JP6692022B2 - Delivery planning system, delivery planning method and program - Google Patents

Description

  The present invention relates to a delivery planning system, a delivery planning method and a program.

  The need for car sharing is increasing. Car sharing is, for example, a system in which members and the like share a vehicle, pay a fee according to boarding time, and use the vehicle at their own convenience. As one form of car sharing, there is a form of use called a one-way type. In the ride-on type car sharing, users can use a shared vehicle up to a predetermined parking lot near the destination and leave the vehicle in the parking lot as it is. In such a form of car sharing, it is necessary to deliver a vehicle that the user has finished using to another parking lot that has new usage needs.

  In addition, in the case of a so-called after-sales service tour in which a service person travels around the customer in order to provide after-sales service for the product purchased by the customer, the same situation may occur regarding the movement of the service person and parts necessary for providing the service. Occurs. For example, each customer has a product for after-sales service installed, and a service person can procure the parts used for after-sales service of the product at a certain place and carry it to the customer, or in one patrol. Service personnel who perform various types of after-sales services are efficient in situations such as moving from one customer who needs the same parts to provide the service to another customer and then returning the used parts to their original positions. It becomes necessary to select a patrol method.

  In order to address such a problem, for example, Patent Document 1 discloses a technique of creating a transportation plan for transporting a package from a plurality of delivery points using a plurality of transportation means at a plurality of dates and times designated as a plurality of delivery destinations. There is. By using this technology, in the case of car sharing, it is possible to create a transportation plan in which a vehicle used by a user is loaded on transportation means such as a truck and transported to each parking lot. Also, in the after-sales service patrol, it is possible to create a delivery plan for delivering the parts used for the service to the customer.

However, when a vehicle is delivered by car sharing, there is also a vehicle delivery method in which a delivery staff boards a delivery target vehicle and drives to a target parking lot. This method of boarding and delivering the delivery itself is called boarding transportation. For delivery including boarding, no technology for optimal delivery planning is provided.
Also, in the after-sales service patrol, when a service person moves with a part, when delivering a part from one customer to another customer, or when a service person has an extra part, the service person carries it to the next customer. As in the case of boarding transportation, there is no technology provided for the optimal patrolling plan of the service person when traveling to the area.
In general, a discrete value combination optimization problem uses a method called linear relaxation, that is, a method in which the problem is temporarily replaced with a continuous value problem to solve, and an optimal solution is obtained from the obtained relaxation solution. If there are many complex constraints like the problem, the calculation time will be too long, so it is necessary to devise a solution in a practical time.

JP, 2013-136421, A

By the way, the applicant of the present application has already filed an application for a delivery planning system capable of solving the above-mentioned problem of delivery planning for delivery including boarding transportation (Japanese Patent Application No. 2016-051550). By using this delivery planning system, an optimal delivery plan for a delivery problem including boarding can be obtained in a practical time.
Regarding this delivery planning system, even if the scale of the problem increases due to the increase in the number of vehicles to be delivered and the number of delivery destinations, it is desirable to further reduce the calculation time so that the optimal delivery plan can be obtained in a practical time. It was rare.

  Therefore, an object of the present invention is to provide a delivery planning system, a delivery planning method, and a program that can solve the above problems.

According to the first to twelfth aspects of the present invention, the delivery planning system divides the delivery problem indicated by the initial condition into smaller delivery problems in the delivery problem of delivering the deliverables to the demanded delivery base. A dividing unit and a delivery plan generating unit that generates a delivery plan for the delivery problem after the dividing unit divides.
By dividing a large-scale delivery problem into smaller-scale delivery problems and calculating a delivery plan in units of small delivery problems, it is possible to generate a delivery plan in a practical time.

In the first aspect of the present invention, the division unit includes one demand point included in a delivery base group that has a demand for the delivery item and one supply point included in a delivery base group that is a supply source of the delivery item. And are associated so that the travel time from the one demand point to the one supply point is minimized, a set of the associated demand points and the supply points is generated, and the initial condition indicates The delivery problem may be divided into a delivery problem from the demand point group to the supply point group included in the generated set.
Based on the supply and demand information for each delivery base included in the initial conditions, the delivery area is divided into delivery area units for each set of delivery bases that exist in a short distance, and a delivery plan is set for each delivery area unit after division. By calculating, the delivery plan can be generated in a practical time.

The dividing unit according to the second aspect of the present invention is configured such that the moving time from one supply point to one demand point is selected from among correspondence relationships between the plurality of supply points and the plurality of demand points included in the generated set. A delivery route from a supply point to a demand point, which is less than or equal to a predetermined value, is calculated, and the delivery plan generation unit determines the travel time of the delivery route from the supply point group to the demand point group included in the generated set. A delivery plan for the small-scale delivery problem may be generated using delivery routes that are equal to or less than the predetermined threshold.
Since the delivery plan is generated using the information of the delivery route between the delivery bases where the travel time is less than or equal to the threshold value, the amount of calculation required to generate the delivery plan can be reduced.

The dividing unit according to the third aspect of the present invention uses a preset delivery route from the departure point to perform delivery related to some of the delivery points and returns to the departure point and the delivery route. When a plurality of unit route information indicating the cost at the time of doing is acquired, the number of the delivery bases included in the combination is within a predetermined number among the plurality of unit route information combinations, and the total cost is The minimum combination is calculated, a set of departure bases and delivery bases included in the combination is generated, and the delivery problem indicated by the initial condition is set to a demand point group included in the generated set of start bases and delivery bases. May be divided into a delivery problem from a to a supply point group.
Based on a certain departure point, calculate a combination of delivery routes that minimizes the delivery cost while satisfying the demands of a plurality of delivery points within a predetermined number, and combine these multiple delivery points and the departure point into one delivery area. And By dividing the delivery area for all the delivery points given in the initial conditions into the delivery areas generated in this way, and calculating the delivery plan for each delivery area, the delivery plan can be created in a practical time. Can be generated.

The dividing unit in the fourth aspect of the present invention calculates a combination of the unit path information by a column generation method.
The delivery area can be generated at high speed by using the column generation method.

The division unit in the fifth aspect of the present invention divides the delivery problem indicated by the initial condition into the delivery problems for each of the divided times by dividing the delivery time limit of the delivery item into a plurality of times, and The delivery plan generation unit is a delivery plan in which the delivery items are delivered to a demand base as much as possible within each time after the division based on the delivery status of the delivery items at the first time of each time after the division. May be generated.

The delivery plan generation unit according to the sixth aspect of the present invention indicates the delivery problem related to the last time formed by the division unit by the initial condition before the end of the last time. A delivery plan may be generated so that the deliverables are delivered to all of the demanded delivery points.
According to the fifth and sixth aspects, the delivery time limit given by the initial condition is divided, and the delivery plan is calculated for the post-division time unit delivery problem, so that the delivery plan is generated in a practical time. be able to.

In the seventh aspect of the present invention, the dividing unit regards the delivery problem indicated by the initial condition as a new delivery time limit with a first delivery time limit shorter than the delivery time limit included in the initial condition by a predetermined time. Then, the delivery plan generation unit may generate a delivery plan in which the delivery item is delivered to a base with a large demand within the first delivery time limit.

The dividing unit according to the eighth aspect of the present invention sets a predetermined length of time following the first delivery time limit as a second delivery time limit, and the delivery plan generating unit sets the second delivery time limit within the second delivery time limit. In addition, a delivery plan may be generated so that the delivered item is delivered to a base having a large demand.

The delivery plan generation unit according to the ninth aspect of the present invention uses the completion time point when the generated delivery plan is executed as a start time, and includes the initial condition on the basis of the start time of the first delivery time limit. As a result of the execution of the delivery plan, a delivery plan that finishes delivery of the deliverable that has not been delivered may be generated within the last time whose end time is the time when the delivery time limit is passed.
According to the seventh to ninth aspects, a time shorter than the delivery time limit given in the initial condition is set as the delivery time limit, and the delivery plan is generated while extending the delivery time limit. By dividing the delivery problem indicated by the initial condition into smaller delivery problems with set or extended delivery time limits, it is possible to generate a delivery plan in a practical time.

In the tenth aspect of the present invention, when generating a delivery plan in which the delivered items are delivered to a base with a large demand, the delivery plan generation unit executes the delivery plan and, as a result, sets the delivery plan to the delivery plan. The delivery plan may be generated on condition that the necessary delivery staff and delivery means do not remain at the delivery site.
In addition to delivering as many deliverables as possible, it is possible to generate a delivery plan that does not leave extra delivery staff and delivery means that are not used in the later time after the division, at the delivery base.

The delivery plan generation unit in the eleventh aspect of the present invention is a delivery base that indicates the initial position of a delivery entity that delivers the delivery item and a delivery means that moves the delivery item or the delivery entity, and the delivery point and the delivery start. Between the point information paired with each time based on the time of time, and two point information items related to the delivery of the delivery object in the point information, the delivery item related to the delivery, the delivery subject, and the Solving an integer programming problem based on a spatiotemporal network model composed of branch information indicating the flow rate of the delivery means, and generating at least one set of branch information relating to the delivery in the delivery problem after the division by the dividing unit. You may.
By modeling the delivery problem with a spatio-temporal network model, it is possible to generate a delivery plan for the delivery problem including boarding.

According to a twelfth aspect of the present invention, the delivery plan generation unit, in the spatiotemporal network model, for one of the delivery bases, point information relating to an entrance that is a combination of the entrance of the delivery base and time. , Point information relating to the exit that forms a pair with the exit of the delivery point and time, and point information relating to the storage location of the delivery that sets the time for each piece of delivery related to the delivery point. , The value of the flow rate of the delivery subject and the delivery item between the point information about the entrance and the point information about the delivery item and between the point information about the exit and the point information about the delivery item. It may be set to 0 or 1.
By handling the inside of the delivery site by dividing it into an entrance, an exit, and a storage space for each delivery item, the situation at each of these places can be represented by 0 and 1, so that the delivery site is treated as a 0-1 integer programming problem. It can be handled and the calculation process can be speeded up.

According to a thirteenth aspect of the present invention, the delivery planning system divides the delivery problem indicated by the initial condition into smaller delivery problems in the delivery problem of delivering the deliverables to the demanded delivery base, A step of generating a delivery plan for the delivery problem after the division, wherein in the step of dividing, one demand point included in a delivery base group having a demand for the delivery item and the supply of the delivery item. One supply point included in the original delivery base group is associated with the one demand point so that the moving time from the one demand point to the one supply point is minimized, and the associated demand point and the supply point are associated with each other. Is a set of combinations of the above, and the delivery problem indicated by the initial condition is divided into a delivery problem from a demand point group to a supply point group included in the generated set .

According to the fourteenth aspect of the present invention, the program causes the computer of the delivery planning system to turn the delivery problem indicated by the initial condition into a smaller-scale delivery problem in the delivery problem of delivering the deliverables to the demanded delivery base. The dividing means functions as a means for dividing, a means for generating a delivery plan for the delivery problem after the dividing, and the dividing means includes one demand point included in a delivery base group in which there is a demand for the delivery item, One supply point included in the delivery base group that is the supply source of the delivery is associated with the one demand point so that the moving time from the one demand point to the one supply point is minimized, and the associated demand point is associated. And a set of combinations of the supply points is generated, and the delivery problem indicated by the initial condition is divided into a delivery problem from a demand point group to a supply point group included in the generated set .

  According to the present invention, it is possible to make a delivery plan that minimizes the cost and travel time for a large-scale delivery problem in a practical time.

It is a functional block diagram which shows an example of the delivery planning system in 1st embodiment of this invention. It is a figure explaining an example of the delivery plan in a first embodiment of the present invention. It is a figure explaining the 1st spatiotemporal network model which concerns on the delivery plan in 1st embodiment of this invention. It is a 1st figure explaining the 2nd spatiotemporal network model which concerns on the delivery plan in 1st embodiment of this invention. It is a 2nd figure explaining the 2nd spatiotemporal network model concerning the delivery plan in 1st embodiment of this invention. It is a 3rd figure explaining the 2nd spatiotemporal network model concerning the delivery plan in 1st embodiment of this invention. It is a 4th figure explaining the 2nd spatiotemporal network model concerning the delivery plan in 1st embodiment of this invention. It is a 5th figure explaining the 2nd spatiotemporal network model concerning the delivery plan in 1st embodiment of this invention. It is a figure which shows an example of the delivery problem in 1st embodiment of this invention. It is a figure which shows an example of the delivery plan produced with respect to a delivery problem. It is a 1st figure explaining the 1st area division process in 1st embodiment of this invention. It is a 2nd figure explaining the 1st area division process in 1st embodiment of this invention. It is a flow chart which shows an example of generation processing of a delivery plan in a first embodiment of the present invention. It is a functional block diagram which shows an example of the delivery planning system in 2nd embodiment of this invention. It is a 1st figure explaining the 2nd area division process of the delivery problem in 2nd embodiment of this invention. It is a 2nd figure explaining the 2nd area division process of the delivery problem in 2nd embodiment of this invention. It is a 3rd figure explaining the 2nd area division process of the delivery problem in 2nd embodiment of this invention. It is a flow chart which shows an example of generation processing of a delivery plan in a second embodiment of the present invention. It is a functional block diagram which shows an example of the delivery planning system in 3rd embodiment of this invention. It is a 1st figure explaining the time division process of the delivery problem in 3rd embodiment of this invention. It is a 2nd figure explaining the time division process of the delivery problem in 3rd embodiment of this invention. It is a flow chart which shows an example of generation processing of a delivery plan in a third embodiment of the present invention.

