JP7591008B2 - Inventory placement optimization system and inventory placement optimization method - Google Patents

Description

The present invention relates to an inventory allocation optimization system and an inventory allocation optimization method.

The concept of combinatorial optimization problems, which involves searching for a solution that maximizes or minimizes desired parameters under given conditions, can also be applied to complex real-world problems such as optimizing the allocation of various resources such as workers and equipment, optimizing operation schedules, eliminating traffic congestion, and reducing logistics costs in global supply chains.

However, because the number of potential solutions to such problems is explosively large, it is difficult to solve the problem within a practical time frame unless a computer with adequate computing power, such as a supercomputer or quantum computer, is used.

For example, a conventional technology related to quantum computers is a computer that enables high-speed calculations for inverse problems and combinatorial optimization problems that require exhaustive search. It uses spin as a variable in the calculation, sets the problem to be solved in terms of spin-spin interactions and local fields acting on each spin, and directs all spins in one direction at time t = 0 using an external magnetic field, gradually decreasing the external magnetic field so that it becomes zero at time t = τ. It also assumes that the direction of each spin is determined by the effective magnetic field determined by the effects of all the external magnetic fields and spin-spin interactions at time t, and evolves over time. In this case, the spins are not perfectly aligned with the effective magnetic field, but are quantum mechanically corrected, so that the system maintains the ground state (see Patent Document 1).

As a conventional technique for optimizing the placement of inventory in a logistics warehouse, which is one of the optimization problems, a product placement system, a product placement method, and a product placement program (see Patent Document 2) have been proposed that improve the efficiency of the process from receiving to shipping products at the logistics site.

This technology relates to a product placement system having a grouping means for acquiring multiple feature amounts for each of a plurality of products from shipping data relating to the products, comparing each of the feature amounts acquired for a certain product with each of the feature amounts acquired for other products with the corresponding feature amounts, calculating the amount of change between the corresponding feature amounts, and classifying the plurality of products into a plurality of product groups based on the magnitude of the calculated amount of change, a shipping prediction means for acquiring past shipping records for each of the products from the shipping data and predicting the shipping quantities of the plurality of products based on the acquired shipping records, and a placement location determination means for determining the placement locations of the classified product groups and the placement locations of the plurality of products based on the shipping prediction by the shipping prediction means.

As mentioned above, a system and method for optimizing product placement in logistics warehouses and the like has also been proposed as a conventional technique for optimizing product placement (see Patent Document 3) that reduces the frequency of replenishing and replacing items.

This technology relates to a system that calculates a recommended capacity value of a product arranged in each of a plurality of front spaces, which a plurality of shelves have and in which a plurality of products are arranged, based on a predicted shipping amount of the product arranged in the front space as a result of a demand forecast for the product in a future specified period. The system determines one or more replacement pairs, which are front space pairs in which product replacement occurs, based on the current capacity value and the recommended capacity value of each of the plurality of front spaces. For each front space, the current capacity value is a value that means the capacity of the front space. For each front space, the recommended capacity value is a value that means the front space capacity that is predicted to be required for the product arranged in the front space in a unit period in a specified period. Each of the one or more replacement pairs described above satisfies the following conditions. (a) The current capacity value of a first front space, which is one front space constituting the replacement pair, is smaller than the recommended capacity value of the first front space, or the current capacity value of a second front space, which is the other front space constituting the replacement pair, is larger than the recommended capacity value of the second front space. (b) the recommended capacity value of the second frontage space satisfies the current capacity value of the first frontage space, (c) the recommended capacity value of the first frontage space satisfies the current capacity value of the second frontage space.

WO2016/157333 Republished 2019-97694 JP 2021-120891 A

In a logistics warehouse along the supply chain, daily operations include extracting products ordered by customers from the picking area and shipping them. Meanwhile, as these extractions are carried out one after another, the amount of inventory in the picking area decreases.

As a result, if the stock level in the picking area falls below the standard and there is a shortage, the product in question will be transported from the storage area to the picking area and replenished up to the replenishment limit (the maximum stock level in the picking area, manually defined according to the size of the shipment).

However, simply determining a replenishment limit based on the number of shipments often results in cases where the actual shelves in the picking area are not able to accommodate all of the products. The storage area of the shelves in the picking area is, of course, finite, and the shape (e.g., the aspect ratio of the shelves or the position of the partitions) and external environment (e.g., the presence of a pillar close to the rear) can vary. Similarly, the shapes and sizes of the products stored on those shelves vary depending on the type of product.

Therefore, the number of items that can be stored on a shelf is not simply the capacity of the shelf divided by the volume of the items to be stored. In such cases, it is possible that, depending on the shape of the item, it may not be possible to store it on the shelf and therefore it may not be possible to place it in the picking area (see Figure 1).

Furthermore, the accuracy of the replenishment limits mentioned above is not very good, and there is a problem that the balance between actual shipments and inventory can easily become unbalanced. This can lead to situations where there are products with a large shipment volume but low inventory in the picking area, and products with a small shipment volume but high inventory in the picking area (see Figure 2).

As a result, product replenishment from the storage area to the picking area occurred more frequently than necessary, while the products brought to the picking area could not be stored on the shelves, which could lead to a significant drop in operational efficiency throughout the logistics warehouse.

The object of the present invention is to provide technology that minimizes the number of times products are replenished in the picking area of a logistics warehouse, thereby making the process more efficient.

The inventory allocation optimization system of the present invention, which solves the above problem, has a memory unit that stores information on each of the constraint conditions, such as the position and size of each storage shelf of the product, the size of each product stored in the storage shelf and the replenishment point as the minimum inventory required, the collection form in which the same type of product is accumulated in a row on the storage shelf, the placement interval between the collections of the products accumulated in a row, and the height and placement length of the collection in the width and depth directions on the storage shelf, and a calculation unit that calculates the value of each of the decision variables that maximizes the storage number, which is the objective function, using a mathematical optimization solver under the constraint conditions, and outputs each of the values of the decision variables based on the results of the calculation.

