CN117035339B - Method and device for calculating material demand planning problem in enterprise resource planning - Google Patents

Abstract

The present invention relates to the field of management science and technology, and in particular to a method and device for calculating material requirement planning problems in enterprise resource planning, the method comprising: S1, summarizing the universal material management requirements of manufacturing enterprises and determining the material supply mode; S2, comprehensively analyzing the material management logic, and using mixed integer programming technology to establish a mathematical model of the material requirement planning problem according to the material supply mode; S3, for large-scale calculation examples, relaxing the integer variables in the mathematical model into linear variables, converting the mathematical model into a pure linear programming model, and using a commercial solver combined with a heuristic method to obtain the final material procurement decision. The present invention fills the gap in the field, uses a mathematical model to accurately describe the problem, and proposes a commercial solver combined with a heuristic method for large-scale calculation examples. The algorithm framework is concise, the speed is fast, the decision quality is high, and it has good expansion capabilities.

Description

A calculation method and device for material requirement planning problems in enterprise resource planning

Technical Field

The invention relates to the field of management science and technology, and in particular to a calculation method and device for material requirement planning problems in enterprise resource planning.

Background Art

Material Resource Planning (MRP) is one of the important modules of the production planning system. After determining the master production plan, that is, the production quantity of each production line at each time point during the planning period, decisions are made on the material supply plan to answer the questions of "what to use, how to use it, what else is there, and what is still missing" for materials in the production system.

For some large manufacturing companies, they have the following characteristics: (1) The production is highly digitalized, and some production links have already acquired digital capabilities; (2) There are many manufacturing plants, and workshops, warehouses, and large warehouses are distributed in multiple cities across the country or even around the world, which brings great challenges to management; (3) Orders fluctuate greatly. As market demand uncertainty increases, combined with policy changes, increased customized demand and other factors, inventory levels need to be accurately controlled. However, the existing calculation methods for MRP problems are mainly based on rules based on simple methods such as prediction or traversal, which have problems such as incomplete scenario induction and poor generalization; the calculation method is simple, overly dependent on prediction, and unsatisfactory results.

Summary of the invention

The present invention provides a method and device for calculating material requirement planning problems in enterprise resource planning, which are used to solve the problems existing in the prior art. The technical solution is as follows:

On the one hand, a calculation method for material requirement planning problem in enterprise resource planning is provided, including:

S1. Summarize the universal material management needs of manufacturing enterprises and determine the material supply method;

S2. Conduct a comprehensive analysis of the material management logic and establish a mathematical model of the material requirement planning problem using mixed integer programming techniques based on the material supply method;

S3. For large-scale examples, the integer variables in the mathematical model are relaxed into linear variables, the mathematical model is transformed into a pure linear programming model, and a commercial solver is used in combination with a heuristic method to obtain the final material procurement decision.

Optionally, the S1 specifically includes:

On the basis of local inventory supply, manufacturing supply and procurement supply, remote inventory transfer, Open PO supply and Liability supply are added. Finally, the material supply methods include five supply methods: inventory supply including local inventory supply and remote inventory transfer, manufacturing supply, procurement supply, Open PO supply and Liability supply. The Open PO supply refers to the part of the purchased materials that have been shipped but not arrived under a signed procurement contract. The Liability supply refers to the estimated part for which a preliminary procurement intention has been reached with the supplier but a specific procurement contract has not been signed.

Optionally, the material requirement planning problem in S2 is to decide on the method and quantity of material supply to each factory when the orders that each factory needs to complete within the planning period are known;

The input of the problem includes: order information, master production plan information, and material information; the order information includes: order quantity and BOM information corresponding to the order; the master production plan information includes: planning period duration, order scheduling plan for each factory during the planning period; the material information includes: whether the material attribute belongs to MPQ/MOQ material, the initial available quantity of each material under each supply mode of each factory at the beginning of the planning period, and the supply cost; the BOM is a bill of materials, and its data structure is a tree, the root node is the final product, the leaf node is the production raw material, and each node in the middle layer corresponds to an intermediate product; the MPQ is the minimum packaging quantity; the MOQ is the minimum order quantity;

The output of the problem includes: the supply decision of each node in the BOM corresponding to each order, the purchase status of each material, and the changes in the local inventory and purchase inventory of each factory during the planning period. The purchase inventory refers to the inventory generated due to the unused part of the purchase, which is calculated independently from the original local inventory.

The optimization objectives of the problem include: minimizing the purchase cost during the planning period, minimizing the cost of transferring Open PO during the planning period, and maximizing the inventory usage excluding purchase inventory during the planning period.

Optionally, the mathematical model in S2 includes:

Collections and Indexes:

Order Collection

The node set contained in the BOM of order i

A collection of time nodes within the planning period

Factory Collection

Material Collection

Supplier Collection

MPQ Material Collection

MOQ Material Collection

The root node collection of all BOMs

The set of leaf nodes in all BOMs

A collection of transfer nodes in all BOMs

A collection of Liability supply nodes in all BOMs

A collection of replacement group nodes in all BOMs

parameter:

D _i demand quantity for order i

CM _k Inventory supply cost of material k

Inv _0sk 0, the local inventory available for material k in factory s

OPO _0sk 0, the Open PO available quantity of material k in plant s

Lia _0k The available amount of liability of material k at time 0

α _ijl Material ratio between node j of order i and its child node L

MPQ _kv MPQ batch size of material k at supplier v

MOQ _k v Minimum order quantity of MOQ material k at supplier v

variable:

_{Xij is} the quantity of node j that needs i to be satisfied through inventory (including local inventory and inventory transfer)

_{Yij is} the number of nodes j that meet demand i by manufacturing

_Zij is the quantity of node j that meets demand i through procurement

EX _ij The number of nodes j whose demand i is satisfied by Open PO

LX _ij is the number of nodes j whose demand i is satisfied by Liability

M _ij is the amount of complete satisfaction of node j for demand i

S _tsk is the local inventory supply of material k in factory s at time node t

ES _tsk Open PO supply of material k in plant s at time node r

N _tsk is the inventory consumption of material k in factory s at time node t.

VN _tsk is the inventory consumption of material k in factory s at time node t.