<First embodiment>
Hereinafter, a delivery planning system according to an exemplary embodiment of the present invention will be described with reference to FIGS.
FIG. 1 is a functional block diagram showing an example of a delivery planning system according to the first embodiment of the present invention. In the present embodiment, the delivery planning system is composed of, for example, one PC or a computer device such as a server device. The computer device includes an arithmetic unit such as a CPU (Central Processing Unit), a storage unit such as a ROM (Read Only Memory), a RAM (Random Access Memory), and an HDD (Hard Disk Drive), and other hardware such as a network interface. It is configured to include clothing.

  The delivery planning device 10 of FIG. 1 is an example of a delivery planning system. The delivery planning device 10 is a device that calculates delivery means, delivery routes, and the like that minimize the cost in a delivery plan including boarding transportation. In the present embodiment, in a case where a vehicle shared by users is delivered to a place where the users start using it in a car-sharing type, the method of making an optimal delivery plan for realizing the delivery will be taken as an example. When delivering a delivery, for example, it is required to select delivery means and delivery routes that minimize the cost. Various methods have been provided in the past for creating a delivery plan that minimizes costs. However, delivery of vehicles in car sharing is different from delivery of parcels, for example, by courier. That is, when delivering a vehicle, a person can board the vehicle and move. For example, it is assumed that the base A, the base B, the base C, the base D, and the base E each have a state in which there is an excess of vehicles or a state in which there are insufficient vehicles. In such a state, for example, the following method can be considered in order to move the vehicle from the surplus base to the shortage base so that the needs of the user can be met. (1) One delivery staff travels around each site by trucks that can load vehicles, installs the surplus vehicles in the trucks, and delivers to the depleted sites. (2) A plurality of delivery staff board a delivery vehicle and move between locations. When some of the delivery staff who boarded the delivery vehicle arrive at the base where the vehicle is surplus, they transfer to the surplus vehicle and drive and deliver the vehicle to the base where the vehicle is short (boarding transportation). In such a case, it is not easy to know which delivery means should be used for delivery, and what route should be used for delivery to minimize the cost. The delivery planning apparatus 10 according to the present embodiment introduces a mathematical model and constraints based on mathematical knowledge into a delivery plan when boarding transportation is possible, thereby quickly and efficiently minimizing cost, for example. Provides a way to generate a shipping plan. Further, the delivery planning apparatus 10 of the present embodiment, when generating a delivery plan for delivering a delivery item to a delivery point, specifies the demand quantity of the delivery item for each delivery point given as an initial condition of the delivery (when there is a shortage, Existing quantity) and supply quantity (remaining quantity), the whole delivery problem indicated by the initial condition is divided into partial delivery problems. As a result, even if the number of vehicles or sites to be delivered is large, it is possible to make a delivery plan in a practical time (for example, 10 minutes).

As shown in FIG. 1, the delivery planning apparatus 10 includes an initial condition setting unit 11, a delivery plan generating unit 12, an input / output unit 13, a first area dividing unit 14, and a storage unit 15.
The initial condition setting unit 11 includes a delivery item (for example, a vehicle used by a user), a delivery entity, a delivery item that can be moved by a delivery entity (for example, a delivery staff member), and a delivery means that moves the delivery entity (for example, a delivery entity). One or a plurality of departure points (for example, car-sharing points) that indicate the demand quantity and supply quantity of deliveries for each delivery point, which is the place where any of the delivery vehicles such as trucks), and the initial position of the delivery entity and delivery means. Information such as the operating base of the company that provides the service, information about the available delivery means and delivery entities at the departure base, and information about the delivery deadline are set as the initial conditions for generating the delivery plan. To do. These parameters will be described later in detail.
The delivery plan generation unit 12 performs delivery related to delivery between point information including a delivery base and a departure base and time based on the time of delivery start, and two point information related to delivery in the point information. At least one branch information set in the case of calculating branch information indicating the flow rate of a product, a delivery subject, and a delivery means, and delivering a delivery product satisfying the demand quantity within the delivery deadline to a delivery site to which the demand quantity is set To generate. The starting point and the delivery point are collectively referred to as a point.
The input / output unit 13 receives an input operation by the user. The input / output unit 13 also outputs, to a display or the like, delivery plan information based on the set of branch information generated by the delivery plan generation unit 12.
The first area dividing unit 14 defines one demand point included in a delivery base group that has a demand for deliverables and one supply point included in a delivery base group that is a supply source of the deliverables as the one demand. The points are associated with each other so that the moving time to the one supply point is minimized, and a set of associated demand point and supply point combinations is generated. That is, the first area division unit 14 delivers the entire delivery problem to all delivery base groups that have demand for deliveries based on the initial condition, in the delivery area unit indicated by the generated set (included in the set. Delivery problem from demand point group to supply point group). Then, the delivery plan generation unit 12 generates a set of branch information for each of the post-division small scale delivery problems.
The storage unit 15 stores various information necessary for generating a delivery plan.
The initial condition setting unit 11, the delivery plan generation unit 12, and the first area division unit 14, for example, a CPU (Central Processing Unit) included in the delivery planning device 10 reads and executes the program from the storage unit 15. Will be realized in.

  The delivery planning apparatus 10 generates a delivery plan for a given delivery problem using a spatiotemporal network model. First, we describe a spatiotemporal network model and a method for generating a delivery plan using the spatiotemporal network model, and then describe a method for dividing the delivery problem when the problem becomes large-scale.

FIG. 2 is a diagram illustrating an example of a delivery plan in the first embodiment of the present invention.
With reference to FIG. 2, a delivery example of a delivery (vehicle) in a drop-off type car sharing will be described. In FIG. 2, a center is a base where a delivery staff of the delivery is present and starts delivering the delivery (departure base). Further, the parking lot A, the parking lot B, and the parking lot C are bases (delivery bases) that are the delivery origins or destinations of the delivered items. The user of the delivery item makes a reservation for the delivery item using a predetermined reservation system or the like. The user inputs information such as the number of items to be used for delivery and the use start place (for example, parking lot B) from the reservation system. When the user wants to use the delivered item from the parking lot B, if the delivered item already exists in the parking lot B, the user can use the delivered item. However, when there is no delivery item in the parking lot B, the delivery staff needs to move the delivery item from another parking lot to the parking lot B. In the drop-off type car sharing, for example, when the user uses the delivered item from the parking lot B to the parking lot A, the user leaves the delivered item to the parking lot A as it is. Then, a situation may occur in which deliveries are ubiquitous, for example, in the parking lot A used by many users. The delivery staff of the center delivers the ubiquitous delivery items to the parking lots A to C where the user needs. In the case of the example in FIG. 2, the parking lot A has two or more delivered items, and the parking lot B and the parking lot C lack one delivered item at a time. The delivery staff of the center delivers the remaining two deliveries in the parking lot A to the parking lot B and the parking lot C one by one so that the user can use the deliverables as desired. FIG. 2 shows an example of realization of delivery that satisfies this condition.

  First, two delivery staff members (k, l) board the delivery vehicle 1 (delivery means) from the center and move to the parking lot A (1). At the parking lot A, the delivery staff k boards one of the remaining two deliveries and moves to the parking lot B. Further, the other delivery staff 1 also board the delivery vehicle 1 and move to the parking lot B (2). In the parking lot B, the delivery staff k parks the deliveries in the parking lot B and board the delivery vehicle 1 operated by the delivery staff l. The delivery staffs k and l return from the parking lot B to the parking lot A (3). When returning to the parking lot A, the delivery staff k boards the remaining one delivery item and moves to the parking lot C. Moreover, the delivery staff 1 boards the delivery vehicle 1 as it is and moves to the parking lot C (4). In the parking lot C, the delivery staff k parks the deliveries in the parking lot C and board the delivery vehicle 1 operated by the delivery staff l. The delivery staffs k and l return from the parking lot B to the center (5). By performing the delivery in such a procedure, it is possible to satisfy the user's request. In the present embodiment, the delivery method for deliveries in such a situation is formulated as the minimum cost flow problem of the spatiotemporal network model, and the method with the smallest cost among the feasible delivery methods is obtained.

<First spatiotemporal network model>
FIG. 3 is a diagram illustrating a first spatiotemporal network model related to a delivery plan in the first embodiment of the present invention.
FIG. 3 is a diagram in which the delivery embodiment described in FIG. 2 is modeled in a spatiotemporal network. The vertical axis of FIG. 3 indicates the passage of time, and the horizontal axis indicates the location of each base. In the figure, the points on the space-time represent each base at each time. In the figure, the arrow connecting two points indicates the movement of the delivered item, the delivery vehicle (delivery means), and the delivery staff (person) in space-time. Each arrow represents the movement origin base, the movement destination base, and the time required for the movement. Solid arrows indicate movements between bases, and double-headed arrows indicate deliverables, delivery vehicles, and delivery staffs who stay at the same base (moving time). In addition, each element of the matrix displayed along with each arrow represents the number of deliveries, delivery vehicles, and delivery staff moved by the delivery indicated by the arrow. Indicates the number of delivery vehicles and the number of delivery staff who have moved. For example, in the case of the solid arrow 31, it indicates that there are 0 deliveries, 1 delivery car, 2 delivery staff, and time t = 0 to t = 1 from the center to the parking lot A. There is. Further, the double-lined arrow 32 indicates that, in the parking lot A, there were two deliveries, zero delivery vehicles, zero delivery staff, and stays from time t = 0 to t = 1. .. Further, in the case of the solid line arrow 33, it is confirmed that one delivery item, one delivery vehicle, two delivery staff members, and two delivery staff members have moved from the parking lot A to the parking lot B between time t = 1 and t = 2. Shows. Further, the double-lined arrow 34 indicates that, in the parking lot A, one delivery item, zero delivery vehicles, zero delivery staff members, and stays between the times t = 1 and t = 2. .. The reason why the number of deliveries in the parking lot A changed from two to one is that the delivery staff boarded one of the two deliveries and moved to the parking lot B. The same applies to the other arrows. One arrow is called a branch. The set of branches in FIG. 3 corresponds to the delivery plan described in FIG. When delivering a delivery item, there may be a time-related action such as waiting for delivery staff or delivery means at some parking lot. In existing mathematical models for delivery planning, the points are often used as points, and the movement of delivery vehicles between points is often used as a branch. In this embodiment, a two-dimensional space-time network is used for modeling. As a result, not only the spatial movement between the bases but also the movement of the vehicle or the person with time intervening can be represented.

<Method of generating delivery plan based on first spatiotemporal network model>
In the present embodiment, a delivery plan that minimizes the cost of delivery in a delivery plan delivery product that satisfies the demand within the time limit described with reference to FIGS. 2 and 3 is obtained. This problem can be formulated as an integer programming problem shown below.
[Objective function]
Minimize the total cost of deliveries, delivery methods, and delivery staff for delivery [restriction condition]
(1) The flow rate at each site satisfies the law of conservation of flow rate.
(2) The number of vehicles in the parking lot does not exceed the parking space in the parking lot.
(3) A delivery staff member will always be on the delivery means except at the departure point.
(4) When moving, the delivery staff always rides on the deliverables or delivery means, and the number of persons on the move is equal to or less than the total number of persons who can board the deliverables and delivery means.

  In order to solve the above integer programming problem, the delivery plan generation unit 12 generates two-dimensional spatio-temporal information as illustrated in FIG. 3 based on the information of the initial condition accepted by the initial condition setting unit 11. Generate a branch between points related to delivery, and generate multiple sets of branch information that can deliver the deliverables to the location where the demand quantity is set so that the demand quantity of each location can be met within the delivery deadline. .. Then, the delivery plan generation unit 12 selects a set of branch information that minimizes the cost from a plurality of sets of branch information.