The inventory allocation optimization method of the present invention is characterized in that the information processing system stores in a memory unit information on the constraint conditions, such as the position and size of each storage shelf of the product, the size of each product stored in the storage shelf and the replenishment point as the minimum inventory required, the collection form in which the same type of product is accumulated in a row on the storage shelf, the arrangement interval between the collections of the products accumulated in a row, and the height and arrangement length of the collection in the width and depth directions on the storage shelf, as an objective function, the number of products stored in the storage shelf, the storage shelf where the collection is stored and the arrangement position on the storage shelf, the number of stacked layers of the products that make up the collection, and the arrangement number in the width and depth directions, as decision variables, calculates each value of the decision variable that maximizes the storage number, which is the objective function, using a mathematical optimization solver under the constraint conditions, and outputs each value of the decision variable to a specified device based on the results of the calculation.

The present invention makes it possible to minimize the number of times products are replenished in the picking area of a logistics warehouse, thereby improving the efficiency of that operation.

FIG. 1 is a diagram showing an example of shelf volume and actual product arrangement in a conventional manner. 1 is a graph showing a conventional relationship between shipping volume and inventory volume. FIG. 1 is a diagram illustrating a network configuration including an inventory placement optimization system according to an embodiment of the present invention. FIG. 2 is a diagram illustrating an example of a hardware configuration of the inventory placement optimization system according to the present embodiment. FIG. 4 is a diagram illustrating an example of a timing chart according to the present embodiment. FIG. 4 is a diagram illustrating an example of a flow according to the present embodiment. 11 is a diagram showing an example of storage shelf information stored in an information DB according to the embodiment; FIG. 4 is a diagram showing an example of product information stored in an information DB according to the embodiment; FIG. 11 is a diagram showing an example of passage information stored in an information DB according to the embodiment; FIG. 1 is a diagram showing an example of weight/capacity limit information stored in an information DB according to the embodiment; 11 is a diagram showing an example of placement restriction information for a best-selling item stored in an information DB according to the present embodiment. FIG. 11 is a diagram showing an example of information on the number of products per column stored in an information DB according to the embodiment; FIG. 11 is a diagram illustrating an example of minimum column number information stored in an information DB according to the embodiment. FIG. 11 is a diagram illustrating an example of maximum column number information stored in an information DB according to the embodiment. FIG. 11 is a diagram showing an example of protruding condition information stored in an information DB according to the embodiment; FIG. FIG. 2 is a diagram showing a conceptual example of a column structure in the present embodiment. FIG. 13 is a diagram illustrating a conceptual example of excess depth in the present embodiment. FIG. 2 is a diagram showing an example of a flow of an inventory placement optimization method according to the present embodiment. FIG. 4 is a diagram showing an example of an output screen in the present embodiment. FIG. 11 is a diagram illustrating an example of an additional constraint condition according to the present embodiment. FIG. 11 is a diagram illustrating an example of an additional constraint condition according to the present embodiment.

<About mathematical optimization solvers and annealing machines>
In the inventory allocation optimization technology of this embodiment, a mathematical optimization solver is used as an engine for solving combinatorial optimization problems. The mathematical optimization solver includes the concepts of a linear programming solver and quantum annealing, either of which can be used in this embodiment.

As mentioned above, there are several common linear programming solver tools, and their application methods are widely known, so here we will explain the concept of quantum annealing and its applications.

As described in the above-mentioned Patent Document 1, the applicant has developed quantum computing technology and has attempted to solve various problems, for example, in exhaustive search problems based on big data (including the concept of combinatorial optimization problems).

Quantum computers are generally expected to solve these exhaustive search problems. Quantum computers are made up of basic elements called quantum bits, which can simultaneously realize "0" and "1". This means that all possible solutions can be calculated simultaneously using the initial value, making it possible to realize an exhaustive search. However, quantum computers must maintain quantum coherence throughout the entire calculation time.

Among these, a method called adiabatic quantum computing has been attracting attention (Reference: E. Farhi, et al., "A quantum adiabatic computing
evolution al gorithm applied to random
instances of an NP-complete problem, "S
science292, 472 (2001). ).

This method transforms the problem so that the ground state of a physical system is the solution, and attempts to obtain a solution by finding the ground state.

Let H^p be the Hamiltonian of the physical system for which the problem is set. However, at the start of the calculation, the Hamiltonian is not H^p, but a different Hamiltonian H^0, whose ground state is clear and easy to prepare. Next, take a sufficient amount of time to transition the Hamiltonian from H^0 to H^p. If enough time is taken, the system will remain in the ground state, and the ground state of the Hamiltonian H^p will be obtained. This is the principle of adiabatic quantum computing. If the calculation time is τ, the Hamiltonian becomes equation (1),

[Equation 1]

A solution is obtained by time evolution based on the Schrödinger equation of equation (2).
[Equation 2]

Adiabatic quantum computing can also be applied to problems that require exhaustive search, and a solution is reached in a one-way process. However, if the computation process needs to follow the Schrödinger equation in equation (2), then quantum coherence must be maintained, just like in a quantum computer.

However, while a quantum computer repeats gate operations between one or two quantum bits, adiabatic quantum computing involves simultaneous interactions across the entire quantum bit system, and the concept of coherence is different.

For example, consider a gate operation on a certain quantum bit. At this time, if there is an interaction between that quantum bit and other quantum bits, it will cause decoherence, but in adiabatic quantum computing, all quantum bits interact simultaneously, so decoherence does not occur in this example. Reflecting this difference, adiabatic quantum computing is thought to be more robust against decoherence than quantum computers.