EN _tsk The consumption of Open PO of material k in factory s at time node t

FN _tsk Open PO transfer quantity of material k in factory s at time node t

GN _tsk is the stock transfer quantity of material k in factory s at time node t.

P _tsk is the purchase quantity of material k in factory s at time node t

LS _tsk is the initial available quantity of Liability supply of material k at time node t.

_LN tLiability consumption of material k at time node t

Inv _tsk: The available inventory of material k in factory s at time node t (T≥1)

OPO _tskOpen PO availability of material k in plant s at time node t (t≥1)

PP _tskv is the purchase volume of MPQ/MOQ material k from supplier v in factory s at time node t

BZ _tskv is the purchase batch of MPQ material k from supplier v at time node t, in plant s, integer variable

PS _tsk is the purchase inventory level of material k in factory s at time t

Objective function:

min J ₁ +J ₂ -J ₃ (1)

constraint:

BZ _tskv ∈N (27)

_{Xij , Yij} , _Zij ,EXij, _{LXij ,} Mij,Stsk, _EStsk , _{Ntsk , VNtsk} , _ENtsk , _FNtsk , _GNtsk ,Ptsk, _LStsk , _{LNt , PPtskv} , PS _tsk ≥0 (28)

Variable part: _Xij , _Yij , _Zij , _EXij , _LXij correspond to the supply decision of each node; _PPtskv , _BZtskv correspond to the purchase decision of materials; _Invtsk , _PStsk correspond to the inventory level change and purchase inventory change during the planning period;

Objective function and constraint part: Formula (2) is the sum of the purchase cost of all materials; Formula (3) is the sum of the Open PO transfer cost of all materials; Formula (4) is the sum of the local inventory level at each moment; Formulas (2)-(4) all contain the time gradient multiplier (T+1-t). As t increases, since T is a constant, (T+1-t) decreases. Therefore, in Formula (2), the earlier the purchase cost is generated, the higher the purchase cost is; in Formula (3), the earlier the Open PO transfer cost is generated, the higher the penalty is; in Formula (4), the earlier the local inventory level is generated, the higher the penalty is; Among them, Formula (2) (3) is the minimization amount, and Formula (4) is the maximization amount. Therefore, the right sides of Formulas (2) (3) are added together, and then the right side of Formula (4) is subtracted to obtain the unified minimization objective function Formula (1). At the same time, the time gradient multiplier is used to impose a soft constraint of "the later the cost is generated, the better";

The left side of formula (5) represents the total inventory supply of each material by each factory at each moment, and the right side represents the total inventory supply demand of each material by each factory at each moment; the left side of formula (6) represents the total manufacturing supply of each material by each factory at each moment, and the right side represents the total manufacturing supply demand of each material by each factory at each moment; the left side of formula (7) represents the total purchase supply of each material by each factory at each moment, and the right side represents the total purchase supply demand of each material by each factory at each moment; the left side of formula (8) represents the total local inventory supply of each material by each factory at each moment, and the right side represents the total local inventory consumption of each material by each factory at each moment; the left side of formula (9) represents the total Open PO transfer supply of each material by each factory at each moment, and the right side represents the Open PO transfer supply of each material by each factory at each moment =Total PO transfer; The left side of formula (10) represents the total inventory transfer supply of each material by each factory at each moment, and the right side represents the inventory transfer consumption of each material by each factory at each moment; The left side of formula (11) represents the total liability supply of each material by each factory at each moment, and the right side represents the liability consumption of each material by each factory at each moment; The left side of formula (12) represents the initial inventory availability of each material of each factory minus the inventory consumption at the initial moment, and the right side represents the inventory availability of each material corresponding to each factory at the next moment; The left side of formula (13) represents the inventory availability of each material of each factory at the non-initial moment plus the newly added inventory of each material of each factory at each moment minus the inventory consumption of each material of each factory at each moment, and the right side represents the inventory availability of each material corresponding to each factory at the next moment; The left side of formula (14) represents the initial OpenPO availability of each material of each factory minus the 0pen PO consumption at the initial moment, and the right side represents the Open PO available quantity; the left side of formula (15) represents the Open PO available quantity of each material in each factory at the non-initial moment plus the newly added OpenPO quantity of each material in each factory at each moment minus the Open PO consumption of each material in each factory at each moment, and the right side represents the Open PO available quantity of each material in each factory at the next moment; the left side of formula (16) represents the Liability available quantity of each material in each factory at the initial moment minus the Liability consumption at the initial moment, and the right side represents the Liability available quantity of each material in each factory at the next moment; the left side of formula (17) represents the Liability available quantity of each material in each factory at the non-initial moment plus the newly added Liability quantity of each material in each factory at each moment minus the Liability consumption of each material in each factory at each moment, and the right side represents the Liability available quantity of each material in each factory at the next moment; formula (18) represents that the complete set satisfaction quantity of the root node of the BOM corresponding to the order should be equal to the quantity of the corresponding order; formula (19) represents that the complete set satisfaction quantity of the non-leaf nodes in the BOM is equal to the inventory supply, manufacturing supply, procurement supply, Open =The sum of the supply quantities of five modes: PO supply, Liability supply; Formula (20) indicates that the complete set satisfaction quantity of the leaf node is equal to the sum of the supply quantities of four modes: inventory supply, purchase supply, Open PO supply, and Liability supply; Formula (21) indicates that the manufacturing supply quantity of the root node of the non-replacement group is equal to the sum of the complete set satisfaction quantity of each leaf node multiplied by the matching coefficient; Formula (22) indicates that the manufacturing supply quantity of the root node of the replacement group is equal to the sum of the complete set satisfaction quantity of all its leaf nodes multiplied by the matching coefficient; Formula (23) is used to calculate the purchase quantity of each MPQ material from each supplier at each time for each factory; Formula (24) is used to calculate the purchase quantity of each MOQ material from each supplier at each time for each factory; Formula (25) indicates that the purchase inventory level of each material for each factory at the initial time of the planning period is 0; The left side of Formula (26) indicates the purchase inventory level of each material at the non-initial time of each factory plus the purchase quantity of each material minus the purchase supply quantity, and the right side is the purchase inventory level at the next time; Formulas (27)-(28) indicate the variable type.

