CN109492810A

CN109492810A - A method of solving greening supply chain collaborative design problem

Info

Publication number: CN109492810A
Application number: CN201811336950.6A
Authority: CN
Inventors: 郭羽含; 姜彦吉; 胡芳霞; 王光; 杨帆
Original assignee: Liaoning Technical University
Current assignee: Liaoning Technical University
Priority date: 2018-11-12
Filing date: 2018-11-12
Publication date: 2019-03-19

Abstract

The present invention provides a kind of method for solving greening supply chain collaborative design problem, is related to supply chains design field.Specific step is as follows by the present invention: step 1: the quantity of product or raw material being converted to corresponding means of transport quantity, using cost, carbon emission, water consumption as optimization aim, establishes the supply chain mathematical model of the quaternary structure of integrated manufacturer's selection and Transportation Planning；The mathematical model includes objective function and qualifications；Step 2: the freight volume between optimal supply chain network structure and the structure every two vertex being obtained according to compound out of kilter method, totle drilling cost is obtained according to freight volume and objective function.This method effectively selects optimal supply chain participant combination on the basis of considering cost and environment, and accurately calculates the traffic program between participant, provides the solution of high quality and high efficiency for complexity supply chain.

Description

A method of solving greening supply chain collaborative design problem

Technical field

The present invention relates to supply chains design fields more particularly to a kind of solution greening supply chain collaborative design to ask The method of topic.

Background technique

Supply chain is the network being made of supplier, production plant, center for distribution, client and shipping channels, for obtaining It takes raw material and is translated into product, finally by these product distributions to client.Network Design of Supply Chain (Supply chain Network design, SCND) be optimal facility (supplier, the production plant and center for distribution) position of selection, quantity and Capacity configuration is in important strategic position in supply chain management.Greening supply chain network design (Green supply Chain network design, GSCND) need to comprehensively consider in the design process environmental factor (carbon emission, water pollution), make It is minimum to obtain entire supply chain process effect on environment, level of resources utilization highest.Greening supply chain collaborative design problem is generally adopted It is solved with two step approach, initially sets up the mathematical model of the problem, then the model is carried out using optimization or approximate algorithm It solves.But existing method fails during supply chain design, effectively comprehensively considers carbon emission, water consumption, cost, Establish the mathematical model based on global optimization.Further, since greening supply chain collaborative design problem model is complicated, it is existing optimal It is lower to change method for solving efficiency, large-scale example can not be solved in a short time；And then there is second-rate, the nothing of solution in approximate algorithm Method provides the problem of high quality solution.

Summary of the invention

The technical problem to be solved by the present invention is in view of the above shortcomings of the prior art, provide a kind of solution greening supply chain The method of collaborative design problem, this method effectively select optimal supply on the basis of considering cost and environment Chain participant combination, and the traffic program between participant is accurately calculated, the solution of high quality and high efficiency is provided for complexity supply chain Certainly scheme；

In order to solve the above technical problems, the technical solution used in the present invention is:

A method of greening supply chain collaborative design problem is solved, is included the following steps:

Step 1: the quantity of product or raw material being converted into corresponding means of transport quantity, is disappeared with cost, carbon emission, water Consumption is used as optimization aim, establishes the supply chain mathematical model of the quaternary structure of integrated manufacturer's selection and Transportation Planning；The mathematics Model includes objective function and qualifications, and the formula of the objective function is as follows:

Wherein, i represents vendor number, i ∈ I；J represents manufacturer's number, j ∈ J；K represents retail trader's number, k ∈ K；l Represent customer number, l ∈ L；M represents raw material number, m ∈ M；N representative products number, n ∈ N；CSM_imRepresentative is adopted from supplier i Purchase the cost of a unit raw material m；CPP_jnRepresent the cost that manufacturer j produces a unit product n；ESM_imIt is raw to represent supplier i Produce carbon emission amount caused by a unit raw material m；EPP_jnIt represents manufacturer j and produces carbon emission caused by a unit product n Amount；WSM_imIt represents supplier i and produces water consumed by a unit raw material m；WPP_jnIt represents manufacturer j and produces unit production Water consumed by product n；DSP_ijRepresent the distance between supplier i and manufacturer j；DPD_jkRepresent manufacturer j and retail trader k The distance between；DDC_klRepresent the distance between retail trader k and client l；CMP_jRepresent operation cost in manufacturer's j period； CMD_kRepresent operation cost in the retail trader k period；ET_spRepresent the cost of 1 kilometer of Freight Transport；ET_spRepresent a lorry Carbon emission caused by 1 kilometer of transport；A, b respectively represent conversion weight when carbon emission, water consumption to be converted to cost；sp_j It indicates whether to select manufacturer j as supply chain cooperation manufacturer, 1 represents selection, and 0 representative does not select；sd_kIndicate whether selection point It sells quotient k and represents selection as supply chain cooperation manufacturer, 1,0 representative does not select；aspm_ijmIt transports from supplier i to manufacturer j's The quantity of raw material m；apdp_jknIt transports from manufacturer j to the quantity of the product n of retail trader k；aSP_ijFormer material is transported from supplier i Expect to the lorry quantity of manufacturer j；aPD_jkThe lorry quantity of product to retail trader k is transported from manufacturer j；aDC_klFrom retail trader k Transport the lorry quantity of product to client l；