As described above, adiabatic quantum computing is effective for difficult problems that require an exhaustive search. Spin is treated as a variable in the calculation, and the problem to be solved is set in terms of spin-spin interactions and local fields acting on each spin.

At time t = 0, an external magnetic field is applied to orient all spins in one direction, and the external magnetic field is gradually reduced so that it becomes zero at time t = τ.

The orientation of each spin evolves over time according to the effective magnetic field determined by the combined effect of the external magnetic field at each site and the spin-spin interactions at time t.

In this case, the spin direction is not perfectly aligned with the effective magnetic field, but is quantum mechanically corrected so that the system remains nearly in the ground state.

In addition, a term (relaxation term) that maintains each spin in its original orientation as time evolves is added to the effective magnetic field, improving the convergence of the solution.

In this embodiment, the inventory placement optimization system is assumed to be an annealing machine that performs the above-mentioned adiabatic quantum computing, but of course this is not limited to this, and any mathematical optimization solver that can appropriately solve combinatorial optimization problems in accordance with the inventory placement optimization method of the present invention can be applied.

Note that the mathematical optimization solver mentioned above can be, for example, existing ones such as CBC (COIN-OR BRAND-and-Cut) solver (registered trademark), Gurobii (registered trademark), and CPLEX (registered trademark).

Other specific examples include not only hardware implemented with electronic circuits (digital circuits, etc.) in the annealing method, but also methods implemented with superconducting circuits, etc.
Hardware that realizes the Ising model using a method other than the annealing method may be used. For example, this includes a laser network method (optical parametric oscillation) and a quantum neural network. In addition, although some of the concepts are different as described above, the present invention can also be realized using a quantum gate method in which the calculations performed by the Ising model are replaced with gates such as a Hadamard gate, a rotation gate, and a controlled NOT gate.

<Network Configuration>
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described in detail below with reference to the accompanying drawings. Fig. 3 is a diagram showing a network configuration including an inventory allocation optimization system 100 according to the present embodiment.

The inventory allocation optimization system 100 shown in FIG. 3 is a computer system that minimizes the number of times products are replenished in a picking area in a logistics warehouse, enabling the efficiency of said operations, and specifically, is an information processing device that implements a mathematical optimization solver. For example, if the information processing device is equipped with a quantum annealing engine, it becomes an annealing machine.

However, the outline of the annealing machine has already been described based on Patent Document 1, and details of its specific configuration, operation, etc. will be omitted as appropriate (as below). Also, when a mathematical optimization solver other than annealing technology is adopted, existing technology will be adopted, so details of its specific configuration, operation, etc. will be omitted as appropriate.

The inventory placement optimization system 100 of this embodiment is connected to a user terminal 200 via an appropriate network 10 such as the Internet, enabling data communication.

The above-mentioned user terminal 200 is a terminal that receives proposals from the inventory placement optimization system 100 about information for minimizing the number of times products are replenished in the picking area of the logistics warehouse and making the relevant operations more efficient, that is, information such as the placement position and number of products (which can be said to be the number of products in the group that makes up the row) on the storage shelf in the picking area when storing products from the storage area on the storage shelf in the picking area.

Specific examples of users of this user terminal 200 include operators of logistics warehouses, logistics companies, and e-commerce site operators.

In any case, any business that stores a wide variety of small quantities of products in a huge logistics warehouse and quickly and reliably ships products in response to orders, and that seeks to minimize the number of times products are replenished in the picking area of the logistics warehouse and to improve the efficiency of that business, could qualify as a user as described above. In other words, the present invention can be said to be applicable to the business operations of such businesses.

<Hardware Configuration>
The hardware configuration of the inventory placement optimization system 100 of this embodiment is as shown in FIG.

That is, the inventory placement optimization system 100 includes a storage unit 101, a memory 103, a calculation unit 104, and a communication unit 105.

The memory unit 101 is composed of an appropriate non-volatile memory element such as a solid state drive (SSD) or a hard disk drive.

In addition, memory 103 is composed of a volatile memory element such as RAM.

The calculation unit 104 is a CPU that executes the program 102 stored in the storage unit 101 by reading it into the memory 103, etc., to perform overall control of the device itself, as well as various judgments, calculations, and control processes.

The communication unit 105 is assumed to be a network interface card or the like that is connected to the network 10 and handles communication processing with the user terminal 200.

If the inventory placement optimization system 100 is a stand-alone machine, it is preferable that it further includes an input device that accepts key input or voice input from the user, and an output device such as a display that displays the processed data.

In addition to the program 102 for implementing the functions required for the inventory allocation optimization system of this embodiment, at least an information DB 125 is stored in the storage unit 101. However, details of this information DB 125 will be described later.

Furthermore, the program 102, i.e., the algorithm that implements the operation as a mathematical optimization solver, holds information about a mathematical model 1021, which is the problem to be solved. This mathematical model 1021 is set in advance by an administrator or the like with respect to various information required for mathematical analysis, such as objective functions, decision variables, and constraint conditions. When the inventory placement optimization system 100 operates as an annealing machine, the mathematical model 1021 is an Ising model.

As described above, the annealing machine that solves the Ising model 1021, which is an example of the inventory placement optimization system 100 of this embodiment, is merely one example, and as already mentioned, it is of course possible to implement other mathematical optimization solvers in the program 102 or call them from an external system and use them to solve the mathematical model 1021 consisting of an objective function, decision variables, and constraint conditions that correspond to the contents of the Ising model 1021.