Optionally, the S3 specifically includes:

S31. Change the type of integer variable BZ _tskv from Integer to Continuous and relax it to a linear variable At this point, the model becomes a pure linear programming model that does not contain integer variables;

S32. Solve the relaxed linear variables using commercial solvers The solution result is recorded using the dictionary BZ ^relax . The solution result is an infeasible solution to the original problem. The solution result is further processed using a heuristic method to obtain the final MPQ material procurement batch, which is recorded as Using the dictionary BZ ^heur record, the heuristic method is based on the Traverse the purchase batches of MPQ materials from various suppliers in chronological order;

S33. The remaining decision variables are linear variables in the original problem. After solving the relaxed pure linear programming model and obtaining the result, they are directly used as the solution to the original problem.

Optionally, the input of the heuristic method is a BZ ^relax dictionary obtained by solving a pure linear programming model, and the output is a BZ ^heur dictionary obtained by the heuristic method and recording feasible solutions to the original problem. The step S32 further processes the solution result using the heuristic method, specifically including:

For each factory and each MPQ material, set a variable rest with an initial value of 0. Use this variable to record the remaining value of the corresponding material in the corresponding factory after meeting the current demand during the traversal process. If the supply is not enough to meet the next traversed demand, new purchases are required. Otherwise, no new purchases are required and the corresponding supply is deducted from rest.

Further traversal: For each moment and each supplier, set a variable PlanPurchase, which represents the original planned purchase quantity of each material purchased by each factory from each supplier at each moment, which is also the purchase quantity of each MPQ material obtained by solving the pure linear programming model. The original planned purchase quantity is equal to the purchase quantity obtained by solving the pure linear programming model. Multiply the minimum packaging quantity of each material at each supplier, and then round it up. If the rest of the current material in the current factory is greater than or equal to the original planned purchase quantity, no new purchase is made, and the corresponding subscript variable is set to If it is 0, it means that the batch of materials purchased by the corresponding factory from the supplier at the current moment is 0, and the original planned purchase quantity is deducted from rest. Otherwise, a variable Lack is set to indicate that rest does not meet the missing part of the supply, which is equal to the original planned supply minus rest. At this time, the corresponding subscript variable It is equal to the ratio of Lack to the minimum package quantity of each material at each supplier, rounded up. After this new purchase, the value of the variable rest is updated, which is equal to the previous remaining quantity rest plus the heuristic purchase batch multiplied by the minimum package quantity minus the original planned purchase quantity.

Repeat the above cycle until all variables After assignment, the output dictionary BZ ^heur is a set of feasible solutions for the integer variable BZ _tskv in the original problem.

Optionally, the method further comprises:

For small and medium-scale examples, commercial solvers are used to solve the mathematical model.

On the other hand, a computing device for material requirement planning problem in enterprise resource planning is provided, characterized in that the device comprises:

The determination module is used to summarize the universal material management needs of manufacturing enterprises and determine the material supply method;

Establish a module for comprehensive analysis of material management logic and establish a mathematical model of the material requirement planning problem using mixed integer programming techniques based on the supply mode of the material;

The solution module is used to relax the integer variables in the mathematical model into linear variables for large-scale calculation examples, transform the mathematical model into a pure linear programming model, and use a commercial solver combined with a heuristic method to obtain the final material procurement decision.

On the other hand, an electronic device is provided, which includes a processor and a memory, wherein the memory stores instructions, and the instructions are loaded and executed by the processor to implement the calculation method of the material requirement planning problem in the above-mentioned enterprise resource planning.

On the other hand, a computer-readable storage medium is provided, wherein instructions are stored in the storage medium, and the instructions are loaded and executed by a processor to implement the calculation method of the material requirement planning problem in the enterprise resource planning.

The beneficial effects brought about by the technical solution provided by the present invention include at least:

The present invention fills the gap in the field, uses mathematical models to accurately describe the problem, and proposes a commercial solver combined with a heuristic method for large-scale examples. The algorithm framework is simple, the speed is fast, the decision quality is high, and it has good expansion capabilities.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

FIG1 is a flow chart of a method for calculating a material requirement planning problem in an enterprise resource planning according to an embodiment of the present invention;

FIG2 is a schematic diagram of a supply method provided in an embodiment of the present invention;

3 is a schematic diagram of a pseudo code of a heuristic algorithm for solving the MRP problem provided by an embodiment of the present invention;

4 is a block diagram of a computing device for material requirement planning in an enterprise resource planning according to an embodiment of the present invention;

FIG. 5 is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention.

DETAILED DESCRIPTION

In order to make the technical problems, technical solutions and advantages to be solved by the present invention more clear, a detailed description will be given below with reference to the accompanying drawings and specific embodiments.

As shown in FIG1 , an embodiment of the present invention provides a method for calculating a material requirement planning problem in an enterprise resource planning, including:

S1. Summarize the universal material management needs of manufacturing enterprises and determine the material supply method;

S2. Conduct a comprehensive analysis of the material management logic and establish a mathematical model of the material requirement planning problem using mixed integer programming techniques based on the material supply method;

S3. For large-scale examples, the integer variables in the mathematical model are relaxed into linear variables, the mathematical model is transformed into a pure linear programming model, and a commercial solver is used in combination with a heuristic method to obtain the final material procurement decision.

2-3, a calculation method for material requirement planning in an enterprise resource planning according to an embodiment of the present invention is described in detail below, including:

S1. Summarize the universal material management needs of manufacturing enterprises and determine the material supply method;

Optionally, as shown in FIG2 , the S1 specifically includes:

On the basis of local inventory supply, manufacturing supply and procurement supply, we added off-site inventory transfer, Open Purchase Orders (Open PO) supply and pre-purchase order liability supply. Finally, the material supply methods include five supply methods: inventory supply including local inventory supply and off-site inventory transfer, manufacturing supply, procurement supply, Open PO supply and Liability supply. The Open PO supply refers to the part of the purchased materials that have been shipped but not arrived after a procurement contract has been signed. The Liability supply refers to the estimated part for which a preliminary procurement intention has been reached with the supplier but a specific procurement contract has not been signed.