  The mathematical models and programs of the delivery plan that have been provided so far are limited to cases where the deliverables are loaded and delivered on transportation means such as trucks and railroads. For cases involving boarding, such as vehicle delivery, existing technologies may be able to solve the problem by adding constraints, but the constraints are complicated and the number of combinations of means and routes is large. It is considered impractical because it grows exponentially. According to this embodiment, the cost is minimized among the feasible delivery methods by formulating the minimum cost flow problem of the spatiotemporal network model when generating the delivery plan of the deliverables that can be boarded. You can request a shipping plan.

<Second spatiotemporal network model>
In the second spatiotemporal network model, a graph (point information and branch information indicating the movement of delivery staff, deliverables, and delivery means) within the delivery point is added to the first spatiotemporal network model. As a result, the inside of the delivery point can be treated as a 0-1 integer programming problem. The 0-1 integer programming problem has a narrower range of variables than the integer programming problem, and can form a tight relaxation problem. Also, by doing so, it becomes easy to insert a valid inequality (cut), and the calculation process can be speeded up (the calculation time can be shortened).

  When the delivery plan generation unit 12 generates a delivery plan using the second spatio-temporal network model, in addition to the spatio-temporal information described in the case of the first spatio-temporal network model, for one delivery base, the delivery base Point information in which the entrance and time of the delivery point are paired, point information in which the exit of the delivery point and the time point are paired, and point information in which the time point is paired for each delivery item related to the delivery point is generated. .. Further, the delivery plan generation unit 12 sets the value of the flow rate of the delivery staff and the delivery item between the point information regarding the entrance and the point information regarding the delivery item to 0 or 1. Further, the delivery plan generation unit 12 sets the value of the flow rate of the delivery staff and the delivery item between the point information regarding the exit and the point information regarding the delivery item to 0 or 1.

Here, the parameters that the delivery planner inputs to the delivery planning apparatus 10 will be described. Input parameters include the following items.
That is, a set of departure points (Depot), a set of delivery points (W), a delivery deadline (dl), a time of one section (h), a set of types of deliverables (P), a set of types of delivery means (D). ), The load amount (cp) of the delivery means, the cost cx (yen / minute) of the delivery item, the cost cy (yen / minute) of the delivery means, the cost cz (yen / minute) of the delivery staff, the travel time matrix M (for example, , The moving time from the delivery base w1 to the w2 by the delivery means d is m [d] [w1] [w2], and the supply quantity supply at each base (for example, the supply quantity of d at the delivery base w is supply [w]. , D]), and the demand quantity demand of each delivery point (for example, the demand quantity of d at the delivery point w is demand [w, d]). The initial condition setting unit 11 acquires these parameters and sets them as the initial conditions of the delivery plan.

  Further, as output items, the delivery plan generation unit 12 has a flow rate x ((v, s), (w, t)) of a delivery item flowing through the spatiotemporal network in the optimized delivery plan, and a flow rate y (of the delivery means). (V, s), (w, t)), and the flow rate z ((v, s), (w, t)) of the delivery staff are output to the input / output unit 13. In addition, a branch that leaves the delivery point v at time s and arrives at the delivery point w at time t is represented by ((v, s), (w, t)). Note that the output items also include the cost of delivery and the like.

FIG. 4 is a first diagram illustrating a second spatio-temporal network model according to the delivery plan in the first embodiment of the present invention.
The second space-time network will be described with reference to FIG. In the following, the place set is N, the time set is T, and the spatiotemporal network graph G = (V, E). V is a point set and E is a branch set. The point set V is defined as follows.
V = {(w, d, p, t) | wεW, dε {0} ∪P, pεS _wd , tεT}
Here, S _wd = {0,1} (d = 0), S _wd = {0,1 ,. ． ． , M} (d ≠ 0). d = 0 indicates the entrance / exit path of the delivery base. When d = 0, S _wd takes a value of 0 or 1, but S _wd = 0 indicates an inlet and S _wd = 1 indicates an outlet. When d ≠ 0, d indicates the type of delivery and S _wd has a value of 0 to m. m is the supply quantity -1 or the demand quantity -1 for the delivered product d at the delivery point w. For example, when the delivery base w has three extra deliveries a (supply quantity = 3), S _wd takes values of 0, 1, and 2. Further, for example, when the delivery base w lacks four deliverables a (demand quantity = 4), S _wd takes values of 0, 1, 2, and 3. For a certain delivery point w, a point of d = 0 is also called a road, and a point of d ≠ 0 is also called a port. The port indicates a place for placing one delivery item d.

FIG. 4 shows that Depot = {0}, W = {1,2}, P = {a}, T = {0,1,2}, S _1a = {0} (delivery for delivery item a at delivery point 1). It is a spatio-temporal network in the case of S _2a = {0} (1 demand quantity for delivery a at the delivery site 2). Next, the branch set E will be described with reference to FIG.

FIG. 5 is a second diagram illustrating the second spatiotemporal network model according to the delivery plan in the first embodiment of the present invention.
Hereinafter, the branch set E is defined as E = E _x ∪E _y ∪E _z . E _x is a branch set of deliveries, E _y is a branch set of delivery means, and E _z is a branch set of delivery staff.
Branch set E _x of delivery was defined as follows.
E _x = E _wwx ∪E _wx ∪E _wpx ∪E _pwx ∪E _px
E _wwx is a set of branches indicating the movement of the delivery item between the bases, E _wx is a set of branches (waiting, etc.) remaining on the way of the delivery _point of the delivery item, and E _wpx is the movement of the delivery item from the path to the port. A set of branches, E _pwx is a set of branches indicating the movement of a delivery from a port to a road, and E _px is a set of branches at which a delivery is _retained at a port.

The branch set E _y of the delivery means is defined as follows.
_{E y = E wwy ∪E wy ∪E} wpy ∪E pwy
_E wwy shows a set of branches showing the movement between the base of the delivery means, the set of E _wy branches that remain in the way of delivery base of the delivery means (such as waiting), the movement of the _E wpy is to port from the way of the delivery means A set of branches, E _pwy, is a set of branches showing the movement of the delivery means from the port to the road.

The branch set E _z of the delivery staff is defined as follows.
E _z = E _wwz ∪E _wz ∪E _wpz ∪E _pwz
E _wwz is a set of branches showing the movement of the delivery staff between the bases, E _wz is a set of branches (waiting etc.) staying on the way of the delivery staff's delivery base, and E _wpz is the movement of the delivery staff from the road to the port. A set of branches, E _pwz, is a set of branches showing the movement of the delivery staff from the port to the road.

FIG. 5 shows a display example of the branch set defined above. The diagonal solid arrows indicate the branches corresponding to each set of E _wwx, E _{wyw, and} E _wwz . Vertical double- _lined arrows indicate branches corresponding to each set of E _wx, E _{wy, and} E _wz . The horizontal two-dot chain line arrow indicates the branch corresponding to each set of E _wpx, E _{wpy, and} E _wpz . The one-dot chain line arrow in the diagonal direction indicates a branch corresponding to each set of E _pwx, E _{pwy, and} E _pwz . Vertical dashed arrows indicate branches corresponding to the set of E _px .
In the second spatiotemporal network model, the inside of the delivery point is treated as a 0-1 integer problem, but the horizontal two-dot chain line arrow, the diagonal one-dot chain line arrow, and the vertical dashed line arrow branch are the 0-1 integer. This is a branch added in this embodiment in relation to the problem.

FIG. 6 is a third diagram illustrating the second spatiotemporal network model according to the delivery plan in the first embodiment of the present invention.
The flow rate vector set for each branch will be described with reference to FIG. As shown in FIG. 6 (a), the flow rate vector is assigned to each branch e.

Is set. In this flow rate vector, x [d, e] (dεP, eεE _x ) is the flow rate of the delivery, y [d, e] (dεD, eεE _y ) is the flow rate of the delivery means, z [e] (eεE _z ) indicates the flow rate of the delivery staff. Here are some examples. When P = {a} and D = {car}, the flow rate vector is

Becomes The branch e illustrated in FIG. 6B indicates movement of one a, one delivery vehicle (vehicle), and two delivery staff (person). When P = {a, b} and D = {car, motorcycle}, the flow rate vector is

Becomes The branch e shown in FIG. 6C shows the movement of one a, one b, one delivery vehicle (car), one motorcycle, and one delivery staff (person).

FIG. 7 is a fourth diagram illustrating the second spatiotemporal network model according to the delivery plan in the first embodiment of the present invention.
In FIG. 7, the flow rate vector is

This is a spatio-temporal network model for moving one delivery item a from delivery point 1 to delivery point 2. First, two delivery staff (people) and one delivery vehicle (vehicle) move from the Depot exit to the delivery site 1 (solid arrow 91). At the delivery point 1, one delivery staff member moves to the storage place (port 0) of the delivery a (two-dot chain line arrow 92). At port 0 of the delivered product a, the delivered product a exists from time 0 to 1 (broken line arrow 93). Subsequently, one delivery staff member and one delivery item a move to the exit of the delivery site 1 (one-dot chain line arrow 94). Next, one delivery item a, one delivery vehicle, and two delivery staffs move from the delivery base 1 exit to the delivery base 2 entrance (solid arrow 95). Next, one delivery staff member and one delivered item a move to port 0 of the delivery point 2 (two-dot chain line arrow 96). Then, one delivery staff moves from the port 0 to the exit of the delivery site 2 (one-dot chain line arrow 97). Next, two delivery staff members and one delivery vehicle move from the exit of the delivery site 2 to the Depot entrance (solid arrow 98). At port 0 of the delivery base 2, the delivery a exists from time 2 to time 3 (broken line arrow 100). As shown in FIG. 7, in the present embodiment, points are assigned to each delivered item a at the delivery point 1 and the delivery point 2, and points are assigned to each of the entrance and the exit of the delivery point. Therefore, the value of each element of the flow rate vector in the delivery point 1 and the delivery point 2 is 0 or 1. As a result, the inside of the delivery site can be treated as a 0-1 integer programming problem, and the calculation time can be shortened.

FIG. 8 is a fifth diagram illustrating the second spatiotemporal network model related to the delivery plan in the first embodiment of the present invention.
FIG. 8 shows the first spatiotemporal network model illustrated in FIG. 3 using the second spatiotemporal network model. In FIG. 8, the point set represented by the column of the parking lot A in FIG. 3 is further subdivided into (1, 0, 0, 0), (1, a, 0, 0), (1, a, 1, 0) is represented by a set of points in each column. The same applies to parking lot B and parking lot C. In addition, a point set corresponding to an entrance / exit is given to each of the center and parking lots A to C.

<Method of generating delivery plan based on second spatiotemporal network model>
In the above, as a measure against the speeding up of the processing in the second spatiotemporal network model, it has been explained that the delivery base has a 0-1 integer programming problem. Next, a method of generating a delivery plan will be described. It should be noted that as delivery means, a case of delivering by a delivery vehicle and a bicycle (including a case of delivering only by a delivery vehicle) and a case of delivering by a truck (on which delivery items are loaded) will be described. In addition, as for the bicycle as a delivery means, the delivery staff rides a bicycle to a delivery base where there is supply, loads the bicycle on the surplus vehicle there, and the delivery staff drives the surplus vehicle to move to the delivery base where there is demand. To be used.

First, the objective function will be described. In FIG. 3, the case where the cost is minimized has been described as an example. Here, the case where the moving time required for delivery is minimized will be described.
(When delivering by delivery car and bicycle)
1. The objective function for minimizing the cost of delivery is the cost per hour of each of the delivered item, the delivery vehicle, and the delivery staff multiplied by the travel time.
2. The objective function in the case of minimizing the travel time required for delivery is to add the travel times of the delivered item, delivery vehicle, and delivery staff.

(When delivering by truck)
1. The objective function to minimize the cost of delivery is the cost per hour of each delivery truck and delivery staff multiplied by the travel time.
2. The objective function for minimizing the travel time required for delivery is to add the travel times of the delivery truck and delivery staff.

Next, the constraint conditions will be described.
(Common for delivery by car and bicycle and delivery by truck)
1. Flow Conservation Law (1) Regarding the flow rate of the delivered product At the start of delivery, the flow rate of the port from which the supply exists is 1. When the delivery is completed, the flow rate entering the port where the demand exists becomes 1. Otherwise, the outgoing and incoming flows are equal.