The adiabatic quantum computing mentioned in the overview of annealing machines is also known as quantum annealing, and is an extension of the classical concept of simulated annealing to quantum mechanics. In other words, adiabatic quantum computing is essentially capable of classical operation, and can be interpreted as adding quantum mechanical effects to improve performance in terms of speed and accuracy rate. Therefore, in this invention, the calculation unit itself is classical, and by introducing parameters determined quantum mechanically into the calculation process, a calculation method and device that is classical but includes quantum mechanical effects is realized. However, it is of course possible to adopt a form in which the calculation unit is composed of a quantum computer.

Based on the above concepts, in the following example we will describe a classical algorithm for obtaining the ground state as a solution, while explaining its relevance to adiabatic quantum computing, and a device for implementing it.

Under these assumptions, the inventory placement optimization system 100 has N variables ^sjz (j=1, 2, ..., N) with a value range of -1≦ ^sjz ≦1, and sets a problem based on local fields gj and inter-variable interactions Jij (i, j=1, 2, ..., N).

The calculation unit 104 divides the time into m parts and performs calculations discretely from t=t. (t.=0) to tm (tm=τ), and when determining the variable ^Sjz (tk) at each time tk, the value of the variable ^Sjz (tk-1) (i=1, 2, .., N) at the previous time tk-1 and the relaxation term coefficient 9pina or 9pinb are used to obtain ^Bjz (tk)={ ^ΣiJijSiz (tk-1)+gj+sgn( ^sjz (tk-1))·9pina}·tk/ ^τ or Bjz(tk)={ ^ΣiJiJSjz (tk-1)+gj+9pinb. ^Sjz (tk-1)}·tk/τ is found, a function f is defined so that the value range of the above-mentioned variable ^Sjz (tk) is -1≦ ^sjz (tk)≦1, and ^Sjz (tk)=f( ^Bjz (tk),tk) is set, and as the time step progresses from t=t0 to t=tm, the above-mentioned variable ^Sjz approaches -1 or 1, and finally, if ^sjz <0, ^Sjzd =-1, and if ^Sjz >0, ^Sjzd =1 are set to determine the solution. However, if it is appropriate that ^{the final solution sjzd} _is a real number, ^the solution may be determined as _sjzd being a real number with a value range of [-1, 1].

The coefficient gpinb is, for example, a value between 50% and 200% of the average value of |Jij|. In addition, for the local field gj in the problem setting, a correction term δgj' can be added to gj' only for a certain site j', and the magnitude of gj' can be increased only for that site j'. In addition, the correction term δgj' is, for example, a value between 10% and 100% of the average value of |Jij|.

Next, we describe the basic principles of annealing machines, starting from a quantum mechanical description and moving to classical formalisms.

The problem of searching for the ground state of the Ising spin Hamiltonian given by equation (3) includes a classification of problems called NP-hard, and is known to be a useful problem (reference: F. Barahona, "On the computational complexity of Isingspin glass models," J. Phys. A: Math. Gen. 15, 3241 (1982)).

[Equation 3]

Jij and gj are the problem setting parameters, and σ^ ^Z is the z component of the Pauli spin matrix, which has an eigenvalue of ±1. i and j represent the spin site. An Ising spin is a variable that can only take on a value of ±1, and in equation (3), the eigenvalue of σ^ ^z is ±1, making it an Ising spin system.

The Ising spin in equation (3) does not have to be a literal spin; it can be anything physically as long as the Hamiltonian is described by equation (3).

For example, the number of stacked products that make up the collection as a row, the number of products arranged in the width and depth directions of the storage shelf, the storage shelf where the collection is stored and the arrangement position on that storage shelf can each be associated with a spin of ±1, the high and low of a logic circuit can be associated with ±1, the vertical and horizontal polarization of light can be associated with ±1, and the phase of 0, π can be associated with ±1.

In the method exemplified here, similar to adiabatic quantum computing, a computational system is prepared in the ground state of the Hamiltonian given by equation (4) at time t = 0.

[Equation 4]

γ is a proportionality constant determined by the magnitude of the external field applied uniformly to all sites j, and σ^j ^x is the x component of the Pauli spin matrix. If the calculation system is the spin itself, the external field means a magnetic field.

Equation (4) corresponds to the application of a transverse magnetic field, and the ground state is when all spins point in the x direction (γ>0). The Hamiltonian in the problem formulation was defined as an Ising spin system with only the z component, but equation (4) includes the x component of spin. Therefore, the spin in the calculation process is not Ising but vectorial (Bloch vector). At t=0, we start with the Hamiltonian in equation (4), but as time t progresses, the Hamiltonian is gradually changed, and finally the Hamiltonian described by equation (3) is obtained, with the ground state being the solution.

[Equation 5]

Here, σ^ represents the three components of the Pauli spin matrix as a vector. The ground state is when the spin is oriented in the direction of the magnetic field, and can be written as <σ^> = B/|B|, where <·> is the quantum mechanical expectation value. In an adiabatic process, the ground state is always maintained, so the direction of the spin always follows the direction of the magnetic field.

The above discussion can be extended to multi-spin systems. At t=0, the Hamiltonian is given by equation (4). This means that a magnetic field ^BjX = γ is applied uniformly to all spins. At t>0, the x component of the magnetic field gradually weakens to ^BjX = γ(1-t/τ). As for the z component, the effective magnetic field is given by equation (6) due to the interaction between spins.

[Equation 6]

Since the spin direction can be defined by <σ^ ^z >/<σ^ ^x >, if the spin direction follows the effective magnetic field, the spin direction is determined by equation (7).

[Equation 7]

Equation (7) is a quantum mechanical description, but it takes the expectation value, so unlike equations (1) to (6), it is a relationship between classical quantities.

