JPH07175504A - Device and method for search for optimum vehicle allocation and distribution order in distribution problem - Google Patents

Abstract

PURPOSE:To provide the device and method for the search for the optimum vehicle allocation and distribution order in distribution problems which can solve two kinds of problem of the vehicle allocation and distribution order under various restriction conditions and lower the cost. CONSTITUTION:The search device is equipped with a 1st determination part 3 which determines an array plan for a two-dimensional array having respective rows corresponding to respective vehicles and respective columns corresponding to the distribution order, a 2nd determination part 5 which determines a cost function showing the cost and restriction conditions at distribution destinations, etc., an arithmetic part 7 which computes and define an energy function with the linear sum of a cost term indicating the cost function and a restriction term showing the restriction conditions, and a minimization part 9 which minimizes the energy function; and data which are required for the distribution problems are inputted from a data input part 1 and an arithmetic result is outputted from an arithmetic result output part 11.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a search apparatus and a search method for optimum vehicle allocation and delivery order in a delivery problem,
In particular, a search device and a search for an optimal vehicle allocation and delivery order in a delivery problem that searches for an optimal vehicle allocation and delivery order that can satisfy various constraints given to the delivery problem and minimize costs Regarding the method.

[0002]

2. Description of the Related Art In order to deliver a large number of parcels to each delivery destination using a plurality of vehicles, what cargo is loaded on which car (delivery), and what delivery destination is assigned to each vehicle? Two problems have to be solved: turn around (delivery order). In particular, the delivery destination may be subject to various constraints such as designation of delivery time, restrictions on the types of vehicles that can be entered, upper limit of vehicle loading capacity, vehicle departure time and return point, etc. Needs to find a solution that satisfies all of these constraints and minimizes the given objective function. As the objective function, the total or deviation of the delivery time spent by each vehicle, or the time when all deliveries are completed, etc. are practically required.

Specific examples of such delivery problems include food, beverages, clothes, sundries, parts by truck,
Examples include delivery of parcels such as products to restaurants, shops, factories, and general households. In such a delivery problem, it is necessary to search for an optimum combination, and conventional mathematical programming has used a general branch and bound method. This branch-and-bound method divides a problem that is difficult to solve directly into easier sub-problems (branches), evaluates the sub-problems and removes unnecessary sub-problems (limits), and removes all possible sub-problems. The idea is to solve.

[0004]

However, in the actual delivery problem, there are many cases where the constraint condition is complicated and the objective function is not a single multi-objective optimization problem.
Therefore, in the branch and bound method, the program needs to be rewritten every time the constraint condition or the objective function changes, and it is rarely used in the actual delivery site, and it depends on the intuition and experience of a skilled delivery staff. The current situation.

However, the type of delivery destination, delivery problem, etc.
Road conditions such as vehicle traveling speed and constraint conditions such as delivery time change day by day, and it is quite difficult for humans to formulate a delivery plan that satisfies these conditions. In fact, it is necessary to process in a short time, and the mental load on the delivery staff is considerable. Moreover, there is little guarantee that a delivery plan drafted by humans will give the minimum value of the objective function such as transportation cost.

Therefore, an object of the present invention is to specify various delivery conditions such as designation of delivery time, restrictions on vehicle types that can be entered, upper limit of loading capacity, vehicle departure time, and return point. Search for the optimal delivery and delivery order by satisfying all of these constraints and minimizing the multipurpose objective function such as the total or deviation of the delivery time spent by each vehicle or the time when all deliveries are completed. It is an object of the present invention to provide a search device and a search method for an optimal vehicle allocation and delivery order in a delivery problem that can be solved.

[0007]

According to a first aspect of the present invention, there is provided an optimal vehicle allocation and delivery order search device for a delivery problem, wherein a plurality of vehicles are delivered by a plurality of vehicles to a plurality of delivery destinations. Optimum vehicle allocation and delivery order in the delivery problem that optimizes the vehicle allocation in which a large number of packages are allocated to each vehicle and the delivery order in which each vehicle delivers each package to the allocated destination among multiple destinations A search device, for formulating a first decision means for deciding a delivery plan showing vehicle allocation and delivery order, constraint conditions to be satisfied by the delivery plan decided by the first deciding means, and a delivery plan Second determining means for determining the cost function to be minimized to, increasing as it deviates from the constraint conditions determined by the second determining means,
It is provided with a calculating means for calculating an energy function that increases as the cost function determined by the second determining means increases, and a minimizing means for minimizing the energy function calculated by the calculating means.