(2) About the flow rate of delivery vehicles At the start of delivery, the flow rate from the road where delivery vehicles exist is the number of delivery vehicles. At the time of completion of delivery, the amount of flow entering the road where delivery vehicles are present is the number of delivery vehicles present. Otherwise, the outgoing and incoming flows are equal.
(3) Flow rate of delivery staff At the start of delivery, the flow rate from the road where the delivery staff exists will be the number of delivery staff. At the time of delivery completion, the amount of flow entering the road where the delivery staff exists will be the number of delivery staff. Otherwise, the outgoing and incoming flows are equal.
2. The amount of deliveries and people moving within the capacity-constrained delivery site is 1 or less.

3. Constraints within the delivery base 1
∀e ∈ E _wp
(E _wp is a set of _deliverables , delivery means, and branches that indicate movement from people's roads to ports)
(1) When the destination of e is the supply point of d The delivered product does not enter the port from the road.
(2) When the destination of e is the demand point of d The flow rates of the delivered product and the delivery staff have the same value (0 or 1).
(3) In either case, the number of bicycles is less than the number of delivery staff.

4. Constraints within the delivery base 2
∀e ∈ E _pw
(E _pw is a set of branches indicating the delivery goods, delivery means, and movement of people from the port to the road)
(1) When the starting point of e is the supply point of d The flow rates of the delivered material and the delivery staff have the same value (0 or 1).
(2) When the starting point of e is the demand point of d: The delivered product does not go out of the way from the port.
(3) In either case, the number of bicycles is less than the number of delivery staff.

In the following, description will be given separately for delivery by car and bicycle and delivery by truck.
(When delivering by delivery car and bicycle)
5. Constraint on branch when moving from base to another base ∀e∈E _ww
(E _ww is a set of branches indicating the delivery goods, delivery means, and movement of people between bases)
(1) When e is a branch of a bicycle and a branch of a car There are cases where the delivery staff rides on the bike and the car, and cases where the bike is loaded on the car and the car is moving. The restrictions are that the delivery staff must be on board, that the number of delivery staff is less than the number of people that can be boarded, and the number of bicycles that cannot be driven is less than the number that can be loaded on the vehicle.
(2) When e is a bicycle branch but not a car branch (moving by bicycle)
The number of bicycles matches the number of people.

6. Constraints on branches that stay in the delivery base It is constrained to have people onboard the car.

(When delivering by truck)
5. Constraints on branches when moving from a delivery site to another delivery site The delivery staff must be on the truck, the number of delivery staff must be less than the boarding capacity, and the total volume of deliveries must be less than the load capacity of the truck. There is a constraint.

6. Constraints on branches that remain in the delivery base The total volume of deliveries is limited to the load capacity of the truck or less.

  Furthermore, a constraint equation called cut can be applied to shorten the calculation time. In integer programming problems, inequalities that can be satisfied by points in the feasible region are called valid inequalities. Since the integer programming problem is difficult to solve, it is often treated as a linear relaxation problem excluding the integer condition. Adding a valid inequality that reduces the solution space of a linear relaxation problem is called adding a cut. The addition of the cut brings the linear relaxation solution closer to the integer optimal solution, which has a powerful effect on speeding up the calculation. In addition, since the feasible area is not cut by the addition of the cut, the optimality of the solution is guaranteed. For example, a cut is added to regulate that one or more delivery vehicles come. Then, it is possible to exclude from the calculation target the unrealistic case of 3/4 delivery vehicles, and it is possible to improve the calculation speed. A specific example of the cut is described in the specification of Japanese Patent Application No. 2016-051550 by the applicant of the present application. With the addition of the cut, it became possible to solve the integer programming problem that took several hours or more without the cut in a few minutes.

  The delivery plan generation unit 12 generates a spatio-temporal network model that divides the delivery base into roads (d = 0) and parking ports (d ≠ 0), and further uses the above-mentioned constraint conditions and the added cuts. Calculate branch information. According to the present embodiment, the inside of the delivery point can be modeled as a 0-1 integer programming problem. Therefore, in addition to the effect of generating the delivery plan using the first spatiotemporal network, calculation of the delivery plan is performed. The effect of reducing the time required for is obtained. Furthermore, the addition of cuts can significantly reduce the calculation time. This improves the convenience of the planner, for example, by comparing delivery plans generated under various initial conditions and selecting a delivery plan at a lower cost.

Next, an example of generating a delivery plan using the second space-time network will be described.
FIG. 9 is a diagram showing an example of the delivery problem in the first embodiment of the present invention.
FIG. 10 is a diagram showing an example of a delivery plan generated for a delivery problem.
Point c0 (depot) in FIG. 9 is a departure point. The other points w1 to w9 are delivery points. For example, "d1: 2" at the point w7 indicates that two delivery items d1 are left over, and "d2: -1" at the point w5 means that one delivery item d2 is insufficient. It shows the state. Further, "d1: -1, d2: 1" at the point w2 indicates that one delivery item d1 is insufficient and one delivery item d2 is left. Consider the problem of delivering the delivered items d1 to d3 so that the delivery items d1 to d3 shown in FIG. An example of the delivery plan generated by the delivery planning apparatus 10 will be given below for each case of delivery by car and bicycle and delivery by truck.

1. When delivering by car and bicycle (1) Input ・ In delivery, 1 delivery vehicle, 3 bicycles, 3 delivery staff ・ Delivery deadline: 120 minutes ・ Delivery vehicle cost: 1.5 yen / minute ・ Delivery staff Cost: 17 yen / minute-d1, d2, d3 cost: 1.5 yen / minute-Delivery vehicle boarding capacity: 4 people, bicycle loadable capacity: 1 vehicle-d1 boarding capacity: 1 person , Number of bicycles that can be loaded: 0, d2 can be loaded: 4 persons, Number of bicycles that can be loaded: 1 vehicle, d3 can be loaded: 2 persons, Number of bicycles that can be loaded: 0 (2) Objective function Cost minimization

When the delivery planning apparatus 10 was calculated by adding the above-mentioned constraint conditions and cuts to this objective function, the following output result was obtained.
(3) As shown in FIG. 10, the output / delivery vehicle, the bicycle, and the delivery staff divide the delivery route shown by S1 to S7 and the delivery route shown by T1 to T9 and deliver. ..
-Delivery cost: 2768 yen-Required time: 60 minutes In this way, it is possible to obtain a delivery plan that minimizes the cost within the conditions of the delivery means, delivery staff, and delivery deadline set in the initial conditions.

  Generation of a delivery plan using the first spatiotemporal network or the second spatiotemporal network by the delivery planning apparatus 10 can also be applied to delivery, procurement, and after-sales service tour of deliverable items that can be boarded. .. For example, in after-sales service, it is necessary to provide the service by procuring parts and the like necessary for the after-sales service before heading to the customer or visiting a plurality of customers. Products that are subject to after-sales service, such as parts that use delivered goods for after-sales service, vehicles that are mainly used for delivery by the service person, delivery vehicles that are used by the service person for transportation, and delivery vehicles that are necessary for transporting parts, etc. As a place to install, the above mathematical model can be applied to solve the integer programming problem, and when a serviceman performs after-sales service at multiple customers, a traveling method (minimizing the traveling cost and traveling time) ( It is possible to calculate a patrol means, a patrol route). In the case of FIG. 2, for example, parking lots A to C (delivery bases), customers who provide after-sales service, vehicles (delivery items) as parts, and passenger vehicles (delivery means) used by service personnel for movement, The delivery person (delivery subject) may be the service person. In addition, in the case of after-sales service, not only the customer is patrolled, but the customer performs inspection and repair work. According to the delivery planning apparatuses 10, 10A, and 10B using the spatiotemporal network model, it is possible to model the patrol behavior of the service person in consideration of these working times.

In addition to the above examples, the present invention can be applied to delivery of deliverables that are not boarded. For example, there is a collection method called milk run. With milk run, when a manufacturer of a product purchases raw materials and parts used for that product from multiple suppliers, the manufacturer goes around each supplier and collects the raw materials, etc. It is a procurement method. When the milk run is used to collect the cargo, for example, by collecting the cargo with one truck, it is possible to reduce costs, reduce traffic congestion around the factory, and reduce the environmental load as compared with the case of delivering to each supplier. In the case of calculating the optimum traveling method of the milk run by the delivery planning apparatus 10 of the present embodiment, for example, the factory of the delivery destination of the product manufacturer is set as the delivery base that has a demand in car sharing, and the factory of the supplier of raw materials and parts. If the vehicle is a delivery base with an excess of vehicles, the delivery plan can be calculated by setting the same objective function, constraint conditions, etc. as in the case of “delivery by truck” described above. Regarding the constraint condition that "the total volume of deliveries is less than or equal to the loading capacity of the truck" when delivering by truck, see "(weight of raw material x amount of raw material + weight of parts x number of parts)" Must be less than or equal to the loading capacity of the truck. ” Further, when a pickup time frame of a certain supplier is designated, it can be dealt with by adding information on the designated pickup time frame to the constraint condition. For example, if the arrival time at a certain supplier must be after 30 minutes (from the start of pickup), adding a constraint condition as follows will generate a pickup plan that complies with the time frame constraint of the supplier. be able to.
Arrival time at a supplier ≥ 30 minutes later

  So far, the delivery planning apparatus 10 of the present embodiment has described the process of creating a delivery plan. According to the method described above, the delivery planning apparatus 10 can obtain a strict optimal solution for the delivery problem. However, when the scale of the problem becomes large (for example, 20 delivery points and 20 vehicles are delivered), it may be difficult to find a solution in a practical time only by the above method. Therefore, the first area dividing unit 14 divides the delivery base into each delivery area, and divides the given delivery problem into the divided delivery problems for each area. Next, the area division processing (first area division processing) by the first area division unit 14 will be described.

FIG. 11 is a first diagram illustrating the first area division processing in the first embodiment of the present invention.
The left diagram of FIG. 11 shows the positions of the delivery bases and the departure bases existing in the area targeted for the delivery plan. In the figure, circle points indicate delivery points (w1 to w17), and square points indicate departure points (c1 to c3). There are demands or surpluses for deliveries at the delivery points w1 to w17, and delivery vehicles and delivery staff exist at the departure points c1 to c3. The first area dividing unit 14 generates a pair of a demanding delivery base (demand point) existing in the neighborhood and a surplus delivery base (supply point), and further sets a pair of the demand point and the supply point. One or a plurality of divided areas are generated. Generation of areas by the first area dividing unit 14 is called first area dividing processing.

  The right diagram of FIG. 11 shows the result of the first area dividing unit 14 performing the first area dividing process. The delivery points w1 to w5 belong to the area j1, the delivery points w6 to w9 belong to the area j2, and the delivery points w10 to w17 belong to the area j3. The delivery plan generation unit 12 generates the delivery plan for each of the divided areas j1 to j3 by the above method. Areas j1 to j3 each include less than 10 delivery points, and are relatively small. Therefore, the delivery plan generation unit 12 can generate the delivery plan in a practical time by using the above-mentioned space-time network model.

  Next, the outline of the first area division processing will be described with reference to FIG. First, the first area dividing unit 14 divides the delivery points w1 to w17 into demand points, supply points, and delivery points that are neither demand points nor supply points. Next, the 1st area division part 14 matches a demand point and a supply point one to one. At this time, the first area dividing unit 14 associates the demand points and the supply points having a short distance (moving time) with each other. For example, at the delivery point w4 in FIG. 11, there is one more delivery item d1, and at the delivery point w5 there is not more than one delivery item d1. Further, at the delivery point w6, one delivery item d1 is left, and at the delivery point w7, one delivery item d1 is insufficient. Further, it is assumed that the delivery point w8 has one extra delivery item d2 and the delivery point w9 has one extra delivery item d2. In this case, the first area dividing unit 14 associates the delivery bases whose supply and demand are the same and whose distances are short with each other. That is, the first area division unit 14 associates the delivery base w4 and the delivery base w5 (set 1), the delivery base w6 and the delivery base w7 (set 2), and the delivery base w8. The delivery base w9 is associated (set 3). The other demand points and supply points are similarly associated.

