Information processing program, information processing method, and information processing device.

Abstract

To find the optimal delivery route that minimizes variations in shipment volume from the shipping source. [Solution] The information processing device 100 generates a set of multiple routes that indicate the order in which multiple moving objects visit a predetermined number of nodes among the multiple nodes when multiple moving objects depart from a specific node and return to the specific node via multiple nodes. Using the generated set of routes, it solves a route selection problem that has constraints on the shipment volume of the specific node or the node among the multiple nodes that will be the source of the shipment, and outputs the result of solving the route selection problem.

Description

[Technical Field]

[0001] This invention relates to an information processing program, etc., for solving a delivery planning problem. [Background technology]

[0002] The Vehicle Routing Problem (VRP) is a problem that seeks to find a route for transporting goods from a specific point called a depot to a destination using multiple moving objects, such as transport vehicles, and returning to the depot. VRP is one of the representative combinatorial optimization problems, and it seeks to find the optimal route that satisfies constraints imposed on the transport vehicles, such as capacity constraints and time constraints.

[0003] In recent years, an increasing number of companies in the logistics industry are aiming to equalize workloads to prevent imbalances in the work of specific employees or warehouses, and to ensure that the burden is distributed as evenly as possible. For example, when delivering goods to multiple customers, if there are multiple warehouses from which the goods originate, a limit may be placed on the amount of goods that can be shipped from each warehouse to avoid concentration of deliveries. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2021-106036 [Overview of the Initiative] [Problems that the invention aims to solve]

[0005] In this situation, it is desirable to find the optimal delivery route when an upper limit is set on the amount of goods shipped from the source, such as a warehouse or factory. However, while general capacity constraints and time constraints are constraints on the transport vehicles, constraints on the upper limit of the amount of goods shipped from each warehouse (hereinafter referred to as the upper limit constraint on the amount of goods shipped) are constraints on the warehouses themselves, making them difficult to handle in delivery planning problems.

[0006] In one aspect, the present invention aims to provide an information processing program, an information processing method, and an information processing device that can determine an optimal delivery route that suppresses variations in the volume of shipments from the shipping source. [Means for solving the problem]

[0007] In the first proposal, the computer performs the following processes: The computer generates a set of multiple paths that indicate the order in which multiple moving objects visit a predetermined number of nodes when multiple moving objects depart from a specific node and return to that specific node via multiple nodes; it solves a path selection problem using the generated set of paths, which is constrained by the shipment volume of the specific node or the node from which the goods are shipped; and it outputs the result of solving the path selection problem. [Effects of the Invention]

[0008] This invention makes it possible to determine the optimal delivery route while suppressing variations in the volume of shipments from the delivery source. [Brief explanation of the drawing]

[0009] [Figure 1] Figure 1 is a diagram illustrating the information processing device according to Example 1. [Figure 2] Figure 2 is a functional block diagram showing the functional configuration of the information processing device according to Example 1. [Figure 3] Figure 3 is a flowchart showing the processing procedure of the information processing device according to Example 1. [Figure 4] Figure 4 shows the configuration information of a test instance related to the application example of Example 1. [Figure 5] Figure 5 shows the solution results of a test instance related to the application example of Example 1. [Figure 6] Figure 6 shows the solution results of a test instance related to the application example of Example 1. [Figure 7] Figure 7 shows the solution results of a test instance related to the application example of Example 1. [Figure 8] Figure 8 shows the results of the shipment volume from each warehouse in the application example of Example 1. [Figure 9] Figure 9 shows an example of a hardware configuration. [Modes for carrying out the invention]

[0010] The following describes in detail, with reference to the drawings, embodiments of the information processing program, information processing method, and information processing apparatus disclosed in this application. However, this invention is not limited by these embodiments.

[0011] [Example 1] (Problem setting) Before describing this embodiment, we will explain the problem setting of the delivery planning problem with a shipment volume limit constraint related to this embodiment. For example, by setting the problem as follows for the delivery planning problem with a shipment volume limit, an efficient delivery route that satisfies each constraint condition, including the shipment volume limit constraint, can be found.

[0012] • Multiple trucks depart from a specific location, visit several nodes (customers or warehouses), and then return to the starting point. Each transport vehicle loads goods at the warehouse and delivers them to customers. There are multiple warehouses, and loading is possible at any of them. Furthermore, it is possible to visit the warehouses multiple times. • We must deliver packages to all customers. Transport vehicles are subject to constraints such as their load capacity (capacity constraints), different delivery time slots for each customer (time slot constraints), and the maximum travel time for the transport vehicle (maximum travel time constraints). Each warehouse has a set limit on the amount of goods it can ship, and it is not possible to ship more than that amount. The delivery cost for each transport vehicle is defined by factors such as travel time, travel distance, fixed costs, etc., or by a weighted linear sum thereof. • Find the route for each transport vehicle that satisfies all the constraints described above and minimizes the total delivery cost.