According to a second aspect of the present invention, the first determining means of the first aspect expresses the delivery plan in a two-dimensional array represented by a plurality of rows and columns, each row in the two-dimensional array corresponding to each vehicle. The columns correspond to the delivery order, and each array element is characterized by a symbol representing a starting point, a symbol representing each delivery destination, or a dummy symbol for matching the number of columns.

In the third aspect, the delivery order of the second aspect includes the case of returning to the starting point between the delivery destination and another delivery destination.

According to a fourth aspect of the present invention, the energy function calculated by the calculating means according to any one of the first to third aspects is calculated as a linear sum of a term representing a constraint condition and a term representing a cost function. .

In claim 5, the minimization means of claim 4 is:
An energy function calculated as a linear sum of a term representing the constraint condition and a term representing the cost function is minimized by using a simulated annealing method.

According to a sixth aspect of the present invention, there is provided a method for searching for an optimal vehicle allocation and delivery order in a delivery problem. In the delivery problem of delivering a large number of packages to a plurality of delivery destinations by a plurality of vehicles, a large number of packages are delivered to each vehicle. A method of searching for an optimal vehicle allocation and delivery order in a delivery problem that optimizes the vehicle allocation to be assigned and the delivery order in which each vehicle delivers each package to the assigned delivery destination among a plurality of delivery destinations. And a first step of determining a delivery plan in which the delivery order is indicated, constraints to be satisfied by the delivery plan determined in the first step, and a cost function that should be minimized to formulate the delivery plan. A second step of determining, an energy function that increases as the cost function determined in the second step increases and deviates from the constraint conditions determined in the second step Delivery plan at that time steps, and the energy function calculated in the third step to minimize contains a fourth step of determining optimal.

In claim 7, the delivery plan determined in the first step of claim 6 is represented by a plurality of rows and columns.
Each row in the two-dimensional array corresponds to each vehicle, each column corresponds to the delivery order, and each array element represents a symbol representing a departure point, a symbol representing each delivery destination, or the number of columns. It is characterized by being a dummy symbol for matching.

In claim 8, the delivery order of claim 7 includes the case of returning to the starting point between the delivery destination and another delivery destination.

In claim 9, the energy function calculated in the third step of any one of claims 6 to 8 is calculated as a linear sum of a term representing a constraint condition and a term representing a cost function. I am trying.

In claim 10, the fourth step of claim 9 includes the step of minimizing the energy function calculated in the third step by using a simulated annealing method.

[0017]

According to the first aspect of the present invention, the optimum vehicle allocation and delivery order search device for a delivery problem can reduce an energy function of the delivery problem and minimize the energy function to search for an optimal vehicle allocation and delivery order.

The optimal vehicle allocation and delivery order search device for the delivery problem according to the second aspect of the present invention expresses the delivery plan in a two-dimensional array, and can solve two types of issues, vehicle delivery and delivery order, at the same time. .

According to the third aspect of the present invention, the optimum vehicle allocation and delivery order search device in the delivery problem enables the drafting of a delivery plan that uses a vehicle having a small upper load limit for two or more revolutions.

Since the optimum vehicle allocation and delivery order search device in the delivery problem according to the fourth aspect of the present invention calculates the energy function as a linear sum of the term representing the constraint condition and the term representing the cost function, the constraint condition and An energy function can be calculated and defined according to the importance of the cost function.

The optimal vehicle allocation and delivery order search device in the delivery problem according to the fifth aspect of the present invention minimizes the energy function by using the simulated annealing method. Therefore, emphasis is placed on a solution having a small energy function value. The approximate solution can be obtained stochastically.

According to the sixth aspect of the present invention, the optimal vehicle allocation and delivery order search method in the delivery problem can be reduced to an energy function and the energy function can be minimized to search for the optimal vehicle allocation and delivery order.

In the method of searching for the optimal vehicle allocation and the delivery order in the delivery problem according to the seventh aspect of the present invention, the delivery plan is represented by a two-dimensional array, and the two problems of vehicle delivery and delivery order can be solved at the same time. .

According to the eighth aspect of the present invention, the optimum dispatching method and the search method for the delivery order in the delivery problem enable the drafting of a delivery plan in which a vehicle having a small upper load limit is used twice or more times.

