CN113033866B - Emergency order distribution scheduling optimization method - Google Patents

Emergency order distribution scheduling optimization method Download PDF

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CN113033866B
CN113033866B CN202110130311.XA CN202110130311A CN113033866B CN 113033866 B CN113033866 B CN 113033866B CN 202110130311 A CN202110130311 A CN 202110130311A CN 113033866 B CN113033866 B CN 113033866B
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谢友财
苏海龙
陈岫
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Huashang College Guangdong University Of Finance & Economics
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Abstract

The invention discloses an emergency order distribution scheduling optimization method, which comprises the following steps: establishing a conventional order distribution model taking the minimum total distribution cost as an objective function; step two: constructing an emergency order distribution model with the minimum insertion cost based on the conventional order distribution model established in the step one and a time axis strategy; step three: designing an SI heuristic algorithm and a dynamic insertion algorithm solving model, applying the SI heuristic algorithm and the dynamic insertion algorithm solving model to the emergency order distribution model obtained in the step two, and carrying out distribution scheduling optimization on the emergency orders; the two-stage model and the algorithm are subjected to example verification, and the result shows that the two-stage model has the characteristics of feasibility, high timeliness of order distribution and quick response in emergency order processing.

Description

Emergency order distribution scheduling optimization method
Technical Field
The invention relates to the technical field of intelligent optimized scheduling of vehicles, in particular to an optimized method for emergency order delivery scheduling.
Background
Along with the rapid development of social economy, the demand for logistics is increased rapidly, and the rapid and efficient development of the logistics industry is effectively promoted; the logistics industry is a combined service type industry integrating related industries such as transportation industry, warehousing industry, information technology and the like, is an important component of national economy, and has the functions of improving the economic structure, enhancing the national economic quality and resisting the risk capability; with the rise of electronic commerce and the improvement of the individuation degree of consumer demands, the requirement on the logistics distribution timeliness is also obviously improved; in logistics distribution, planning and selecting a distribution path are important components, and conventional order distribution and emergency order distribution are divided according to the difference of acquisition time of distribution orders; conventional order delivery refers to delivering orders that have been determined to need delivery the day before, emergency order delivery refers to delivering orders that are temporarily scheduled on the day of delivery, different order types have different delivery targets, and a large amount of research is conducted by scholars;
for regular orders, such orders strive to deliver the lowest total cost, since the relevant delivery information is known; zhou Xianchun, and the like, analyzing the vehicle path optimization problem under the current complex vehicle road condition, and designing an ant colony improvement algorithm based on multi-constraint optimization by introducing path quality parameters; huang and the like establish a model with the aim of determining the number of sub-fleets and the optimal route by researching the problem of branch vehicle paths so as to reduce the total cost to the maximum extent; zhang Liyi and the like construct a relevant mathematical model by taking the lowest carbon emission cost as a target from the perspective of low-carbon logistics, and provide a simulated annealing ant colony algorithm solution model with mixed disturbance; the Heng hong Jun et al considers the scheduling problem of airport luggage transport vehicles and constructs a path optimization model with the shortest vehicle travel distance as a target; liu Bo provides an improved artificial fish school algorithm for solving the cold chain distribution problem with a soft time window by researching the cold chain distribution problem and aiming at minimizing the total cost; kalayci and the like construct a model aiming at minimizing the total travel and design a mixed meta-heuristic algorithm solving model for solving the problem of vehicle paths of simultaneous goods taking and delivery;
for the emergency order distribution, due to the uncertainty of order information and the limitation of distribution center resources, the order is more focused on the distribution timeliness and the effective utilization of the existing resources; li Nan for dynamic demands generated in the vehicle distribution process, a mathematical model with minimized distribution time as a target is constructed, and the model is solved by improving a VNS algorithm; yan Dong, etc. propose a new method for inserting emergency demands and solving data packets for dynamic order problems occurring in the distribution process; cheng Xingxing [11] Aiming at the dynamic order demand change of customers in the express delivery process, the delivery vehicle is combinedConstructing a dynamic vehicle path planning mathematical model which can be repeatedly used by the vehicle under the condition of limited resources; he Xiaohan constructs a mathematical model with consumption cost and customer satisfaction as targets, and designs two algorithms of an improved large neighborhood algorithm and a mixed particle swarm algorithm for solving; mandzuik et al propose an effective algorithm for dynamically requesting a vehicle path problem solution based on a memory algorithm;
it can be seen from the above studies that in the conventional order delivery, mostly, the minimum cost is used as an objective function, the model is solved by improving the algorithm, but the length of time for solving the algorithm is Cheng Hao, and in the emergency order, more vehicles which utilize the remaining vehicle resources of the delivery center or have completed the delivery task are returned to the delivery center to deliver the emergency order in a special delivery manner, so that the delivery cost is high.
Disclosure of Invention
Aiming at the existing problems, the method for optimizing the delivery scheduling of the emergency order is characterized in that in order to improve the timeliness of the delivery of the emergency order, a conventional order delivery model taking the minimum total delivery cost as an objective function is established; on the basis, an emergency order distribution model with the minimum insertion cost is constructed based on a time axis strategy; secondly, designing an SI heuristic algorithm and a dynamic insertion algorithm solving model, and finally carrying out example verification on the two-stage model and the algorithm, wherein the result shows that the two-stage model has the characteristics of feasibility, high timeliness of order distribution and quick response to the emergency order processing.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
an emergency order delivery scheduling optimization method comprises
The method comprises the following steps: establishing a conventional order distribution model taking the minimum total distribution cost as an objective function;
step two: constructing an emergency order distribution model with the minimum insertion cost on the basis of the conventional order distribution model established in the step one;
step three: and designing an SI heuristic algorithm and a dynamic interpolation algorithm solving model, applying the SI heuristic algorithm and the dynamic interpolation algorithm solving model to the emergency order distribution model obtained in the step two, and carrying out distribution scheduling optimization on the emergency orders.
