Methods and hybrid storage systems for optimizing storage costs

Abstract

The invention relates to a method and a hybrid storage system (1) for optimizing storage costs comprising a digital computer (2) with a set of virtual warehouses, (i, j E {1,..., NF} = : I), as well as a set of virtual components (t, t' ∈ {1,...,NP} = : P),

Description

The invention relates to a method and a hybrid storage system for optimizing storage costs.Components and goods must be stored in warehouses until they are used and have caused storage costs. Storage costs are thus incurred for most companies and represent a considerable financial burden. It is thus of interest for each company to reduce its storage costs as much as possible and thus to save money.Each company also seeks to optimally manage the resources, in particular with regard to specific components or raw materials such as steel or iron, in order to avoid production shutdown.Fixed storage costs may represent a significant portion of the total cost of storage. To reduce them, redesign or modernization measures may help. In contrast, there are the variable storage costs which are only generated when the bearing is used. They are dependent on the intensity of the use of the bearing.There is therefore a need to minimize storage costs. Storage costs are minimized, for example, by accelerating storage and storage processes and by enlarging and centralizing stores. At the same time, there is a need to keep stored goods as close as possible to the production facilities.There are many proposals in the prior art to minimize storage costs. However, with respect to globalization and the plurality of components, optimum storage is difficult to realize with respect to storage costs. Therefore, current optimizations are usually aimed at the quantity of components to be ordered or at the delivery routes.WO 1997021180 A1 discloses a method in which management data are converted as parameters in at least two modules of computer programs linked to one another into corresponding control data for controlling conveying means. The at least two modules are a storage module and an acquisition module. The basic method can be extended by an input / output module and a statistics module. There are alternating effects between the "inner" modules with one another and between the modules and the environment. The inventory is monitored by the inventory module, orders are initiated in accordance with certain ordering criteria established in rules, and the internal inventory structure is "organized". The acquisition module assigns a type of business to each article according to certain business criteria established in rules, and orders are manifested and sent according to a certain lot size formula. Goods acceptance and delivery are authorized, initiated and reported by the input / output module.It is therefore an object of the invention to specify an improved method and a hybrid storage system for optimizing storage costs and a use.The object is achieved by a method with the features of claim 1 and a hybrid storage system with the features of claim 7 as well as a use with the features of claim 11.The object is achieved by a method for optimizing storage costs comprising the steps:providing a digital computer,virtually providing a set of warehouses on the digital computer,virtually providing a set of components on the digital computer,generating a transport cost function by the digital computer, said transport cost function indicating the costs incurred when transporting a component from one warehouse to another warehouse,generating a profit function by the digital computer, which specifies the profit of the component at the respective virtual warehouse,generating a cost reduction function by the digital computer, said cost reduction function indicating the cost reduction when two components are transported together during transport from the one warehouse to the other warehouse,generating an energy function by the digital computer on the basis of the transport cost function, the profit function and the cost reduction function using the following binary variables: with t ∈P the set of all virtual components and i,jE I the set of all warehouses,providing an adiabatic quantum system, wherein the quantum system is associated with a corresponding energy landscape, wherein the quantum system is coupled to the digital computer,generating an initial initial state for the quantum system based on the energy function by the digital computer and initializing the energy landscape based on the initial state by the digital computer,changing the initial state to a fundamental energetic state by the adiabatic quantum system using the energy function, wherein the fundamental energetic state encodes a minimum of the energy function,measuring the initial state of energy after adiabatic change by the digital computer,encoding the measurement by the digital computer,causing or omitting a transport of the component or a transport of the two components from the one warehouse to the other warehouse on the basis of the encoding.A digital computer can be understood to mean a conventional computer / computing system / computer.In this case, i, j ∈{1,..., N F} = : I are referred to below as the set of warehouses; t, t' ∈{1,..., N p} = : : P are referred to below as the set of components.In this case, d(t, i, j) is referred to as a transport cost function which specifies the costs which arise during the transport of a component