Delivery plan determination device, delivery plan determination method, and computer program

Abstract

The present invention acquires an objective function including first to ninth functions and optimizes the objective function using an annealing quantum computer to thereby determine a luggage delivery plan.　First function: represents a required delivery time. Second function: represents the number of delivery points. Third function: relates to prohibiting movement between points in less than a required movement time. Fourth function: limits the number of visits to each delivery point by each vehicle to one or less, and relates to prohibiting a plurality of vehicles from visiting each delivery point in a plurality of time frames. Fifth function: relates to prohibiting a plurality of vehicles from visiting each delivery point in each time frame. Sixth function: relates to prohibiting each vehicle from visiting a departure point, a delivery point, and a return point before a departure time from the departure point. Seventh function: relates to prohibiting each vehicle from visiting a departure point, a delivery point, and a return point after a return time to the return point. Eighth function: relates to prohibiting each vehicle from visiting a departure point multiple times. Ninth function: relates to prohibiting each vehicle from visiting a return point multiple times.

Description

Delivery plan determination device, delivery plan determination method, and computer program

[0001] This disclosure relates to a delivery plan determination device, a delivery plan determination method, and a computer program. This application claims priority to Japanese Application No. 2022-207861, filed December 26, 2022, and incorporates by reference all of the contents of that Japanese application.

[0002] A method for creating an operation plan for production equipment in a factory using an annealing machine has been proposed (see, for example, Patent Document 1). The annealing machine is also called an Ising machine or a quadratic unconstrained binary optimization (QUBO) solver, and is a device in which specialized hardware for combinatorial optimization is implemented using circuits such as a field-programmable gate array (FPGA) or a graphics processing unit (GPU).

[0003] Furthermore, the practical application of quantum computers, which can instantly solve combinatorial optimization problems, is becoming a reality. Using such quantum computers, the above-mentioned operation plans can also be created instantly.

[0004] Japanese Patent Application Laid-Open No. 2020-140615

[0005] A delivery plan determination device according to one aspect of the present disclosure is a delivery plan determination device that determines a delivery plan for a package by a plurality of vehicles from a departure point to a destination point via a package delivery point, and includes an objective function acquisition unit that acquires objective functions including a first function, a second function, a third function, a fourth function, a fifth function, a sixth function, a seventh function, an eighth function, and a ninth function shown below, and a delivery plan determination unit that determines the delivery plan by optimizing the objective function using an annealing quantum computer or an Ising machine. First function: a function that represents the time required for delivery of a package. Second function: a function that represents the number of delivery points. Third function: a penalty function related to prohibiting movement of the vehicle between points that the vehicle may travel to within the time required for movement. Fourth function: a penalty function related to prohibiting multiple vehicles from visiting each of the delivery points in multiple time frames when the number of visits to each of the delivery points by each of the vehicles is one or less and the planned time of the delivery plan is divided into multiple time frames. Fifth function: a penalty function related to prohibiting multiple vehicles from visiting each of the delivery points in each of the time frames. Sixth function: a penalty function related to prohibiting each of the vehicles from visiting the departure point, the delivery point, and the return point before the departure time of each of the vehicles from the departure point. Seventh function: a penalty function related to prohibiting each of the vehicles from visiting the departure point, the delivery point, and the return point after the return time of each of the vehicles to the return point. Eighth function: a penalty function related to prohibiting each of the vehicles from visiting the departure point multiple times. Ninth function: a penalty function related to prohibiting each of the vehicles from visiting the return point multiple times.

[0006] FIG. 1 is a diagram illustrating an example of the overall configuration of a delivery plan determination system according to a first embodiment of the present disclosure. FIG. 2 is a diagram illustrating an example of a delivery plan for a package. FIG. 3 is a block diagram illustrating an example of the configuration of a delivery plan determination device according to the first embodiment of the present disclosure. FIG. 4 is a diagram illustrating a first function. FIG. 5 is a diagram illustrating a second function. FIG. 6 is a diagram illustrating a third function. FIG. 7 is a diagram illustrating a fourth function. FIG. 8 is a diagram illustrating a fifth function. FIG. 9 is a diagram illustrating a sixth function. FIG. 10 is a diagram illustrating a seventh function. FIG. 11 is a diagram illustrating an eighth function. FIG. 12 is a diagram illustrating a ninth function. FIG. 13 is a sequence diagram illustrating an example of the operation of the delivery plan determination system according to the first embodiment of the present disclosure. FIG. 14 is a block diagram illustrating an example of the configuration of a delivery plan determination device according to a second embodiment of the present disclosure. FIG. 15 is a diagram illustrating an example of designated delivery time information for a package. FIG. 16 is a diagram illustrating an example of a decision variable. FIG. 17 is a sequence diagram illustrating an example of the operation of the delivery plan determination system according to the second embodiment of the present disclosure.

[0007] [Problem to be Solved by the Present Disclosure] Various methods for determining a delivery plan for packages using vehicles have been proposed. However, the method disclosed in Patent Literature 1 does not reflect movement between points in the combinatorial optimization problem. For this reason, the above method cannot be directly applied to the creation of a delivery plan.

[0008] The present application has been made in view of the above circumstances, and has as its object to provide a delivery plan determination device, a delivery plan determination method, and a computer program that are capable of determining a delivery plan at high speed.

[0009] Effect of the Present Disclosure According to the present disclosure, a delivery plan can be determined quickly.

[0010] [Outline of Embodiments of the Present Disclosure] First, an outline of embodiments of the present disclosure will be listed and described. (1) A delivery plan determination device according to an embodiment of the present disclosure is a delivery plan determination device that determines a package delivery plan by a plurality of vehicles from a departure point to a destination point via package delivery points, and includes an objective function acquisition unit that acquires objective functions including a first function, a second function, a third function, a fourth function, a fifth function, a sixth function, a seventh function, an eighth function, and a ninth function shown below, and a delivery plan determination unit that determines the delivery plan by optimizing the objective function using an annealing quantum computer or an Ising machine. First function: a function that represents the time required for delivery of a package. Second function: a function that represents the number of delivery points. Third function: a penalty function related to prohibiting movement of the vehicle between points that the vehicle may travel to within the time required for movement. Fourth function: a penalty function related to prohibiting multiple vehicles from visiting each of the delivery points in multiple time frames when the number of visits to each of the delivery points by each of the vehicles is one or less and the planned time of the delivery plan is divided into multiple time frames. Fifth function: a penalty function related to prohibiting multiple vehicles from visiting each of the delivery points in each of the time frames. Sixth function: a penalty function related to prohibiting each of the vehicles from visiting the departure point, the delivery point, and the return point before the departure time of each of the vehicles from the departure point. Seventh function: a penalty function related to prohibiting each of the vehicles from visiting the departure point, the delivery point, and the return point after the return time of each of the vehicles to the return point. Eighth function: a penalty function related to prohibiting each of the vehicles from visiting the departure point multiple times. Ninth function: a penalty function related to prohibiting each of the vehicles from visiting the return point multiple times.