Preferably, the process of establishing the conventional order distribution model in step one includes:
s1-1, setting the order delivery to be from the same delivery center or a goods taking point, wherein the number of available delivery vehicles is m, unified vehicle types are adopted, the vehicle capacity is Q, the average vehicle running speed is v, each delivery task corresponds to a user demand i, and the commodity volume corresponding to each demand i is Q i Each task requires that the user expect to get a commodity time window of [ e ] i ,l i ]，
Wherein: e.g. of the type i Is expected to arrive at the earliest point in time,/ i Is expected to arrive at the latest time point;
s1-2, setting a symbol and a variable: n represents the total number of all order tasks; m represents the total number of delivery vehicles, k =1,2,3 …, m; i, j represents the corresponding order number, i =1,2,3 …, n; c. C 1 Representing that the vehicle is early in penalty coefficient relative to the user expected time window; c. C 2 Representing that the vehicle is late relative to the user expected time window to a penalty factor; c. C 3 Representing the distribution cost corresponding to the unit distance of the vehicle; v represents the speed at which the delivery vehicle travels; q. q.s i Representing the commodity volume corresponding to the task point i; w is a 2ij Represents the delivery cost from delivery point i to delivery point j; w is a 3i Represents the penalty cost due to the vehicle not arriving on time at delivery point i; w represents the cost incurred in the entire distribution process; w 1 Represents a fixed cost required to start the vehicle; w 2 Represents the total distribution cost generated in the distribution process; w 3 Representing the total penalty cost generated in the distribution process; q represents the maximum load volume that the delivery vehicle can carry; s ij Represents the distance from order i to order j; t is t ij Represents the time taken by the vehicle from delivery point i to delivery point j; t is t i Represents the time point, t, corresponding to the arrival of the vehicle at the delivery point i 0 =0; i =0 represents the delivery center corresponding order number;
s1-3, aiming at minimizing cost, designing a conventional order vehicle distribution model as follows:
Figure BDA0002924868970000041
Figure BDA0002924868970000042
Figure BDA0002924868970000043
Figure BDA0002924868970000044
/>
Figure BDA0002924868970000045
Figure BDA0002924868970000046
Figure BDA0002924868970000047
Figure BDA0002924868970000048
Figure BDA0002924868970000049
Figure BDA00029248689700000410
Figure BDA00029248689700000411
Figure BDA0002924868970000051
Figure BDA0002924868970000052
Figure BDA0002924868970000053
wherein: the above equation (1) represents the total cost minimization; equation (2) represents the total delivery cost resulting from vehicle delivery; equations (3) and (4) represent the total penalty cost incurred by vehicle delivery; formula (5) indicates that there is only one vehicle coming out from any order and comes out once; (6) Indicating that only one vehicle is scheduled for delivery per order; formula (7) indicates that each order is processed only once and no duplication occurs; equation (8) indicates that each order must be scheduled for delivery; formula (9) indicates that the order volume carried by each vehicle in the distribution process does not exceed the maximum capacity volume of the vehicle; formula (10) shows that all vehicles start from the distribution center to be distributed; formula (11) represents that the vehicle finishes the delivery of the order, namely the delivery is finished, and then the vehicle returns to the delivery center; equation (12) represents the time relationship between the arrival of the two delivery points before and after the delivery process.
Preferably, the process of establishing the emergency order distribution model in step two includes:
s2-1, when the time 1 is set, an emergency order i 'is generated, and the commodity volume corresponding to the order is q' i Delivery time window of order demand is [ e' i ,l’ i ](ii) a The emergency order i ' arranges the vehicle to return to the distribution center for picking up goods among the order groups (a, b), arranges the distribution among the order groups (u, z), and arranges the distribution among the order groups (a, b) before the order groups (u, z), if b = u is overlapped and is 0, the vehicle receives the emergency order i ' and returns to the distribution center for picking up goods, and immediately distributes the emergency order i ';
and S2-2, on the basis of the conventional order, taking the minimum insertion cost as an objective function, considering the delivery cost of the emergency order, and constructing an emergency order model by the penalty cost of the conventional order caused by the insertion of the emergency order.
Preferably, the specific steps of step S2-2 include:
s2-2.1, setting the distribution cost generated by inserting the emergency newly-added order as g (1): after the goods taking of the emergency order i' is inserted into the middle of the order group (a, b), the original distribution path a → b is changed into a → 0 → b; similarly, after the delivery of the emergency order i 'is inserted into the middle of the order group (u, z), the original delivery path u → z is changed to u → i' → z, so that the delivery distance is increased, and the corresponding increased delivery path cost is as follows:
Figure BDA0002924868970000061
wherein: w is a 2ij Representing the delivery cost required for orders i to j; s is ij Represents the distance from order i to order j;
s2-2.2, setting the penalty cost generated when the emergency order i' exceeds the delivery time window as g (2): the emergency order i 'is scheduled for delivery among the order group (u, z), so that the delivery vehicle needs to return to the delivery center to pick up the goods for delivery, and the actual delivery time of the emergency order i' is:
t i' ＝t u +t a0 +t 0b +t ui' (14)
combined with emergency order i 'customer expected time window [ e ] to place order' i ,l’ i ]The penalty cost for the available emergency order i' is:
Figure BDA0002924868970000062
then:
Figure BDA0002924868970000063
wherein: e.g. of a cylinder i' Indicating an emergency order customer expected earliest arrival time; l i' Indicating an emergency order customer expected latest orderThe arrival time;
s2-2.3, setting the total change penalty cost of the conventional order due to the change of the arrival time as g (3): the impact of an emergency order on the regular order time window is two: one is an order with arrival time variation caused only by picking, then the original penalty cost for regular order b is:
Figure BDA0002924868970000071
the time of arriving at the delivery point of the order b is t b' ＝t a +t a0 +t 0b The penalty cost generated by the corresponding time window is as follows:
Figure BDA0002924868970000072
the penalty change cost of the order b due to the urgent order is: Δ w 3b ＝w 3b' -w 3b Namely:
Figure BDA0002924868970000073
n orders with time change of arrival at the delivery point caused by only returning the emergency dynamic order i' to the delivery center for taking goods are set 1 (including orders b, u, n) 1 =0,1,2,3 …), i.e. order [ b, u]Between is provided with n 1 Individual order, pair n 1 The order is distributed according to the sequence 1,2,3 …, and the penalty cost of the time window change is:
Figure BDA0002924868970000074
similarly, the change penalty cost g (3 ') due to the change in arrival time of subsequent regular orders caused by the pick and delivery of the urgent order i' can be obtained:
Figure BDA0002924868970000075
Figure BDA0002924868970000076
thus, the penalty charges for regular orders due to urgent order insertion are:
g(3)＝g(3')+g(3”)；
s2-2.4, obtaining a distribution model of the emergency order as follows:
ming＝g(1)+g(2)+g(3)。
preferably, the design process of the SI heuristic algorithm and the dynamic interpolation algorithm solution model in the third step includes:
s3-1, designing an SI heuristic algorithm to solve a conventional order model;
and S3-2, designing a dynamic insertion heuristic algorithm to solve the emergency order model.