[0013] (method of expression) Next, we will explain how the delivery planning problem handled by the delivery optimization system implemented by the information processing device according to this embodiment is represented. Below, we will first explain the definitions of "tasks," "task groups," and "maximum sum constraints" that are introduced when representing the delivery planning problem.

[0014] Let's explain the definition of a "task." A task is the work of collecting and delivering packages. For example, a task includes the following information: *Collection node: A node that collects packages. *Delivery node: A node that handles the delivery of packages. *Time slot: Time slots related to collection and delivery. *Size: The size of the package.

[0015] Let's explain the definition of a "task group." A task group is a subset of the task set that contains all tasks. For each task group, at least one task from that group must be assigned to a transport vehicle. For example, if task groups G1={1,2} and G2={3,4}, then either task 1 or 2 must be assigned to a transport vehicle, and either task 3 or 4 must be assigned to a transport vehicle.

[0016] The definition of the "maximum sum constraint" is explained below. The maximum sum constraint is defined as satisfying equation (1) below for any determined paths r1, ..., rm, given a function f(r) that determines a non-negative value and a maximum sum M (>0) for any given path r of a transport vehicle.

[0017]

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[0018] Incorporating the concepts described above, the delivery optimization system according to this embodiment expresses the delivery planning problem as follows. V: Set of nodes. · s ∈ V: The departure node of the transport vehicle and the node to return to. · T: The set of tasks. · G i (i = 1, …, n) ⊆ T: n task groups. · f j (r): A function that determines a non - negative value for the route r of the transport vehicle to represent the maximum total value constraint. · M j (j = 1, …, m): The maximum total value. · g(r): A function that calculates the delivery cost (positive value) for the route r of the transport vehicle. · List of constraint conditions for each transport vehicle: For example, the following apply. - Capacity constraint: The capacity that can be loaded on the transport vehicle (time - frame constraint). - Time - frame constraint: The deliverable time - frame of the goods set at different times for each customer. - Maximum travel time constraint: The maximum travel time of the transport vehicle.

[0019] Next, the correspondence between the above - described expression method and the delivery planning problem with an upper limit on the shipment quantity according to this embodiment will be described respectively. · Let the set of customer nodes be C = {c1, …, c n}, the set of warehouse nodes be P = {p1, …, p m}, and the departure point be the node s. · Define V = C ∪ P ∪ {s}. · For each warehouse node p j ∈ P and each customer node c i ∈ C, define a task with the following information. * Collection node: Warehouse node p j . * Delivery node: Customer node c i . * Time - frame: The delivery time - frame of customer node c i . * Size: The size of the goods to be delivered to customer node c i . · Define the (n × m) total tasks defined above as the task set T. · For each customer node c i (i = 1, …, n), the delivery node is c iA set of tasks that is a task group G i It is stipulated that... • Each warehouse node p j For (j=1,…,m), the route r of the transport vehicle leads to the warehouse node p j Function f to calculate the shipment volume j Define (r), and warehouse node p j The upper limit of the shipment volume is M j It is stipulated that... Let g(r) be the delivery cost for each transport vehicle along route r. • Constraints on each transport vehicle, such as capacity constraints, time constraints, and maximum travel time constraints, are included in the "List of Constraints for Each Transport Vehicle".

[0020] (Processing details of the information processing device 100) Next, we will describe the information processing device 100 that performs the aforementioned constrained delivery planning problem with a shipment volume limit. Figure 1 is a diagram illustrating the information processing device according to Embodiment 1. The information processing device 100 shown in Figure 1 is an example of a computer device that outputs an optimal transportation route that takes into account the upper limit of the shipment volume for each warehouse by solving the aforementioned constrained delivery planning problem with a shipment volume limit.

[0021] As shown in Figure 1, the information processing device 100 generates a set of multiple paths that represent the order in which multiple mobile entities visit nodes when they depart from a specific node and return to that specific node via multiple nodes. The information processing device 100 then uses the generated set of paths to solve a path selection problem that has constraints on the shipment volume of a given node, and outputs the solution result.

[0022] For example, the information processing device 100 shows that a transport vehicle carrying goods departs from the starting point node s and moves to the warehouse node P. j The packages collected are sent to customer node c i After delivery to node P, a set of multiple routes (route 1 to route n) is generated for the return to node s. Then, the information processing device 100 generates a set of multiple routes for each warehouse node P j The upper limit of the shipment volume is M jThe system generates a route selection problem based on the given settings, and by solving this problem, it selects the optimal route that takes into account the upper limit of the shipping volume for each warehouse.