t ∈Pfrom one warehouse i ∈Ito another warehouse j ∈I. In this case, w(t, i) is referred to as a profit function which specifies the profit of the component t ∈P at the virtual warehouse i ∈I. Further, R c( t, t', i, j) is referred to as a cost reduction function indicating the cost reduction when two parts t, t' ∈P are transported together from one warehouse i ∈I to another warehouse j ∈I, and H as an energy function.Heretofore, storage costs have been optimized only such that only the order amount has been varied so that sufficient components have been stored in each store. Optimizing the storage costs taking into account the profit which a component achieves in a store and the transport of several components together has not been possible up to now on account of the large number of variables (quantity of components / warehouses and possible combinations during transport); rather, technical knowledge has been used in this case.According to the invention, a sufficiently accurate (as well as reasonable) approximation for the quantum system, for example for a quantum channel, must be found, so that adiabatic optimization is made possible and which describes the technical task sufficiently accurately.Furthermore, the task must be formulated as a QUBO (Quadratic Unconstrained Binary Optimization) task with binary variables via a quadratic objective function without constraints.According to the invention, the problem is approximated by the method in such a way that it can be described by a maximum binary energy function. This means that the energy function is present as a quadratic uncontracted binary optimization function with binary variables, thus enabling a start with coupled qubits.The object can now be achieved technically by the invention to optimize costs with regard to the redistribution of already stored components / goods.With the aid of the method according to the invention, global inventory optimization is possible for the first time with the aid of a quantum system using a classic digital computer.In this case, both the costs for the storage in the storage hall i and j for each component t and the profit which each component t achieves in the respective storage hall i, j E I are considered.According to the invention, the profit is thus taken into account by the profit function in each warehouse i, jE I.According to the invention, the transport costs are also considered in view of the cost reduction potential when parts batches can be sent together.By means of the method according to the invention, it is now possible for the first time, on the basis of a displacement of the components t or of the components t, t', to achieve an optimization of the storage costs and thus a maximizing of the profit, wherein the minimum reserve quantity is covered by the profit function.For this purpose, according to the invention, an energy function is generated by the digital computer on the basis of the transport cost function d(t, i, j), the profit function w(t, i) and the cost reduction function R c( t, t', i, j) using binary variables.The initial state of the quantum computer typically corresponds to a detachable quantum system in which the qubits are initialized in the ground state. This initial state is then transferred into the matrix of the problem location, whereby the qubits are ideally also brought into the basic state of the problem location. The matrix is translated into a coupling strength of the qubits with each other in the adiabatic quantum computer.The minimum of the energy function can then be found on the basis of the quantum channel. According to the invention, encoding, i.e. global inventory optimization, can be carried out on the basis of the found basic state and the transport of components t, t' into other warehouses can be initiated or omitted by the digital computer.By using a profit function on the at least two warehouses and the transport cost function and the cost reduction function, an efficient maximum quadratic energy function can be generated, by means of which both the supply (higher profit) and, as it were, little used components (lower profit) and the transport costs are balanced against one another over all components and over all warehouses.The method according to the invention makes it possible to achieve optimum management of the resources by optimizing storage costs with regard to winning and loss. Thus, resources can be handled gently to increase sustainability aspect and to take best advantage of the components.The method according to the invention now takes into account storage costs for the first time not with regard to the ordering behavior or a space utility, but rather takes into account the storage costs with regard to its location.In a further embodiment, the energy function is given by: where w(t, j) specifies the profit of the component t ∈Pat the virtual warehouse j ∈ I, where w(t, i) specifies the profit of the component t ∈Pat the virtual warehouse i ∈ I, with b(t, i, j) and b(t', i, j) as binary variables, with R c( t, t', i, j) as cost reduction function and d(t, i, j) as transport cost function.By such a configuration, the profit of the component t ∈P at a storage hall i ∈Ias well as in a possible storage at the storage hall j ∈Iare taken into account. Thus, for example, it is taken into account whether the component t ∈Pis required more at the warehouse j E Iand thus introduces more profit (and whether this is, for example, at the warehouse i ∈ I, a