In classical systems, there is no nonlocal correlation (quantum stitching) in quantum mechanics, so the spin direction should be completely determined by the local field at each site, and equation (7) determines the behavior of the classical spin system. In quantum systems, equation (7) is transformed due to the existence of nonlocal correlation, but this will be discussed later. Here, we will describe the classical system defined by equation (7) to explain the basic form of the invention.

Figure 5 shows a timing chart (1) for obtaining the ground state of the spin system. Since the description in Figure 5 is related to classical quantities, the spin of site j is expressed by sj rather than σ^j. Accordingly, the effective magnetic field Bj in Figure 5 is a classical quantity. At t = 0, a rightward effective magnetic field Bj is applied to all sites, and all spins Sj are initialized to the right.

As time t passes, the magnetic field in the z-axis direction and the spin-spin interaction are gradually added, and finally the spins are in the +z or -z direction, and the z component of the spin Sj becomes sj ^z = +1 or -1. Ideally, time t is continuous, but in the actual calculation process, it can be made discrete to improve convenience. The discrete case is described below.

The spin shown here is a vectorial spin because it includes not only the z component but also the x component. Its vectorial behavior can also be understood from Figure 5. The y component has not appeared so far, but this is because the external field direction is taken to be on the xz plane, so there is no y component of the external field, and therefore <σ^ ^Y > = 0.

The spin of the computational system is assumed to be a three-dimensional vector of magnitude 1 (called a Bloch vector, which can describe the state as a point on a sphere), but the axis selection in the example shown in the figure requires that only two dimensions be considered (the state can be described as a point on a circle).

Furthermore, since γ is constant, Bj ^x (t)>0 (γ>0) or Bj ^x (t)<0 (γ<0) holds. In this case, the two-dimensional spin vector can be described using only a semicircle, and if Sj ^z is specified as [-1, 1], the two-dimensional spin vector is determined by the single variable Sj ^z . Therefore, although the spin is a two-dimensional vector in this example, it can also be expressed as a one-dimensional continuous variable with a range of [-1, 1].

In the timing chart of Figure 5, the effective magnetic field is calculated for each site at time t = tk, and the spin direction at t = tk is calculated using this value according to equation (8).

[Equation 8]

Equation (8) is equation (7) rewritten in terms of classical quantities, so there is no < > symbol. Next, the effective magnetic field at t = tk + l is found using the value of the spin at t = tk. If we write the effective magnetic field at each time in concrete terms, we get equations (9) and (10).

[Equation 9]

[Equation 10]

Below, we alternately find the spin and effective magnetic field following the procedure shown diagrammatically in the timing chart of Figure 5.

In the classical system, the magnitude of the spin vector is 1. In this case, each component of the spin vector is described as ^Sjz (tk) = sin θ and ^Sjx (tk) = cos θ, using the parameter θ defined as tan θ = ^Bjz (tk)/ ^Bjx (tk).

Rewriting this, Sj ^z (tk) = sin(arctan(Bj ^z (tk)/Bj ^x (tk))), Sj ^x (tk) = cos(arctan(Bj ^z (tk)/Bj ^x (tk) )).

As is clear from equation (9), the only variable of ^Bjx (tk) is tk, and τ and γ are constants. Therefore, ^Sjz (tk)=sin(arctan( ^Bjz (tk)/ ^Bjx (tk))) and Sjx(tk)=cos(arctan( ^Bjz (tk)/ ^Bjx (tk))) can also be generalized as functions with ^Bjz (tk) and tk as variables, such as ^Sjz (tk)=f1( ^Bjz (tk),tk) and ^Sjx (tk)=f2( ^Bjz (tk),tk).

Since the spin is described as a two-dimensional vector, two components Sj ^z (tk) and sj ^x (tk) appear, but if Bj ^z (tk) is determined based on equation (10), Sj ^x (tK) is not necessary.

This corresponds to the fact that the spin state can be described only by Sj ^z (tk) with a range of [-1, 1]. The final solution Sj ^zd needs to be Sj ^zd =-1 or 1, and if Sj ^z (τ) > 0, Sj ^zd = 1, and if Sj ^z (τ) < 0, Sj ^zd =-1. However, if it is appropriate for the final solution s _j ^zd to be a real number, s _j ^zd may be extracted as a real number with a range of [-1, 1].

FIG. 6 shows a flowchart summarizing the above algorithm. Here, tm=τ. Each step s1 to s9 in the flowchart in FIG. 6 corresponds to a process at a certain time in the timing chart in FIG. 5 from time t=0 to t=τ. That is, steps s2, s4, and s6 in the flowchart correspond to the above equations (9) and (10) at t=t1, tk+l, and tm, respectively. The final solution is determined in step s8 by setting Sj ^zd =-1 if sj ^z <0, and Sj ^zd =1 if Sj ^z >0 (s9). However, if it is appropriate for the final solution to be a real number, s _j ^zd may be determined as a real number with a range of [-1, 1]. Note that the flow in FIG. 6 shows a general example, and the description of extracting it as a real number is omitted.

So far, we have shown how the problem is solved when it is expressed by equation (3). Next, we will use a concrete example to explain how a specific problem is expressed by equation (3) including the local field gj and the variable interactions Jij (i, j = 1, 2, ..., N).

The specific problem here, that is, the Ising model 1021, is an Ising model in which, for example, the number of stacked layers of the products constituting the above-mentioned collection and the number of products arranged in the width and depth directions, the storage shelf where the collection is stored and the arrangement position on the storage shelf are each set as spins, and the sensitivity between variables in the above-mentioned constraint function is set as the strength of interaction between the spins, with respect to an objective function including, as terms, a constraint function that maximizes the number of products stored on the storage shelf when each of the constraint conditions for the picking area in a logistics warehouse, the position and size of each product storage shelf, the size of each product stored on the storage shelf and the replenishment point as the minimum number of products required, the collection form in which the same type of product is accumulated in a row on the storage shelf, the arrangement interval between the collections of the products accumulated in a row, and the height of the collection on the storage shelf and the arrangement length in the width and depth directions, is satisfied.