S2. Conduct a comprehensive analysis of the material management logic and establish a mathematical model of the material requirement planning problem using mixed integer programming techniques based on the material supply method;

Optionally, the material requirement planning (MRP) problem in S2 is to make decisions on the method and quantity of material supply to each factory when the orders that each factory needs to complete within the planning period are known;

The input, output and optimization objectives of the problem are shown in Table 1:

Table 1 Input, output and optimization target of MRP problem

Right now:

The input of the problem includes: order information, master production plan information, and material information; the order information includes: order quantity, bill of material (BOM) information corresponding to the order; the master production plan information includes: planning period duration, order scheduling plan for each factory during the planning period; the material information includes: whether it belongs to the material attributes of MPQ (Minimum Pack Quantity, MPQ)/MOQ (Minimum Order Quantity, MOQ), the initial available quantity of each material under each supply mode at each factory at the beginning of the planning period, and the supply cost; the BOM is a bill of materials, and its data structure is a tree, the root node is the final product, the leaf node is the production raw material, and each node in the middle layer corresponds to an intermediate product; the MPQ is the minimum packing quantity; the MOQ is the minimum order quantity;

The output of the problem includes: the supply decision of each node in the BOM corresponding to each order, the purchase status of each material, and the changes in the local inventory and purchase inventory of each factory during the planning period. The purchase inventory refers to the inventory generated due to the unused part of the purchase, which is calculated independently from the original local inventory.

The optimization objectives of the problem include: minimizing the purchase cost during the planning period, minimizing the cost of transferring Open PO during the planning period, and maximizing the inventory usage excluding purchase inventory during the planning period.

Optionally, the mathematical model in S2 includes:

Collections and Indexes:

Order Collection

The node set contained in the BOM of order i

A collection of time nodes within the planning period

Factory Collection

Material Collection

Supplier Collection

MPQ Material Collection

MOQ Material Collection

The root node collection of all BOMs

The set of leaf nodes in all BOMs

A collection of transfer nodes in all BOMs

A collection of Liability supply nodes in all BOMs

A collection of replacement group nodes in all BOMs

parameter:

D _i demand quantity for order i

CM _k Inventory supply cost of material k

_Invosk 0, the local inventory availability of material k in factory s

OPO _0sk 0, the Open PO available quantity of material k in plant s

Lia _0k The available amount of liability of material k at time 0

α _ijl Material ratio between node j of order i and its child node l

MPQ _kv MPQ batch size of material k at supplier v

MOQ _kv Minimum order quantity of MOQ material k at supplier v

variable:

_{Xij is} the quantity of node j that needs i to be satisfied through inventory (including local inventory and inventory transfer)

_{Yij is} the number of nodes j that meet demand i by manufacturing

_Zij is the quantity of node j that meets demand i through procurement

EX _ij The number of nodes j whose demand i is satisfied by Open PO

LX _ij is the number of nodes j whose demand i is satisfied by Liability

M _ij is the amount of complete satisfaction of node j for demand i

S _tsk is the local inventory supply of material k in factory s at time node T

ES _tsk Open PO supply of material k in plant s at time node t

N _tsk is the inventory consumption of material k in factory s at time node t.

VN _tsk is the inventory consumption of material k in factory s at time node t.

EN _tsk The consumption of Open PO of material k in factory s at time node t

FN _tsk Open PO transfer quantity of material k in factory s at time node t

GN _tsk is the stock transfer quantity of material k in factory s at time node t.

P _tsk is the purchase quantity of material k in factory s at time node t

LS _tsk is the initial available quantity of Liability supply of material k at time node t.

_LN tLiability consumption of material k at time node t

Inv _tsk: The available inventory of material k in factory s at time node t (T≥1)

oPO _tskOpen PO availability of material k in plant s at time node t (t≥1)

PP _tskv is the purchase volume of MPQ/MOQ material k from supplier v in factory s at time node t

BZ _tskv is the purchase batch of MPQ material k from supplier v at time node t, in plant s, integer variable

PS _tsk is the purchase inventory level of material k in factory s at time t

Objective function:

min J ₁ +J ₂ -J ₃ (1)

constraint:

BZ _tskv ∈N (27)

_{Xij , Yij} , _Zij ,EXij, _{LXij ,} Mij,Stsk, _EStsk , _{Ntsk , VNtsk} , _ENtsk , _FNtsk , _GNtsk ,Ptsk, _LStsk , _{LNt , PPtskv} , PS _tsk ≥0 (28)

Variable part: _Xij , _Yij , _Zij , _EXij , _LXij correspond to the supply decision of each node; _PPtskv , _BZtskv correspond to the purchase decision of materials; _Invtsk , _PStsk correspond to the inventory level change and purchase inventory change during the planning period;

Objective function and constraint part: Formula (2) is the sum of the purchase cost of all materials; Formula (3) is the sum of the Open PO transfer cost of all materials; Formula (4) is the sum of the local inventory level at each moment; Formulas (2)-(4) all contain the time gradient multiplier (T+1-t). As t increases, since T is a constant, (T+1-t) decreases. Therefore, in Formula (2), the earlier the purchase cost is generated, the higher the purchase cost is; in Formula (3), the earlier the Open PO transfer cost is generated, the higher the penalty is; in Formula (4), the earlier the local inventory level is generated, the higher the penalty is; Among them, Formula (2) (3) is the minimization amount, and Formula (4) is the maximization amount. Therefore, the right sides of Formulas (2) (3) are added together, and then the right side of Formula (4) is subtracted to obtain the unified minimization objective function Formula (1). At the same time, the time gradient multiplier is used to impose a soft constraint of "the later the cost is generated, the better";