Preferably, the algorithm step of solving the conventional order model by the SI heuristic algorithm includes:
s3-1.1, establishing a rectangular coordinate system by taking the distribution center as an original point, determining coordinates of each delivery point, and taking an x-axis forward line as a scanning start line;
s3-1.2, selecting a starting line in the step S3-1.1, rotating counterclockwise, and grouping orders:
taking the volume of the vehicle-mounted capacity as a constraint, and enabling each order in the scanning area to correspond to a volume q i Summing Q, if the volume sum Q is not less than the maximum volume Q of the vehicle, dividing the orders into a group, completing the distribution by one vehicle, continuing to scan, grouping the rest orders, and redistributing the vehicle for distribution; if the volume sum Q is smaller than the maximum volume Q of the vehicle, continuing to scan;
s3-1.3, checking whether the order set of the residual unscanned area is empty, and if the order set of the residual unscanned area is empty, turning to the step S3-1.4; otherwise, continuing to scan according to the step S3-1.2;
all orders are grouped, assuming that m groups are obtained in total, counting the orders of each group, turning to the step S3-1.5, and planning a vehicle path according to the orders of each group;
s3-1.5, selecting a group of unplanned order groups m i Considering the distance and time factors, and aiming at minimizing the cost W, searching for an order i, wherein a connection point i and an origin (distribution center) form a directional vehicle driving path 0 → i → 0,m i ＝m i -i；
S3-1.6.m i If the value is 0, turning to the step S3-1.9 if the value is 0; otherwise, turning to the step S3-1.7;
s3-1.7 from m i Continuously searching a point j, wherein the cost W of the point j meeting the distance on the path is minimum, inserting the point j into the path, and m i ＝m i -j；
S3-1.8: repeating the step S3-1.6 and the step S3-1.7 until all points are planned into the route, wherein m = m-1, and turning to the step S3-1.9;
s3-1.9, judging whether the set m is 0, and if so, turning to the step S3-1.10; otherwise, turning to the step S3-1.5;
s3-1.10, all orders are arranged, and the algorithm is finished.
Preferably, the step of the algorithm for solving the emergency order model by the dynamic insertion heuristic algorithm includes:
s3-2.1, processing the dynamic order based on a time axis, and acquiring a dynamic newly-added order set N each time the dynamic order appears;
s3-2.2, updating the vehicle information, the distribution condition and the key points of the running path of each vehicle in real time;
s3-2.3, setting a larger cost g j #；
S3-2.4, considering the time window of order distribution, sequencing all new orders according to the time point of the time window expected by the user, and then finding the order N with the earliest delivery time of the expected goods j ；
S3-2.5, comprehensively analyzing the newly added order volume and the vehicle loading volume constraint to find a candidate path set D capable of being inserted into the newly added order;
s3-2.6, analyzing the condition of the path set D, and if the set D is empty, searching the vehicle which completes the delivery task earliest to arrange the delivery order N of the vehicle j (ii) a Otherwise, find a line D from the set D i Calculating an order N j After insertion, minimum of generationChanging the cost g;
s3-2.7, if g is less than g j #, then g j # = g (indicating order N) j Is given by g j Change # distribution method to g corresponding distribution method), while removing line D from path set D i I.e. D = D-D i Otherwise D = D-D i ；
S3-2.8, when the set D is empty, g is selected j The order N corresponds to the delivery policy # j The distribution method of (1);
s3-2.9, take N = N-N j If the order set N is empty, turning to the step S3-2.10; if not, turning to the step S3-2.4;
and S3-2.10, finishing the algorithm.
The invention has the beneficial effects that: the invention discloses an emergency order dispatching optimization method, compared with the prior art, the improvement of the invention is as follows:
the invention designs an emergency order delivery scheduling optimization method for improving the timeliness of emergency order delivery, and carries out optimization research on emergency order delivery scheduling by constructing a two-stage model, wherein the method comprises the following steps: firstly, a conventional order distribution model is constructed, and an SI heuristic algorithm is designed to solve to obtain a conventional order distribution path with the lowest cost; secondly, an emergency order distribution model is built, and emergency orders are inserted into a conventional order distribution path in a dynamic insertion mode so as to seek the lowest insertion cost to complete the distribution of the emergency orders; and finally, case data is used for verifying the two-stage model to obtain that the two-stage model is feasible and effective when the emergency order is processed, and the method can provide reference basis for logistics related enterprises in the aspect of emergency order distribution route optimization, so that distribution vehicles are reasonably arranged to reduce the total distribution cost, and the two-stage model has the advantages of feasibility, high timeliness of order distribution and quick response to the emergency order processing.