[0023] As a result, the information processing device 100 can solve the route selection problem when an upper limit is set on the shipment volume from the shipping source, and can find the optimal delivery route that suppresses variations in the shipment volume from the shipping source.

[0024] (Functional configuration of the information processing device 100) Figure 2 is a functional block diagram showing the functional configuration of the information processing device according to Embodiment 1. As shown in Figure 2, the information processing device 100 has a communication unit 110, a display unit 120, a storage unit 130, and a control unit 140.

[0025] The communication unit 110 is a processing unit that controls communication between other devices, and is implemented, for example, by a communication interface. For example, the communication unit 110 performs the transmission and reception of various data with external devices, such as devices used by administrators.

[0026] The display unit 120 is a processing unit that displays various information and is implemented by, for example, a display or a touch panel. For example, the display unit 120 displays the final output route data list and the data associated with each route.

[0027] The memory unit 130 is a processing unit that stores various data and programs executed by the control unit 140, and is implemented by, for example, memory or a hard disk. This memory unit 130 includes a VRP data storage unit 131, a solution parameter storage unit 132, and a path set storage unit 133.

[0028] The VRP data storage unit 131 stores various types of data used by VRP. For example, the VRP data storage unit 131 stores cargo data, node data, and transport vehicle data. Here, cargo data includes, for example, collection nodes, delivery nodes, collection time slots, and delivery time slots. Node data includes, for example, depot nodes, shipment volume limits, travel time between nodes, and available edge data. Transport vehicle data includes, for example, maximum load capacity, visitable nodes, maximum travel time, step function cost, and fixed costs.

[0029] The solution parameter storage unit 132 stores the parameters used by the information processing device 100 to solve each optimization problem. For example, the solution parameter storage unit 132 stores path generation parameters and path selection parameters. Here, the path generation parameters include parameters related to time limits and dual problem solvers. The path selection parameters include, for example, parameters related to time limits and path selection problem solvers.

[0030] The route set storage unit 133 stores a set of multiple routes r that indicate the order in which multiple mobile entities visit nodes, representing the paths taken when multiple mobile entities depart from a specific node generated by the information processing device 100 and return to that specific node via multiple nodes. For example, the route set storage unit 133 stores a set of routes that are the target of route selection by the route selection problem solving unit 144, which is generated by the initial route generation unit 141 and the route generation unit 142, which will be described later.

[0031] The control unit 140 is a processing unit that oversees the entire information processing device 100 and is implemented by, for example, a processor. This control unit 140 includes an initial path generation unit 141, a path generation unit 142, a termination determination unit 143, a path selection problem solving unit 144, and an output data generation unit 145. The path generation unit 142 includes a dual problem solving unit 142a and a reduced cost minimization problem solving unit 142b. The initial path generation unit 141, the path generation unit 142, the dual problem solving unit 142a, the reduced cost minimization problem solving unit 142b, the termination determination unit 143, the path selection problem solving unit 144, and the output data generation unit 145 are implemented by electronic circuits of the processor or processes executed by the processor.

[0032] The initial route generation unit 141 generates initial routes to be processed by the route selection problem solving unit 144, which will be described later. For example, the initial route generation unit 141 generates a delivery route that satisfies the condition of delivering packages to all customers and stores it in the route set storage unit 133. Here, the method of generating initial routes by the initial route generation unit 141 is not particularly limited, but as the simplest method, one example is to generate a simple initial route that repeats collection at a warehouse node and delivery at a customer node for each customer.

[0033] Here, the solution performed by the delivery optimization system implemented by the information processing device 100 consists of two main phases: (1) generating efficient route candidates, and (2) selecting the optimal one from among those candidates. Below, we will first explain the processing of the route selection problem solving unit 144, and then explain the processing of the route generation unit 142 and the termination determination unit 143.

[0034] The route selection problem solving unit 144 selects the optimal route from the route set by solving the route selection problem. For example, when the route selection problem solving unit 144 receives notification of the completion of the route generation process by the termination determination unit 143 (described later), it selects the optimal route from the routes stored in the route set storage unit 133. Here, the route selection problem is defined as follows. Let R be the set of paths generated. • Constant air We define it as shown in equation (2) below. For each path r ∈ R, the 0-1 variable xr in the path selection problem is defined as shown in equation (3) below.

[0035]

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[0036]

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[0037] The path selection problem can then be formulated as shown in equation (4) below.