In the method of searching for the optimum vehicle allocation and delivery order in the delivery problem according to the ninth aspect of the present invention, the energy function is calculated as a linear sum of the term representing the constraint condition and the term representing the cost function. An energy function can be calculated and defined according to the importance of the cost function.

The optimal vehicle allocation and delivery order search method in the delivery problem according to the tenth aspect of the present invention minimizes the energy function by using the simulated annealing method. Therefore, emphasis is placed on a solution having a small energy function value. It can be obtained from probabilistic detection.

[0027]

1 is a schematic block diagram of an apparatus for searching an optimal vehicle allocation and delivery order in a delivery problem according to an embodiment of the present invention, and FIG. 2 is a schematic block diagram showing a configuration of an arithmetic unit of FIG. It is a figure.

Referring to FIGS. 1 and 2, the search device
A data input unit 1 for inputting data necessary for solving a delivery problem, a first determining unit 3 for determining a delivery plan proposal, a second determining unit 5 for determining a cost function and constraint conditions, and a first
A calculation unit 7 that calculates and defines an energy function using the information of the determination unit 3 and the second determination unit 5, and a minimization unit 9 that minimizes the energy function defined by the calculation unit 7. The calculation result is output from the calculation result output unit 11. Further, a control unit 13 for controlling the data input unit 1, the first determination unit 3, the second determination unit 5, the calculation unit 7, the minimization unit 9 and the calculation result output unit 11 is provided. Further, particularly in the minimization unit 9, as shown in FIG. 2, a random number generation unit 15, a parameter storage unit 17, and a trial deformation prohibition condition storage unit 19 necessary for minimizing the energy function.
And are provided.

FIG. 3 is a flow chart showing a process of searching for an optimal vehicle allocation and delivery order by the search device shown in FIGS. 1 and 2, and FIG. 4 is determined by the determination unit of FIG. It is the figure which showed the state which expressed the delivery plan by the two-dimensional array,
It is the figure which showed the initial state. Hereinafter, FIG. 1 and FIG.
The operation of the device will be described in detail with reference to FIGS. 3 and 4.

Basically, the delivery plan is represented by a two-dimensional array of symbols representing stores, the two-dimensional array is regarded as a system, and the energy function in that state is defined.
Simulated annealing method for the minimum state of energy function (S.Kirkpatrick, CDGelatt Jr., MPVecchi:
“Optimization by Simulated Annealing”, Science, V
It is roughly determined by ol.220, No.4598, pp.671-680 (1983)). Therefore, the flow diagram shown in FIG. 3 is summarized in the following three steps.

In step (represented by S in the drawing) 1, an initial state of the delivery plan proposal represented by a two-dimensional array is set. Then, since the two-dimensional array is regarded as a system, the two-dimensional array has energy.

Therefore, in step 2, under constant temperature conditions, the system is brought to a thermal equilibrium state using the metropolis method which will be described in detail later. Among the states (feasible solutions) in which all the constraints are satisfied, the state having the minimum energy value is recorded. Assuming that the system is in thermal equilibrium with a given probability distribution over temperature T, the temperature T
The lower the value, the higher the probability of being in the low energy state, and the higher the temperature T, the higher the probability of being in the high energy state.

Therefore, in step 3, the temperature is lowered. To lower the temperature, specifically, a temperature sequence {T _i } (i = 0, 1, ..., N) is set and i →
You can lower it as i + 1. If i> n, the process ends. If not, the process returns to step 2 and the process of step 2 is performed again.

More specifically, step 1 to step 3 will be described in detail. First, from the data input section 1, information on the shortest moving time between stores at the delivery destination and its route, temperature schedule, weights of constraint and cost terms, and random numbers. Values of necessary parameters such as seeds, initial values of the system (matrix X that is a two-dimensional array), and the like are read.

Next, the matrix X representing the current two-dimensional array is read from the first determining unit which determines the delivery plan. Here, the state of the two-dimensional array will be described in detail. Figure 4
Consider an M × L matrix X as shown in. The elements of the matrix X are represented by x _{i, j} (i = 1, ..., M, j = 1, ..., L). i identifies the vehicle and j corresponds to the shipping order. M is the number of vehicles used for delivery and is a constant.
L is a constant defined by L = N + N _rot +1. However, N is an integer obtained by adding 1 to the total number of stores, and N _rot
Is a constant defined by the equation (1).

X _{i, j} is {-1, 0, 1, ..., N-1}
Takes one of the values. Here, 0 represents the distribution center at the starting point, and 1 to (N-1) represent the number of each store. For example, in the case of 46 stores, N = 47.