  Next, the first area dividing unit 14 collects a plurality of pairs of demand points and supply points which are associated with each other and has a close distance to each other to generate one area. At this time, if there is no other pair having a short distance, one pair may be set as one area. For example, in the case of the example given above, the first area dividing unit 14 calculates the distance between the delivery base w4 of the set 1 and the delivery base w6 of the set 2. Then, if the calculated distance is smaller than the predetermined threshold value, the set 1 and the set 2 are classified into the same area, and if the calculated distance is larger than the predetermined threshold value, the set 1 and the set 2 are determined as different areas. .. Regarding the calculation of the distance between the sets, for example, in the case of the distance between the set 1 and the set 2, the distance between the delivery base w4 and the delivery base w7 may be calculated, or between the delivery base w4 and the delivery base w6, and the delivery base. The distances between w4 and delivery point w7, between delivery points w5 and w6, and between delivery points w5 and w7 may be respectively calculated, and the average of the calculated distances may be used as the distance between group 1 and group 2. Alternatively, the largest (or smallest) distance among the calculated distances may be set as the distance between the set 1 and the set 2. In the case of the example in FIG. 11, the first area dividing unit 14 classifies, for example, the set 2 and the set 3 into the same area j2 and the set 1 into another area j1. The first area dividing unit 14 performs the same processing for the other delivery bases, classifies the delivery bases w1 to w17 for each area, and generates areas j1 to j3 shown in FIG. 11.

When the areas are generated by the first area division processing, the delivery plan generation unit 12 sets, for each of the areas j1 to j3, the supply quantity, the demand quantity, and the like of the deliveries at each delivery base in each area as initial conditions. For the delivery problem, the delivery plan may be generated using the first spatiotemporal network model or the second spatiotemporal network model. However, calculation using the spatiotemporal network model from a completely initial state is possible. Even if not performed, the correspondence between the demand point and the supply point at the time of the first area division processing can be used as the branch information. In other words, the delivery plan generation unit 12 can generate branch information from the associated demand points to the supply points and connect them to generate a delivery plan that satisfies all demands. However, the delivery routes that connect the closest delivery points are too limited, and when viewed from the overall delivery plan that moves between multiple locations, it is possible to move away from the optimized state. There is a nature. Therefore, the first area dividing unit 14 performs a process of adding a delivery route that may be selected when the delivery plan generating unit 12 generates the branch information. Then, the delivery plan generation unit 12 selects the appropriate delivery route from among all the delivery routes that are selected and added to the delivery routes that connect the closest delivery bases that meet the demand and supply. Select a suitable delivery route to generate branch information and generate a delivery plan for each area.
In addition, in FIG. 11, the demand point and the supply point are described as the delivery points, but they may be ports with demand and ports with supply, respectively.

Next, the first area division processing will be described in detail.
FIG. 12 is a second diagram illustrating the first area division processing in the first embodiment of the present invention.
The algorithm of the first area division processing of this embodiment will be described below. The first area division unit 14 performs each process in the following procedure.
1. First, each port of each delivery point (the delivery point in the case of the first spatiotemporal network model) is divided into a supply point and a demand point, and a set A of supply points and a set B of demand points are generated. Let V ₁ = A∪B.
2. Then new point s, the t added to _{V 1,} and _{V = V 1 ∪ {s,} t}.
3. The delivery routes e _{11 to} e ₁₉ are created from A to B, and the cost function c (e) based on the travel time when each delivery route is delivered by the route indicated by the delivery route is defined.
4. A delivery route is created from s to A and B to t, and their costs are set to 0. Let E ₂ be the set of delivery routes from s to A and B to t, and let E be the union of E ₁ and E ₂ .
5. The bipartite graph G = (V, E) is constructed by the processing up to this point.
6. The minimum weight maximum matching of G, that is, the path from s to t that minimizes the cost is calculated. More specifically, in the route from s to t, the number of delivery routes from each supply point included in the set A is 1, and the number of delivery routes from each demand point included in the set B is 1. Below, the delivery route is calculated when the total cost of the delivery routes connecting s, each supply point of the set A, each demand point of the set B, and t is the minimum (main problem). 4. Since the cost from s to each supply point of the set A and the cost from each demand point of the set B to t are 0, the supply point a1 to the supply point a3 and the demand point b1 to demand when the cost is the minimum It is possible to determine how to associate with the point b3. Here, since the cost is a function based on the traveling time, it is possible to obtain the one-to-one matching between the supply point and the demand point having the shortest distance. In the example of FIG. 12, for example, the combination of the delivery route e ₁₁ connecting a1 and b1, the delivery route e ₁₆ connecting a2 and b3, and the delivery route e ₁₈ connecting a3 and b2 has the smallest total cost. In the case of a route, a1 is associated with b1, a2 is associated with b3, and a3 is associated with b2.
7. Next, all ports are divided into areas so that the two associated ports are included in the same area. At this time, if the moving time between the two associated ports is less than or equal to a predetermined value, it is classified into one area. In the example of FIG. 12, of the associated a1 and b1, a2 and b3, a3 and b2, for example, a1 and b1 are one area (j4), a2 and b3, a3 and b2 are one area (j5). Classify as.

8. Then 1. ~ 5. Re-create the bipartite graph created in the procedure of 6. Generate a dual problem for (a dual problem can be created by a mathematical operation). If the optimal solution X ^* (e) of the main problem is 1 for the branch e = (u, v), and the optimal solution of the dual problem is Y, then c (e) −Y ^* (u ) -Y ^* (v) = 0 (complementary slackness), where c ^ (e) is c ^ (e) = c (e) -Y ^* (u) -Y ^* (v) Define,
0 ≤ c ^ (e) ≤ ε (ε is a predetermined constant)
Depending on the condition of, c ^ (e) has a width. This condition means that not only c ^ (e) = 0 but also the case where c ^ (e) is ε or less is recognized as a delivery route candidate. That is, not only when the cost is minimized in the main problem, but also a solution with a range is obtained. By relaxing the condition of this solution, in the example of FIG. 12, for example, a delivery route candidate e ₁₉ that connects a1 and b1 is newly obtained.

This completes the first area division processing. When the first area division process is completed, the delivery plan generation unit 12 generates a delivery plan for each divided area. At this time, the delivery plan generation unit 12 uses the delivery route candidates obtained in the first area division process to generate a delivery plan that satisfies the conditions. Specifically, in addition to the above-mentioned “1. Flow rate conservation law” to “6. Constraints on branches remaining in the delivery base”, delivery route candidates (e ₁₁ , e) obtained by the first area division processing ₁₆ , e ₁₈ , e ₁₉ ) is used as a constraint condition to calculate a set of branch information.

Next, the flow of the delivery plan generation processing of this embodiment will be described.
FIG. 13 is a flowchart showing an example of delivery plan generation processing according to the first embodiment of the present invention.
First, the delivery staff who makes the delivery plan inputs the initial conditions of the delivery plan to the delivery planning apparatus 10. The input / output unit 13 receives the input and outputs the received information to the initial condition setting unit 11. The initial condition setting unit 11 acquires the information on the initial condition input by the delivery staff (step S11). The initial condition setting unit 11 sets the acquired initial condition information as the initial condition of the delivery plan. The initial conditions include, for example, the supply quantity (surplus quantity) of deliveries at each base, the demand quantity (insufficient quantity), the number of delivery vehicles at the departure base, the number of delivery staff, and the distance between bases. Travel time, delivery deadline, etc.
Next, the first area dividing unit 14 performs the first area dividing process using the supply quantity and the demand quantity of the deliveries at each delivery base (or port) included in the initial condition information (step S12). .. The first area division processing is as described with reference to FIGS. 11 and 12.

  Next, the delivery plan generation unit 12 sets the branch information for each area obtained by the first area division processing on the spatiotemporal network model illustrated in FIG. 3 and FIG. 8 so as to satisfy the above constraint conditions. Then, a plurality of sets of branch information that satisfy the conditions such as the delivery deadline are generated (step S13). Specifically, the delivery plan generation unit 12 adds information on the number of deliveries, the number of delivery vehicles, and the number of delivery staffs to the delivery route candidates obtained by the first area division processing, and each constraint condition is added. Branch information satisfying (“1. Flow rate conservation law” to “6. Constraints on branches remaining in delivery base”) is generated. Further, the delivery plan generation unit 12 combines the generated branch information to generate a plurality of sets of branch information indicating delivery that satisfies the demanded number of each site by the delivery deadline.

  Next, the delivery plan generation unit 12 calculates the total cost for each set of generated branch information for each area (step S14). For example, the unit cost generated per unit time for each delivery vehicle, delivery staff, and delivery item is recorded in the storage unit 15 in advance, and the delivery plan generation unit 12 uses the unit cost for delivery vehicle, delivery staff, and delivery item as the unit cost. Multiply the time indicated by each branch to calculate the cost for each branch (the total cost of the delivery car, delivery staff, and deliverables). The delivery plan generation unit 12 calculates the cost for each branch included in the set of branch information and sums them. The totaled cost is the cost for one set of branch information. The delivery plan generation unit 12 calculates a cost for each set of all branch information for each area.

  Next, the delivery plan generation unit 12 compares the calculated costs for each calculated set for each area and selects the set of branch information having the smallest total cost (step S15). The selected set of branch information represents the movement of the delivered item, the delivery means, and the delivery staff with the passage of time from the state of the departure point and each delivery point indicated by the initial condition (FIGS. 3 and 8). Therefore, if the delivery is performed based on the set of branch information, the delivery according to the demand from the user becomes possible. That is, this set of branch information is a delivery plan to be obtained for one area after division. When the delivery plan generation unit 12 finishes generating the delivery plan for each area, it means that the delivery plans for all the delivery bases given as the initial conditions have been generated.

According to the present embodiment, by dividing the entire delivery base given in the initial condition into a set (area) of delivery bases located in a short distance, it is possible to reduce the scale of the delivery problem, and in each area. It is possible to reduce the amount of calculation of the delivery plan generation process. Further, when the area division is performed, delivery route candidates are calculated, and a delivery route is selected from the candidates to generate branch information, so that the calculation amount can be further reduced. As a result, even if the number of deliveries and delivery bases is large and the delivery problem becomes large, the delivery plan can be generated in a practical time (for example, 10 minutes).
The delivery plan generation unit 12 may generate the branch plan by generating branch information without using delivery route candidates in step S13.
Further, the area may be reconfigured in consideration of the cost of the area delivery plan. For example, for a pair of areas where the difference in shipping cost is significantly different, if the area where delivery is completed early is made large and the area where delivery is completed late is made small, the overall cost can be reduced. There is.

<Second embodiment>
Next, a delivery planning system according to another method (second embodiment) for generating a delivery plan in a practical time for a large-scale delivery problem will be described with reference to FIGS. 14 to 18. In the first embodiment, attention is paid to a demand point and a supply point existing in a relatively short distance, and a pair of demand point and supply point are collected to generate a small area. In the second embodiment, area division processing is performed centering on the departure point, and a delivery plan is generated in each area after division. The area division processing in the second embodiment is called the second area division processing.

FIG. 14 is a functional block diagram showing an example of the delivery planning system according to the second embodiment of the present invention.
Of the configurations according to the second embodiment of the present invention, the same parts as the functional units configuring the delivery planning apparatus 10 according to the first embodiment of the present invention are designated by the same reference numerals, and description thereof will be omitted. The delivery planning apparatus 10A according to the second embodiment includes a second area dividing unit 16 instead of the first area dividing unit 14 in the configuration of the first embodiment.
The second area dividing unit 16 sets a preset delivery route from the departure point to perform delivery between some delivery points and returns to the original departure point, and the cost when the delivery is performed by the delivery route. A plurality of unit route information indicating and are acquired. In addition, the second area dividing unit 16 selects, from the combinations of the plurality of unit path information, a combination in which the number of delivery points included in the combination is within a predetermined number and the cost is the minimum. The set of the departure point and the delivery point included in the combination of the unit route information is the area after the division.
The second area dividing unit 16 is realized by the CPU included in the delivery planning apparatus 10A by reading the program from the storage unit 15 and executing the program.