The left side of formula (5) represents the total inventory supply of each material by each factory at each moment, and the right side represents the total inventory supply demand of each material by each factory at each moment; the left side of formula (6) represents the total manufacturing supply of each material by each factory at each moment, and the right side represents the total manufacturing supply demand of each material by each factory at each moment; the left side of formula (7) represents the total purchase supply of each material by each factory at each moment, and the right side represents the total purchase supply demand of each material by each factory at each moment; the left side of formula (8) represents the total local inventory supply of each material by each factory at each moment, and the right side represents the total local inventory consumption of each material by each factory at each moment; the left side of formula (9) represents the total Open PO transfer supply of each material by each factory at each moment, and the right side represents the Open PO transfer supply of each material by each factory at each moment =Total PO transfer amount; The left side of formula (10) represents the total inventory transfer supply of each material by each factory at each moment, and the right side represents the inventory transfer consumption of each material by each factory at each moment; The left side of formula (11) represents the total liability supply of each material by each factory at each moment, and the right side represents the liability consumption of each material by each factory at each moment; The left side of formula (12) represents the initial inventory available quantity of each material of each factory minus the inventory consumption at the initial moment, and the right side represents the inventory available quantity of each material corresponding to each factory at the next moment; The left side of formula (13) represents the inventory available quantity of each material of each factory at the non-initial moment plus the newly added inventory quantity of each material of each factory at each moment minus the inventory consumption quantity of each material of each factory at each moment, and the right side represents the inventory available quantity of each material corresponding to each factory at the next moment; The left side of formula (14) represents the Open PO available quantity of each material of each factory at the initial moment minus the Open PO consumption at the initial moment, and the right side represents the Open PO consumption quantity of each material corresponding to each factory at the next moment PO available quantity; the left side of formula (15) represents the available quantity of Open PO of each material in each factory at the non-initial moment plus the newly added Open PO quantity of each material in each factory at each moment minus the Open PO consumption of each material in each factory at each moment, and the right side represents the available quantity of Open PO of each material in each factory at the next moment; the left side of formula (16) represents the available quantity of Liability of each material in each factory at the initial moment minus the Liability consumption at the initial moment, and the right side represents the available quantity of Liability of each material in each factory at the next moment; the left side of formula (17) represents the available quantity of Liability of each material in each factory at the non-initial moment plus the newly added Liability of each material in each factory at each moment minus the Liability consumption of each material in each factory at each moment, and the right side represents the available quantity of Liability of each material in each factory at the next moment; formula (18) represents that the complete set satisfaction quantity of the root node of the BOM corresponding to the order should be equal to the quantity of the corresponding order; formula (19) represents that the complete set satisfaction quantity of the non-leaf nodes in the BOM is equal to the inventory supply, manufacturing supply, procurement supply, Open =The sum of the supply quantities of five modes: PO supply, Liability supply; Formula (20) indicates that the complete set satisfaction quantity of the leaf node is equal to the sum of the supply quantities of four modes: inventory supply, purchase supply, Open PO supply, and Liability supply; Formula (21) indicates that the manufacturing supply quantity of the root node of the non-replacement group is equal to the sum of the complete set satisfaction quantity of each leaf node multiplied by the matching coefficient; Formula (22) indicates that the manufacturing supply quantity of the root node of the replacement group is equal to the sum of the complete set satisfaction quantity of all its leaf nodes multiplied by the matching coefficient; Formula (23) is used to calculate the purchase quantity of each MPQ material from each supplier at each time for each factory; Formula (24) is used to calculate the purchase quantity of each MOQ material from each supplier at each time for each factory; Formula (25) indicates that the purchase inventory level of each material for each factory at the initial time of the planning period is 0; The left side of Formula (26) indicates the purchase inventory level of each material at the non-initial time of each factory plus the purchase quantity of each material minus the purchase supply quantity, and the right side is the purchase inventory level at the next time; Formulas (27)-(28) indicate the variable type.

S3. For large-scale examples, the integer variables in the mathematical model are relaxed into linear variables, the mathematical model is transformed into a pure linear programming model, and a commercial solver is used in combination with a heuristic method to obtain the final material procurement decision.

After testing different scale examples, it was found that for small and medium scale examples (generally speaking, commercial solvers can solve small scale examples in minutes, medium scale examples in 30 minutes, and large scale examples in more than 30 minutes), commercial solvers can accurately solve the problems in an acceptable fast time, and the solution results meet the expected material supply logic; however, for large scale examples, commercial solvers cannot accurately solve the problems. Therefore, for large scale examples, the embodiment of the present invention proposes a commercial solver combined with a heuristic method, which can obtain a high-quality feasible solution in a short time and directly use it for decision-making guidance, specifically including:

S31. Change the type of integer variable BZ _tskv from Integer to Continuous and relax it to a linear variable At this point, the model becomes a pure linear programming model that does not contain integer variables;

Since the integer variable BZ _tskv increases the complexity of the model and the solution, the embodiment of the present invention changes the type of the integer variable BZ _tskv from Integer to Continuous and relaxes it to a linear variable

S32. Solve the relaxed linear variables using commercial solvers The solution result is recorded using the dictionary BZ ^relax . The solution result is an infeasible solution to the original problem. The solution result is further processed using a heuristic method to obtain the final MPQ material procurement batch, which is recorded as Using the dictionary BZ ^heur record, the heuristic method is based on the Traverse the purchase batches of MPQ materials from various suppliers in chronological order;

The heuristic method can ensure sufficient procurement while minimizing procurement and procuring as late as possible. Since the optimization goal of the objective function in the original problem is to minimize procurement supply and allocation, maximize local inventory supply, and hope that necessary procurement will occur as late as possible, the heuristic optimization logic of the embodiment of the present invention is consistent with the optimization goal of the original problem, while greatly shortening the calculation time and achieving efficient decision-making.

S33. The remaining decision variables are linear variables in the original problem. After solving the relaxed pure linear programming model and obtaining the result, they are directly used as the solution to the original problem.

Optionally, the input of the heuristic method is a BZ ^relax dictionary obtained by solving a pure linear programming model, and the output is a BZ ^heur dictionary obtained by the heuristic method and recording feasible solutions to the original problem, as shown in FIG3 . The heuristic method is used in S32 to further process the solution result, specifically including:

For each factory (pseudo code line 2), for each MPQ material (pseudo code line 3), set a variable rest with an initial value of 0 (pseudo code line 4). Use this variable to record the remaining value of the corresponding material in the corresponding factory after meeting the current demand during the traversal process. If the supply is not enough to meet the next traversed demand, new purchases are required. Otherwise, no new purchases are required and the corresponding supply is deducted from rest.