In FIG. 4, in the first line, the first value is 0.
It is fixed to the (delivery center), and from the second, the numbers representing the stores are arranged in ascending order from 1 to (N-1). Next, 0s are arranged by the number obtained by subtracting 1 from the maximum rotation speed n ⁽¹⁾ _rot designated for the vehicle number 1. Finally, only -1 is arranged. In the second and subsequent rows, immediately after n ⁽ⁱ⁾ _rot 0s are arranged, all -1s are arranged. However, the search results do not depend much on these initial states.

One delivery plan is thus represented by a two-dimensional matrix. The column of numbers in each row represents the delivery order that each vehicle should perform from the left. However, 0 represents returning to the delivery center (rotation), and -1 is a dummy symbol which is skipped regardless of the delivery order. The dummy symbol -1 is introduced because the size of the two-dimensional array is fixed and the memory area secured in computer calculation is fixed. Further, there is an advantage that the trial modification of inserting a certain store in the delivery order of a certain vehicle can be easily realized by a swapping (compatibility) operation of two matrix elements which will be described in detail later.

Next, the second deciding unit 5 for deciding the cost function and the constraint condition, for example, when the parcel is loaded from a certain distribution center and delivered to a plurality of stores by truck, the cost function and the constraint condition shown below. To decide.

Taking three types of cost functions as examples,
Is a total of required time (constraint time) required for delivery by each vehicle, which is delivery cost such as labor cost and fuel cost for delivery. The second is the objective function required when the delivery time is important, such as perishables, and is the time until the completion of all delivery and unloading. Third,
This is the first objective function that should be first applied when equal allocation of working hours among drivers is required for labor management, and it is the standard deviation of the required time (constraint time) required for delivery by a specified vehicle. . The cost function is weighted according to the degree of importance, and a plurality of cost functions may be superposed. There are two types of constraint conditions, for example, those relating to stores (delivery destinations) and those relating to vehicles (trucks).

As constraints on the store, there are eaves conditions and arrival time designation conditions, for example. The eaves conditions include a vehicle stop time set for each store and an upper limit of vehicles that can be stopped specified by the tonnage and the like for each store. Further, the arrival time designation condition includes the arrival time of the vehicle designated by the upper limit time and the lower limit time for each store.

The constraint conditions for the vehicle include the upper limit of the load capacity, the starting point, the departure time, the ending condition, and the like.
The upper limit of the load capacity may be specified for each vehicle. The time of departure may be fixed at the distribution center, for example. The departure time may be specified for each vehicle. Examples of the termination condition include a return point after the delivery specified for each vehicle.

Next, the calculation unit 7 for defining the energy function
Calculates the energy function E of the system based on the matrix X read by the first decision unit 3 and the cost function and the constraint conditions decided by the second decision unit. Here, the energy function E will be described. The energy function E is, as shown in the equation (2), a cost term E _cost representing a cost function to be minimized and a constraint term E representing a constraint condition.
It is expressed as a linear sum of two types of terms with _cnst . Here, the coefficients {a _k } (k = 1, 2, 3), {b _k } (k =
1, 2, 3) are the importance degrees between cost terms and constraint terms to be considered, and are decided in advance according to the importance degree between cost functions and constraint conditions.

[0044] E in cost terms E _cost ⁽¹⁾ _cost, the starting point of the (distribution center) from the time that was starting for each vehicle, the time until one of the completion time or return time of work t _i (the restraint time) Represent. This restraint time is summed over all the tracks and the total restraint time is regarded as energy. When the termination condition is free, this restraint time is the time when the unloading work is completed at the last delivery destination from the time when the departure point is started. Further, when the ending condition is the departure point, the restraint time is the time from the time of departure from the departure point to the time of return to the departure point. Furthermore, in the case of a store that has an end condition, the restraint time is the time from the time of departure from the departure point to the time of return to the designated return point. There may be three cases as described above, but the user may freely select them according to the usage conditions.

The second cost term E ⁽²⁾ _cost is the unloading completion time at the store with the latest unloading completion time. For example, if the elapsed time from midnight, the sum of the times can be regarded as energy. The 3 E ⁽³⁾ the cost term _cost, as shown in (3), the standard deviation of the duty time t _i at the given vehicle (n stand).