Drawings
FIG. 1 is a flowchart of an emergency order delivery scheduling optimization method based on a two-stage model according to the present invention.
FIG. 2 is a diagram of the order information at time 1 of the present invention.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the following further describes the technical solution of the present invention with reference to the drawings and the embodiments.
In order to solve the problems of long time consumption and high delivery cost of emergency order delivery in the prior art and improve the timeliness of the emergency order delivery, the invention designs an emergency order delivery scheduling optimization method.
Referring to FIGS. 1-2, an emergency order delivery scheduling optimization method includes
The method comprises the following steps: establishing a conventional order distribution model taking the minimum total distribution cost as an objective function, wherein the specific process is as follows:
s1-1, setting the order delivery from the same delivery center or a goods taking point, wherein the available delivery vehicle number is m, unified vehicle types are adopted, the vehicle capacities are Q (mainly considering the vehicle capacity), the vehicle average running speed is v, each delivery task corresponds to a user demand i, and the commodity volume corresponding to each demand i is Q i Each task requires that the user expect to get a commodity time window of [ e ] i ,l i ]；
Wherein e i Is expected to arrive at the earliest point in time,/ i Is expected to arrive at the latest time point; starting a total of m delivery vehicles from a common delivery center, enabling goods carried by each vehicle not to exceed the maximum capacity Q of the vehicle, driving according to a planned route, completing tasks, delivering the goods to users, namely when the delivery is finished, and then returning to the delivery center;
simultaneously: in combination with the order delivery features, assume: (1) The whole distribution system is provided with one distribution center, all vehicles start from the same place, all orders can be distributed only by the distribution center, and the vehicles finish the orders after completing the distribution, namely the tasks are finished, and the orders are returned to the distribution center(ii) a (2) Each order has only one delivery point, the position of each delivery point is different, the position information of the delivery point of each order delivery is known, and repeated delivery points can not appear; (3) The vehicle types of all vehicles are unified and standard, namely the vehicle types are the same, the running speeds v of all vehicles are the same, and the running distance of the vehicles and the volume of commodities carried by the vehicles do not influence the speed of the vehicles; (4) The running cost of the vehicle is only related to the running distance of the vehicle and is not related to the self load capacity and the like; (5) Each order can be completed by only one delivery person, the delivery can be performed only by taking the order first, and one vehicle can complete the delivery of a plurality of orders; (6) Each distribution vehicle can bear a plurality of orders of commodities, but the total volume cannot exceed the volume Q of the vehicle, and the volume of the commodities corresponding to each order cannot exceed the volume Q of the vehicle; (7) The deliverer delivers the goods to a delivery point or delivers the goods to the user, and the service time of delivery of each order is negligible; (8) The information for each initial order is known, except for the dynamic orders that occur during the delivery process; (9) When the distribution is started, all order commodities are loaded on the vehicle, the dynamic orders appearing in the distribution process need to be returned to the distribution center to pick up the commodities and then distributed without returning to a distribution network to pick up the commodities; (10) All vehicles for order delivery generate a fixed startup cost W 1 ；
S1-2, setting a symbol and a variable:
setting n to represent the total number of all order tasks;
m represents the total number of delivery vehicles, k =1,2,3 …, m;
i, j represents the corresponding order (point of delivery) number, i =1,2,3 …, n;
c 1 representing that the vehicle is early in penalty coefficient relative to the user expected time window;
c 2 representing that the vehicle is late relative to the user expected time window to a penalty factor;
c 3 representing the distribution cost corresponding to the unit distance of the vehicle;
v represents the speed at which the delivery vehicle travels;
q i representing the volume of the commodity corresponding to the task point (order) i;
w 2ij represents the delivery cost for delivery point (delivery order) i to delivery point (delivery order) j;
w 3i represents penalty costs at delivery point (order) i due to vehicle not being delivered on time;
w represents the cost incurred in the entire distribution process;
W 1 represents a fixed cost required to start the vehicle;
W 2 represents the total distribution cost generated in the distribution process;
W 3 representing the total penalty cost generated in the distribution process;
q represents the maximum load volume that the delivery vehicle can carry;
s ij represents the distance from order (point of delivery) i to order (point of delivery) j;
t ij represents the time taken by the vehicle from delivery point i to delivery point j;
t i representing the point in time, t, at which the vehicle arrives at the delivery point i 0 ＝0；
i =0 represents the delivery center corresponding order number;
s1-3, aiming at minimizing cost, designing a conventional order vehicle distribution model as follows:
Figure BDA0002924868970000131
Figure BDA0002924868970000132
Figure BDA0002924868970000133
Figure BDA0002924868970000134
Figure BDA0002924868970000135
Figure BDA0002924868970000136
Figure BDA0002924868970000137
Figure BDA0002924868970000138
Figure BDA0002924868970000139
Figure BDA00029248689700001310
Figure BDA00029248689700001311
Figure BDA00029248689700001312
Figure BDA0002924868970000141
Figure BDA0002924868970000142
wherein: the above equation (1) represents the total cost minimization; equation (2) represents the total delivery cost resulting from vehicle delivery; equations (3) and (4) represent the total penalty cost incurred by vehicle delivery; formula (5) indicates that there is only one vehicle coming out from any order and comes out once; (6) Indicating that only one vehicle is scheduled for delivery per order; formula (7) indicates that each order is processed only once and no duplication occurs; equation (8) indicates that each order must be scheduled for delivery; formula (9) shows that the order volume carried by each vehicle in the distribution process does not exceed the maximum capacity volume of the vehicle; formula (10) shows that all vehicles start from the distribution center to be distributed; formula (11) represents that the vehicle finishes the delivery of the order, namely the delivery is finished, and then the vehicle returns to the delivery center; equation (12) represents the time relationship between the arrival of the two delivery points before and after the delivery process.