In this case, the local field gj is assumed to be set as the degree of influence that the values of the variables in the constraint function that maximizes the number of products stored in the storage shelf when the following constraint conditions are satisfied with respect to the picking area in the logistics warehouse: the position and size of each product storage shelf, the size of each product stored in the storage shelf and the replenishment point as the minimum required inventory number, the collection form in which the same type of product is accumulated in a row on the storage shelf, the arrangement interval between the collections of products accumulated in a row, and the height of the collection on the storage shelf and the arrangement length in the width and depth directions.

Through the above considerations, the variable interactions Jij and the local fields gj (between each term of the objective function described above) are specifically set, and the ground state search of the Ising model 1021 expressed by equation (3) is performed, that is, through a search for a ground state in which the number of products stored in the storage shelf is maximized when the constraint conditions regarding the picking area in the logistics warehouse described above, namely, the position and size of each product storage shelf, the size of each product stored in the storage shelf and the replenishment point as the required minimum inventory number, the collection form in which the same type of product is accumulated in a row on the storage shelf, the arrangement interval between the collections in which the products are accumulated in a row, and the height of the collection on the storage shelf and the arrangement length in the width direction and depth direction, are each satisfied, the storage shelf in which the collection of products is stored and the arrangement position on the storage shelf, and the number of stacked layers and the arrangement number in the width direction and depth direction of the products constituting the collection are each specified.

<Data structure example>
Next, a description will be given of various types of information used by the inventory placement optimization system 100 of this embodiment. Figures 7A to 7D and 9A to 9E show examples of each type of information held in the information DB 125 of this embodiment.

The storage shelf information 125A of this embodiment shown in FIG. 7A is a table that stores the output information of each storage shelf in the picking area.

The information stored here is a collection of records that use the identification information of the storage shelf as a key to associate values such as the position of the storage shelf in the picking area, the number of shelves it has, the shelf size, load capacity, height per shelf, and surrounding conditions.

Product information 125B in this embodiment, shown in FIG. 7B, is a table that stores various information about products that are stocked on the shelves in the picking area and are subject to shipping. This product information is a collection of records that use the product's identification information as a key and associate values such as the product's size, volume, weight, number shipped in the most recent specified period (average), and number shipped (maximum).

Also, the aisle information 125C of this embodiment shown in FIG. 7C is a table that stores information about the aisles that run around the above-mentioned storage shelves in the picking area. This aisle information is a collection of records that associate values such as the position, width, and length in the picking area with the aisle identification information as a key.

In addition, weight/capacity limit information 125D of this embodiment shown in FIG. 7D is a table that stores restrictions such as load capacity and capacity limits for each of the above-mentioned storage shelves. This weight/capacity limit information 125D is a collection of records that use the identification information of a storage shelf as a key to associate each value of the load capacity and capacity limit for each shelf of the storage shelf.

The best-selling product placement restriction information 125E of this embodiment shown in FIG. 8A is a table that specifies placement restrictions for best-selling products with a shipping volume above a certain level among the products extracted and shipped from the picking area. This best-selling product placement restriction information 125E is a collection of records that specify whether or not each best-selling product can be placed on a storage shelf and on the number of shelves.

In addition, the number of products per row information 125F in this embodiment shown in FIG. 8B is a table that stores information on the number of products per row, which is determined according to the size of the product and the size of the storage shelf when the products are piled up to form a row structure on the storage shelf in the picking area.

When products are piled up on a storage shelf to form a row structure, as shown in the example of Figure 9, the products are arranged in a row in the storage space on the shelf of the storage shelf, with specific faces of the products (e.g., faces that are easy to pick) facing the opening of the storage space in the depth direction, and are stacked in the height direction, for example, up to the height of the storage space -5 cm. The rules for generating these row structures are also expressed in a mathematical formula and are stored in information DB 125 as one of the constraints. In the example of Figure 9, one row of product A is composed of a total of six products, with three products connected in the depth direction and two stacked in the height direction.

The minimum row number information 125G of this embodiment shown in Fig. 8C is a table that specifies the minimum number of row structures in which each product can be accumulated on the storage shelves in the picking area. The maximum row number information 125H shown in Fig. 8D is a table that specifies the maximum number of row structures in which each product can be accumulated on the storage shelves in the picking area.

The protruding condition information 125I of this embodiment shown in FIG. 8E is a table that specifies information regarding the length by which the row structure of each product may protrude beyond the end of the storage shelf in the picking area. Based on this protruding condition information 125I, if the row structure of each product protrudes beyond the storage area of the storage shelf, it is determined whether this satisfies the allowable conditions specified in this table (see FIG. 10). In other words, the protruding condition information 125I is one of the constraint conditions.

In this embodiment, the information stored in the information DB 125 is configured as each condition equation (such as a constraint function in the case of the Ising model 1021) of the constraint conditions, decision variables, and objective functions to be applied to the mathematical model 1021. In addition, users are assumed to appropriately adopt a description method (known) for each condition equation to generate the condition equations, and the inventory placement optimization system 100 is assumed to store this in advance.

<Flow example>
The actual procedure of the inventory placement optimization method in this embodiment will be described below with reference to the drawings. Various operations corresponding to the inventory placement optimization method described below are realized by a program that is read into a memory or the like and executed by the inventory placement optimization system 100. This program is composed of codes for performing the various operations described below.