Further traversal: For each moment (pseudo code line 5), for each supplier (pseudo code line 6), set a variable PlanPurchase, which represents the original planned purchase quantity of each material purchased by each factory from each supplier at each moment, which is also the purchase quantity of each MPQ material obtained by solving the pure linear programming model. The original planned purchase quantity is equal to the purchase quantity obtained by solving the pure linear programming model. Multiply the minimum packaging quantity of each material at each supplier, and then round it up (pseudo code line 7). If the rest of the current material in the current factory is greater than or equal to the original planned purchase quantity (pseudo code line 8), no new purchase is made, and the corresponding subscript variable is set is 0, indicating that the batch of materials purchased by the corresponding factory from the supplier at the current moment is 0 (pseudo code line 9), and the original planned purchase quantity is deducted from rest (pseudo code line 10). Otherwise (pseudo code line 11), a variable Lack is set to indicate that rest does not meet the missing part of the supply, which is equal to the original planned supply minus rest (pseudo code line 12). At this time, the variable corresponding to the subscript It is equal to the ratio of Lack to the minimum packaging quantity of each material at each supplier, and then rounded up to the integer, to ensure that the heuristically obtained purchase quantity can fill the missing quantity of rest (pseudo code 13). After this new purchase, the value of the variable rest is updated, which is equal to the previous remaining quantity rest plus the heuristic purchase batch multiplied by the minimum packaging quantity minus the original planned purchase quantity (pseudo code line 14);

Repeat the above cycle until all variables After assignment, the output dictionary BZ ^heur is a set of feasible solutions for the integer variable BZ _tskv in the original problem.

As shown in FIG4 , an embodiment of the present invention further provides a computing device for material requirement planning problems in enterprise resource planning, the device comprising:

The determination module 410 is used to summarize the universal material management requirements of the manufacturing enterprise and determine the material supply method;

Establishing module 420 for comprehensively analyzing the material management logic and establishing a mathematical model of the material requirement planning problem using mixed integer programming technology according to the material supply mode;

The solution module 430 is used to relax the integer variables in the mathematical model into linear variables for large-scale calculation examples, transform the mathematical model into a pure linear programming model, and use a commercial solver combined with a heuristic method to obtain the final material procurement decision.

The functional structure of a computing device for a material requirement planning problem in an enterprise resource planning provided by an embodiment of the present invention corresponds to the computing method for a material requirement planning problem in an enterprise resource planning provided by an embodiment of the present invention, which will not be described in detail here.

Figure 5 is a structural diagram of an electronic device 500 provided in an embodiment of the present invention. The electronic device 500 may have relatively large differences due to different configurations or performances, and may include one or more processors (central processing units, CPU) 501 and one or more memories 502, wherein the memories 502 store instructions, and the instructions are loaded and executed by the processor 501 to implement the steps of the calculation method of the material requirement planning problem in the above-mentioned enterprise resource planning.

In an exemplary embodiment, a computer-readable storage medium is also provided, such as a memory including instructions, which can be executed by a processor in a terminal to complete the calculation method of the material requirement planning problem in the enterprise resource planning. For example, the computer-readable storage medium can be a ROM, a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, etc.

A person skilled in the art will understand that all or part of the steps to implement the above embodiments may be accomplished by hardware or by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, and the above-mentioned storage medium may be a read-only memory, a disk or an optical disk, etc.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (7)