[0011] According to this configuration, an objective function is optimized using an annealing quantum computer or an Ising machine. The objective function includes a first function related to the required delivery time of the package and a second function related to the number of delivery points of the package. The objective function also includes penalty functions shown as the third to ninth functions. These penalty functions indicate constraints on the vehicle's movement between points. Therefore, it is possible to quickly determine a package delivery plan that optimizes the required delivery time of the package and the number of delivery points while satisfying these constraints.

[0012] (2) In (1) above, the objective function may be expressed as a sum of functions obtained by multiplying the first function, the second function, the third function, the fourth function, the fifth function, the sixth function, the seventh function, the eighth function, and the ninth function by a predetermined weight coefficient.

[0013] For example, by setting the weights for the third to ninth functions to values ​​that are sufficiently larger than the weights for the first and second functions (for example, 100 to 1000 times larger), the value of the objective function can be increased when the constraints are not satisfied. Therefore, by minimizing the objective function, it is possible to determine a package delivery plan that reliably satisfies the constraints.

[0014] (3) In the above (1) or (2), the third function may be expressed as H3 below.

[0015] According to this configuration, the third function can be formulated as a Hamiltonian H3 using the decision variables shown in the following equation 1. The decision variables indicate whether or not the vehicle k visits the point p in the time frame τ by using 0 or 1. Therefore, the objective function can be optimized using an annealing-type quantum computer or an Ising machine.

[0016] (4) In any of (1) to (3) above, the fourth function may be expressed as H4 below.

[0017] According to this configuration, the fourth function can be formulated as a Hamiltonian H4 using the decision variable of Equation 1, which indicates whether or not the point p is visited in the time frame τ of the vehicle k by 0 or 1. Therefore, the objective function can be optimized using an annealing-type quantum computer or an Ising machine.

[0018] (5) In any of (1) to (4) above, the fifth function may be expressed as H5 below.

[0019] According to this configuration, the fifth function can be formulated as a Hamiltonian H5 using the decision variable of Equation 1, which indicates whether or not the point p is visited in the time frame τ of the vehicle k by 0 or 1. Therefore, the objective function can be optimized using an annealing-type quantum computer or an Ising machine.

[0020] (6) In any of (1) to (5) above, the sixth function may be expressed as H6 below.

[0021] According to this configuration, the sixth function can be formulated as a Hamiltonian H6 using the decision variable of Equation 1, which indicates whether or not the point p is visited in the time frame τ of the vehicle k by 0 or 1. Therefore, the objective function can be optimized using an annealing-type quantum computer or an Ising machine.

[0022] (7) In any of (1) to (6) above, the seventh function may be expressed as H7 below.

[0023] According to this configuration, the seventh function can be formulated as a Hamiltonian H7 using the decision variable of Equation 1, which indicates whether or not the point p has been visited in the time frame τ of the vehicle k by 0 or 1. Therefore, the objective function can be optimized using an annealing-type quantum computer or an Ising machine.

[0024] (8) In any of (1) to (7) above, the eighth function may be expressed as H8 below.

[0025] According to this configuration, the eighth function can be formulated as a Hamiltonian H using the decision variable of Equation 1, which indicates whether or not the point p has been visited in the time frame τ of the vehicle k by 0 or 1. Therefore, the objective function can be optimized using an annealing-type quantum computer or an Ising machine.

[0026] (9) In any of (1) to (8) above, the ninth function may be expressed as H9 below.

[0027] According to this configuration, the ninth function can be formulated as a Hamiltonian H9 using the decision variable of Equation 1, which indicates whether or not the point p is visited in the time frame τ of the vehicle k by 0 or 1. Therefore, the objective function can be optimized using an annealing-type quantum computer or an Ising machine.

[0028] (10) In any of (1) to (9) above, the delivery point may be associated with the package and a designated delivery time for the package.

[0029] There are cases where different delivery times are specified for multiple packages delivered to the same delivery point. With this configuration, even if the delivery points are the same, if the specified delivery times for the packages are different, the objective function can be optimized by treating them as different delivery points. This makes it possible to determine a delivery plan for delivering packages with different specified delivery times to the same delivery point without being restricted by the number of visits due to the fourth function.

[0030] (11) In any of (1) to (10) above, the objective function may include a decision variable that represents, as a binary value, whether or not each vehicle will visit each delivery point during each time slot, and the delivery plan determination unit may optimize the objective function after determining, based on the specified delivery time of the package, the values ​​of the decision variables other than the specified delivery time of the delivery point of the package to values ​​corresponding to no visit.

[0031] This configuration reduces the number of decision variables whose values ​​need to be determined, allowing for the rapid determination of a delivery plan that does not deliver packages during times when delivery is prohibited.

[0032] (12) A delivery plan determination method according to another embodiment of the present disclosure is a delivery plan determination method for determining a delivery plan for a package from a departure point to a destination point by a plurality of vehicles via a package delivery point, the delivery plan determination method including: a step in which a delivery plan determination device obtains an objective function including a first function, a second function, a third function, a fourth function, a fifth function, a sixth function, a seventh function, an eighth function, and a ninth function shown below; and a step in which the delivery plan determination device determines the delivery plan by optimizing the objective function using an annealing quantum computer or an Ising machine. First function: a function that represents the time required for delivery of a package. Second function: a function that represents the number of delivery points. Third function: a penalty function related to prohibiting movement of the vehicle between points that the vehicle may travel to within the time required for movement. Fourth function: a penalty function related to prohibiting multiple vehicles from visiting each of the delivery points in multiple time frames when the number of visits to each of the delivery points by each of the vehicles is one or less and the planned time of the delivery plan is divided into multiple time frames. Fifth function: a penalty function related to prohibiting multiple vehicles from visiting each of the delivery points in each of the time frames. Sixth function: a penalty function related to prohibiting each of the vehicles from visiting the departure point, the delivery point, and the return point before the departure time of each of the vehicles from the departure point. Seventh function: a penalty function related to prohibiting each of the vehicles from visiting the departure point, the delivery point, and the return point after the return time of each of the vehicles to the return point. Eighth function: a penalty function related to prohibiting each of the vehicles from visiting the departure point multiple times. Ninth function: a penalty function related to prohibiting each of the vehicles from visiting the return point multiple times.