Step two: and on the basis of the conventional order distribution model established in the step one, establishing an emergency order distribution model with the minimum insertion cost based on a time axis strategy, wherein the specific construction process comprises the following steps:
time axis: since the emergency orders appear randomly over time, a timeline-based order processing strategy is adopted to process the emergency orders appearing in real time, and a timeline is established for the whole distribution cycle by introducing the concept of the timeline, as shown in fig. 2; at the moment 1, the vehicle information is updated every time an emergency order appears, and the distribution information of the current emergency order and the conventional order can be clearly known; the conventional order distribution vehicle plans a distribution path before starting and distributes according to a certain order distribution sequence; from the perspective of recycling vehicles and reducing cost, when an emergency order appears, the minimum insertion cost is taken as a target by combining with the conventional order distribution condition, assuming that the specification of emergency order goods and the specification of vehicle remaining order goods meet the vehicle-mounted capacity volume constraint, and based on the condition, searching the most appropriate vehicle from all distribution vehicles to complete the distribution of the emergency order;
s2-1. Model assumptions:
assume that 1: at time 1, an emergency order i' is generated, which corresponds to a product volume q i ', delivery time window of order demand is [ e' i ,l’ i ]；
Assume 2: the emergency order i ' arranges the vehicle to return to the distribution center for picking up goods among the order groups (a, b), arranges the distribution among the order groups (u, z), and arranges the distribution among the order groups (a, b) before the order groups (u, z), if b = u is overlapped and is 0, the vehicle receives the emergency order i ' and returns to the distribution center for picking up goods, and immediately distributes the emergency order i ';
s2-2, an emergency order distribution model is built, namely on the basis of a conventional order, the distribution cost of the emergency order is comprehensively considered by taking the minimum insertion cost as an objective function, and the penalty cost of the conventional order caused by the insertion of the emergency order is built:
s2-2.1, setting the distribution cost generated by inserting the emergency newly-added order as g (1): after the goods taking of the emergency order i' is inserted into the middle of the order group (a, b), the original distribution path a → b becomes a → 0 → b; similarly, after the delivery of the emergency order i 'is inserted into the middle of the order group (u, z), the original delivery path u → z is changed to u → i' → z, so that the delivery distance is increased, and the corresponding increased delivery path cost is as follows:
Figure BDA0002924868970000151
wherein: w is a 2ij Representing the delivery cost required for orders i to j; s ij Represents the distance from order i to order j;
s2-2.2, setting penalty cost g (2) generated when the emergency order i' exceeds the delivery time window: since the insertion and delivery of the emergency order are considered from the delivery route as a whole, the delivery of the emergency order may exceed the time window, the delivery of the emergency order i 'is scheduled between the order groups (u, z), and therefore the delivery vehicle needs to return to the delivery center to pick up the goods for delivery, and the actual delivery time of the emergency order i' is:
t i' ＝t u +t a0 +t 0b +t ui' (14)
expected time window [ e ] of customer placing order in combination with emergency order i' i ,l’ i ]The penalty cost for the available emergency order i' is:
Figure BDA0002924868970000161
then:
Figure BDA0002924868970000162
wherein: e.g. of the type i' Indicating an emergency order customer expected earliest arrival time; l i' Indicating the time of arrival of the latest order expected by the emergency order customer;
s2-2.3, setting the total change penalty cost g (3) of the conventional order due to the change of the arrival time: the impact of an emergency order on the regular order time window is two: one is an order with arrival time changes caused only by picking, and the original penalty cost for regular order b is:
Figure BDA0002924868970000163
the time of arriving at the delivery point of the order b is t b' ＝t a +t a0 +t 0b The penalty cost generated by the corresponding time window is as follows:
Figure BDA0002924868970000164
the penalty change cost of the order b due to the urgent order is: Δ w 3b ＝w 3b' -w 3b Namely:
Figure BDA0002924868970000165
n orders with time change of arrival at the delivery point caused by only returning the emergency dynamic order i' to the delivery center for taking goods are set 1 (including orders b, u, n) 1 =0,1,2,3 …), i.e. order [ b, u)]Between is provided with n 1 Individual order, pair n 1 The order is distributed according to the sequence 1,2,3 …, and the penalty cost of the time window change is:
Figure BDA0002924868970000171
similarly, the change penalty cost g (3 ') due to the change in arrival time of subsequent regular orders caused by the pick and delivery of the urgent order i' can be obtained:
Figure BDA0002924868970000172
Figure BDA0002924868970000173
thus, the penalty charge for a regular order due to an urgent order insertion is:
g(3)＝g(3')+g(3”)
s2-2.4, obtaining a distribution model of the emergency order as follows:
ming＝g(1)+g(2)+g(3)。
step three: designing an SI heuristic algorithm and a dynamic interpolation algorithm solving model, applying the SI heuristic algorithm and the dynamic interpolation algorithm solving model to an emergency order distribution model, and carrying out distribution scheduling optimization on emergency orders, wherein the specific steps comprise:
s3-1.2.1 conventional order model algorithm design: the heuristic algorithm has the advantages of simple algorithm structure, high solving speed and capability of obtaining a better solution or a satisfactory solution in a short time, so that the heuristic algorithm SI is designed to solve the conventional order model by combining the characteristics of the scanning algorithm and the nearest interpolation algorithm;
(1) Scanning algorithm
The scanning Algorithm (Sweep Algorithm) is a "group-before-line route" type of Algorithm, the basic principle being: regarding the whole distribution system as a plane, taking a distribution center as an origin, and representing each conventional order delivery point in a two-dimensional coordinate mode; all orders are grouped by taking the volume of the delivery vehicle as a constraint, dividing a delivery plane taking a delivery center as an origin into a plurality of areas, distributing each area order to one vehicle for completion, and then planning a specific route in each area. All orders are grouped by adopting the method, if the unallocated points exist, the grouping is continued until all the points are allocated, and the grouping is not finished.