1. A method for calculating material requirement planning problems in enterprise resource planning, characterized in that the method comprises: S1. Summarize the universal material management needs of manufacturing enterprises and determine the material supply method; S2. Conduct a comprehensive analysis of the material management logic and establish a mathematical model of the material requirement planning problem using mixed integer programming techniques based on the material supply method; S3. For large-scale examples, the integer variables in the mathematical model are relaxed into linear variables, the mathematical model is transformed into a pure linear programming model, and the final material procurement decision is obtained by using a commercial solver combined with a heuristic method; The S1 specifically includes: On the basis of local inventory supply, manufacturing supply, and procurement supply, remote inventory transfer, OpenPO supply, and liability supply were added. The final material supply methods include five supply methods: inventory supply including local inventory supply and remote inventory transfer, manufacturing supply, procurement supply, Open PO supply, and liability supply. The Open PO supply refers to the part of the purchased materials that have been shipped but not yet arrived after the procurement contract has been signed. The liability supply refers to the estimated part of the preliminary procurement intention reached with the supplier but no specific procurement contract has been signed; The material requirement planning problem in S2 is to decide the method and quantity of material supply to each factory when the orders that each factory needs to complete within the planning period are known; The input of the problem includes: order information, master production plan information and material information; the order information includes: order quantity and BOM information corresponding to the order; the master production plan information includes: planning period and order scheduling plan of each factory during the planning period; the material information includes: whether it belongs to MPQ/MOQ material attributes, the initial available quantity and supply cost of each material under each supply mode of each factory at the beginning of the planning period; the BOM is a bill of materials, and its data structure is a tree, the root node is the final product, the leaf node is the production raw material, and each node in the middle layer corresponds to an intermediate product; the MPQ is the minimum packaging quantity; the MOQ is the minimum order quantity; The output of the problem includes: the supply decision of each node in the BOM corresponding to each order, the purchase status of each material, and the changes in the local inventory and purchase inventory of each factory during the planning period. The purchase inventory refers to the inventory generated due to the unused part of the purchase, which is calculated independently from the original local inventory. The optimization objectives of the problem include: minimizing the purchase cost during the planning period, minimizing the cost of transferring Open PO during the planning period, and maximizing the inventory usage excluding the purchase inventory during the planning period; The mathematical model in S2 includes: Collections and Indexes: Order Collection The node set contained in the BOM of order i A collection of time nodes within the planning period Factory Collection Material Collection Supplier Collection MPQ Material Collection MOQ Material Collection The root node collection of all BOMs The set of leaf nodes in all BOMs A collection of Open PO transfer nodes in all BOMs A collection of Liability supply nodes in all BOMs A collection of replacement group nodes in all BOMs parameter: D _i demand quantity for order i CM _k Inventory supply cost of material k Inv _0sk 0, the local inventory available for material k in factory s OPO _0sk 0, the Open PO available quantity of material k in plant s PS _0sk 0, the purchase inventory level of material k in factory s Lia _0k The available amount of liability of material k at time 0 α _ijl Material ratio between node j of order i and its child node l MPQ _kv MPQ batch size of material k at supplier v MOQ _kv Minimum order quantity of MOQ material k at supplier v variable: _Xij is the quantity of node j that meets demand i through local inventory and remote inventory transfer _{Yij is} the number of nodes j that meet demand i by manufacturing _Zij is the quantity of node j that meets demand i through procurement EX _ij The number of nodes j whose demand i is satisfied by Open PO LX _ij is the number of nodes j whose demand i is satisfied by Liability M _ij is the amount of complete satisfaction of node j for demand i S _tsk is the local inventory supply of material k in factory s at time node t ES _tsk Open PO supply of material k in plant s at time node t N _tsk is the inventory consumption of material k in factory s at time node t. VN _tsk is the inventory consumption of material k in factory s at time node t. EN _tsk The consumption of Open PO of material k in factory s at time node t FN _tsk Open PO transfer quantity of material k in factory s at time node t GN _tsk is the stock transfer quantity of material k in factory s at time node t. P _tsk is the purchase supply of material k in factory s at time node t LS _tk is the available supply of material k at time node t. LN _tkLiability consumption of material k at time node t Inv _tsk is the available inventory of material k in factory s at time node t, t≥1 OPO _tsk Open PO availability of material k in plant s at time node t, t≥1 PP _tskv is the purchase volume of MPQ/MOQ material k from supplier v in factory s at time node t BZ _tskv is the purchase batch of MPQ material k from supplier v at time node t, in plant s, integer variable PS _tsk is the purchase inventory level of material k in factory s at time t Objective function: min J ₁ +J ₂ -J ₃ (1) constraint: BZ _tskv ∈N (27) _{Xij , Yij} , _Zij ,EXij, _{LXij ,} Mij,Stsk _{, EStsk} , _{Ntsk , VNtsk} ,ENtsk, _FNtsk , _GNtsk , _Ptsk , _LStk , _LNtk , _PPtskv , PS _tsk ≥0(28) Variable part: _Xij , _Yij , _Zij , _EXij , _LXij correspond to the supply decision of each node; _PPtskv , _BZtskv correspond to the purchase decision of materials; _Invtsk , _PStsk correspond to the inventory availability and purchase inventory level during the planning period; Objective function and constraint part: Formula (2) is the sum of the purchase costs of all materials; Formula (3) is the sum of the OpenPO transfer costs of all materials; Formula (4) is the sum of the local inventory levels at each moment; Formulas (2)-(4) all contain the time gradient multiplier (T+1-t). Formulas (2) and (3) are the minimization quantities, and Formula (4) is the maximization quantity. Therefore, the right sides of Formulas (2) and (3) are added together, and then the right side of Formula (4) is subtracted to obtain the uniform minimization objective function Formula (1). At the same time, the time gradient multiplier is used to impose a soft constraint of "the later the cost is generated, the better". 2. The method according to claim 1, characterized in that said S3 specifically comprises: S31. Change the type of integer variable BZ _tskv from Integer to Continuous and relax it to a linear variable At this point, the model becomes a pure linear programming model that does not contain integer variables; S32. Solve the relaxed linear variables using commercial solvers The solution result is recorded using the dictionary BZ ^relax . The solution result is an infeasible solution to the original problem. The solution result is further processed using a heuristic method to obtain the final MPQ material procurement batch, which is recorded as Using the dictionary BZ ^heur record, the heuristic method is based on the Traverse the purchase batches of MPQ materials from various suppliers in chronological order; S33. The remaining decision variables are linear variables in the original problem. After solving the relaxed pure linear programming model and obtaining the result, they are directly used as the solution to the original problem. 