[0033] This configuration includes the characteristic processing steps of the above-described delivery plan determination device, and therefore can achieve the same functions and effects as the above-described delivery plan determination device.

[0034] (13) A computer program according to another embodiment of the present disclosure is a computer program for causing a computer to function as a delivery plan determination device that determines a package delivery plan for a plurality of vehicles from a departure point to a destination point via a package delivery point, and causes the computer to function as an objective function acquisition unit that acquires objective functions including a first function, a second function, a third function, a fourth function, a fifth function, a sixth function, a seventh function, an eighth function, and a ninth function shown below, and a delivery plan determination unit that determines the delivery plan by optimizing the objective function using an annealing quantum computer or an Ising machine. First function: a function that represents the time required for delivery of a package. Second function: a function that represents the number of delivery points. Third function: a penalty function related to prohibiting movement of the vehicle between points that the vehicle may travel to within the time required for movement. Fourth function: a penalty function related to prohibiting multiple vehicles from visiting each of the delivery points in multiple time frames when the number of visits to each of the delivery points by each of the vehicles is one or less and the planned time of the delivery plan is divided into multiple time frames. Fifth function: a penalty function related to prohibiting multiple vehicles from visiting each of the delivery points in each of the time frames. Sixth function: a penalty function related to prohibiting each of the vehicles from visiting the departure point, the delivery point, and the return point before the departure time of each of the vehicles from the departure point. Seventh function: a penalty function related to prohibiting each of the vehicles from visiting the departure point, the delivery point, and the return point after the return time of each of the vehicles to the return point. Eighth function: a penalty function related to prohibiting each of the vehicles from visiting the departure point multiple times. Ninth function: a penalty function related to prohibiting each of the vehicles from visiting the return point multiple times.

[0035] According to this configuration, the computer can function as the delivery plan determination device described above, and therefore, the same functions and effects as those of the delivery plan determination device described above can be achieved.

[0036] [Details of the Embodiments of the Present Disclosure] Hereinafter, embodiments of the present disclosure will be described with reference to the drawings. Note that each of the embodiments described below represents a specific example of the present disclosure. The numerical values, shapes, materials, components, component placement and connection configurations, steps, and step order shown in the following embodiments are examples and do not limit the present disclosure. Furthermore, among the components in the following embodiments, components not recited in independent claims are components that can be added arbitrarily. Furthermore, each figure is a schematic diagram and is not necessarily a precise illustration.

[0037] The same components are denoted by the same reference numerals, and their functions and names are also the same, so their explanations will be omitted where appropriate.

[0038] 1 is a diagram illustrating an example of the overall configuration of a delivery plan determination system according to embodiment 1 of the present disclosure. The delivery plan determination system 10 includes a delivery plan determination device 100 and a quantum computer 200.

[0039] The delivery plan determination device 100 and the quantum computer 200 are connected via a network 300 such as a local area network (LAN), a wide area network (WAN), the Internet, etc. However, the delivery plan determination device 100 and the quantum computer 200 may also be directly connected via a dedicated line.

[0040] The quantum computer 200 is an annealing quantum computer, and is capable of quickly calculating solutions to combinatorial optimization problems. The combinatorial optimization problem is formulated as QUBO (quadratic unconstrained binary optimization) represented by the following equation 2. Note that an Ising machine may be used instead of the quantum computer 200. Similar to the quantum computer 200, an Ising machine can also quickly calculate solutions to QUBO combinatorial optimization problems.

[0041] where xi(xj) is a decision variable, Ji,j,hi are parameters, and const. is a constant.

[0042] In QUBO, the possible values ​​of a decision variable are 0 or 1. Furthermore, the objective function of QUBO is a polynomial of degree up to 2. Furthermore, QUBO does not explicitly have any constraints.

[0043] The delivery plan determination device 100 uses the quantum computer 200 to determine a delivery plan for a plurality of vehicles to transport packages from a departure point to a destination point via delivery points for the packages. That is, the delivery plan determination device 100 creates a QUBO objective function (described below) and provides it to the quantum computer 200. The quantum computer 200 probabilistically determines the values ​​of decision variables that optimize (here, minimize) the objective function. The delivery plan determination device 100 obtains the values ​​of the decision variables from the quantum computer 200 and determines the delivery plan. Here, points to which the vehicles may travel include the departure point, delivery point, and destination point.

[0044] [Explanation of Variables] Here, each variable used in determining a package delivery plan will be described. In the first embodiment, a delivery plan is determined in which V vehicles are used within a predetermined time period (for example, between 9:00 and 19:00) to deliver packages to more delivery points in a shorter time.

[0045] FIG. 2 is a diagram showing an example of a package delivery plan. Delivery plan 20 is a three-dimensional matrix showing the delivery plans for all vehicles. Delivery plan 20 is composed of multiple two-dimensional matrices showing the delivery plans for each vehicle. For example, delivery plan 21 shows the delivery plan for vehicle 1, delivery plan 22 shows the delivery plan for vehicle 2, and delivery plan 23 shows the delivery plan for vehicle V.

[0046] The first axis of the delivery plan 20 indicates the location p, the second axis indicates the time frame τ, and the third axis indicates the vehicle k. The time frame τ refers to a time frame obtained by dividing the planned time of the delivery plan by a predetermined time frame (for example, one hour).

[0047] Each cell of the delivery plan 20 indicates a value expressed by the following formula 3. However, if point p is a return point, 1 indicates arrival at the return point, and 0 indicates not arrival at the return point.

[0048] The travel time, waiting time, working time, rest time, and time slots are all known values.

[0049] For example, the delivery plan 21 indicates that vehicle 1 will depart from the departure point in the 9:00 time slot, arrive at delivery point A, and then depart delivery point A in the 12:00 time slot. The delivery plan 21 then indicates that vehicle 1 will arrive at delivery point F, and then depart delivery point F in the 16:00 time slot. The delivery plan 21 then indicates that vehicle 1 will arrive at the return point in the 18:00 time slot.

[0050] [Configuration of Delivery Plan Determination Device 100] FIG. 3 is a block diagram showing an example of the configuration of the delivery plan determination device 100 according to the first embodiment of the present disclosure.