(2) Nearest insertion algorithm
The algorithm idea is as follows: selecting the optimal points from all the selectable aggregation points, forming a sub-loop with the initial point (distribution center), and then continuously searching the point which is the closest to the middle point of the sub-loop from the rest points to form a loop until all the points are arranged;
based on the principle, the algorithm process for solving the conventional order model by the designed SI heuristic algorithm comprises the following steps:
s3-1.1, establishing a rectangular coordinate system by taking a distribution center as an original point, determining coordinates of each delivery point, and taking an x-axis forward line as a scanning start line;
s3-1.2, selecting a starting line in the step S3-1.1, rotating anticlockwise, and grouping orders:
taking the volume of the vehicle-mounted capacity as a constraint, and enabling each order in the scanning area to correspond to a volume q i Summing Q, if the volume sum Q is not less than the maximum volume Q of the vehicle, dividing the orders into a group, completing the distribution by one vehicle, continuing to scan, grouping the rest orders, and redistributing the vehicle for distribution; if the volume sum Q is smaller than the maximum volume Q of the vehicle, continuing to scan;
s3-1.3, checking whether the order set of the residual unscanned area is empty, and if the order set of the residual unscanned area is empty, turning to the step S3-1.4; otherwise, continuing to scan according to the step S3-1.2;
all orders are grouped, assuming that m groups are obtained in total, counting the orders of each group, turning to the step S3-1.5, and planning a vehicle path according to the orders of each group;
s3-1.5, selecting a group of unplanned order groups m i Considering the distance and time factors, and aiming at minimizing the cost W, searching for an order i, wherein a connection point i and an origin (distribution center) form a directional vehicle driving path 0 → i → 0,m i ＝m i -i；
S3-1.6.m i If the value is 0, turning to the step S3-1.9 if the value is 0; otherwise, turning to the step S3-1.7;
s3-1.7 from m i Continuously searching for a point j, wherein the point j satisfies the distance pathThe cost W for the point on the path is minimized, and the point j is inserted into the path, m i ＝m i -j；
S3-1.8: repeating the step S3-1.6 and the step S3-1.7 until all points are planned into the route, wherein m = m-1, and turning to the step S3-1.9;
s3-1.9, judging whether the set m is 0, if so, turning to the step S3-1.10; otherwise, turning to the step S3-1.5;
s3-1.10, all orders are arranged, and the algorithm is ended;
s3-2, designing an emergency order model algorithm: because the emergency order distribution model inserts the emergency order into the conventional order distribution path, the insertion rule is proposed by reference and improvement of Solomon, a dynamic insertion heuristic algorithm is designed to solve the emergency order model, and the algorithm step of solving the emergency order model by the dynamic insertion heuristic algorithm comprises the following steps:
s3-2.1, processing the dynamic order based on a time axis, and acquiring a dynamic newly-added order set N each time the dynamic order appears;
s3-2.2, updating the vehicle information, the distribution condition and the key points of the running path of each vehicle in real time;
s3-2.3, setting a larger cost g j #；
S3-2.4, considering the time window of order delivery, sequencing all new orders according to the time point of the time window expected by the user, and then finding the order N with the earliest expected commodity delivery time j ；
S3-2.5, comprehensively analyzing the newly added order volume and the vehicle loading volume constraint to find a candidate path set D capable of being inserted into the newly added order;
s3-2.6, analyzing the condition of the path set D, and if the set D is empty, searching the vehicle which completes the delivery task earliest to arrange the delivery order N of the vehicle j (ii) a Otherwise, find a line D from the set D i Calculating an order N j The minimum change cost g generated after insertion;
s3-2.7, if g is less than g j #, then g j # = g (indicating order N) j Is given by g j Change # delivery method to g corresponding delivery method), while from the path set DRemoving the line D i I.e. D = D-D i Otherwise D = D-D i ；
S3-2.8, when the set D is empty, g is selected j The order N corresponds to the delivery policy # j The distribution method of (1);
s3-2.9, taking N = N-N j If the order set N is empty, turning to the step S3-2.10; if not, turning to the step S3-2.4;
and S3-2.10, finishing the algorithm.