FIG. 15 is a first diagram illustrating the second area division processing of the delivery problem in the second embodiment of the present invention.
In FIG. 15, circle points indicate delivery points w1 to w17, and square points indicate departure points c1 to c3. In the present embodiment, first, all possible supply / demand patterns are enumerated, and then a large number of simple delivery routes that satisfy the supply / demand of each pattern are created for each departure point. Here, there are a sufficient number of delivery vehicles (trucks) and delivery staff at the departure points c1 to c3, and the delivery points w1, w3, w6, w8, and w10 are the supply points, and the delivery points w2. It is assumed that w5, w7, w9, and w11 are demand points. In addition, it is assumed that the types of deliveries related to delivery are the same. In this case, a simple delivery route that satisfies the demand and supply for each departure point is, for example, that the departure point c1 is reached to the delivery point w1 (R1), the delivery item is picked up at the delivery point w1, and the delivery point is set to the delivery point w2. This is a delivery route (delivering route 1) that carries a delivery item (R2) and returns to the starting point c1 when delivery is completed (R3). Similarly, a route returning from the departure point c1 to the departure point c1 via the delivery point w3 and the delivery point w5 (delivery route 2), a departure point c1 from the departure point c1 to the delivery point w6, and a departure point c1 via the delivery point w7. To the delivery route (referred to as delivery route 3), from the departure point c2 to the departure point c2 via the delivery point w8 and the delivery point w9, the delivery route (referred to as delivery route 4), from the departure point c3 to the delivery point w10, A delivery route (referred to as delivery route 5) returning to the departure site c3 via the delivery site w11. A large number of these simple routes are created in advance and recorded in the storage unit 15. Although not shown, for example, the following routes are also created and recorded in the storage unit 15 in advance. A delivery route from the departure point c1 to the departure point c1 via the delivery points w1 and w5, a delivery route from the departure point c1 to the departure point c1 via the delivery points w1 and w7, and a departure point c1 A delivery route returning to the departure point c1 via the delivery point w3 and the delivery point w2, a delivery route returning from the departure point c1 to the delivery point w10 and a departure point c1 via the delivery point w11, a departure point c2 to the delivery point w1 A delivery route returning to the departure point c2 via the delivery point w2, a delivery route returning from the departure point c3 to the departure point c3 via the delivery point w1 and the delivery point w2, and the like.

  Also, a simple delivery route is only a delivery route that returns to the original departure point via one supply point and one demand point (a route that goes around two delivery points and returns to the original departure point). Instead of pointing to, the departure route c1 is taken, two delivery items are picked up at the delivery point w1, one delivery item is delivered to each of the delivery points w2 and w4, and the delivery route is returned to the departure point c1. May be present (example with 3 delivery sites). Alternatively, the customer departs from the departure point c1, picks up one delivery item at the delivery point w1 and delivers it to the delivery point w2, subsequently takes one delivery item at the delivery point w3, delivers it to the delivery point w4, and sends it to the departure point c1. It may be a delivery route of returning (example of four delivery bases).

FIG. 16 is a second diagram illustrating the second area division process of the delivery problem in the second embodiment of the present invention.
As shown in FIG. 16, the storage unit 15 records a plurality of simple delivery routes prepared in advance. In addition, the cost of delivery by the delivery route is recorded in association with the simple delivery route. The cost is given as a function of traveling time, for example. The more the pre-recorded simple delivery route and cost information, the more accurate (close to the exact optimal solution) the delivery plan can be generated. Information including the simple delivery route illustrated in FIG. 16 and the cost corresponding to the delivery route is referred to as unit route information.

FIG. 17 is a third diagram illustrating the second area division process of the delivery problem in the second embodiment of the present invention.
Next, the second area division processing by the second area division unit 16 will be described with reference to FIGS.
As a premise, the storage unit 15 records the unit path information illustrated in FIG. Further, it is assumed that initial conditions of delivery requirements (demand quantity, supply quantity, number of delivery vehicles at departure point, number of delivery staff, etc. for each delivery point) are given.
1. First, the second area dividing unit 16 reads from the storage unit 15 unit route information including a delivery route that partially satisfies the delivery request (demand) given in the initial condition.
2. Next, the second area division unit 16 combines the delivery routes included in the read unit route information to create a route that satisfies all delivery requests, and sets it as a provisional solution. Here, a mathematical method called a set partitioning approach is used as a method for obtaining a combination that satisfies all requirements and has the lowest cost by combining simple delivery routes recorded in advance, but in the case of this method, When the number of simple delivery routes becomes huge, the optimization problem of the combination may not be solved in a practical time. Therefore, the second area dividing unit 16 generates an initial solution using a small number of delivery routes among the many simple delivery routes stored in the storage unit 15, and uses a mathematical method called a column generation method. , Add the simple delivery route to find the optimal solution. It should be noted that a small number of simple delivery routes for generating the initial solution may be selected by any method. A generally provided solver can be used to generate the initial solution. At this time, a restriction is placed on the number of delivery bases handled by one departure base (for example, within 6 bases including demand points and supply points). Here, the reason why the number of delivery bases is restricted (upper limit) is to reduce the amount of calculation and to speed up the processing. The number of delivery bases to be constrained may be set, for example, by performing an actual calculation and setting the upper limit to the number of delivery bases when a solution is obtained within a practical time. As the initial solution, for example, the solution (delivery route 1 to delivery route 5) shown in FIG. 15 is obtained.

  3. Next, the second area dividing unit 16 selects one or a plurality of delivery routes from the unselected simple delivery routes by the column generation method (known mathematical method), and selects a certain already selected simple delivery route. Calculate the reduction cost when the route and the selected simple delivery route are replaced. The reduction cost is the original simple delivery selected before the replacement from the total of the costs (the cost column in FIG. 16) recorded in association with the simple delivery route newly selected as the solution by the replacement. It is a value obtained by subtracting the total cost recorded in association with the route.

  4. The second area dividing unit 16 has three steps. If the reduction cost calculated in step 3 is a negative value (lower after replacement), 3. Update some of all existing shipping routes with the simple shipping route selected in. For example, regarding the delivery to the delivery base w7, the delivery route 3 is selected in the initial solution shown in FIG. 15, but the second area dividing unit 16 replaces the delivery route 3 and starts from the departure base c2 to the delivery base. The reduction cost in the case of switching to a route (delivery route 6) returning to the departure site c2 via w6 and the delivery site w7 is calculated. Since the cost of the delivery route 3 is 2500 and the cost of the delivery route 6 is 1500 according to FIG. 16, the reduction cost is −1000. Therefore, the second area dividing unit 16 updates the delivery route 3 with the delivery route 6. FIG. 17 shows a combination of updated simple delivery routes. In addition, also when calculating the reduction cost, the second area division unit 16 selects the delivery route so that the number of bases in charge of one departure base is within the constraint.

  Further, in this example, an example in which the simple delivery route is moved from the range in charge of the departure site c1 to the range in charge of the departure site c3 is described, but the update of the delivery route is not limited to this example. For example, in the state of FIG. 15, a combination of the delivery route 1 and the delivery route 2 in the route which the departure point c1 is in charge of is a route from the departure point c1 to the departure point c1 via the delivery point w3 and the delivery point w2. A method of updating to a combination of routes returning from the departure point c1 to the departure point c1 via the delivery point w1 and the delivery point w5 may be used. Alternatively, assuming that there are two target deliverables at the delivery point w1, the combination of the delivery route 1 and the delivery route 2 is set from the departure point c1 via the delivery point w1, the delivery point w2, the delivery point w3, and the delivery point w5. Alternatively, a method of updating to a delivery route that returns to the departure point c1 may be used.

  5. The second area dividing unit 16 has three steps. ~ 4. The above process is repeated and the second area division process ends when there is no route that can reduce the cost. When the second area division process ends, the delivery bases within the constraint condition (for example, 6 bases) are associated with each departure base. A set of a plurality of associated delivery bases and departure bases (for example, each of area j6 to area j8) is an area obtained by the second area division processing.

Next, the flow of the delivery plan generation processing of this embodiment will be described.
FIG. 18 is a flowchart showing an example of delivery plan generation processing according to the second embodiment of the present invention. Processing similar to that of FIG. 13 will be briefly described.
First, the initial condition setting unit 11 acquires information on initial conditions input by the delivery staff or the like (step S11).
Next, the second area dividing unit 16 uses the supply quantity, the demand quantity, the number of delivery staff at the departure location, the type and number of delivery vehicles included in the information of the initial condition, and the Two-area division processing is performed (step S121). The second area division processing is as described with reference to FIGS.

  Next, the delivery plan generation unit 12 determines, for each area obtained by the second area division processing (a departure point obtained by the second area division processing and a set of a plurality of delivery points associated with the departure point). On the spatiotemporal network model illustrated in FIG. 3 and FIG. 8, the branch information is generated so as to satisfy the above constraint conditions, and a plurality of sets of branch information satisfying the conditions such as the delivery deadline are generated (step S131). In the example of FIG. 17, the delivery plan generation unit 12 generates a plurality of sets of branch information for each of the areas j6 to j8. The delivery plan generation unit 12 may generate the branch information regardless of the simple delivery route and the combination thereof used in the second area division process, or the branch information may be generated by using the simple delivery route and the combination thereof. Information may be generated.

Next, the delivery plan generation unit 12 calculates the total cost for each of the generated pieces of branch information (step S14). In the example of FIG. 17, the delivery plan generation unit 12 calculates the total cost for each set of generated branch information for each of the areas j6 to j8.
Next, the delivery plan generation unit 12 compares the calculated total costs and selects a set of branch information having the minimum total cost (step S15). In the example of FIG. 17, the delivery plan generation unit 12 selects, for each of the areas j6 to j8, a set of branch information that minimizes the total cost. The set of selected branch information indicates the delivery plan in each area. That is, when the delivery plan generation unit 12 finishes generating the delivery plan for each area, it means that the delivery plans for all the delivery bases before the division are generated.

  According to the present embodiment, it is possible to divide each of the delivery bases having the demand and supply given in the initial condition into the delivery base by associating each of the delivery bases with the departure base. Compared to the case of generating a delivery plan for all the demanded delivery bases given in the initial conditions, by dividing the delivery area into small delivery areas and generating the delivery plan for each delivery area. , It is possible to reduce the amount of calculation required to generate a delivery plan. As a result, even when the number of deliveries and delivery bases is large and the delivery problem becomes large, it is possible to make a delivery plan in a practical time (for example, 10 minutes).

<Third embodiment>
A delivery planning system according to another method (third embodiment) for generating a delivery plan for a large-scale delivery problem in a practical time will be described with reference to FIGS. 19 to 22. In the first embodiment and the second embodiment, the delivery problem is divided into small-scale delivery problems by spatially dividing the delivery problem (area division) based on the supply and demand information for each delivery base included in the initial condition. , It was a method to realize high-speed processing by solving a small-scale delivery problem. In the third embodiment, the delivery problem is made into a small problem by time division based on the information of the delivery time limit of the delivery included in the initial condition, and the delivery plan is generated every time after the division.

FIG. 19 is a functional block diagram showing an example of the delivery planning system in the third embodiment of the present invention.
Among the configurations according to the third embodiment of the present invention, the same components as the functional units configuring the delivery planning apparatus 10B according to the first embodiment of the present invention will be denoted by the same reference numerals, and description thereof will be omitted. The delivery planning apparatus 10B according to the third embodiment includes a time division unit 17 instead of the first area division unit 14 in the configuration of the first embodiment. The delivery planning apparatus 10B includes a delivery plan generating unit 12a instead of the delivery plan generating unit 12.
The time division unit 17 divides the delivery problem into a plurality of times by dividing the delivery time limit given in the initial condition, and divides the delivery problem into delivery problems of small scale for each time. Each time divided by the time division unit 17 is called a section.
The delivery plan generation unit 12a solves the delivery problem in which different objective functions and constraints are set according to the section created by the time division unit 17 to generate a delivery plan. For example, the delivery plan generation unit 12a starts the delivery from the delivery status of the delivery at the first time of each section after the division (the progress status of the delivery when the immediately preceding section is finished), and A delivery plan is created so that as many deliverables as possible will be delivered to a delivery base with a high demand. In addition, the time division unit 17 determines, for the last section of the divided sections, a delivery point that has not been delivered among the demanded delivery points indicated by the initial conditions in the last section. Generate a delivery plan where deliveries are delivered to all of the.
The time division unit 17 and the delivery plan generation unit 12a are realized by the CPU included in the delivery planning device 10B by reading the program from the storage unit 15 and executing the program.

FIG. 20 is a first diagram illustrating the time division processing of the delivery problem in the third embodiment of the present invention.
The left diagram of FIG. 20 shows an initial state of a certain delivery problem. The delivery base w1 has two extra deliveries d1, and the delivery base w2 has three extra deliveries d1. In addition, the delivery base w3 lacks four deliverables d1, and the delivery base w4 lacks one deliverable d1. Consider the problem of delivering the delivered product d1 from the initial state within 120 minutes so as to satisfy the demand at the delivery site w3 and the delivery site w4. In the first and second embodiments, the delivery base w1 to the delivery base w4 are divided for each area. In this embodiment, the delivery time limit 120 minutes given as the initial condition is divided.
Specifically, the time division unit 17 divides the delivery time limit of 120 minutes into a plurality of times (sections). For example, the time division unit 17 divides the delivery time limit of 120 minutes into two sections of 60 minutes in the first half and 60 minutes in the second half. The time length of one section formed by the time division unit 17 and the number of sections may be arbitrary. For example, the time division unit 17 may divide 120 minutes into 90 minutes and 30 minutes, or may divide the 120 minutes into three intervals of 40 minutes. Further, the time division unit 17 may set a time shorter than the delivery time limit given in the initial condition by a predetermined time as the first section after the division and the remaining time as the last section.