[0051] The delivery plan determination device 100 includes a communication unit 110, a storage device 120, and a processor 130. The communication unit 110, the storage device 120, and the processor 130 are connected to each other via an internal bus 140. The delivery plan determination device 100 is a von Neumann type computer (classical computer).

[0052] The communication unit 110 includes a communication interface for connecting the delivery plan determination device 100 to the network 300 by wire or wirelessly. When the delivery plan determination device 100 and the quantum computer 200 are directly connected, the communication unit 110 includes a communication interface for connecting the delivery plan determination device 100 to the quantum computer 200 by wire or wirelessly.

[0053] The storage device 120 is composed of a volatile memory element such as an SRAM (Static Random Access Memory) or a DRAM (Dynamic Random Access Memory), a non-volatile memory element such as a flash memory or an EEPROM (Electrically Erasable Programmable Read Only Memory), or a magnetic storage device such as a hard disk.

[0054] The storage device 120 stores a computer program 121 that is executed by the processor 130. The storage device 120 also stores data that is used or generated during execution of the computer program 121. For example, the storage device 120 stores an objective function 122 that is to be optimized by the quantum computer 200.

[0055] The processor 130 is configured by a CPU (Central Processing Unit), a GPU, etc. The processor 130 includes an objective function acquisition unit 131 and a delivery plan determination unit 132 as functional processing units realized by reading and executing the computer program 121 stored in the storage device 120.

[0056] The objective function acquisition unit 131 acquires the objective function of QUBO. Specifically, the objective function acquisition unit 131 reads the objective function 122 from the storage device 120. The objective function 122 is formulated as a Hamiltonian H shown in the following equation 4. The Hamiltonian H is expressed as the sum of functions obtained by multiplying the first function H1, the second function H2, the third function H3, the fourth function H4, the fifth function H5, the sixth function H6, the seventh function H7, the eighth function H8, and the ninth function H9 by weights w1, (-w2), w3, w4, w5, w6, w7, w8, and w9, respectively. Here, w1 to w9 are all positive values.

[0057] [First Function] The first function (Hamiltonian H1) is expressed by the following equation 5.

[0058] Fig. 4 is a diagram for explaining the first function. Fig. 4 shows an example of a delivery plan 21 for vehicle 1 and a delivery plan 22 for vehicle 2. Note that delivery plans for other vehicles are similarly shown. Hamiltonian H1 indicates the total required time obtained by adding up the required times for all vehicles from the departure point to the arrival point of each vehicle.

[0059] For example, the time frame to which the cell with value 1 in box 31 belongs corresponds to the time when vehicle 1 departs from the starting point, and the time frame to which the cell with value 1 in box 32 belongs corresponds to the time when vehicle 1 arrives at the destination point. Similarly, the time frame to which the cell with value 1 in box 33 belongs corresponds to the time when vehicle 2 departs from the starting point, and the time frame to which the cell with value 1 in box 34 belongs corresponds to the time when vehicle 2 arrives at the destination point.

[0060] [Regarding the Second Function] The second function (Hamiltonian H2) is expressed by the following equation 6.

[0061] FIG. 5 is a diagram for explaining the second function. FIG. 5 shows an example of a delivery plan 21 for vehicle 1 and a delivery plan 22 for vehicle 2. Note that delivery plans for other vehicles are similarly shown. Hamiltonian H2 calculates the number of vehicle visits to each delivery point of the luggage, excluding the departure point and return point, among the points that each vehicle may travel to, and indicates the total number of visits (the total number of points visited by all vehicles) obtained by adding up the number of vehicle visits to each delivery point for all delivery points. The sum of the values ​​of the cells in box 41 indicates the number of visits to delivery point A, and the sum of the values ​​of the cells in box 42 indicates the number of visits to delivery point F. The number of visits to each delivery point is shown in box 43. The sum of the values ​​of the cells in box 43 is equal to the value of Hamiltonian H2.

[0062] [Regarding the Third Function] The third function (Hamiltonian H3) is expressed by the following equation 7.

[0063] Fig. 6 is a diagram for explaining the third function. Fig. 6 shows an example of a delivery plan 21 for vehicle 1 and a delivery plan 22 for vehicle 2. Note that delivery plans for other vehicles are shown in the same manner.

[0064] Hamiltonian H3 is a penalty function for prohibiting travel between points that each vehicle may travel within the travel time required for travel.

[0065] For example, suppose vehicle 1 departs from delivery point F in the 10:00 time slot. In this case, the value of the cell in frame 51 is 1. Then, suppose vehicle 1 heads to each location. For example, suppose vehicle 1 heads from delivery point F to delivery point A and the number of time slots required before it departs from delivery point A is four. In this case, vehicle 1 is scheduled to depart delivery point A in the 13:00 time slot, so the values ​​of three cells in frame 52 must be 0. Also, suppose vehicle 1 heads to its destination and the number of time slots required before it arrives at the destination is three. In this case, vehicle 1 is scheduled to arrive at the destination in the 12:00 time slot, so the values ​​of two cells in frame 53 must be 0.

[0066] Similarly, suppose vehicle 2 departs from delivery point A in the 9:00 time slot. In this case, the value of the cell in box 54 is 1. Then, suppose vehicle 2 heads to each location. For example, suppose vehicle 2 heads to delivery point F and the number of time slots required before it departs from delivery point F is four. In this case, vehicle 2 is scheduled to depart delivery point F in the 12:00 time slot, so the value of the cell in box 55 must be 0. Also, suppose vehicle 2 heads to its return point and the number of time slots required before it arrives at the return point is three. In this case, vehicle 2 is scheduled to arrive at the return point in the 11:00 time slot, so the value of the cell in box 56 must be 0.

[0067] Hamiltonian H3 is a function that becomes 0 when the time it takes for each vehicle to travel between possible points is equal to or greater than the required travel time, but its value increases according to the combination of points that are traveled between in a time less than the required travel time.

[0068] The third function can be formulated as a Hamiltonian H3 using the decision variables in Equation 3, where 0 or 1 indicates whether vehicle k visits point p in time slot τ. Thus, the objective function 122 can be optimized using a quantum computer 200 or an Ising machine.

[0069] [Regarding the Fourth Function] The fourth function (Hamiltonian H4) is expressed by the following equation 8.

[0070] Fig. 7 is a diagram for explaining the fourth function. Fig. 7 shows examples of a delivery plan 21 for vehicle 1, a delivery plan 22 for vehicle 2, and a delivery plan 23 for vehicle V. Note that delivery plans for other vehicles are shown in the same manner.