Example 1: s4, example verification
And (3) taking an order distribution task of a branch store of the K company in the morning on a certain day as case data, verifying a model and an algorithm, wherein the distribution order data is shown in a table 1:
table 1: order data
Figure BDA0002924868970000201
Figure BDA0002924868970000211
The parameters in the model are set as follows: q =15; v =15km/h =0.25km/min; w 1 ＝15，c 3 ＝0.5；c 1 ＝0.1，c 2 ＝0.15；
Distance s between orders ij The calculation formula is as follows:
Figure BDA0002924868970000212
wherein: (lat) i ,lng i ) And (lat) j ,lng j ) Longitude and latitude coordinates of the corresponding points i and j respectively, wherein R represents the earth radius and takes 6371KM;
the results of solving the conventional order model using the SI heuristic are shown in table 2:
table 2: conventional order model solution results
Figure BDA0002924868970000213
The distribution center is characterized in that 8: at 38, 1 emergency order is accepted, for which delivery needs to be scheduled as soon as possible, and the emergency order information is shown in table 3:
table 3: dynamic newly-added order information
Figure BDA0002924868970000214
The dynamic insertion heuristic algorithm and the conventional order model are used for respectively carrying out distribution arrangement on the emergency orders, and the result is shown in table 4:
table 4: two models solution results
Total cost of Total time/min Number of vehicles
Conventional order model 185.3 247 4
Two-stage model 169.3 245 3
As can be seen from Table 4, the two-stage model handles emergency order delivery more economically, less costly, and uses fewer vehicles than the conventional order model;
therefore, it is feasible and effective to adopt the two-stage model to process the emergency order delivery problem, namely, the superiority and feasibility of the emergency order delivery scheduling optimization method based on the two-stage model are proved.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (4)

1. An emergency order delivery scheduling optimization method is characterized by comprising the following steps: comprises that
The method comprises the following steps: establishing a conventional order distribution model taking the minimum total distribution cost as an objective function;
the process for establishing the conventional order distribution model in the step one comprises the following steps:
s1-1, setting the order delivery to be from the same delivery center or a goods taking point, wherein the number of available delivery vehicles is m, unified vehicle types are adopted, the vehicle capacity is Q, the average vehicle running speed is v, each delivery task corresponds to a user demand i, and the commodity volume corresponding to each demand i is Q i Each task requires that the user expect to get the commodity time window as [ e ] i ,l i ]，
Wherein: e.g. of the type i Is expected to arrive at the earliest point in time, l i Is expected to arrive at the latest time point;
s1-2, setting a symbol and a variable: n represents the total number of all order tasks; m represents the total number of delivery vehicles, k =1,2,3 …, m; i, j represents the corresponding order number, i =1,2,3…,n；c 1 Representing that the vehicle is early in penalty coefficient relative to the user expected time window; c. C 2 Representing that the vehicle is late relative to the user expected time window to a penalty factor; c. C 3 Representing the distribution cost corresponding to the unit distance of the vehicle; v represents the speed at which the delivery vehicle travels; q. q of i Representing the commodity volume corresponding to the task point i; w is a 2ij Represents the delivery cost from delivery point i to delivery point j; w is a 3i Represents the penalty cost due to the vehicle not arriving on time at delivery point i; w represents the cost incurred in the entire distribution process; w 1 Represents a fixed cost required to start the vehicle; w 2 Represents the total distribution cost generated in the distribution process; w 3 Representing the total penalty cost generated in the distribution process; q represents the maximum load volume that the delivery vehicle can carry; s ij Represents the distance from order i to order j; t is t ij Represents the time taken by the vehicle from delivery point i to delivery point j; t is t i Representing the point in time, t, at which the vehicle arrives at the delivery point i 0 =0; i =0 represents the delivery center corresponding order number;
s1-3, aiming at minimizing cost, designing a conventional order vehicle distribution model as follows:
Figure FDA0003988599830000011
Figure FDA0003988599830000012
Figure FDA0003988599830000013
Figure FDA0003988599830000014
Figure FDA0003988599830000021
Figure FDA0003988599830000022
Figure FDA0003988599830000023
Figure FDA0003988599830000024
Figure FDA0003988599830000025
Figure FDA0003988599830000026
Figure FDA0003988599830000027
Figure FDA0003988599830000028
Figure FDA0003988599830000029
Figure FDA00039885998300000210
Figure FDA00039885998300000211
wherein: the above equation (1) represents the total cost minimization; equation (2) represents the total delivery cost resulting from vehicle delivery; equations (3) and (4) represent the total penalty cost resulting from vehicle delivery; formula (5) indicates that there is only one vehicle coming out from any order and comes out once; (6) Indicating that only one vehicle is scheduled for delivery per order; formula (7) indicates that each order is processed only once and no duplication occurs; equation (8) indicates that each order must be scheduled for delivery; formula (9) indicates that the order volume carried by each vehicle in the distribution process does not exceed the maximum capacity volume of the vehicle; formula (10) shows that all vehicles start from the distribution center to be distributed; formula (11) represents that the vehicle finishes the delivery of the order, namely the delivery is finished, and then the vehicle returns to the delivery center; formula (12) represents the time relationship between the two delivery points before and after the delivery process;
step two: constructing an emergency order distribution model with the minimum insertion cost on the basis of the conventional order distribution model established in the step one;
the establishment process of the emergency order distribution model in the step two comprises the following steps:
s2-1, when the time 1 is set, an emergency order i 'is generated, and the commodity volume corresponding to the order is q' i Delivery time window of order demand is [ e' i ,l' i ](ii) a The emergency order i ' arranges the vehicle to return to the distribution center for picking up goods among the order groups (a, b), arranges the distribution among the order groups (u, z), and arranges the distribution among the order groups (a, b) before the order groups (u, z), if b = u is overlapped and is 0, the vehicle receives the emergency order i ' and returns to the distribution center for picking up goods, and immediately distributes the emergency order i ';
s2-2, on the basis of a conventional order, taking the minimum insertion cost as an objective function, considering the delivery cost of the emergency order, and constructing an emergency order model by the penalty cost of the conventional order caused by the insertion of the emergency order;
step three: designing an SI heuristic algorithm and a dynamic insertion algorithm solving model, applying the SI heuristic algorithm and the dynamic insertion algorithm solving model to the emergency order distribution model obtained in the step two, and carrying out distribution scheduling optimization on the emergency orders;
the design process of the SI heuristic algorithm and the dynamic insertion algorithm solution model comprises the following steps:
s3-1, designing an SI heuristic algorithm to solve a conventional order model;
and S3-2, designing a dynamic insertion heuristic algorithm to solve the emergency order model.