[0038]

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[0039] The route selection problem solving unit 144 selects the optimal route from the route set R by solving the route selection problem formulated in equation (4) above. Here, by constructing an inequality (maximum sum constraint) with respect to the maximum sum M in equation (4) above, the route selection problem solving unit 144 can select the optimal route that takes into account the upper limit of the shipment volume of each warehouse.

[0040] The path selection problem in this embodiment is an optimization problem of a class called a 0-1 integer programming problem, and the software used to solve the 0-1 integer programming problem is not particularly limited.

[0041] The path generation unit 142 generates paths to be processed by the path selection problem solving unit 144, which will be described later, using a method based on the column generation method. Here, the column generation method has two steps: (1) solving the dual problem of the linear relaxation problem of the path selection problem for the current set of paths R, and (2) solving the reduced cost minimization problem for that dual problem. The path generation unit 142 generates new efficient path candidates by having the dual problem solving unit 142a perform step (1) and the reduced cost minimization problem solving unit 142b perform step (2).

[0042] The dual problem solving unit 142a solves the dual problem of the linear relaxation problem of the path selection problem for the current path set R. Below, specific examples of each problem related to the solving of the dual problem solving unit 142a are described.

[0043] First, the path selection relaxation problem is the path selection problem for each variable x r This is obtained by removing the integer constraint and is expressed as shown in equation (5) below.

[0044]

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[0045] Here, x r Even without the constraint ≤ 1, the optimal solution to the relaxation problem is x r Note that the condition ≤ 1 is met, x r The ≤1 can be removed. Therefore, the relaxed path selection problem can be rewritten as shown in equation (6) below.

[0046]

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[0047] The relaxation problem described above is classified as an optimization problem called a linear relaxation problem. Linear programming problems have a defined dual problem, and the dual problem for the above relaxation problem is given by equation (7) below.

[0048]

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[0049] The dual problem solving unit 142a solves the dual problem shown in equation (7) above, thereby obtaining the optimal solution (y) of the dual problem in a certain iteration of the column generation method. * ,z * Calculate ).

[0050] The reduced cost minimization problem solving unit 142b finds the optimal solution (y) obtained by the dual problem solving unit 142a. * ,z * This section solves the problem of minimizing the reduced cost of ). Below, we will explain specific examples of problems related to the solution of the reduced cost minimization problem solving unit 142b.

[0051] The optimal solution (y) obtained by the dual problem solving unit 142a * ,z * If we assume that ), the problem of minimizing the reduced cost in that iteration can be expressed as shown in equation (8) below.

[0052]

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[0053] Generally, finding the optimal solution in a reduced cost minimization problem is difficult. Therefore, the reduced cost minimization problem solving unit 142b does not aim to find the optimal solution, but rather processes the problem by obtaining the best possible solution through local search.

[0054] For example, a path r that satisfies the constraints in the constraint list for each transport vehicle. * The path r * Assign any unassigned task t to it. The following are examples of assignment methods: · Route r * Assign task t without adding a node. · Route r *Add a collection node or a delivery node for task t (including adding both), and assign task t to it.

[0055] By the above method, route r * Among the routes assigned to task t, the set of routes that satisfy the constraints in the constraint list for each transport vehicle is N(r * Defined as ,t). The reduced cost minimization problem solving unit 142b calculates the current path r in each iteration of the local search. * Task t offers the best improvement in contracted costs. * and a new path r'∈N(r * Search for ,t).

[0056] Next, we will explain an example of an efficient calculation method implemented by the reduced cost minimization problem solving unit 142b. The efficient calculation method utilizes the following assumptions of the problem setting. • Assumption (1) - Any path r * Task t and path r∈N(r * For ,t), g(r * )≦g(r) holds true. • Assumption (2) - Any path r * Task t and path r∈N(r * For t), f j (r * )≦f j (r)(j=1,…,k) holds. • Assumption (3) - Each task group G i The sets (i=1,…,n) are sparse (their intersection is the empty set).

[0057] Here, assuming that the reduced cost for any path r is given by equation (9) below, the reduced cost minimization problem solving unit 142b uses the above assumptions (1) to (3) to perform efficient calculations using the following techniques (1) to (4).

[0058]

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[0059] First, let's explain the method (1). Method (1) uses assumptions (1) and (2) as usage conditions. Method (1) is y i * For any i=1, ..., n and t∈G such that =0 = 0 i For the path r, * When considering assigning task t to y, i * =0, Assumption (1), Assumption (2), z j * Since ≥ 0 (j=1,…,k), any r ∈ N(r * For ,t) F(r * )≦F(r) holds true. In other words, in modification 1, y i * Task group G = 0 i This shows that assigning tasks included in this category does not improve the contracted costs, and therefore calculating the contracted costs for such a path is unnecessary.