[0071] Here, the constraints are that each vehicle visits each delivery point no more than once, and that when the planned time of the delivery plan is divided into multiple time slots, multiple vehicles do not visit each delivery point in multiple time slots. Hamiltonian H4 is a penalty function that imposes a penalty if these constraints are not met.

[0072] For example, suppose vehicle 1 departs from delivery point F in the 16:00 time slot. In this case, the value of the cell in box 61 is 1. Since the number of visits by vehicle 1 to delivery point F must be one or less, the values ​​of the cells in boxes 62 and 63 must be 0. Furthermore, multiple vehicles are prohibited from visiting delivery point F. For this reason, the values ​​of the cells in boxes 64 and 65 of delivery plan 22 must be 0. Similarly, the values ​​of the cells in boxes 66 and 67 of delivery plan 23 must be 0. The same applies to delivery plans for vehicles other than vehicles 1, 2, and V. However, Hamiltonian H4 allows multiple vehicles to visit each point in the same time slot.

[0073] Hamiltonian H4 is a function that is 0 when the above constraints are satisfied, but whose value (penalty) increases according to combinations that do not satisfy the constraints.

[0074] The fourth function can be formulated as a Hamiltonian H4 using the decision variables in Equation 3, where 0 or 1 indicates whether vehicle k visits point p in time slot τ. Thus, the objective function 122 can be optimized using a quantum computer 200 or an Ising machine.

[0075] [Regarding the Fifth Function] The fifth function (Hamiltonian H5) is expressed by the following equation 9.

[0076] Fig. 8 is a diagram for explaining the fifth function. Fig. 8 shows examples of a delivery plan 21 for vehicle 1, a delivery plan 22 for vehicle 2, and a delivery plan 23 for vehicle V. Note that delivery plans for other vehicles are shown in the same manner.

[0077] Hamiltonian H5 is a penalty function that imposes a penalty if the constraint condition is not met, with the constraint condition being that multiple vehicles do not visit each delivery point in each time frame.

[0078] For example, suppose vehicle 1 departs from delivery point F in the 16:00 time slot. In this case, the value of the cell in frame 71 is 1. Other vehicles are prohibited from visiting delivery point F within the same time slot. For this reason, the value of the cell in frame 72 of delivery plan 22 must be 0. Also, the value of the cell in frame 73 of delivery plan 23 must be 0. The same applies to delivery plans for vehicles other than vehicles 1, 2, and V.

[0079] Hamiltonian H5 is a function that is 0 when the above constraints are satisfied, but whose value (penalty) increases according to combinations that do not satisfy the above constraints.

[0080] The fifth function can be formulated as a Hamiltonian H5 using the decision variables in Equation 3, where 0 or 1 indicates whether or not vehicle k visits location p in time slot τ. Thus, the objective function 122 can be optimized using a quantum computer 200 or an Ising machine.

[0081] [Regarding the Sixth Function] The sixth function (Hamiltonian H6) is expressed by the following equation 10.

[0082] Fig. 9 is a diagram for explaining the sixth function. Fig. 9 shows an example of a delivery plan 21 for vehicle 1 and a delivery plan 22 for vehicle 2. Note that delivery plans for other vehicles are shown in the same manner.

[0083] Hamiltonian H6 is a penalty function that imposes a penalty if the constraint is not met, with the constraint being that the departure point, delivery point, and return point are not visited before the departure time from the departure point of each vehicle.

[0084] For example, suppose vehicle 1 departs from the departure point in the 11:00 time slot. Therefore, the value of the cell in frame 81 of the delivery plan 21 becomes 1. In this case, vehicle 1 is prohibited from visiting the departure point, delivery point, and return point in time slots before 11:00 (here, the 9:00 and 10:00 time slots). Therefore, the value of the cell in frame 82 of the delivery plan 21 must become 0.

[0085] Similarly, assume that vehicle 2 departs from the departure point in the 10:00 time slot. Therefore, the value of the cell in window 83 of the delivery plan 22 becomes 1. In this case, vehicle 2 is prohibited from visiting the departure point, delivery point, and return point in a time slot before 10:00 (here, the 9:00 time slot). Therefore, the value of the cell in window 84 of the delivery plan 22 must become 0.

[0086] Hamiltonian H6 is a function that is 0 when the above constraints are satisfied, but whose value (penalty) increases according to combinations that do not satisfy the constraints.

[0087] The sixth function can be formulated as a Hamiltonian H6 using the decision variables in Equation 3, where 0 or 1 indicates whether or not vehicle k visits point p in time slot τ. Thus, the objective function 122 can be optimized using the quantum computer 200 or an Ising machine.

[0088] [Regarding the Seventh Function] The seventh function (Hamiltonian H7) is expressed by the following equation 11.

[0089] Fig. 10 is a diagram for explaining the seventh function. Fig. 10 shows an example of a delivery plan 21 for vehicle 1 and a delivery plan 22 for vehicle 2. Note that delivery plans for other vehicles are shown in the same manner.

[0090] Hamiltonian H7 is a penalty function that imposes a penalty if the constraint is not met, with the constraint being that the departure point, delivery point, and return point are not visited after the return time of each vehicle to the return point.

[0091] For example, suppose vehicle 1 arrives at the destination point in the 16:00 time slot. Therefore, the value of the cell in slot 85 of the delivery plan 21 becomes 1. In this case, vehicle 1 is prohibited from visiting the departure point, delivery point, and destination point in time slots after 16:00 (here, the 17:00 and 18:00 time slots). Therefore, the value of the cell in slot 86 of the delivery plan 21 must be 0.

[0092] Similarly, assume that vehicle 2 arrives at the return point in the 17:00 time slot. Therefore, the value of the cell in slot 87 in the delivery plan 22 becomes 1. In this case, vehicle 2 is prohibited from visiting the departure point, delivery point, and return point in any time slot after 17:00 (here, the 18:00 time slot). Therefore, the value of the cell in slot 88 in the delivery plan 22 must be 0.

[0093] Hamiltonian H7 is a function that is 0 when the above constraints are satisfied, but whose value (penalty) increases according to combinations that do not satisfy the constraints.

[0094] The seventh function can be formulated as a Hamiltonian H7 using the decision variable in Equation 3, where 0 or 1 indicates whether or not vehicle k visits point p in time slot τ. Thus, the objective function 122 can be optimized using a quantum computer 200 or an Ising machine.

[0095] [Regarding the Eighth Function] The eighth function (Hamiltonian H8) is expressed by the following equation 12.