Figure 11 is a diagram showing an example of the flow of the inventory placement optimization method in this embodiment. In this case, the inventory placement optimization system 100 uses the number of products stored in a storage shelf as the objective function for the mathematical model 1021 (or Ising model 1021) to be processed, the storage shelf that stores the row structure of the products and the placement position on the storage shelf, the number of stacked products that make up the row structure of the products, and the placement number in the width direction and depth direction, as decision variables, and calculates each value of the decision variable that maximizes the storage number, which is the objective function, by a mathematical optimization solver included in the program 102 or appropriately called from an external system under constraints (the position and size of each storage shelf of the products in the picking area in the logistics warehouse, the size of each product stored in the storage shelf and the replenishment point as the minimum stock required, the collection form in which the same type of product is accumulated in a row on the storage shelf, the placement interval between the row structures (assemblies) in which the products are accumulated in a row, and the height of the row structure on the storage shelf and the placement length in the width direction and depth direction).

When an Ising model is adopted as the mathematical model 1021 and the inventory placement optimization system 100 is an annealing machine, a model is calculated in which the above-mentioned decision variables are set as spins and the sensitivity between variables in the objective function is set as the strength of interaction between the spins for the constraint condition function that is maximized when each of the above-mentioned constraint conditions is satisfied.

Therefore, the inventory placement optimization system 100 extracts information corresponding to the above-mentioned constraint conditions and decision variables (including formulas defined based on this) from the information stored in the information DB 125 of the storage device 101, and stores this in the memory 103 (s10).

In addition, similar to s10, the inventory placement optimization system 100 extracts objective function information (a mathematical formula that defines the storage quantity) from the information held in the above-mentioned information DB 125, and stores this in the memory 103 (s11).

Next, the inventory placement optimization system 100 provides the above-mentioned objective function, decision variables, and constraint conditions to the mathematical optimization solver, and calculates the values of the decision variables that maximize the storage quantity, which is the objective function (s12). Here, the maximized storage quantity is the maximum value of the replenishment limit.

Next, the inventory placement optimization system 100 calculates the number of times the product will be replenished from the storage area to the picking area by dividing the total number of shipments of the product in a specified past period (the value of the (average) number of shipments in product information 125B in Figure 7B) by the value obtained by subtracting the replenishment point (the value of the (maximum) number of shipments in product information 125B in Figure 7B) from the replenishment limit identified in s12 (s13).

Then, the inventory placement optimization system 100 outputs the values of the decision variables obtained up to this point, i.e., the storage shelf where the products in the row structure will be stored and their placement positions on that storage shelf, the number of layers of the products that make up the row structure and the number of placements in the width and depth directions, the number of replenishments calculated in s13 above, and the replenishment limit value to the user terminal 200 (see Figure 12) (s14), and ends the process.

In addition, the information on constraints stored in the information DB 125 may further include information on constraints that prohibit product placement in a specific portion (e.g., the position at the beginning of the second tier; see FIG. 13) facing the opening of the storage shelf among products forming a row structure (assembly) in order to ensure space for picking operations.

In this case, the inventory placement optimization system 100 performs calculations using a mathematical optimization solver under information on constraint conditions, including constraint conditions that prohibit the above-mentioned product placement. In this case, product placement that hinders the removal of products from storage shelves is avoided, making picking operations easier and ultimately making it possible to further improve the efficiency of picking operations in logistics warehouses.

In addition, the constraint information stored in the information DB 125 may further include information on constraint conditions related to an upper limit on the number of items that may be moved on the shelves based on the results of calculations performed by the mathematical optimization solver (see FIG. 14).

In this case, the inventory placement optimization system 100 performs calculations using a mathematical optimization solver under constraint information, including the constraint on the upper limit of the number of items that can be moved. This makes it possible to appropriately reduce the burden of moving items on workers when changing the existing item placement on a storage shelf. This in turn makes it possible to further improve the efficiency of picking operations in logistics warehouses.

The above describes in detail the best mode for carrying out the present invention, but the present invention is not limited to this, and various modifications are possible without departing from the spirit of the present invention.

This embodiment minimizes the number of times products need to be replenished in the picking area of a logistics warehouse, making it possible to improve the efficiency of this operation.

The description in this specification makes clear at least the following. That is, in the inventory placement optimization system of this embodiment, the calculation unit may calculate the number of times the product is replenished from the storage area to the picking area by dividing the total number of shipments of the product in a specified past period by a value obtained by subtracting the replenishment point from the storage number, which is the replenishment limit, and output the result to a specified device.

This outputs information on the number of replenishments that is minimized based on the maximized replenishment limit, allowing users such as warehouse managers to clearly recognize the results and effects of optimizing inventory placement. Furthermore, by implementing operations such as inventory placement based on this information, the number of times products are actually replenished in the picking area of the warehouse can be minimized, making it possible to improve the efficiency of this work.

In addition, in the inventory placement optimization system of this embodiment, the storage unit may further store, as the constraint information, information on a constraint that prohibits product placement in a specific portion of the assembly that faces the opening of the storage shelf in order to ensure space for picking operations, and the calculation unit may perform the calculation under the constraint information that also includes the constraint that prohibits the product placement.

This makes it easier to remove products from storage shelves, i.e., to perform the picking operation, and ultimately makes picking operations in logistics warehouses more efficient.

In addition, in the inventory placement optimization system of this embodiment, the storage unit may further store, as the constraint information, information on a constraint on a protrusion length by which the product can exceed the placement length and protrude from the storage shelf, and the calculation unit may perform the calculation under the constraint information including the protrusion length constraint.

This makes it possible to respond appropriately to situations and shapes where products are placed with their ends hanging off the shelves, improving the storage efficiency of products on the shelves and increasing the replenishment limit. This in turn minimizes the number of times products need to be replenished in the picking area of the logistics warehouse, making it possible to further improve the efficiency of the relevant operations.