On the other hand, one of the constraint terms E _cnst is E ⁽¹⁾
_cnst is the total sum of the excess amounts of the load w ^(k) _i of each vehicle at the distribution center, as shown in equation (4). As this total amount, for example, the number of cases can be considered. However, k is a rotation identification symbol, and w ⁰ _i represents the upper limit of the load capacity of the vehicle i.

The second constraint term E⁽²⁾ _cnstEach shipping
This is a constraint condition regarding the arrival time set earlier. Tato
For example, the arrival time of the delivery destination k is t_k, Lower bound on arrival time
t^l _kAnd the upper limit t^u _kE⁽²⁾ _cnstIs the
It is defined as in equation (5). If you do this,
When the arrival time is not met, the constraint term E⁽²⁾ _cnstIs big
Become.

The third constraint term, E ⁽³⁾ _cnst, is a constraint condition regarding the weight of the receiving vehicle set at each delivery destination. Letting g _{i be} the weight of each vehicle, G _k be the maximum weight of the vehicle that can be accepted at each delivery destination k, and i (k) be the truck that can be loaded at each delivery destination k, the constraint term E ⁽³⁾ _cnst is It is defined as in equation (5). If you do this,
If the condition is not satisfied, the constraint term E ⁽³⁾ _cnst will increase.

After all, the plurality of cost terms and the plurality of constraint conditions which are desired to be minimized are expressed in the form of a linear sum in the energy function, and the cost term and constraint term other than the predetermined ones are newly added. Easy to do.

Next, the minimization unit 9 for minimizing the energy function is simulated based on the values generated or stored by the random number generation unit 15, the parameter storage unit 17, and the trial deformation constraint condition storage unit 19. The annealing method is used to search for the minimum energy state while slowly lowering the temperature. Here, the simulated annealing method is
This is one method for finding the minimum energy state of a system.

It is assumed that x represents the state of the system and the energy of the system at this time is defined by the energy function E (x). Furthermore, the Gibbs distribution (Boltzmann distribution) whose system probability distribution has a temperature T
It is assumed to be in a thermal equilibrium state given by The temperature T of the system in this thermal equilibrium state is calculated by the temperature schedule {T _i } (i =
0, 1, ..., n), slowly lowering while maintaining thermal equilibrium. In general, the simulated annealing method using the metropolis method is summarized in five steps.

The first step is the state x of the system,
Choose the initial state of the system temperature T (T = T ₀ ). Second
In the step of (1), the state x is trial-deformed to select the state x ′. The third step is assuming that ΔE = E (x ′) − E.
When (x) <0, the state is changed to the state x '. In other cases, the state is changed to the state x ′ with the probability of exp (−ΔE / T). The fourth step sufficiently repeats the second and third steps until the system reaches thermal equilibrium. The fifth step ends the process if i = n. In other cases, the temperature T is changed from i → i, for example.
Increase by one step such as +1, T = T _i , and return to the second step.

Among the states appearing in the process by such an annealing method, if there are particular constraint conditions, the state with the lowest energy value is determined as the optimum solution among all the conditions satisfying the constraint conditions. . In addition, as a trial modification of the above-mentioned second step, it is general to select a state near the current state x.

Next, the trial deformation required in the simulated annealing method will be described.

The trial transformation is performed by randomly selecting two elements of one matrix X determined by the first determining unit 3 for determining the delivery plan and exchanging the values. However,
The value of the first column of the matrix X is fixed to 0, since it is assumed that the starting point of all vehicles is the distribution center. Further, in trial deformation, there is a prohibition condition in trial deformation in order to speed up the processing. This prohibition condition is stored in the trial deformation prohibition condition storage unit 19. First, with respect to two randomly selected matrix elements x _{i, j} , x _{i ′, j ′} , x _{i, j} = x _{i, j} = −1 or x _{i, j} = x _{i ′, j ′.} =
0, or if i ≠ i ', x _{i, j} = 0 or x
_{If i ', j'} = 0, the trial transformation is redone. This is because, in the former case, the delivery order has not changed at all, and in the latter case, the condition of the maximum rotation speed given to each vehicle is changed. If such trial transformations are rejected, the search space is further limited, and the optimum solution can be obtained at high speed.

Next, the state with the lowest energy value in the trial deformation given the prohibition condition of the trial deformation as described above is determined as the optimum solution, and the calculation result output unit 10 outputs the result.