[0060] Next, I will explain the method (2). In method (1), assumptions (1), (2), and (3) are used as usage conditions. In method (2), the path r * When considering assigning a task to a i (r * For any i ∈ {1, ..., n} such that ) = 1, task t ∈ G i , path r∈N(r * For t), by assumption (3), equation (10) below holds. Therefore, in modification (2), assumption (1), assumption (2), z j * Since ≥ 0 (j=1,…,k), F(r * )≦F(r) holds true. In other words, in method (2), a i (r * Task group G where )=1 i This shows that assigning tasks included in this category does not improve the contracted costs, and therefore calculating the contracted costs for such a path is unnecessary.

[0061]

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[0062] Next, I will explain the method (3). In method (3), we use assumption (2) as the usage condition. In method (3), any path r * When considering assigning an arbitrary task t∈T to a path r∈N(r) satisfying equation (11) below, * For ,t), by assumption (2), F(r * )≦F(r) holds. In other words, in technique (3), when assigning tasks to a path to improve the reduced cost, we can determine whether the reduced cost can be improved from the current path without calculating the part of equation (12) below in equation (9) which shows the reduced cost.

[0063]

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[0064]

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[0065] Next, we will explain the method (4). In method (4), for any paths r',r that satisfy equation (13) below, z j * f j (r)≧0(j=1,…,k) Therefore, F(r * )≦F(r) holds. In other words, in technique (4), similar to technique (3), we show that we can determine whether the reduced cost can be improved from the current route without calculating the part of equation (12) above in equation (9) which shows the reduced cost.

[0066]

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[0067] The constrained cost minimization problem solving unit 142b executes local search for the cost minimization problem by the search procedure from step (1) to step (4) below, including the above device. Note that the constrained cost minimization problem solving unit 142b is given the initial route r0, the task set T, and the optimal solution (y * , z * ) of the dual problem as input and outputs the searched route.

[0068] First, the processing of step (1) will be described. In step (1), the initializations from step (1)-1 to step (1)-4 below are executed in order.

[0069] In step (1)-1, set r * := r0, r´ := r0, α´ := F(r´), T´ := T, and set β * as the following equation (14).

[0070]

Equation

[0071] In step (1)-2 (device (1)), when assumptions (1) and (2) are satisfied, let the set of i such that y i * = 0 (i = 1,..., n) be I1, and define D1 by the following equation (15). Then, redefine T´ as T´ \ D1.

[0072]

Equation

[0073] In step (1)-3 (device (2)), when assumptions (1), (2), and (3) are satisfied, let the set of i such that a i (r * ) = 1 (i = 1,..., n) be I2, and define D2 by the following equation (16). Then, redefine T´ as T´ \ D2.

[0074]

Equation

[0075] In step (1)-4, when none of the assumptions (1), (2), and (3) are satisfied, the task assigned to path r * is removed from T´.

[0076] Next, the process of step (2) will be described. In step (2), for each path r ∈ N(r * , t) of each task t ∈ T´, the processes from step (2)-1 to step (2)-4 below are executed in order.

[0077] In step (2)-1, the following equation (17) is calculated.

[0078]

Equation

[0079] In step (2)-2 (Ingenuity (3)), when assumption (2) is satisfied and α * ≤ γ + β * , the cost savings of path r cannot be improved, so step (2)-1 is executed for the next r ∈ N(r * , t).

[0080] In step (2)-3 (Ingenuity (4)), when α´ ≤ γ, the cost savings of path r cannot be improved, so step (2)-1 is executed for the next r ∈ N(r * , t).

[0081] In step (2)-4, when α´ > F(r), update α´ := F(r) and r´ := r.

[0082] Subsequently, the process of step (3) will be described. In step (3), when α´ = α * , end the search and output path r * .

[0083] Next, we will explain the process in step (4). In step (4), the task assigned in step (2) is t * Then, perform the updates by executing the processes from step (4)-1 to step (4)-3 below, and return to the process in step (2).

[0084] In step (4)-1, r * :=r', α * Let :=α', then β * Let this be represented by equation (18) below.

[0085]

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[0086] In step (4)-2 (Ingenuity (2)), if assumption (1), assumption (2), and assumption (3) are met, then task t * Task group G i Remove from T'.

[0087] In step (4)-3, if none of assumptions (1), (2), or (3) are met, then task t * Remove the task from T'.

[0088] The reduced cost minimization problem solving unit 142b performs a local search on the cost minimization problem by executing the processing procedures from step (1) to step (4) described above, and obtains the optimal solution (y) obtained by the dual problem solving unit 142a. * ,z * The reduced cost minimization problem is solved. As a result, the reduced cost minimization problem solving unit 142b can generate new efficient route candidates and store them in the route set storage unit 133.