2. The method of claim 1, wherein the method comprises the steps of: the specific steps of step S2-2 include:
s2-2.1, setting the distribution cost generated by inserting the emergency newly-added order as g (1): after the goods taking of the emergency order i' is inserted into the middle of the order group (a, b), the original distribution path a → b is changed into a → 0 → b; similarly, after the delivery of the emergency order i 'is inserted into the middle of the order group (u, z), the original delivery path u → z is changed to u → i' → z, so that the delivery distance is increased, and the corresponding increased delivery path cost is as follows:
Figure FDA0003988599830000041
wherein: w is a 2ij Representing the delivery cost required for orders i to j; s ij Represents the distance from order i to order j;
s2-2.2, setting the penalty cost generated when the emergency order i' exceeds the delivery time window as g (2): the emergency order i 'is scheduled for delivery among the order group (u, z), so that the delivery vehicle needs to return to the delivery center to pick up the goods for delivery, and the actual delivery time of the emergency order i' is:
t i' ＝t u +t a0 +t 0b +t ui' (14)
combined with emergency order i 'customer expected time window [ e ] to place order' i ,l' i ]The penalty cost for the available emergency order i' is:
Figure FDA0003988599830000042
then:
Figure FDA0003988599830000043
wherein: e.g. of the type i' Indicating an emergency order customer expected earliest arrival time; l i' Indicating the time of arrival of the latest order expected by the emergency order customer;
s2-2.3, setting the total change penalty cost of the conventional order due to the change of the arrival time as g (3): the impact of an emergency order on the regular order time window is two: one is an order with arrival time variation caused only by picking, then the original penalty cost for regular order b is:
Figure FDA0003988599830000044
the time of arriving at the delivery point of the order b is t b' ＝t a +t a0 +t 0b The penalty cost generated by the corresponding time window is as follows:
Figure FDA0003988599830000045
the penalty change cost of the order b due to the urgent order is: Δ w 3b ＝w 3b' -w 3b Namely:
Figure FDA0003988599830000051
n orders with time change of arrival at the delivery point caused only by the emergency dynamic order i' returning to the delivery center for taking goods are set 1 I.e. the order [ b, u ]]Between is provided with n 1 Individual order, pair n 1 The order is distributed according to the sequence 1,2,3 …, and the penalty cost of the time window change is:
Figure FDA0003988599830000052
similarly, the change penalty cost g (3 ') due to the change in arrival time of subsequent regular orders caused by the pick and delivery of the urgent order i' can be obtained:
Figure FDA0003988599830000053
Figure FDA0003988599830000054
thus, the penalty charges for regular orders due to urgent order insertion are:
g(3)＝g(3')+g(3”)；
s2-2.4, obtaining a distribution model of the emergency order as follows:
min g＝g(1)+g(2)+g(3)。
3. the method of claim 1, wherein the method comprises the steps of: the algorithm step of solving the conventional order model by the SI heuristic algorithm comprises the following steps:
s3-1.1, establishing a rectangular coordinate system by taking a distribution center as an original point, determining coordinates of each delivery point, and taking an x-axis forward line as a scanning start line;
s3-1.2, selecting a starting line in the step S3-1.1, rotating counterclockwise, and grouping orders:
taking the volume of the vehicle-mounted capacity as a constraint, and enabling each order in the scanning area to correspond to a volume q i If the volume sum Q is not less than the maximum volume Q of the vehicle, dividing the orders into a group, completing distribution by one vehicle, continuing scanning, dividing the rest orders into groups, and dispatching the vehicles for distribution; if the volume sum Q is smaller than the maximum volume Q of the vehicle, continuing to scan;
s3-1.3, checking whether the order set of the residual unscanned area is empty, and if the order set of the residual unscanned area is empty, turning to the step S3-1.4; otherwise, continuing to scan according to the step S3-1.2;
all orders are grouped, assuming that m groups are obtained in total, counting the orders of each group, turning to the step S3-1.5, and planning a vehicle path according to the orders of each group;
s3-1.5, selecting a group of unplanned order groups m i Considering the distance and time factors, and aiming at minimizing the cost W, searching for an order i, wherein a connection point i and an origin form a directional vehicle driving path 0 → i → 0,m i ＝m i -i；
S3-1.6.m i If the value is 0, turning to the step S3-1.9 if the value is 0; otherwise, turning to the step S3-1.7;
s3-1.7 from m i Continuously searching a point j, wherein the point j meets the minimum cost W of the point on the distance path, inserting the point j into the path, and m i ＝m i -j；
S3-1.8: repeating the step S3-1.6 and the step S3-1.7 until all points are planned into the route, wherein m = m-1, and turning to the step S3-1.9;
s3-1.9, judging whether the set m is 0, and if so, turning to the step S3-1.10; otherwise, turning to the step S3-1.5;
s3-1.10, all orders are arranged, and the algorithm is finished.
4. The method of claim 1, wherein the method further comprises the steps of: the algorithm for solving the emergency order model by dynamically inserting the heuristic algorithm comprises the following steps:
s3-2.1, processing the dynamic order based on a time axis, and acquiring a dynamic newly-added order set N each time the dynamic order appears;
s3-2.2, updating the vehicle information, the distribution condition and the key points of the running path of each vehicle in real time;
s3-2.3, setting a cost g j #；
S3-2.4, considering the time window of order distribution, sequencing all new orders according to the time point of the time window expected by the user, and then finding the order N with the earliest delivery time of the expected goods j ；
S3-2.5, comprehensively analyzing the newly added order volume and the vehicle loading volume constraint to find a candidate path set D capable of being inserted into the newly added order;
s3-2.6, analyzing the condition of the path set D, and if the set D is empty, searching the vehicle which completes the delivery task earliest and arranges the delivery order N j (ii) a Otherwise, find a line D from the set D i Calculating an order N j The minimum change cost g generated after insertion;
s3-2.7, if g is less than g j #, then g j # = g, while removing line D from the path set D i I.e. D = D-D i Otherwise D = D;
s3-2.8, when the set D is empty, g is selected j The order N corresponds to the delivery policy # j The distribution method of (1);
s3-2.9, take N = N-N j If the order set N is empty, turning to the step S3-2.10; if not, turning to the step S3-2.4;
and S3-2.10, finishing the algorithm.
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