[0096]

[0097] Fig. 11 is a diagram for explaining the eighth function. Fig. 11 shows an example of a delivery plan 21 for vehicle 1 and a delivery plan 22 for vehicle 2. Note that delivery plans for other vehicles are shown in the same manner.

[0098] Hamiltonian H8 is a penalty function that imposes a penalty if the constraint is not met, with the constraint being that each vehicle does not visit the starting point multiple times.

[0099] For example, vehicle 1 departs from the starting point only once. Therefore, the sum of the values ​​of the cells in box 91 of the dispatch plan 21 must be 1. Similarly, vehicle 2 departs from the starting point only once. Therefore, the sum of the values ​​of the cells in box 92 of the dispatch plan 22 must be 1.

[0100] Hamiltonian H8 is a function that becomes 0 when the above constraints are satisfied, but its value (penalty) increases depending on the combination that does not satisfy the constraints. For example, if the sum of the values ​​of the cells in box 91 is not 1, the value of Hamiltonian H8 will not become 0.

[0101] The eighth function can be formulated as a Hamiltonian H using the decision variable in Equation 3, where 0 or 1 indicates whether or not vehicle k visits point p in time slot τ. Thus, the objective function 122 can be optimized using a quantum computer 200 or an Ising machine.

[0102] [Regarding the Ninth Function] The ninth function (Hamiltonian H9) is expressed by the following equation 13.

[0103] Fig. 12 is a diagram for explaining the ninth function. Fig. 12 shows an example of a delivery plan 21 for vehicle 1 and a delivery plan 22 for vehicle 2. Note that delivery plans for other vehicles are shown in the same manner.

[0104] Hamiltonian H9 is a penalty function that imposes a penalty if the constraint condition is not met, with each vehicle constrained to not visit the destination point multiple times.

[0105] For example, vehicle 1 will arrive at the destination only once. Therefore, the sum of the values ​​of the cells in box 93 of dispatch plan 21 must be 1. Similarly, vehicle 2 will arrive at the destination only once. Therefore, the sum of the values ​​of the cells in box 94 of dispatch plan 22 must be 1.

[0106] Hamiltonian H9 is a function that becomes 0 when the above constraints are satisfied, but its value (penalty) increases depending on the combination that does not satisfy the constraints. For example, if the sum of the values ​​of the cells in box 93 is not 1, the value of Hamiltonian H9 will not be 0.

[0107] The ninth function can be formulated as a Hamiltonian H9 using the decision variables of Equation 3, each of which indicates whether or not vehicle k visits point p in time slot τ, as 0 or 1. Thus, the objective function 122 can be optimized using a quantum computer 200 or an Ising machine.

[0108] Referring again to Figure 3, the delivery plan determination unit 132 determines a delivery plan for each vehicle by using the quantum computer 200 to optimize (here, minimize) the objective function 122 acquired by the objective function acquisition unit 131.

[0109] That is, the objective function acquisition unit 131 transmits the QUBO objective function 122 expressed by Equation 4 to the quantum computer 200 via the communication unit 110. In the quantum computer 200, the values ​​of the decision variables that minimize the objective function 122 are calculated probabilistically.

[0110] The objective function acquisition unit 131 receives values ​​of decision variables from the quantum computer 200 via the communication unit 110. The objective function acquisition unit 131 determines a delivery plan based on the values ​​of the decision variables. For example, the objective function acquisition unit 131 determines a delivery plan 20 as shown in FIG. 2 based on the values ​​of the decision variables.

[0111] [Operation of Delivery Plan Determination System 10] FIG. 13 is a sequence diagram showing an example of the operation of the delivery plan determination system 10 according to the first embodiment of the present disclosure.

[0112] The delivery plan determination device 100 acquires the objective function 122 (step S11).

[0113] The delivery plan determination device 100 transmits the acquired objective function 122 to the quantum computer 200, and the quantum computer 200 receives the objective function 122 (step S12).

[0114] The quantum computer 200 calculates the values ​​of the decision variables that minimize the value of the received objective function 122 (step S13).

[0115] The quantum computer 200 transmits the calculated values ​​of the decision variables to the delivery plan determination device 100, and the delivery plan determination device 100 receives the values ​​of the decision variables (step S14).

[0116] The delivery plan determination device 100 determines a delivery plan based on the received values ​​of the decision variables (step S15).

[0117] As described above, the objective function 122 is optimized using the annealing quantum computer 200 or the Ising machine. The objective function 122 includes a first function related to the required delivery time for the package and a second function related to the number of delivery points for the package. The objective function 122 also includes penalty functions shown as the third to ninth functions. These penalty functions indicate constraints on the vehicle's movement between points. Therefore, it is possible to quickly determine a package delivery plan that optimizes the required delivery time for the package and the number of delivery points while satisfying these constraints.

[0118] As shown in Equation 4, objective function 122 is expressed as the sum of functions obtained by multiplying the first, second, third, fourth, fifth, sixth, seventh, eighth, and ninth functions by a predetermined weight coefficient. For example, by setting the weights for functions three through ninth to values ​​sufficiently larger than the weights for functions one and two (e.g., 100 to 1000 times), the value of 16 can be increased if the constraints are not satisfied. Therefore, by minimizing objective function 122, a package delivery plan that reliably satisfies the constraints can be determined.

[0119] Second Embodiment In a second embodiment, a method for determining a delivery plan when a delivery time for a package is specified will be described.

[0120] The configuration of the delivery plan determination system 10 is the same as that shown in Fig. 1. In the following explanation, differences from the first embodiment will be mainly described.

[0121] FIG. 14 is a block diagram illustrating an example of the configuration of a delivery plan determination device 100 according to the second embodiment of the present disclosure.

[0122] The delivery plan determination device 100 has the same configuration as the delivery plan determination device 100 shown in Fig. 3. However, the storage device 120 further stores designated delivery time information 123 for packages.

[0123] FIG. 15 is a diagram showing an example of the designated delivery time information 123 for a package.

[0124] The designated delivery time information 123 indicates the designated delivery time for a package for each delivery point. A time frame with a cell value of 1 indicates the designated delivery time, and a time frame with a cell value of 0 indicates a time other than the designated delivery time. For example, the cell values ​​for the 13:00, 14:00, and 15:00 time frames for delivery point A are 1, and the cell values ​​for the other time frames are 0. This indicates that the designated delivery time for a package to delivery point A is between 13:00 and 16:00. Similarly, it indicates that the designated delivery time for a package to delivery point C is between 9:00 and 13:00. It also indicates that the designated delivery time for a package to delivery point D is between 16:00 and 19:00.