[0089] The termination determination unit 143 determines whether to terminate the process by which the route generation unit 142 generates new efficient route candidates. For example, the termination determination unit 143 determines whether the route generation unit 142 has generated a route with a negative reduced cost. If a route with a negative reduced cost has been generated, the termination determination unit 143 determines whether the time required for route generation exceeds the time limit related to the route generation parameters stored in the solution parameter storage unit 132.

[0090] Then, if no route with a negative contracted cost has been generated, or if the time required for route generation exceeds the time limit related to the route generation parameters, the termination determination unit 143 notifies the route selection problem solving unit 144 that the route generation process has ended. If the time required for route generation does not exceed the time limit related to the route generation parameters, the termination determination unit 143 notifies the route generation unit 142 to continue the route generation process.

[0091] The output data generation unit 145 generates route data based on the optimal route selected by the route selection problem solving unit 144. For example, the output data generation unit 145 generates a route data list of the route selected by the route selection problem solving unit 144, as well as output data such as the node visit order, node visit time, and task data for each route.

[0092] (Processing procedure of the information processing device 100) Next, an example of the processing procedure of the information processing device 100 according to Example 1 will be described. Figure 3 is a flowchart showing the processing procedure of the information processing device according to Example 1. Note that each step in the flowchart shown in Figure 3 can be executed in a different order, and additional or omitted processes may be included.

[0093] First, the information processing device 100 generates an initial path and sets the path set to R (S101). Then, the information processing device 100 solves the dual of the linear relaxation problem of the path selection problem for the path set R (S102). Then, by solving the reduced cost minimization problem for the optimal solution of the dual problem, it generates a new path and adds it to the path set R (S103).

[0094] Next, the information processing device 100 determines whether or not a route with a negative redeemable cost has been generated (S104). If a route with a negative redeemable cost has been generated (S104; Yes), the information processing device 100 determines whether or not the time required for route generation exceeds the given time limit (S105). If no route with a negative redeemable cost has been generated (S104; No), or if the time required for route generation exceeds the given time limit (S105; Yes), the information processing device 100 selects the optimal route from the set of routes R generated by solving the route selection problem (S106).

[0095] If the time required for route generation does not exceed the given time limit (S105; No), the information processing device 100 returns to S102 and continues processing. Then, after S106, the information processing device 100 outputs route information related to the selected optimal route (S107) and terminates the process.

[0096] (effect) As described above, the information processing device 100 generates a set of multiple routes that represent the order in which multiple moving objects, departing from a specific node and returning to that specific node via multiple nodes, visit a predetermined number of nodes among the multiple nodes. Using the generated set of routes, it solves a route selection problem that imposes constraints on the shipment volume of the specific node or the node that serves as the source of the shipment, and outputs the solution result of the route selection problem. As a result, the information processing device 100 can select a route that minimizes the number of violations of the inequality constraints on the shipment volume of the predetermined node, thereby suppressing variations in the shipment volume of warehouse nodes. In other words, the information processing device 100 can find an optimal delivery route that suppresses variations in the shipment volume of the source.

[0097] Furthermore, the information processing device 100 solves the dual of the linear relaxation problem of the route selection problem for the set of routes, and if the reduced cost of the solution obtained by solving the reduced cost minimization problem on the solution result of the dual problem is negative, it adds the route corresponding to the solution result of the reduced cost minimization problem to the set of routes. As a result, the information processing device 100 can find the optimal delivery route after adding an efficient route to the set of routes when an upper limit is set on the shipment volume.

[0098] (Examples of application) Next, we will explain an example of applying the delivery optimization system using the aforementioned information processing device 100 to a delivery planning problem with a shipment volume limit. Here, the instance of the delivery planning problem with a shipment volume limit is set as follows. Figure 4 shows the configuration information of a test instance related to the application example of Example 1. Let the coordinates of the starting node be (0,0). There are four warehouse nodes, with their coordinates set to (10,10), (10,-10), (-10,10), and (-10,-10). The customer node generates coordinates (x,y) randomly within the range of -30≦x≦30 and -30≦y≦30. The size of each customer's package is set to 1. The constraints on each transport vehicle are capacity constraints and constraints on maximum travel distance. Each warehouse is subject to the same shipping volume limit (an instance without a limit is also created for comparison). • Delivery costs are calculated based on distance traveled. • Set the actual numerical settings for the six test instances as shown in Figure 4.