FIG. 5 shows 4 from the distribution center (No. 0).
It is a figure showing the state of each delivery center and 46 stores for explaining the problem of delivering goods to five stores by six trucks. 6 to 8 are diagrams showing the input data necessary for solving the delivery problem, in particular, FIG. 6 is a diagram showing the input data regarding the delivery destination store, and FIG. FIG. 9 is a diagram showing input data relating to used tracks, and FIG. 8 is a diagram showing input data such as parameters. FIG. 9 is a diagram showing the final processing result.

FIG. 6 shows the stop time at each store, the types of trucks that can be entered (the number of tons that can be loaded), the amount of luggage (the number of cases), and the upper and lower limits of the designated arrival time.

In FIG. 7, the type of each truck (loadable tonnage), loadable load amount (case number), end conditions (-1: no specific return point, 0: return to the starting point, i: A certain store i is set as the return point. One of these three points is specified), the maximum number of rotations allowed, the time of departure from the delivery point, and the target truck when equalizing the restraint time are specified. Identifier for (1: target,
0: Not applicable) is specified. In this example, the track number No. Only the tracks of 1, 2, and 3 have their restraint times equalized. The restraint time is not equalized for the 4th and 5th tracks.

[0060] In FIG. 8, the value of the weighting factor of cost claim _{{a k} (k = 1,2,3} ), the value of the weighting factor constraints section _{{b k} (k = 1,2,3} ), The temperature schedule {t _i } and the number of trial deformations at each temperature are shown.
The number of trial deformations at each temperature represents the number of times the system state was actually trial deformed without touching the forbidden conditions.If this number of trial deformations is performed, the system will reach a thermal equilibrium state at each temperature. It is considered that the state has been reached, the update of the state is terminated, and the temperature is lowered. In this example, 20,000 trial deformations were performed at each temperature, and the temperature was 2
Annealing is performed in 13 temperature steps from 0.0 to 0.001.

In FIG. 9, under the input data shown in FIGS. 6 to 8, the obtained results are the allocation of stores to be delivered by the five trucks, the delivery order, the required time (minutes), The total load (number of cases) loaded by the truck and the value for each term of the energy function are shown. Since the values of E ^(k) _cnst are all 0, it can be seen that this solution satisfies all the given constraints. If a solution that satisfies the constraint condition is not obtained, the value of {b _k } may be increased according to the value of E ^(k) _cnst and re-executed.

As described above, under the complicated constraint conditions such as the eaves condition, the arrival time designation, and the upper limit of the loaded luggage amount, the importance of various cost functions is considered by adjusting the weighting coefficient,
The desired optimal solution is sought. Therefore, it has a great effect on drafting an optimal delivery plan according to various purposes under such complicated constraint conditions, and it is easy to change or add these constraint conditions and cost functions as described above. Since it is carried out at the same time, it has a considerable effect on the delivery problem.

To briefly explain the above, first, the concept of energy of physics, which is difficult to conceive, is applied to the delivery problem. The energy function is determined such that the energy increases as the constraint condition in the delivery problem is removed, and the energy increases as the cost function used as the objective function increases. Then, if the constraint condition is satisfied and the cost function is obtained as the minimum solution, it is determined that the energy function is optimized. If, for example, a simulated annealing method is used as the minimization of the cost function, in other words, the minimization of the energy function, an approximate solution is stochastically obtained by focusing on the solution having a small objective function value. Therefore, it is not necessary to count all basically possible combinations as in the conventional branch and bound method, and the optimal dispatch and delivery order can be obtained that is processed at high speed and is reliable.

Further, the vehicle allocation and the delivery order are determined by a two-dimensional array of a plurality of rows and columns without individually treating the vehicle allocation and the delivery order. Each row in the two-dimensional array corresponds to each vehicle, and each column corresponds to each delivery order. Since the determined delivery plan is simply expressed by this two-dimensional array, it is possible to handle two types of problems, that is, vehicle allocation and delivery order, at the same time as the method using the concept of energy. Get dispatch and delivery order.

The two-dimensional array used in the first determining unit 3 for determining the delivery plan shown in FIG. 1 can be considered other than the one shown in the embodiment. For example, the length of the column can be made variable, and a state in which only one dummy symbol is inserted between the symbols indicating the delivery destination and the rotation can be considered as a two-dimensional array expressing the delivery plan proposal. However, in this case, a process of inserting or deleting the dummy symbol after the state update by trial transformation is performed each time so that only one dummy symbol is inserted between the symbols indicating the delivery destination and the rotation. is necessary.