[0125] For each of delivery points B, E, and F, the cell value is 1 in all time slots. This indicates that no delivery time is specified for delivery points B, E, and F.

[0126] 3, the delivery plan determination unit 132 fixes the values ​​of some of the decision variables of the objective function 122 to 0 based on the specified delivery time information 123. A method for fixing the values ​​of the decision variables will be described below.

[0127] 16 is a diagram showing an example of decision variables. A decision variable set 124 indicates a set of decision variables for each location and time frame to which vehicle k may move. The decision variable set 124 is the same for all vehicles except for the value of the subscript k.

[0128] The delivery plan determination unit 132 fixes the values ​​of decision variables corresponding to cells with a value of 0 in the specified delivery time information 123 to 0. For example, in the specified delivery time information 123 shown in FIG. 15, for delivery point A, the values ​​of the cells for the time slots of 9:00, 10:00, 11:00, 12:00, 16:00, 17:00, and 18:00 are 0. Therefore, the delivery plan determination unit 132 fixes the values ​​of decision variables corresponding to the time slots of 9:00, 10:00, 11:00, 12:00, 16:00, 17:00, and 18:00 for delivery point A to 0, as shown in FIG. 16. This makes it possible to determine a delivery plan in which no vehicles visit delivery point A during this time slot.

[0129] The delivery plan determination unit 132 similarly fixes the values ​​of the decision variables for other delivery points.

[0130] The delivery plan determination unit 132 transmits the objective function 122 to the quantum computer 200 along with a set of decision variables 124 some of whose values ​​are fixed to zero.

[0131] 17 is a sequence diagram showing an example of the operation of the delivery plan determination system 10 according to the second embodiment of the present disclosure. The same step numbers are assigned to steps that are the same as those shown in FIG.

[0132] The delivery plan determination device 100 acquires the objective function 122 (step S11).

[0133] The delivery plan determination device 100 acquires the designated delivery time information 123 (step S21). The delivery plan determination unit 132 of the delivery plan determination device 100 may acquire the designated delivery time information 123 by reading out the designated delivery time information 123 from the storage device 120. Alternatively, the delivery plan determination unit 132 may acquire the designated delivery time information 123 by receiving the designated delivery time information 123 input by a user operating an input device via an input / output interface.

[0134] The delivery plan determination unit 132 of the delivery plan determination device 100 fixes some of the decision variables of the objective function 122 to 0 based on the acquired designated delivery time information 123 (step S22).

[0135] The delivery plan determination unit 132 of the delivery plan determination device 100 transmits the objective function 122 to the quantum computer 200 together with the decision variable set 124 in which some decision variables are fixed to 0. The quantum computer 200 receives the decision variable set 124 and the objective function 122 (step S23).

[0136] The quantum computer 200 calculates the values ​​of the decision variables that minimize the objective function 122 without changing the fixed value 0 indicated in the decision variable set 124 (step S24).

[0137] The quantum computer 200 transmits the calculated values ​​of the decision variables to the delivery plan determination device 100, and the delivery plan determination device 100 receives the values ​​of the decision variables (step S14).

[0138] The delivery plan determination device 100 determines a delivery plan based on the received values ​​of the decision variables (step S15).

[0139] As described above, the number of decision variables whose values ​​need to be determined can be reduced, and therefore a delivery plan that does not deliver packages during times when delivery is prohibited can be determined quickly.

[0140] <Variation> The fourth function is a penalty function that includes constraints that each vehicle visits each delivery point no more than once, and that when the planned time of the delivery plan is divided into multiple time slots, multiple vehicles are prohibited from visiting each delivery point in multiple time slots.

[0141] However, there are cases where multiple packages with different designated delivery times are delivered to the same delivery point. In such cases, one vehicle may visit the delivery point more than once, or multiple vehicles may visit the delivery point in multiple time slots, which does not satisfy the constraints shown in the fourth function.

[0142] For this reason, in this modified example, a delivery point is associated with a package and its designated delivery time. In other words, even if the delivery point is the same, packages with different designated delivery times are treated as different delivery points. For example, suppose that package P1, which has a designated delivery time between 9:00 and 12:00, and package P2, which has a designated delivery time between 11:00 and 15:00, are scheduled to be delivered to delivery point A. In this case, the delivery point A of package P1 is designated as delivery point A1, and the delivery point A of package P2 is designated as delivery point A2, and the objective function is optimized in the same manner as in the above embodiment.

[0143] This makes it possible to determine a delivery plan for delivering packages with different designated delivery times to the same delivery point without being restricted by the number of visits due to the fourth function.

[0144] [Additional Notes] Although the delivery plan determination system 10 according to the embodiment of the present disclosure has been described above, the present disclosure is not limited to this embodiment.

[0145] For example, in the above-described embodiment, the combinatorial optimization problem solved by the quantum computer 200 or the Ising machine is formulated using QUBO, but it may also be formulated using an Ising model. The Ising model is the same as QUBO except that the possible values ​​of the decision variables are 1 or -1. Therefore, the Ising model and QUBO are mutually convertible.

[0146] In addition, some or all of the components that make up the delivery plan determination device 100 may be configured using hardware such as one or more FPGAs (Field Programmable Gate Arrays) or ASICs (Application Specific Integrated Circuits).

[0147] The computer program described above may be distributed by recording it on a computer-readable non-transitory recording medium, such as a HDD, a CD-ROM, a semiconductor memory, etc. The computer program may also be distributed by transmitting it via a telecommunications line, a wireless or wired communication line, a network such as the Internet, data broadcasting, etc.

[0148] Furthermore, the delivery plan determination device 100 may be realized by a plurality of computers or a plurality of processors.

[0149] Furthermore, some or all of the functions of the delivery plan determination device 100 may be provided by cloud computing. That is, some or all of the functions of the delivery plan determination device 100 may be realized by a cloud server.

[0150] Furthermore, at least some of the above-described embodiments and modifications may be combined in any manner.

[0151] The present invention can be realized not only as a delivery plan determination device 100 having the above-described characteristic processing units, but also as a delivery plan determination method including such characteristic processing steps, or as a computer program for causing a computer to execute such steps. Furthermore, the present invention can be realized as a semiconductor integrated circuit that realizes part or all of the delivery plan determination device 100, or as a delivery plan determination system including the delivery plan determination device 100.

[0152] The embodiments disclosed herein should be considered to be illustrative in all respects and not restrictive. The scope of the present invention is defined by the claims, not by the above meaning, and is intended to include all modifications within the meaning and scope of the claims.