[0099] Here, we will explain examples of actual numerical settings for the six test instances shown in Figure 4. As shown in Figure 4, in the application example, the process of outputting the optimal delivery route is executed for each of the six test instances. Here, "test1" corresponds to "test2", "test3" to "test4", and "test5" to "test6", and by comparing the delivery routes of both setting examples, we will explain the change in the route when a shipping volume limit is set and when a shipping volume limit is not set.

[0100] For example, "test1" outputs the optimal delivery route when delivering packages to 5 customers, with a capacity constraint of 3 packages, and no constraints on shipment volume or maximum travel distance. In contrast, "test2" outputs the optimal delivery route when delivering packages to 5 customers, with a capacity constraint of 3 packages and a shipment volume limit constraint of 2 packages, and no constraint on maximum travel distance.

[0101] Next, we will explain the solution results for the six test instances mentioned above. Figures 5 to 7 show the solution results for the test instances related to the application example of Example 1. In Figures 5 to 7, node 0 is the departure node for the transport vehicle, nodes 1, 2, 3, and 4 are warehouse nodes, and nodes 5 onwards are customer nodes.

[0102] First, let's explain the solution results for "test1" and "test2" using Figure 5. As shown in the solution result for "test1" in Figure 5(1), the route for "test1," which does not have a shipment volume limit constraint, has a shipment volume of 3 from the warehouse at node 1. Therefore, the solution result for "test1" does not satisfy the conditions for "test2," which has a shipment volume limit set to "2."

[0103] In contrast, the "test2" route, by passing through node 2 after node 5, ensures that the shipment volume from all warehouses is 2 or less. In other words, in "test2," where a shipment volume limit constraint is set, it is confirmed that a route that satisfies the shipment volume limit is selected.

[0104] Next, we will explain the solution results for "test3" and "test4" using Figure 6. As shown in the solution result for "test3" in Figure 6(1), the route for "test3," which does not have a shipment volume limit constraint, has a shipment volume of 7 from the warehouse at node 2. Therefore, the solution result for "test3" does not satisfy the conditions for "test4," which has a shipment volume limit set to "5".

[0105] In contrast, the "test4" route efficiently passes through each warehouse node, resulting in a total shipment volume of 5 or less from all warehouses. This confirms that in "test4," where a shipment volume limit constraint is set, a route is selected that satisfies the shipment volume limit.

[0106] Next, we will explain the solution results for "test5" and "test6" using Figure 7. Here, since the solution results for "test5" and "test6" are complex because the number of customers is set to 100, we will explain by focusing on the shipment volume of each warehouse. Figure 8 is a diagram showing the results of the shipment volume of each warehouse related to the application example of Example 1.

[0107] As shown in Figure 8, in "test5," the shipment volume from each warehouse node is 35 for node 1. Therefore, the solution result for "test5" does not satisfy the conditions for "test6," where the shipment volume limit is set to "30." In contrast, the route in "test6" uses node 3 more actively than in "test5," resulting in shipment volumes from all warehouses being 30 or less. In other words, in "test6," where a shipment volume limit constraint is set, it is confirmed that a route that satisfies the shipment volume limit is selected.

[0108] As shown in the application example above, the information processing device 100 can output an optimal delivery route that satisfies the condition that the shipment volume of each warehouse does not exceed the set upper limit by solving a delivery planning problem with a shipment volume limit constraint set as a constraint condition.

[0109] [Example 2] Now, although embodiments of the present invention have been described, the present invention may be implemented in various other forms besides those described above.

[0110] (Numerical values, etc.) The number of rows and columns in the matrix and the values ​​of the elements used in the above examples are merely examples and can be changed as needed. Furthermore, the processing flow described in each flowchart can also be modified as appropriate, within a range that maintains consistency.

[0111] (system) Unless otherwise specified, the processing procedures, control procedures, specific names, and various data and parameters shown in the above documents and drawings may be changed at will.

[0112] Furthermore, the components of each illustrated device are functionally conceptual and do not necessarily need to be physically configured as shown. In other words, the specific forms of distribution and integration of each device are not limited to those shown. That is, all or part of them can be functionally or physically distributed and integrated in any unit according to various loads and usage conditions.

[0113] Furthermore, each processing function performed by each device can be implemented, in whole or in part, by a CPU and a program executed for analysis by that CPU, or by wired logic hardware.

[0114] (Hardware) Figure 9 shows an example of a hardware configuration. As shown in Figure 9, the information processing device 100 includes a communication device 100a, an HDD (Hard Disk Drive) 100b, memory 100c, and a processor 100d. Furthermore, the components shown in Figure 9 are interconnected by a bus or the like.

[0115] The communication device 100a is a network interface card or the like, and communicates with other devices. The HDD 100b stores programs and databases that operate the functions shown in Figure 4.