The second determining unit 5 for determining the cost function and the constraint condition and the calculating unit 7 for defining the energy function.
As for, the cost and the constraint condition can be expressed by a function other than the function used as the cost term and the constraint term shown in the embodiment. Furthermore, it is also possible to use a function other than the linear sum of the cost term and the constraint term as the energy function.

Further, for the minimization unit 9 that minimizes the energy function, in addition to the simulated annealing method, the state is randomly transformed to find a lower state and transition is made (or a random method). Monte Carlo method), iterative improvement method that limits the range of deformation to the vicinity of the current state is also considered.

Further, although a truck is used as the delivery means used in the embodiment, in the case where various delivery means other than the truck, such as an automobile, a ship, an aircraft, a railroad, and a person, are used, depending on the problem to be addressed. Also in, the effective effect can be obtained. Further, the delivery destination is not limited to a store such as a company, a public facility, or a general household.

Furthermore, not only the delivery of luggage, but also the problem of collecting luggage, the problem of planning a visit schedule for salespeople and repair service personnel, the problem of planning transportation routes such as school buses, and the problem of determining the route of garbage trucks. The present invention is applied to a problem having the same structure as the delivery problem including the vehicle dispatch and the delivery order shown in the present embodiment, such as a road sweeping vehicle planning problem.

[0070]

[Equation 1]

[0071]

According to the first aspect of the present invention, the delivery problem is reduced to an energy function, and the energy function is minimized to find the optimum vehicle allocation and delivery order. Is satisfied, and the cost can be reduced, which is economical.

According to the invention of claim 2, the delivery plan is set to 2
Since it was possible to solve the two problems of vehicle allocation and delivery order at the same time by expressing it in a dimensional array, it is possible to quickly deliver parcels and the like to the delivery destination.

According to the invention of claim 3, it is possible to make a delivery plan in which a vehicle having a small upper limit of loading capacity is used twice or more, so that the constraint conditions such as the delivery destination and the vehicle are satisfied, and the cost is also increased. The optimal vehicle allocation and delivery order solution considered are obtained.

According to the invention of claim 4, the energy function is calculated as a linear sum of the term representing the constraint condition and the term representing the cost function, so that the energy function can be calculated in accordance with the constraint condition and the importance of the cost function. Furthermore, it is easy to add new constraint conditions and cost functions.
Therefore, for example, when the energy function is calculated by a computer, the program or the like can be easily rewritten, and the range of application can be expanded.

According to the fifth aspect of the present invention, the energy function is minimized by the simulated annealing method, and an approximate solution can be stochastically obtained by focusing on the solution having a small energy function value, which is optimal for high speed. It is possible to obtain a solution for various vehicle allocations and delivery orders.

According to the sixth aspect of the present invention, the delivery problem is reduced to an energy function, and the energy function is minimized to find the optimum vehicle allocation and delivery order. Therefore, the constraint condition with the delivery destination and the vehicle is satisfied. In addition, it is economical because it can reduce the cost.

According to the invention of claim 7, the delivery plan is set to 2
Since it was possible to solve the two problems of vehicle allocation and delivery order at the same time by expressing it in a dimensional array, it is possible to quickly deliver parcels, etc.

According to the invention of claim 8, it is possible to make a delivery plan in which a vehicle having a small upper limit of loading capacity is used twice or more, so that the constraint condition with the delivery destination and the vehicle is satisfied and the cost is reduced. The optimal vehicle allocation and delivery order solution considered are obtained.

According to the invention of claim 9, since the energy function is calculated as a linear sum of the term representing the constraint condition and the term representing the cost function, the energy function can be calculated in accordance with the constraint condition and the importance of the cost function. Furthermore, it is easy to add new constraint conditions and cost functions.
Therefore, for example, when a computer calculates an energy function, the program and the like can be easily rewritten, and the range of application can be expanded.

According to the tenth aspect of the present invention, the energy function is minimized by the simulated annealing method, and the approximate solution can be stochastically obtained by placing emphasis on the solution having a small energy function value. It is possible to obtain a solution for various vehicle allocations and delivery orders.

[Brief description of drawings]

FIG. 1 is a schematic block diagram of an optimum vehicle allocation and delivery order search device in a delivery problem according to an embodiment of the present invention.

FIG. 2 is a schematic block diagram showing an internal configuration of a minimization unit in FIG.

FIG. 3 is a flowchart showing a process of searching for an optimal vehicle allocation and delivery order by the search device shown in FIGS. 1 and 2.