In addition, in the inventory placement optimization system of this embodiment, the storage unit may further store, as the constraint information, information on a constraint condition related to an upper limit on the number of items that will be moved on the storage shelf based on the results of the calculation, and the calculation unit may perform the calculation under the constraint information including the constraint condition on the upper limit on the number of items.

Accordingly, by applying the present invention, in cases where the existing product layout on a storage shelf is changed, it is possible to appropriately reduce the burden on workers of moving products. This in turn makes it possible to further improve the efficiency of picking operations in logistics warehouses.

In addition, in the inventory placement optimization system of this embodiment, the calculation unit may calculate an Ising model in which the number of stacked layers of the products constituting the collection, the number of products arranged in the width direction and the depth direction, the storage shelf where the collection is to be stored, and the arrangement position on the storage shelf are each set as spins, with the sensitivity between variables in the constraint condition function set as the strength of interaction between the spins, for an objective function that includes as a term a constraint condition function that maximizes the number of products stored in the storage shelf when each of the constraint conditions is satisfied.

This makes it possible to reduce the time required for calculations compared to when using existing linear programming solvers, thereby making it possible to further improve the efficiency of picking operations in logistics warehouses.

In addition, in the inventory placement optimization system of this embodiment, a CMOS annealing machine that solves combinatorial optimization problems with respect to the Ising model may be used.

This makes it possible to simulate the operation of the Ising model using a circuit that uses semiconductor elements such as CMOS (Complementary Metal Oxide Semiconductor), and efficiently obtain practical solutions to combinatorial optimization problems that take into account mutually influencing constraint conditions, i.e. nonlinear constraint conditions, at room temperature. This in turn makes it possible to minimize the number of times products are replenished in the picking area of a logistics warehouse, further improving the efficiency of that business.

10 Network 100 Inventory placement optimization system 101 Storage unit 102 Program 1021 Mathematical model 103 Memory 104 Calculation unit 105 Communication unit 125 Information DB
200 User terminal

Claims (8)

a storage unit that stores information on each of the constraints regarding a picking area in a logistics warehouse, such as the position and size of each storage shelf for the products, the size of each product stored in the storage shelf and a replenishment point that is the minimum number of products required, a collection form in which the same type of products are accumulated in a row on the storage shelf, the arrangement intervals between the collections in which the products are accumulated in a row, and the height and the arrangement length in the width direction and depth direction of the collection on the storage shelf;
a calculation unit that calculates values of the decision variables that maximize the storage number, which is the objective function, using a mathematical optimization solver under the constraint conditions, and that defines the number of products stored in the storage shelf as an objective function, and the storage shelf in which the collection is stored and the arrangement position in the storage shelf, the number of stacked layers of the products that make up the collection, and the arrangement number in the width direction and the depth direction as decision variables;
The calculation unit outputs each value of the decision variable to a predetermined device based on a result of the calculation.
The inventory placement optimization system is characterized by: The calculation unit is
The number of times the product is replenished from the storage area to the picking area is calculated by subtracting the replenishment point from the replenishment limit, which is the number of storages, and dividing the total number of shipments of the product in a specified period in the past by the value obtained, and outputting the calculated number to a specified device.
2. The inventory placement optimization system according to claim 1 . The storage unit is
As the information on the constraint condition, information on a constraint condition that prohibits product placement in a specific portion of the assembly facing an opening surface of the storage shelf in order to secure a space for picking operations is further stored;
The calculation unit is
The calculation is performed under information of the constraint conditions including a constraint condition that prohibits the product placement.
2. The inventory placement optimization system according to claim 1 . The storage unit is
As the information on the constraint condition, information on a constraint condition on a protruding length by which the product can protrude from the storage shelf in excess of the arrangement length is further stored;
The calculation unit is
The calculation is performed under information of the constraint conditions including the constraint condition of the protrusion length.
2. The inventory placement optimization system according to claim 1 . The storage unit is
As the information on the constraint condition, information on a constraint condition regarding an upper limit of the number of products that may be moved in the storage shelf based on the result of the calculation is further stored;
The calculation unit is
The calculation is performed under information of the constraint conditions including a constraint condition of an upper limit of the number of products.
2. The inventory placement optimization system according to claim 1 . The calculation unit is
the number of stacked layers of the products constituting the collection, the number of products arranged in the width direction and the depth direction, the storage shelf in which the collection is stored, and the arrangement position on the storage shelf are each set as spins, and an Ising model is calculated in which the sensitivity between variables in the constraint function is set as the strength of interaction between the spins, with respect to an objective function including, as a term, a constraint function that maximizes the number of products that can be stored in the storage shelf when each of the constraint conditions is satisfied,
2. The inventory placement optimization system according to claim 1 . The inventory allocation optimization system according to claim 6, characterized in that it is a CMOS annealing machine that solves combinatorial optimization problems with respect to the Ising model. The information processing system
a storage unit stores information on each of the constraints regarding a picking area in a logistics warehouse, the position and size of each storage shelf for the products, the size of each product stored in the storage shelf and a replenishment point that is the minimum number of products required, a collection form in which the same type of products are accumulated in a row on the storage shelf, the arrangement intervals between the collections in which the products are accumulated in a row, and the height and the arrangement length in the width direction and depth direction of the collection on the storage shelf;
The number of the products stored in the storage shelf is an objective function, and the storage shelf in which the collection is stored and the arrangement position in the storage shelf, the number of stacked layers of the products constituting the collection, and the arrangement number in the width direction and depth direction are each decision variables, and a mathematical optimization solver is used to maximize the storage number, which is the objective function, and values of the decision variables are output to a specified device based on the results of the calculation.
The inventory allocation optimization method according to the present invention is characterized in that

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