[0116] The processor 100d operates a process that performs the functions described in Figure 2 by reading a program that performs the same processing as each processing unit shown in Figure 2 from the HDD 100b or the like and loading it into memory 100c. For example, this process performs the same functions as each processing unit of the information processing device 100. Specifically, the processor 100d reads a program from the HDD 100b or the like that has the same functions as the initial path generation unit 141, the path generation unit 142, the dual problem solving unit 142a, the reduced cost minimization problem solving unit 142b, the termination determination unit 143, the path selection problem solving unit 144, the output data generation unit 145, etc. Then, the processor 100d executes a process that performs the same operations as the initial path generation unit 141, the path generation unit 142, the dual problem solving unit 142a, the reduced cost minimization problem solving unit 142b, the termination determination unit 143, the path selection problem solving unit 144, the output data generation unit 145, etc.

[0117] Thus, the information processing device 100 operates as an information processing device that executes an information processing method by reading and executing a program. Furthermore, the information processing device 100 can also achieve the same functionality as the above-described embodiment by reading the program from a recording medium using a media reader and executing the read program. It should be noted that the program referred to in this other embodiment is not limited to being executed by the information processing device 100. For example, the above embodiment may also be applied similarly when another computer or server executes the program, or when they collaborate to execute the program.

[0118] This program may be distributed via a network such as the Internet. Alternatively, this program may be recorded on a computer-readable recording medium such as a hard disk, flexible disk (FD), CD-ROM, MO (Magneto-Optical disk), or DVD (Digital Versatile Disc), and executed by being read from the recording medium by a computer. [Explanation of Symbols]

[0119] 100 Information Processing Devices 110 Communications Department 120 Display section 130 Storage section 131 VRP Data Storage Unit 132 Solution Parameter Storage Unit 133 Path set storage unit 140 Control Unit 141 Initial path generation unit 142 Path generation unit 142a Dual Problem Solving Section 142b Contracted cost minimization problem solving part 143 Termination Determination Unit 144 Route Selection Problem Solving Section 145 Output data generation unit

Claims

1. A set of multiple paths is generated that indicates the order in which multiple mobile entities visit a predetermined number of nodes among the multiple nodes, in which multiple mobile entities depart from a specific node and return to the specific node via multiple nodes. Using the generated set of routes, we solve a route selection problem that imposes constraints on the shipment volume of the specific node or the node among the multiple nodes that serves as the source of the shipment. Output the solution result of the aforementioned path selection problem. An information processing program characterized by having a computer perform the processing.

2. The information processing program according to claim 1, characterized in that it causes a computer to further perform a process to generate a route to be newly added to the set of routes, such that the route satisfies the constraints regarding the shipment volume.

3. The process for generating the aforementioned route is: A process for solving the dual of the linear relaxation problem of the path selection problem for the set of paths, The process of solving the reduced cost minimization problem with respect to the solution result of the aforementioned dual problem, If the reduced cost of the solution obtained by solving the reduced cost minimization problem is negative, the process of adding the path corresponding to the solution result of the reduced cost minimization problem to the set of paths, The information processing program according to claim 2, characterized in that it causes a computer to execute it.

4. The aforementioned process for solving the problem is: A transport vehicle for carrying the goods is assigned to at least one task within each task group, which is a subset of all tasks representing the work of collecting and delivering goods. The transport vehicle travels along a route to perform its assigned task. The route selection problem is solved such that, for each node that serves as the source of the shipment, the sum of the shipment quantities along each route passing through that node is less than or equal to the maximum total constraint, which is a constraint on the shipment quantities. The information processing program according to feature 1.

5. The aforementioned task includes, The collection node, which collects the cargo from the specified node or the plurality of nodes, the delivery node, which delivers the cargo from the specified node or the plurality of nodes, the volume of cargo to be collected and delivered, and the time frame for collection and delivery are included. The information processing program according to feature 4.

6. Computers A set of multiple paths is generated that indicates the order in which multiple mobile entities visit the nodes, in which they depart from a specific node and return to the specific node via multiple nodes. Using the generated set of routes, a route selection problem is generated with constraints on the shipment volume of the node that will be the source of the shipment. Solve the generated path selection problem, Output the solution result of the aforementioned path selection problem. An information processing method characterized by including processing.

7. A set of multiple paths is generated that indicates the order in which multiple mobile entities visit the nodes, in which they depart from a specific node and return to the specific node via multiple nodes. Using the generated set of routes, a route selection problem is generated with constraints on the shipment volume of the node that will be the source of the shipment. Solve the generated path selection problem, Output the solution result of the aforementioned path selection problem. An information processing apparatus characterized by having a control unit that performs processing.

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