  The right diagram of FIG. 20 shows that the time division unit 17 divides the delivery time limit of 120 minutes into two sections of 60 minutes each. When the time division unit 17 divides the delivery time limit, the delivery plan generation unit 12a generates the delivery plan for the first section created by the division. At this time, the delivery plan generation unit 12a does not aim to satisfy all the requests, but generates a delivery plan that can satisfy as many requests as possible at the end point of the first section. It should be noted that, in the case of this example, the aim of satisfying all the requirements is to deliver the delivered product d1 in 60 minutes so as to satisfy the demanded quantities of the delivery site w3 and the delivery site w4. A delivery plan that can satisfy as many requests as possible is, for example, 60 minutes after the delivery is started, there are three shortages of the delivery item d1 at the delivery point w3 and the delivery item d1 at the delivery point w4. When a delivery plan in which the shortage is 0 and a delivery plan in which the delivery d1 is short in the delivery base w3 is 2 and the delivery d1 is short in the delivery base w4 is 0, the latter delivery is generated. It refers to a plan.

  Next, the objective function and constraints set for the first section will be described. It should be noted that, more generally, when the time division unit 17 divides the delivery time limit into N pieces, the objective function and the like to be described next are all sections (except the last section (Nth section)). It is an objective function or the like to be used in order from the first section to the (N-1) th section in the order of time.

(Objective function)
The sum of the following (1) to (7) is minimized.
(1) Transfer cost between bases The transfer cost between bases can be suppressed.
(2) Time to meet demand supply Reduce the number of solution options by urging the time to meet demand supply as soon as possible (even if similar delivery is possible at a later time, only the earliest delivery should be the solution) Can reduce the number of choices, leading to a reduction in the amount of calculation).
(3) Port number to supply when demand is met Reduce the number of solution options by encouraging supply from the port with the smallest number (even if there is no problem delivering to the port with the largest number, the port with the smallest number) It is possible to reduce the choice of solutions and reduce the amount of calculation by setting).
(4) Number of persons existing at the delivery base and delivery means that are not used in the subsequent section (g [w])
At the last time of the section under calculation, it is urged to move the extra person / delivery means not used for delivery of the delivered article to the departure point in the next section. For example, at the last time of the first section, if there is no delivery means that can carry a bicycle on the second section, the bicycle is not used for delivery in the second section and is moved to the departure point.
(5) Number of persons and delivery means existing in those delivery points when the demand at the demand point and the supply at the supply point are satisfied. At the delivery point where demand and supply are satisfied, people and delivery means remain. Encourage them not to. In this embodiment, since the delivery plan is calculated independently for each time-divided section (although the delivery status in the immediately preceding section is handed over), extra delivery staff not used in the later section. It is also possible that the delivery method remains at the delivery site. Therefore, (4) and (5) are added to prevent excess delivery staff and the like from remaining at the delivery site.
(6) The number of deliveries remaining at the supply point, the number of deliveries that are insufficient at the demand point (7) The number of demand points that are insufficient at the deliver point, and the demand at the end time of the section is as much as possible according to (6) and (7). You can encourage them to meet as many supply conditions as possible.
Although the objective function is expressed as minimizing the sum of the functions corresponding to the contents of the items (1) to (7), any term (function of each item) of the objective function can be used. Weighting may be performed by multiplying by a coefficient.

Next, restrictions will be described.
1. Flow Preservation Law (a) In the case of each section after the division other than the last section (1) About the flow rate of delivered goods At the start of the section, the flow rate from the port where the supply exists is 1, the supply exists The flow rate from the non-use port is zero. Otherwise, if it is not the end of the section, the outgoing and incoming flows are equal.
(2) Flow rate of delivery vehicles At the start of the section, the flow rate from the road is the number of delivery vehicles existing at the base. Otherwise, if it is not the end of the section, the outgoing and incoming flows are equal.
(3) Flow rate of delivery staff At the start of the section, the flow rate leaving the road will be the number of delivery staff at the base. Otherwise, if it is not the end of the section, the outgoing and incoming flows are equal.

(A) In the case of the last section of each section after division (1) About the flow rate of delivered goods At the start of the section, the flow rate from the port with supply is 1 and the flow rate from the port without supply is It becomes 0. At the end of the section, the flow rate entering the port with demand is 1 and the flow rate entering the port with no demand is 0. Otherwise, the outgoing and incoming flows are equal.
(2) Flow rate of delivery vehicles At the start of delivery in a section, the flow rate from the road is the number of delivery vehicles existing at that point. At the end of the section, the flow rate entering from the road is the number of delivery vehicles in demand at the base. Otherwise, the outgoing and incoming flows are equal.
(3) Flow rate of delivery staff At the start of delivery in a section, the flow rate from the road is the number of delivery staff at the site. At the end of the section, the flow rate entering from the road will be the number of delivery staff in demand at the base. Otherwise, the outgoing and incoming flows are equal.

2. The amount of deliveries and people moving within the capacity-constrained delivery site is 1 or less.

3. Constraints within the delivery base 1
∀e ∈ E _wp
(E _wp is a set of _deliverables , delivery means, and branches that indicate movement from people's roads to ports)
(1) When the destination of e is the supply point of d The delivered product does not enter the port from the road.
(2) When the destination of e is the demand point of d The flow rates of the delivered product and the delivery staff have the same value (0 or 1).
(3) In either case, the number of bicycles is less than the number of delivery staff.

4. Constraints within the delivery base 2
∀e ∈ E _pw
(E _pw is a set of branches indicating the delivery goods, delivery means, and movement of people from the port to the road)
(1) When the starting point of e is the supply point of d The flow rates of the delivered material and the delivery staff have the same value (0 or 1).
(2) When the starting point of e is the demand point of d: The delivered product does not go out of the way from the port.
(3) In either case, the number of bicycles is less than the number of delivery staff.

5. Constraints on variables relating to penalties at the last time of an interval For an arbitrary road w, if the number of people and delivery means not used in the next interval is g [w], then g [w] ≤ f [w] Put a constraint.
f [w] represents an arbitrary number. By adjusting the value of f [w], the number of people and delivery means that can be allowed to remain at the end of the section can be changed.

6. Constraints on branches from road to road (1) When the branches from road to road are car branches (possibly riding a bicycle)
The restrictions are that the delivery staff must be on the delivery vehicle, that the number of delivery staff members is less than the number of people that can be boarded, and that the number of bicycles that cannot be driven is less than the number that can be loaded on the vehicle.
(2) When the branch from road to road is a branch of a bicycle and a branch of walking, not a branch of a car (moving by bicycle or walking)
The sum of the number of bicycles and the number of people moving on foot is equal to the number of delivery staff moving on that branch.
(3) When the branch from road to road is a bicycle branch but not a car branch or a walking branch (moving by bicycle)
The number of bicycles is equal to the number of delivery staff moving along the branch.
(4) When the branch from road to road is a walking branch but not a car branch or a bicycle branch (moves on foot)
The number of people moving on foot is equal to the number of shipping staff moving on that branch.

7. Restrictions on branches staying in the delivery base Restrictions are that people should always be in the car, bicycles should not be parked on the road, and the total volume of deliveries should be less than the capacity of the truck.

  The delivery plan generation unit 12a solves the delivery problem (integer programming problem) formulated by these objective functions and constraints using the first or second space-time network. In the actual calculation, a cut may be added to further speed up the calculation. The right side of FIG. 20 shows an example of the result of the delivery plan generation unit 12a generating the delivery plan for the first section. According to this plan, 60 minutes after the delivery is started, the delivery point w1 and the delivery point w2 have one extra delivery item d1 and the delivery point w3 lacks two delivery items d1. It can be seen that the shortage of the delivered product d1 has been resolved in w4.

  The following points can be cited as advantages of the method of calculating by dividing time in this way. First, by setting the delivery time limit from 120 minutes to 60 minutes, it is possible to reduce the number of parameters required for calculation and reduce the amount of calculation. For convenience of explanation, FIG. 20 shows an example in which both the delivery bases and the number of deliveries are small. However, when calculating the problem of delivering 20 or more deliveries within 120 minutes to 20 delivery bases. It has been found that, for example, there are 41000 variables and 61000 constraints. On the other hand, when the time is divided into the first 60 minutes and a delivery plan that can satisfy as many requests as possible is generated, for example, the number of variables can be reduced to 14,000 and the number of constraints can be reduced to about 18,000. By reducing the number of parameters in this way, the amount of calculation can be reduced and the processing speed can be increased. Next, the latter half of the 60-minute delivery plan generation process will be described.

FIG. 21 is a second diagram illustrating the time division processing of the delivery problem in the third embodiment of the present invention.
FIG. 21 shows a delivery plan generation process performed using the latter half 60 minutes after division. The demand quantity and supply quantity at each delivery point at the start of the latter half 60 minutes will be summarized. The delivery base w1 and the delivery base w2 at the start of the latter half have one extra deliverable d1 and the delivery base w3 lack two deliverables d1. The delivery plan that the delivery plan generation unit 12a has to generate in the latter half 60 minutes is such that the delivery items d1 at the delivery points w1 and w2 satisfy the demand at the delivery point w3 within the remaining 60 minutes. It's a delivery issue. Regarding the delivery point w4, the shortage of the delivery point w4 has been resolved in the first half 60 minutes, so it is not included in the delivery problem in the second half 60 minutes.

  Next, the objective function and the constraint set for the delivery problem for the last section when the delivery time limit is divided into N pieces will be described. The objective function and constraints in this case are the same as those described using the first spatiotemporal network model (FIG. 3) and the second spatiotemporal network model (FIG. 8). In other words, the delivery plan generation unit 12a minimizes the cost and the travel time required for delivery among the delivery plans that finish delivering the deliverables so as to satisfy all the demands by the last time of the last section. To generate.

  As for the advantages of the processing in the latter half of 60 minutes (the last section), first, as in the first half of 60 minutes, by setting the delivery time limit to 60 minutes, the number of parameters is reduced and the calculation amount is reduced. It can be pointed out that the processing speed can be increased. Furthermore, the remaining demand is reduced by the delivery plan that satisfies as many demands as possible calculated in each section up to the last section, which reduces the scale of the delivery problem to be solved. I can mention that. For example, in the examples shown in FIG. 20 and FIG. 21, not only the demand quantity at each demand point decreases but also the demand at the delivery point w4 is satisfied, so that the number of delivery points has been successfully reduced. This can further reduce the scale of the delivery problem. When the problem of delivering 20 or more deliveries to 20 delivery sites within 120 minutes is divided every 60 minutes, for example, in the latter half 60 minutes, the number of variables is 8000 and the number of constraints is 12000. Can be reduced to a degree. As described above, according to the present embodiment, it is possible to reduce the scale of the delivery problem in the later section by the reduction of the parameter due to the time division and the delivery plan generated in the section earlier in time. , It is possible to speed up the process of generating a delivery plan. In addition, since the area division is not performed in the third embodiment, it is possible to generate a delivery plan while securing the globality of the distribution base distribution, as compared with the first embodiment and the second embodiment, which is more optimized. A shipping plan can be generated.

Next, the flow of the delivery plan generation processing of this embodiment will be described.
FIG. 22 is a flowchart showing an example of the delivery plan generation processing in the third embodiment of the present invention. Processing similar to that in FIGS. 13 and 18 will be briefly described.
First, the delivery staff who makes the delivery plan inputs the initial conditions of the delivery plan to the delivery planning apparatus 10B. The input / output unit 13 receives the input and outputs the received information to the initial condition setting unit 11. The initial condition setting unit 11 acquires the information on the initial condition input by the delivery staff (step S11).
Next, the time division unit 17 performs the time division process using the delivery time limit included in the information of the initial condition (step S122). The time division process is as described with reference to FIG. For example, the time division unit 17 divides the delivery time limit of the initial condition into two or three. Alternatively, if the time (eg, 75 minutes) at which delivery completion to a demanded delivery site can be expected at a certain rate is known based on an empirical rule or the like, the time division unit 17 sets the time unit (eg, 75 minutes) according to the user setting. ), The original delivery time limit may be divided, and the remaining time may be set as the last section. Alternatively, the time division unit 17 may set a time shorter than the delivery time limit given in the initial condition by a predetermined time as the first section after the division and the remaining time as the last section. Next, the delivery plan generation unit 12a generates a delivery plan for each of the divided sections in time order. First, the delivery plan generation unit 12a sets 1 to the counter variable n (step S123). Next, the delivery plan production | generation part 12a sets the delivery problem of the nth area (step S124). For example, in the case of the first section, the delivery plan generation unit 12a determines that the demand quantity, the supply quantity, the quantity of delivery means existing at the departure location, the number of delivery staff members, and the like of each delivery base included in the initial condition information. By using the time of the 2nd section as the delivery time limit, we formulate the integer programming problem with the objective function and constraints for the generation of the delivery plan that satisfies as many demands as possible and has the lowest cost.