3. The method according to claim 2, characterized in that the input of the heuristic method is a BZ ^relax dictionary obtained by solving a pure linear programming model, and the output is a BZ ^heur dictionary obtained by the heuristic method that records feasible solutions to the original problem, and the heuristic method is used in S32 to further process the solution result, specifically comprising: For each factory and each MPQ material, set a variable rest with an initial value of 0. Use this variable to record the remaining value of the corresponding material in the corresponding factory after meeting the current demand during the traversal process. If the supply is not enough to meet the next traversed demand, new purchases are required. Otherwise, no new purchases are required and the corresponding supply is deducted from rest. Further traversal: For each moment and each supplier, set a variable PlanPurchase, which represents the original planned purchase quantity of each material purchased by each factory from each supplier at each moment, which is also the purchase quantity of each MPQ material obtained by solving the pure linear programming model. The original planned purchase quantity is equal to the purchase quantity obtained by solving the pure linear programming model. Multiply by the minimum packaging quantity of each material at each supplier, and then round up. If the rest of the current material in the current factory is greater than or equal to the original planned purchase quantity, no new purchase is made, and the corresponding subscript variable is set. If it is 0, it means that the batch of materials purchased by the corresponding factory from the supplier at the current moment is 0, and the original planned purchase quantity is deducted from rest. Otherwise, a variable Lack is set to indicate that rest does not meet the missing part of the supply, which is equal to the original planned supply minus rest. At this time, the corresponding subscript variable It is equal to the ratio of Lack to the minimum packaging quantity of each material at each supplier, rounded up. After a new purchase, the value of the variable rest is updated. The updated value of the variable rest is equal to the previous remaining quantity rest plus the heuristic purchase batch multiplied by the minimum packaging quantity minus the original planned purchase quantity. Repeat the above cycle until all variables After assignment, the output dictionary BZ ^heur is a set of feasible solutions for the integer variable BZ _tskv in the original problem. 4. The method according to claim 1, characterized in that the method further comprises: For small or medium scale cases, the mathematical model is solved using commercial solvers. 5. A computing device for material requirement planning problems in enterprise resource planning, characterized in that the device comprises: The determination module is used to summarize the universal material management needs of manufacturing enterprises and determine the material supply method; Establish a module for comprehensive analysis of material management logic and establish a mathematical model of the material requirement planning problem using mixed integer programming techniques based on the supply mode of the material; A solution module, for large-scale calculation examples, relaxes integer variables in the mathematical model into linear variables, transforms the mathematical model into a pure linear programming model, and uses a commercial solver combined with a heuristic method to obtain a final material procurement decision; The determination module is specifically used for: On the basis of local inventory supply, manufacturing supply, and procurement supply, remote inventory transfer, OpenPO supply, and liability supply were added. The final material supply methods include five supply methods: inventory supply including local inventory supply and remote inventory transfer, manufacturing supply, procurement supply, Open PO supply, and liability supply. The Open PO supply refers to the part of the purchased materials that have been shipped but not yet arrived after the procurement contract has been signed. The liability supply refers to the estimated part of the preliminary procurement intention reached with the supplier but no specific procurement contract has been signed; The material requirement planning problem is to make decisions on the method and quantity of material supply to each factory when the orders that each factory needs to complete within the planning period are known; The input of the problem includes: order information, master production plan information and material information; the order information includes: order quantity and BOM information corresponding to the order; the master production plan information includes: planning period length and order scheduling plan of each factory during the planning period; the material information includes: whether it belongs to MPQ/MOQ material attributes, the initial available quantity and supply cost of each material under each supply mode of each factory at the beginning of the planning period; the BOM is a bill of materials, and its data structure is a tree, the root node is the final product, the leaf node is the production raw material, and each node in the middle layer corresponds to an intermediate product; the MPQ is the minimum packaging quantity; the MOQ is the minimum order quantity; The output of the problem includes: the supply decision of each node in the BOM corresponding to each order, the purchase status of each material, and the changes in the local inventory and purchase inventory of each factory during the planning period. The purchase inventory refers to the inventory generated due to the unused part of the purchase, which is calculated independently from the original local inventory. The optimization objectives of the problem include: minimizing the purchase cost during the planning period, minimizing the cost of transferring Open PO during the planning period, and maximizing the inventory usage excluding purchase inventory during the planning period; The mathematical model includes: Collections and Indexes: Order Collection The node set contained in the BOM of order i A collection of time nodes within the planning period Factory Collection Material Collection Supplier Collection MPQ Material Collection MOQ Material Collection The root node collection of all BOMs The set of leaf nodes in all BOMs A collection of Open PO transfer nodes in all BOMs A collection of Liability supply nodes in all BOMs A collection of replacement group nodes in all BOMs parameter: D _i demand quantity for order i CM _k Inventory supply cost of material k Inv _0sk 0, the local inventory available for material k in factory s OPO _0sk 0, the Open PO available quantity of material k in plant s PS _0sk 0, the purchase inventory level of material k in factory s Lia _0k The available amount of liability of material k at time 0 α _ijl Material ratio between node j of order i and its child node l MPQ _kv Batch size of MPQ material k at supplier v MOQ _kv Minimum order quantity of MOQ material k at supplier v variable: _Xij is the quantity of node j that meets demand i through local inventory and remote inventory transfer _{Yij is} the number of nodes j that meet demand i by manufacturing _Zij is the quantity of node j that meets demand i through procurement EX _ij The number of nodes j whose demand i is satisfied by Open PO LX _ij is the number of nodes j whose demand i is satisfied by Liability M _ij is the amount of complete satisfaction of node j for demand i S _tsk is the local inventory supply of material k in factory s at time node t ES _tsk Open PO supply of material k in plant s at time node t N _tsk is the inventory consumption of material k in factory s at time node t. VN _tsk is the inventory consumption of material k in factory s at time node t. EN _tsk The consumption of Open PO of material k in factory s at time node t FN _tsk Open PO transfer quantity of material k in factory s at time node t GN _tsk is the stock transfer quantity of material k in factory s at time node t. P _tsk is the purchase supply of material k in factory s at time node t LS _tk is the available supply of material k at time node t. LN _tkLiability consumption of material k at time node t Inv _tsk is the available inventory of material k in factory s at time node t, t≥1 OPO _tsk Open PO availability of material k in plant s at time node t, t≥1 PP _tskv is the purchase volume of MPQ/MOQ material k from supplier v in factory s at time node t BZ _tskv is the purchase batch of MPQ material k from supplier v at time node t, in plant s, integer variable PS _tsk is the purchase inventory level of material k in factory s at time t Objective function: min J ₁ +J ₂ -J ₃ (1) constraint: BZ _tskv ∈N (27) _{Xij , Yij} , _Zij ,EXij, _{LXij ,} Mij,Stsk _{, EStsk} , _{Ntsk , VNtsk} ,ENtsk, _FNtsk , _GNtsk , _Ptsk , _LStk , _LNtk , _PPtskv , PS _tsk ≥0(28) Variable part: _Xij , _Yij , _Zij , _EXij , _LXij correspond to the supply decision of each node; _PPtskv , _BZtskv correspond to the purchase decision of materials; _Invtsk , _PStsk correspond to the inventory availability and purchase inventory level during the planning period; Objective function and constraint part: Formula (2) is the sum of the purchase costs of all materials; Formula (3) is the sum of the OpenPO transfer costs of all materials; Formula (4) is the sum of the local inventory levels at each moment; Formulas (2)-(4) all contain the time gradient multiplier (T+1-t). Formulas (2) and (3) are the minimization quantities, and Formula (4) is the maximization quantity. Therefore, the right sides of Formulas (2) and (3) are added together, and then the right side of Formula (4) is subtracted to obtain the uniform minimization objective function Formula (1). At the same time, the time gradient multiplier is used to impose a soft constraint of "the later the cost is generated, the better". 6. An electronic device comprising a processor and a memory, wherein the memory stores instructions, wherein the instructions are loaded and executed by the processor to implement the calculation method for material requirement planning problems in enterprise resource planning as described in any one of claims 1-4. 7. A computer-readable storage medium, wherein instructions are stored in the storage medium, wherein the instructions are loaded and executed by a processor to implement the calculation method for material requirement planning problems in enterprise resource planning as described in any one of claims 1 to 4.