so-called store container which only occupies valuable space and thus causes costs). Furthermore, the transport costs and possibly reduced transport costs are taken into account if a plurality of components can be transported together. Furthermore, by such a configuration of the energy function, the energy function is formed to be maximally square and can thus be solved by means of a quantum channel.In a further embodiment, the components are specified as individual components or as consolidated component charge when the components are consolidated. A consolidated component load indicates the amount of article load, series or variety that is merged and transported. Consolidation in logistics thus describes, among other things, the bundling of products in order to be able to configure their storage and transport in a uniform manner. This is often the case with very small components such as screws or the like.In a further embodiment, the energy function is minimized under the secondary condition that an existing storage capacity C(t, j) at the other storage hall j ∈ Imust not be exceeded when a component t ∈P is removed at the one storage hall i ∈ Ifor storage in the storage hall j ∈ I.The constraint can be given by: with b(t, i, j) as binary variables, j ∈I as virtual warehouse, and t ∈P as virtual component.This can be the entire storage capacity or a restriction specified by the storage operator with respect to the component itself in favor of storing other components.In a further embodiment, the constraint is added as a penalty term to the energy function, in order to generate a QUBO (Quadratic Uncontracted Binary Optimization) model. As a result, the maximum quadratic configuration of the energy function can be maintained, which enables the use of a quantum channel.The object is furthermore achieved by a hybrid storage system for optimizing storage costs, comprising a digital computer having a set of virtual storage halls and a set of virtual components, wherein the digital computer is designed to generate a transport cost function which specifies the costs which arise during the transport of a component from one storage hall to another storage hall, and wherein the digital computer is furthermore designed to generate a profit function which specifies the profit of the component at the respective virtual storage hall, and wherein the digital computer is furthermore designed to generate a cost reduction function which specifies the cost reduction if two components can be transported together during the transport from one storage hall to another storage hall, furthermore having an adiabatic quantum system, wherein the quantum system is associated with a corresponding energy landscape, wherein the quantum system is coupled to the digital computer, and wherein the digital computer is configured to generate an energy function on the basis of the transport cost function, the profit function and the cost reduction function using the following binary variables: with t ∈ P the set of all virtual components and i,j E I the set of all warehouses, and wherein the digital computer is configured to generate an initial initial state for the quantum system on the basis of the energy function, and to initialize the energy landscape on the basis of the initial state, and wherein the adiabatic quantum system is configured to change the initial state into an energetic basic state using the energy function, wherein the energetic basic state encodes a minimum of the energy function, and wherein the digital computer is designed to perform a measurement of the basic state of energy after adiabatic change and an encoding of the measurement, and to cause or to omit a transport of the component or a transport of the two components from the one warehouse to the other warehouse on the basis of the encoding.The hybrid storage system is in particular designed to carry out the method according to the invention.The advantages of the method and the advantageous embodiments can be transferred to the hybrid storage system.In this case, the set of virtual warehouses / components can be stored on a memory unit in the digital computer.Furthermore, in a further embodiment, a display unit can be provided, wherein the digital computer is configured to display the quantity of virtual warehouses present and to display the quantity of virtual components on the display unit.This allows the encodings to be illustrated.In a further embodiment, it is provided as a secondary condition that an existing storage capacity of the other warehouse must not be exceeded when removing a component from the one warehouse for storage in the other warehouse, wherein the digital computer is configured to form the secondary condition by: with b(t, i, j) as binary variables, j ∈ I as virtual warehouse, and t ∈ P as virtual component, wherein the minimization of the energy function takes place under the secondary condition.Furthermore, the object is achieved by using a hybrid logistics management system as described above or a method as described above for optimizing storage costs.Both the costs for storing a component in a first warehouse and the profit which the respective component achieves in the warehouse are considered by the method according to the invention and the hybrid logistics management system according to the invention, and the profit which the component could achieve in another warehouse. Further, the transportation costs are taken into account.By means of