  Next, the delivery plan generation unit 12a uses the first or second spatiotemporal network model illustrated in FIGS. 3 and 8 for the formulated integer programming problem while satisfying each constraint and delivering each delivery. A plurality of sets of branch information that satisfy the demand of the base as much as possible are generated (step S132). Next, the delivery plan generation unit 12a calculates the total cost for each set of generated branch information (step S14). Next, the delivery plan generation unit 12a compares the calculated total costs and selects a set of branch information having the minimum total cost (step S15). As a result, a delivery plan for the n-th (first time this time) section is generated.

  Next, the delivery plan generation unit 12a determines whether n is equal to N (step S16). When n is equal to N (step S16; Yes), it means that the distribution plans for all the sections after the division have been generated, so the generation process of the distribution plan ends. When n is not equal to N (step S16; No), the delivery plan production | generation part 12a adds 1 to n (step S17), and repeats the process from step S124.

  Specifically, for example, when the value of n after adding 1 is 2, the delivery plan generation unit 12a determines, in step S124, the delivery plan of each delivery base as a result of executing the delivery plan generated for the first section. The integer programming problem is formulated by using the demand quantity, the supply quantity, the quantity of delivery means existing at the departure point, the number of delivery staff, and the time of the second section as the delivery time limit. At this time, if n is equal to N, the delivery plan generation unit 12a formulates an integer programming problem with an objective function and constraints for generation of a delivery plan that satisfies all the requirements (first embodiment, second embodiment). Objective function similar to morphology). If n is not equal to N, the delivery plan generation unit 12a formulates an integer programming problem with an objective function and constraints for generating a delivery plan that can satisfy as many requests as possible. The delivery plan generation unit 12a solves the integer programming problem to generate a delivery plan for the nth section. The delivery plan generation unit 12a repeats the processing of steps S124 to S17 until the delivery plan is generated for all the sections (until n becomes equal to N). The entire delivery plan sequentially generated for each of the first section to the Nth (last) section is a delivery plan that satisfies the requirements given in the initial conditions.

In the flowchart of FIG. 22, the delivery time limit given as the initial condition is first divided into some sections, but the delivery planning process may be configured as follows, for example.
1. First, a section (first delivery time limit) shorter than the delivery time limit given in the initial condition is set, and a delivery plan that can deliver as much and cheaply as possible within the section is generated.
2. Next, for the deliverables that cannot be delivered within the first delivery time limit, a section of a predetermined length (second delivery time limit) following the first delivery time limit is set, and within the set section Create a delivery plan that delivers as many deliverables as possible.
3.1. ~ 2. The above step is repeated until the total length of sections from the start of delivery does not exceed the delivery time limit. In other words, find the solution while extending the time (time expansion method). The length of the first section or the section to be extended may be arbitrarily set according to the delivery situation.
4. If the total time from the start of delivery is about to exceed the delivery time limit, the next section is set as the end and the last section is set (the completion time of the delivery plan generated immediately before is set as the start time, and the first delivery restriction is set. A delivery plan is created that satisfies all demands and minimizes the cost at the end time when the delivery time limit included in the initial conditions elapses based on the time start time.

  When the delivery plan generation process of the present embodiment is actually performed, a sub-optimal solution (exactly within 10 minutes) is solved in a practical time (within 10 minutes) for a delivery problem with 20 delivery bases and about 20 deliverables. The difference in the value of the objective function was 10% or less compared with the optimum solution).

  The delivery plan generation method of this embodiment can also be used in the following situations. For example, if all vehicles must be delivered to a demanding parking lot in 120 minutes, first create a delivery plan for the first 60 minutes. When the delivery plan is generated, vehicle delivery is actually started based on the delivery plan. While the vehicle is being delivered, generate a delivery plan for the remaining 60 minutes. In this way, by performing the delivery plan generation process and the delivery in parallel, it is possible to effectively use the time, for example, at the site where the car sharing service is provided.

  It should be noted that the process of each process in the delivery planning apparatuses 10, 10A, and 10B described above is stored in a computer-readable recording medium in the form of a program, and the program of the delivery planning system reads and executes the program. The above processing is performed. Here, the computer-readable recording medium refers to a magnetic disk, a magneto-optical disk, a CD-ROM, a DVD-ROM, a semiconductor memory, or the like. Further, the computer program may be distributed to the computer via a communication line, and the computer that receives the distribution may execute the program.

Further, the program may be for realizing a part of the functions described above. Further, it may be a so-called difference file (difference program) that can realize the above-mentioned functions in combination with a program already recorded in the computer system.
Further, the delivery planning apparatuses 10, 10A, 10B may be configured by one computer, or may be configured by a plurality of computers communicably connected.

  In addition, it is possible to appropriately replace the components in the above-described embodiments with known components without departing from the spirit of the present invention. Further, the technical scope of the present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the spirit of the present invention.

  The delivery staff is an example of a delivery entity, a delivery vehicle, a truck, and a bicycle are examples of delivery means, and a shared vehicle in car sharing is an example of deliverables. Each of the first area dividing unit 14, the second area dividing unit 16, and the time dividing unit 17 is an example of a dividing unit.

10, 10A, 10B ... Delivery planning device 11 ... Initial condition setting unit 12, 12a ... Delivery plan generating unit 13 ... Input / output unit 14 ... First area dividing unit 15 ... Storage Part 16 ... Second area division unit 17 ... Time division unit

Claims (14)

In the delivery problem of delivering a delivery to a demanded delivery base, a division unit that divides the delivery problem indicated by the initial condition into a smaller-scale delivery problem,
A delivery plan generation unit that generates a delivery plan for the delivery problem after the division unit has divided;
Equipped with
The dividing unit defines one demand point included in a delivery base group in which there is a demand for the delivery product and one supply point included in a delivery base group that is a supply source of the delivery product as the one demand point. From the above to the one supply point so as to minimize the movement time, and generate a set of combinations of the demand point and the supply point that are associated with each other, and deliver the delivery problem indicated by the initial condition to the generated set. It divides into the delivery problem from the demand point group included in the to the supply point group,
Delivery planning system. The dividing unit is a supply point in which the movement time from one supply point to one demand point is equal to or less than a predetermined value among the corresponding relationships between the plurality of supply points and the plurality of demand points included in the generated set. Calculate the delivery route from
The delivery plan generation unit uses the delivery route in which the travel time is equal to or less than the predetermined threshold value among the delivery routes from the supply point group to the demand point group included in the generated set to use the small scale delivery problem. Generate a shipping plan for,
The delivery planning system according to claim 1 . In the delivery problem of delivering a delivery to a demanded delivery base, a division unit that divides the delivery problem indicated by the initial condition into a smaller-scale delivery problem,
A delivery plan generation unit that generates a delivery plan for the delivery problem after the division unit has divided;
Equipped with
The division unit is a unit indicating a preset delivery route from the departure point to a delivery between some delivery points and returning to the departure point, and a cost when the delivery is performed on the delivery route. Obtaining a plurality of route information, among the combinations of the plurality of unit route information, the number of the delivery bases included in the combination is within a predetermined number, and calculate a combination in which the total cost is the minimum, A set of a departure point and a delivery point included in the combination is generated, and the delivery problem indicated by the initial condition is set to a delivery problem from the demand point group to the supply point group included in the generated set of the departure point and the delivery point. Split into,
Distribution transmission planning system. The division unit calculates a combination of the unit path information by a column generation method,
The delivery planning system according to claim 3 . In the delivery problem of delivering a delivery to a demanded delivery base, a division unit that divides the delivery problem indicated by the initial condition into a smaller-scale delivery problem,
A delivery plan generation unit that generates a delivery plan for the delivery problem after the division unit has divided;
Equipped with
The dividing unit divides the delivery problem indicated by the initial condition into the delivery problems for each of the divided times by dividing the delivery time limit of the delivery item into a plurality of times,
The delivery plan generation unit is a delivery system in which the delivery state is delivered to a demanded site as much as possible within each time after the division based on the delivery status of the delivery item at the first time of each time after the division. Generate plans,
Distribution transmission planning system. Regarding the delivery problem related to the last time that the dividing unit divided,
The delivery plan generation unit generates a delivery plan so that the delivery is delivered to all of the demanded delivery bases indicated by the initial condition by the end of the last time.
The delivery planning system according to claim 5 . In the delivery problem of delivering a delivery to a demanded delivery base, a division unit that divides the delivery problem indicated by the initial condition into a smaller-scale delivery problem,
A delivery plan generation unit that generates a delivery plan for the delivery problem after the division unit has divided;
Equipped with
The dividing unit divides the delivery problem indicated by the initial condition into a delivery problem in which a first delivery time limit shorter than a delivery time limit included in the initial condition is a new delivery time limit,
The delivery plan generation unit generates a delivery plan in which the delivered items are delivered to a demand base as much as possible within the first delivery time limit,
Distribution transmission planning system. The dividing unit sets a predetermined length of time following the first delivery time limit as a second delivery time limit,
The delivery plan generation unit generates a delivery plan in which the delivered items are delivered to a demand base as much as possible within the second delivery time limit.
The delivery planning system according to claim 7 . The delivery plan generation unit sets the completion time when the generated delivery plan is executed as the start time, and the time when the delivery time limit included in the initial condition elapses based on the start time of the first delivery time limit. As a result of the execution of the delivery plan, a delivery plan that finishes delivery of the delivery item that has not been delivered is generated within the last time with the end time as
Delivery planning system according to claim 7 or claim 8. In generating a delivery plan for delivering the delivered items to a base having a demand as much as possible, the delivery plan generating unit executes the delivery plan, and as a result, the delivery staff and the delivery means required to execute the delivery plan. Generates a delivery plan on the condition that the item does not remain at the delivery point,
The delivery planning system according to any one of claims 5 to 9 . The delivery plan generation unit has a departure point indicating an initial position of a delivery entity that delivers the delivery item and a delivery means that moves the delivery item or the delivery entity, and each time based on the delivery point and the time when the delivery starts. And branch information indicating the flow rate of the delivered item related to the delivery, the delivery subject, and the delivery means between two point information related to delivery of the delivered item of the point information. Solving an integer programming problem based on a spatiotemporal network model composed of, and generating at least one set of branch information relating to the delivery in the delivery problem after the division by the division unit,
The delivery planning system according to any one of claims 1 to 10 . In the spatiotemporal network model, the delivery plan generation unit sets, for each of the delivery bases, point information related to an entrance that is a combination of an entrance and a time of the delivery base, and an exit and a time of the delivery base. The point information relating to the exit and the point information relating to the storage place of the delivery, which forms a set of time for each delivery corresponding to the delivery base, are generated, and the point information relating to the entrance and the delivery The value of the flow rate of the delivery entity and the flow rate of the delivery item between the point information regarding the exit and the point information regarding the delivery item are set to 0 or 1.
The delivery planning system according to claim 11 . The delivery planning system
In the delivery problem of delivering the deliverables to a demanded delivery base, a step of dividing the delivery problem indicated by the initial condition into a smaller-scale delivery problem ,
Generating a delivery plan for the delivery problem after the division ;
Have
In the step of dividing, one demand point included in a delivery base group that has a demand for the delivery item and one supply point included in a delivery base group that is a supply source of the delivery item are included in the one demand point. Points so as to minimize the time required to move to the one supply point, generate a set of associated demand points and supply points, and generate the delivery problem indicated by the initial condition. Divide into a delivery problem from the demand point group included in the set to the supply point group,
Delivery planning method. Computer of the delivery planning system,
A method of dividing the delivery problem indicated by the initial condition into a smaller-scale delivery problem in the delivery problem of delivering the deliverables to a demanding delivery base,
Means for generating a delivery plan for the delivery problem after the division,
To function as,
The dividing means includes one demand point included in a delivery base group that has a demand for the delivery item and one supply point included in a delivery base group that is the supply source of the delivery item. Points so as to minimize the time required to move to the one supply point, generate a set of associated demand points and supply points, and generate the delivery problem indicated by the initial condition. Divide into a delivery problem from the demand point group included in the set to the supply point group,
program.

Images