FIG. 4 is a diagram showing a state in which a delivery plan proposal determined by the first determining unit in FIG. 1 is expressed in a two-dimensional array, showing an initial state thereof.

FIG. 5 is a diagram showing a state of a delivery center and a delivery destination store.

FIG. 6 is a diagram showing an example of input data regarding a delivery destination store.

FIG. 7 is a diagram showing an example of input data regarding a track.

FIG. 8 is a diagram showing an example of input data such as parameters.

FIG. 9 is a diagram showing an example of processing results processed based on the input data of FIGS. 6 to 8;

[Explanation of symbols]

 3 1st determination part 5 2nd determination part 7 Calculation part 9 Minimization part

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Claims (10)

[Claims] 1. In a delivery problem of delivering a large number of parcels to a plurality of delivery destinations by a plurality of vehicles, a vehicle allocation in which the plurality of parcels are allocated to the respective vehicles, and a case where the respective vehicles are among the plurality of delivery destinations. A search device for an optimal vehicle allocation and delivery order in a delivery problem that optimizes a delivery order for delivering each package to an assigned delivery destination, which determines a delivery plan that indicates the vehicle delivery and the delivery order. 1 determining means, 2nd determining means for determining a constraint condition that should be satisfied by the delivery plan determined by the 1st determining means, and a cost function to be minimized in order to draft the delivery plan, The calculating means for calculating an energy function that increases as the cost deviates from the constraint condition determined by the second determining means, and increases as the cost function determined by the second determining means increases, and the calculating means. An optimal vehicle allocation and delivery order search device in a delivery problem, which is provided with a minimization means for minimizing the calculated energy function. 2. The first determining means expresses the delivery plan by a two-dimensional array represented by a plurality of rows and columns, each row in the two-dimensional array corresponds to each vehicle, and each column has a delivery order. Corresponding to, each array element is a symbol representing a starting point, a symbol representing each delivery destination, or a dummy symbol for matching the number of columns, optimal in the delivery problem according to claim 1. Device for automatic dispatch and delivery order. 3. The optimal vehicle allocation and delivery order search device in the delivery problem according to claim 2, wherein the delivery order includes a case where the delivery destination and the other delivery destination return to the starting point. 4. The energy function calculated by the calculation means is calculated as a linear sum of a term representing the constraint condition and a term representing the cost function. Optimal vehicle allocation and delivery order search device for the delivery problem described in. 5. The minimization means minimizes an energy function calculated as a linear sum of a term representing the constraint condition and a term representing the cost function by using a simulated annealing method. An optimal vehicle allocation and delivery order search device in the delivery problem according to claim 4. 6. In a delivery problem in which a large number of packages are delivered to a plurality of delivery destinations by a plurality of vehicles, among the plurality of delivery destinations in which the plurality of packages are allocated to each of the vehicles, A method for searching for an optimal vehicle allocation and delivery order in a delivery problem that optimizes a delivery order for delivering each package to an assigned delivery destination, which determines a delivery plan that indicates the vehicle delivery and the delivery order. 1st step, 2nd step of determining the constraint condition that the delivery plan determined in said 1st step should satisfy and the cost function that should be minimized in order to plan said delivery plan, said 2nd A third operation for calculating an energy function that increases as the cost condition determined in the second step increases and deviates from the constraint condition determined in the step
And the fourth step of minimizing the energy function calculated in the third step to determine that the delivery plan at that time is optimal, and searching for an optimal vehicle allocation and delivery order in the delivery problem. Method. 7. The delivery plan determined in the first step is represented by a two-dimensional array represented by a plurality of rows and columns, each row in the two-dimensional array corresponds to each vehicle, and each column is 7. The delivery problem according to claim 6, wherein each array element corresponds to a delivery order and is a symbol representing a departure point, a symbol representing each delivery destination, or a dummy symbol for matching the number of columns. Method of Optimal Vehicle Allocation and Delivery Order in Japan. 8. The method for searching for an optimal vehicle allocation and delivery order in a delivery problem according to claim 7, wherein the delivery order includes a case where the delivery destination returns to a starting point between a delivery destination and another delivery destination. 9. The energy function calculated in the third step is calculated as a linear sum of a term representing the constraint condition and a term representing the cost function. A method for searching for an optimal vehicle allocation and delivery order in any one of the delivery problems. 10. The optimal vehicle allocation in the delivery problem according to claim 9, wherein the fourth step includes a step of minimizing the energy function calculated in the third step by using a simulated annealing method. How to search the shipping order.