the method according to the invention and also the hybrid logistics management system according to the invention, an optimization can now be accomplished with a completely new approach, which goes beyond a pure ordering optimization.The method according to the invention and the hybrid logistics management system according to the invention also achieve a reduction in storage costs with regard to maximizing the profit which each component in a warehouse achieves.Further characteristics and advantages of the present invention will become apparent from the following description with reference to the attached figures. The following are shown schematically in the drawing: FIG. 1 : a method according to the invention, FIG. 2 : shows the hybrid logistics management system schematically.FIG. 1 schematically shows the method according to the invention for optimizing storage costs.In a first step S 1, this provides a set of warehouses, i,j ∈{1,..., N F} = : : I, and a set of components t, t' ∈{1,..., N p} = : : P. The components t, t' ∈P and the warehouses, i, j ∈Ican be provided virtually on a digital computer 2. In a second step S 2, the digital computer 2 generates a transport cost function d(t, i, J) which specifies the costs which arise during the transport of a component t ∈P from a first warehouse i ∈Ito a second warehouse j ∈I.Furthermore, in the third step S 3, the digital computer 2 generates a profit function w(t, i) which indicates the profit of the component t ∈P at the virtual warehouse i ∈I, and a cost reduction function R c( t, t', i, j) which indicates the cost reduction when two components t, t' ∈P are transported together during transport from the first warehouse i ∈I to the second warehouse j ∈I.Furthermore, in a fourth step S4, an energy function H is generated by the digital computer 2 on the basis of the transport cost function d(t, i, j), the profit function w(t, i) and the cost reduction function R c( t, t', i, j) using the following binary variables:The energy function H is given by: where w(t, j) specifies the profit of the component t ∈P at the virtual warehouse j ∈ I, where w(t, i) specifies the profit of the component t ∈P at the virtual warehouse i ∈ I, with b(t, i, j) and b(t', i, j) as binary variables, with R C( t, t', i, j) as cost reduction function and d(t, i, j) as transport cost function.Thus, the energy function is present as a quadratic unconstrained binary optimization function with binary variables.The profit of the component t ∈Pat a warehouse i ∈Iis thus taken into account and also in the case of a possible mounting at the warehouse j ∈I. Thus, for example, it is taken into account whether the component t ∈Pis required more at the warehouse j ∈Iand thus enters more profit, and whether this is, for example, at the warehouse i ∈I, a so-called store container, which only occupies valuable space and thus causes costs. Furthermore, the transport costs and possibly reduced transport costs are taken into account if a plurality of components can be transported together.The components can be specified as individual components or consolidated component load, for example in the case of bolts or nuts.Furthermore, in a fifth step S 5, an adiabatic quantum system in the form of a quantum channel 3 is provided, wherein the quantum channel 3 is associated with a corresponding energy landscape. The quantum channel 3 is coupled to the digital computer 2.In a sixth step S 6, the digital computer 2 generates an initial state for the quantum channel 3 on the basis of the energy function H and initializes the energy landscape (for example by coupling the qubits in the quantum channel 3, for example the spins) on the basis of the initial state. The initial state of the quantum computer typically corresponds to a detachable quantum system in which the qubits are initialized in the ground state. This initial state is then transferred into the matrix of the problem location, whereby the qubits are ideally also brought into the basic state of the problem location. The matrix is translated into a coupling strength of the qubits with each other in the adiabatic quantum computer.Thus, for example, quantum chips can be used in which circulating currents each represent a qubit. Here, the qubits are measured by microwave radiation. Also, individual spins may be included in semiconductor quantum dots and then used as qubits.In a seventh step S 7, a change of the initial state into an energetic ground state is achieved in the quantum channel 3, wherein the energetic ground state encodes a minimum of the energy function H.In an eighth step S 8, the achieved energetic ground state after adiabatic change is measured and encoded by the digital computer 2.In a ninth step S9, the digital computer 2 can subsequently cause one or more components t, t' ∈P to be transported from one warehouse i ∈Ito another warehouse j ∈Ibased on the encoding.Alternatively, in an additional step S 4 a, a constraint may be added to the energy function H, which constraint is added as a penalty term of the energy function H. An existing storage capacity C(t,j) of the storage hall j ∈Iis taken into account, wherein the storage capacity C(t,j) of the storage hall j ∈Imust not be exceeded when a component t ∈P is removed from the storage hall i ∈Ifor storage in the storage hall j ∈I.In this case, the penalty term can be given by b(t, i, j) as binary variables, i, j E {1,..., N F} = : : I as virtual warehouse, and t ∈ P as component.FIG. 2 