[0153] 10 Delivery plan determination system 20, 21, 22, 23, 24 Delivery plan 31, 32, 33, 34, 41, 42, 43, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66, 67, 71, 72, 73, 81, 83, 84, 85, 86, 87, 88, 91, 92, 93, 94 Frame 100 Delivery plan determination device 110 Communication unit 120 Storage device 121 Computer program 122 Objective function 123 Designated delivery time information 124 Decision variable set 130 Processor 131 Objective function acquisition unit 132 Delivery plan determination unit 140 Internal bus 200 Quantum computer 300 Network

Claims

1. A delivery plan determination device that determines a delivery plan for a package from a departure point to a destination point via a package delivery point by a plurality of vehicles, an objective function acquisition unit that acquires objective functions including a first function, a second function, a third function, a fourth function, a fifth function, a sixth function, a seventh function, an eighth function, and a ninth function shown below; a delivery plan determination unit that determines the delivery plan by optimizing the objective function using an annealing type quantum computer or an Ising machine. First function: A function that represents the time required for package delivery Second function: a function representing the number of delivery points Third function: a penalty function for prohibiting movement of each vehicle between points that may be traveled within the travel time required for that vehicle. Fourth function: A penalty function relating to prohibition of multiple vehicles from visiting each of the delivery points in multiple time slots when the number of visits to each of the delivery points by each of the vehicles is one or less and the planning time of the delivery plan is divided into multiple time slots. Fifth function: a penalty function for prohibiting a plurality of vehicles from visiting each of the delivery points in each of the time slots. Sixth function: a penalty function for prohibiting each of the vehicles from visiting the departure point, the delivery point, and the return point before the departure time from the departure point. Seventh function: a penalty function for prohibiting each of the vehicles from visiting the departure point, the delivery point, and the return point after the return time to the return point. Eighth function: a penalty function for prohibiting each vehicle from visiting the starting point multiple times Ninth function: a penalty function for prohibiting each of the vehicles from visiting the destination point multiple times

2. 2. The delivery plan determination device according to claim 1, wherein the objective function is represented by a sum of functions obtained by multiplying the first function, the second function, the third function, the fourth function, the fifth function, the sixth function, the seventh function, the eighth function, and the ninth function by a predetermined weight coefficient.

3. 3. The delivery plan determination device according to claim 1, wherein the third function is expressed as H3 below. [Equation 1]

4. The delivery plan determination device according to claim 1 or 2, wherein the fourth function is expressed by the following H4. [Equation 2]

5. 3. The delivery plan determination device according to claim 1, wherein the fifth function is expressed by the following H5. [Equation 3]

6. 3. The delivery plan determination device according to claim 1, wherein the sixth function is expressed as H6 below. [Equation 4]

7. 3. The delivery plan determination device according to claim 1, wherein the seventh function is expressed as H7 below. [Equation 5]

8. 3. The delivery plan determination device according to claim 1, wherein the eighth function is expressed as H8 below. [Equation 6]

9. 3. The delivery plan determination device according to claim 1, wherein the ninth function is expressed as H9 below. [Equation 7]

10. 3. The delivery plan determination device according to claim 1, wherein the delivery point is associated with the package and a designated delivery time for the package.

11. the objective function includes a decision variable that represents, as a binary value, whether or not each of the vehicles visits each of the delivery points in each of the time slots; 3. The delivery plan determination device according to claim 1, wherein the delivery plan determination unit optimizes the objective function after determining values ​​of decision variables other than the specified delivery time of the delivery point of the package to values ​​corresponding to no visit, based on the specified delivery time of the package.

12. A delivery plan determination method for determining a delivery plan for a package from a departure point to a destination point via a package delivery point by a plurality of vehicles, comprising: A step in which the delivery plan determination device acquires objective functions including a first function, a second function, a third function, a fourth function, a fifth function, a sixth function, a seventh function, an eighth function, and a ninth function shown below; a step in which the delivery plan determination device determines the delivery plan by optimizing the objective function using an annealing type quantum computer or an Ising machine. First function: A function that represents the time required for package delivery Second function: a function representing the number of delivery points Third function: a penalty function for prohibiting movement of each vehicle between points that may be traveled within the travel time required for that vehicle. Fourth function: A penalty function relating to prohibition of multiple vehicles from visiting each of the delivery points in multiple time slots when the number of visits to each of the delivery points by each of the vehicles is one or less and the planning time of the delivery plan is divided into multiple time slots. Fifth function: a penalty function for prohibiting a plurality of vehicles from visiting each of the delivery points in each of the time slots. Sixth function: a penalty function for prohibiting each of the vehicles from visiting the departure point, the delivery point, and the return point before the departure time from the departure point. Seventh function: a penalty function for prohibiting each of the vehicles from visiting the departure point, the delivery point, and the return point after the return time to the return point. Eighth function: a penalty function for prohibiting each vehicle from visiting the starting point multiple times Ninth function: a penalty function for prohibiting each of the vehicles from visiting the destination point multiple times

13. A computer program for causing a computer to function as a delivery plan determination device that determines a delivery plan for a package from a departure point to a destination point by a plurality of vehicles via a package delivery point, the computer program comprising: The computer an objective function acquisition unit that acquires objective functions including a first function, a second function, a third function, a fourth function, a fifth function, a sixth function, a seventh function, an eighth function, and a ninth function shown below; a computer program that causes the computer to function as a delivery plan determination unit that determines the delivery plan by optimizing the objective function using an annealing quantum computer or an Ising machine. First function: A function that represents the time required for package delivery Second function: a function representing the number of delivery points Third function: a penalty function for prohibiting movement of each vehicle between points that may be traveled within the travel time required for that vehicle. Fourth function: A penalty function relating to prohibition of multiple vehicles from visiting each of the delivery points in multiple time slots when the number of visits to each of the delivery points by each of the vehicles is one or less and the planning time of the delivery plan is divided into multiple time slots. Fifth function: a penalty function for prohibiting a plurality of vehicles from visiting each of the delivery points in each of the time slots. Sixth function: a penalty function for prohibiting each of the vehicles from visiting the departure point, the delivery point, and the return point before the departure time from the departure point. Seventh function: a penalty function for prohibiting each of the vehicles from visiting the departure point, the delivery point, and the return point after the return time to the return point. Eighth function: a penalty function for prohibiting each vehicle from visiting the starting point multiple times Ninth function: a penalty function for prohibiting each of the vehicles from visiting the destination point multiple times

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