shows a hybrid storage system 1 for optimizing storage costs, having a digital computer 2 and a quantum channel 3.In this case, the encoding by the digital computer 2 is used to initiate a transport of a component t from the warehouse i E I to the warehouse j ∈ I.With the aid of the method according to the invention and the hybrid storage system 1 according to the invention, global inventory optimization is possible for the first time with the aid of a quantum channel 3 using a classic digital computer 2.Due to the large number of possible combinations, a solution by means of a conventional computer is not possible and has therefore not been taken into account in the previous optimizations of storage costs. Up to now, storage costs have only been optimized in such a way that only the order quantity has been varied. Optimizing the storage costs in consideration of the profit which a component achieves in a warehouse and the transport of several components together has not been possible up to now because of the large number of variables (quantity of components / warehouses and possible combinations during transport); rather, technical knowledge has been used in this case.According to the invention, the costs for the storage in the storage hall i ∈ Iand j ∈ Iand also the profit which each component t ∈Pin the respective storage hall i, j ∈ I erzielt are considered.According to the invention, the profit is taken into account by the profit function in each warehouse i, j ∈ I.According to the present invention, the transport cost is considered in view of cost reduction potential when parts batches can be sent together.By means of the method according to the invention, it is now possible for the first time, on the basis of a displacement of the components t ∈P or of the components t, t' ∈P, to achieve an optimization of the storage costs and thus a maximizing of the profit, wherein the minimum amount of conservation is covered by the profit function.With the aid of the method according to the invention, global inventory optimization is possible for the first time with the aid of a quantum system using a classic digital computer 2.List of reference characters1 Hybrid storage system 2 Digital computer 3 Quantum channel i, j ∈ I Storage halls t, t' ∈ P Components d(t, i, j) Transport cost function w(t, i) Profit function R C( t, t', i, j) Cost reduction function b(t, i, j) Binary variables H Energy functionReferences included in the specificationThis list of documents cited by the applicant has been produced in an automated manner and is only included for the better information of the reader. The list is not part of the German patent application or utility model application. The DPMA does not take any adhesion for any faults or omissions.Patent Literature citedWO 1997021180 A1

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Claims

Method for optimizing storage costs characterized bythe steps: - providing a digital computer (2), - virtually providing a set of storage halls (i, j ∈ {1,..., N F} =: I) on the digital computer (2), - virtually providing a set of components (t, t' ∈ {1,..., N p} = : P) on the digital computer (2), - generating a transport cost function (d(t, i, j)) by the digital computer (2) which specifies the costs which arise during the transport of a component (t ∈ P) from one storage hall (i ∈ I) to another storage hall (j ∈ I), generating a profit function (w(t, i)) by the digital computer (2) which indicates the profit of the component (t ∈ P) at the respective virtual warehouse (i ∈ I), generating a cost reduction function (R c( t, t', i, j)) by the digital computer (2) which indicates the cost reduction when two components (t, t' ∈ P) are transported together during transport from one warehouse (i ∈ I) to another warehouse (j ∈ I), generating an energy function (H) by the digital computer (2) on the basis of the transport cost function (d(t, i, j)), the profit function (w(t, i)) and the cost reduction function R c( t, t', i, j) using subsequent binary variables (b(t, i, j): b (t, i, j) = { 1, d a s B a u t e i l t w i r d v o n i n a c h j t r a n s p o r t i e r t, ≅ i, j ∈ I, t ∈ P 0, w e n n k e i n T r a n s p o r t s t a t f i n d e t - providing an adiabatic quantum system, the quantum system being associated with a corresponding energy landscape, the quantum system being coupled to the digital computer (2), generating an initial initial state for the quantum system on the basis of the energy function (H) by the digital computer (2) and initializing the energy landscape on the basis of the initial state by the digital computer (2), changing the initial state into an energetic ground state by the adiabatic quantum system using the energy function (H), wherein the energetic ground state encodes a minimum of the energy function (H), measuring the energetic ground state after adiabatic change by the digital computer (2), encoding the measurement by the digital computer (2), causing or omitting a transport of the component (t' ∈ P) or a transport of the components (t, t' ∈ P) from one warehouse (i ∈ I) to the other warehouse (j ∈ I) based on the encoding.Method according to claim 1, characterised in that the energy function (H) is given by: H = ∑ t = 1 N P ∑ i, j = 1 N F ( ( b ( t, i, j) d ( t, i, j) + w ( t, j) - w ( t, i) ) - ∑ t = 1 N P R C ( t, t ', i, j) b ( t ', i, j) ( b ( t, i, j) ) ) wherein (w(t, j)) indicates the profit of the component (t ∈ P) at the virtual warehouse (j ∈ I), wherein (w(t, t, i)) which represents the profile of the component (t ∈ P) on the virtual warehouse (i ∈ I), with (b(t, i, j)) and (b(t', i, j)) as binary variables, with (R c( t, t', i, j)) as cost reduction function and (d(t, i, j)) as transport cost function.Method according to one of the preceding claims, characterized in that the components (t ∈ P) are specified as individual components or consolidated component charge.Method according to one of the preceding claims, characterized in that the minimization of the energy function (H) takes place under the secondary condition that an existing storage capacity (C(t, j)) of the other storage hall (j ∈ I) must not be exceeded when a component (t ∈ P) is removed from the one storage hall (i ∈ I) for storage in the storage hall (j ∈ I).Method according to claim 4, characterized in that the constraint is given by: ∑ i = 1 N F b ( t, i, j) ≤ C ( t, j ) ∀ t, j with (b(t, i, j)) as binary variables, (j ∈ I) as virtual warehouse, and (t ∈ P) as virtual component.Method according to Claim 5, characterized in that the constraint is added as a penalty term to the energy function (H), in order to generate a QUBO (Quadratic Unconstrained Binary Optimization) model.Hybrid storage system (1) for optimizing storage costs, comprising a digital computer (2) having a set of virtual storage halls (i, j ∈ {1,..., N F} = : : I) and a set of virtual components (t, t' ∈ {1,..., N P} = : P), characterized in that the digital computer (2) is designed to generate a transport cost function (d(t, i, j)) which specifies the costs which arise during the transport of a component (t ∈ P) from one storage hall (i ∈ I) to another storage hall (j ∈ I), and wherein the digital computer (2) is furthermore designed to generate a profit function (w(t, t, i)) which specifies the profit of the component (t ∈ P) at the virtual warehouse (i ∈ I) and wherein the digital computer (2) is designed to generate a cost reduction function R C( t, t', i, j) which specifies the cost reduction if two components (t, t' ∈ P) are transportable together during transport from one warehouse (i ∈ I) to another warehouse (j ∈ I), further comprising an adiabatic quantum system, wherein the quantum system is associated with a corresponding energy landscape, wherein the quantum system is coupled to the digital computer (2), and wherein the digital computer (2) is designed to generate an energy function on the basis of the transport cost function (d(t, i, j)), the profit function (w(t, i)) and the cost reduction function (R c( t, t', i, j)) are formed using the following binary variables: b (t, i, j) = { 1, w e n d a s B a u t e i l t v o n i n a c h j t r a n s p o r t i e r t w i r d, ⁢ i, j ∈ I, t ∈ P 0, w e n k e i n t r a n s p o r t s t a t f i n d e t and wherein the digital computer (2) is furthermore designed to generate an initial state for the quantum system on the basis of the energy function (H) and to initialize the energy landscape on the basis of the initial state, and wherein the adiabatic quantum system is designed to bring about a change of the initial state into an energetic base state using the energy function (H), wherein the energetic base state encodes a minimum of the energy function (H), and wherein the digital computer (2) is designed to bring about a measurement of the energetic base state after adiabatic change and an encoding of the measurement, and also to cause or to omit a transport of the component (t ∈ P) or a transport of the two components (t, t' ∈ P) from the one warehouse (i ∈ I) to the other warehouse (j ∈ I) on the basis of the encoding.Hybrid storage system (1) according to Claim 7, characterized in that the digital computer (2) for generating the energy function (H) is given by: H = ∑ t = 1 N P ∑ i, j = 1 N F ( ( b ( t, i, j) d ( t, i, j) + w ( t, j) - w ( t, i) ) - ∑ t = 1 N P R C ( t, t ', i, j) b ( t ', i, j) ( b ( t, i, j) ) where (w(t, j)) specifies the profit of the component (t ∈ P) at the virtual storage hall (j ∈ I), where (w(t, t, i)) indicates the profit of the component (t ∈ P) at the virtual warehouse (i ∈ I), with (b(t, i, j)) and (b(t', i, j)) as binary variables, with (R C( t, t', i, j)) as cost reduction function and (d(t, i, j)) as transport cost function.Hybrid storage system (1) according to Claim 7 or 8, characterized in that a display unit is provided, and the digital computer (2) is designed to display the set of virtual storage halls (i, j ∈ {1,..., N F} = : I) present and to display the set of virtual components (t, t' ∈ {1,..., N P} = : P) on the display unit.Hybrid storage system (1) according to one of the preceding claims 8 to 10, characterized in that it is provided as a secondary condition that an existing storage capacity C(t,j) of the other storage hall (j ∈ I) must not be exceeded when a component (t ∈ P) is removed from the one storage hall (i ∈ I) for storage in the other storage hall (j ∈ I), wherein the digital computer (2) is designed to form the secondary condition by: ∑ i = 1 N F b ( t, i, j) ≤ C ( t, j ) ∀ t, j with (b(t, i, j)) as binary variables, (j ∈ I) as virtual storage hall, and (t ∈ P) as a virtual component, wherein the minimization of the energy function (H) takes place under the constraint.Use of a hybrid logistics management system (1) according to one of the preceding claims 7 to 10 or of a method according to one of the preceding claims 1 to 6 for optimizing storage costs.

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