The qualifications include precondition and constraint condition；

The precondition are as follows: the order of all clients must all meet；Supplier constrains with the supply upper limit, raw Business men has production upper limit constraint, and retail trader has storage upper limit constraint；Each manufacturer, operation cost is solid in retail trader's period It is fixed；Different raw material or product can be merged into same lorry；

The constraint condition are as follows:

Constraint between lorry quantity and raw material, product quantity:

Wherein,ATM_mRaw material m can be delivered most by representing a lorry Big quantity；ATP_nThe maximum quantity of product n can be delivered by representing a lorry；adcp_klnRepresentative is transported from retail trader k to client l Product n quantity；

The order demand of client must satisfy constraint:

Wherein,D_lnRepresent the order total amount of client's l ordering products n；

Retail trader inventory constraint:

Wherein,UBStock_knRetail trader k is represented to the maximum inventory of product n；

Manufacturer produces force constraint:

Wherein,UBPP_jnManufacturer j is represented to the largest production quantity of product n；

Supplier is for stress constraint:

WhereinUBSM_imRepresent the maximum quantity for the raw material m that supplier i can be provided；

Retail trader's amount of stocking up, shipment amount are consistent:

Wherein,

Materials procurement quantity and production quantity keep proportion consistent:

∑_i∈Iaspm_ijm=MPR_mn×∑_k∈Kapdp_jkn (10)

Wherein,MPR_mnRepresent the quantitative relation ratio between raw material m and product n Example；

Nonnegative integer and binary system constraint:

sp_j∈{0,1}(17)

sd_k∈{0,1}(18)

Wherein,

Step 2: being obtained between optimal supply chain network structure and the structure every two vertex according to compound out of kilter method Freight volume obtains totle drilling cost according to objective function；

The compound out of kilter method is to be integrated by the alternative manufacturer to supply quotient sheaf, raw vendor level and distributor level Assessment obtains the manufacturer with preferably assessment score；The manufacturer includes supply quotient sheaf, production quotient sheaf, distributor level；It enumerates The all possible combinations being made of these manufacturers delete the candidate solution for not being able to satisfy customer order wherein as candidate disaggregation；And To remaining each candidate solution calculating target function approximation, the smallest candidate solution of selection target function approximation is as final confession Chain network structure is answered, branch and bound method is reapplied to calculate the freight volume between every two vertex, freight volume is brought into target Totle drilling cost is acquired in function.

Specific step is as follows for the step 2:

Step 2.1: the high supply quotient set S of comprehensive score, production quotient set P, distribution are obtained according to partner's out of kilter method Quotient set D；

Partner's out of kilter method is assessment score to be calculated for candidate manufacturer, and obtain each candidate manufacturer using weighting adduction Comprehensive score；Using the top k algorithm based on quicksort, the high preceding η supplier of comprehensive score, raw factory are selected respectively Quotient and retail trader obtain supply quotient set S, production quotient set P, distribution quotient set D；

Step 2.2: candidate disaggregation CS is obtained according to candidate solution enumeration；

The candidate solution enumeration be preferentially after supply quotient set S, production quotient set P, distribution quotient set D and client Set C；It finds out respectively and is made of set S ', P ', D ' all subsets in addition to empty set of S, P, D, the set C ' that the complete or collected works of C are constituted, Then all candidate solutions of GSCND are obtained by the orderly cartesian product of S ', P ', D ', C '；

Step 2.3: infeasible candidate solution is deleted according to infeasible solution deletion algorithm；

The infeasible solution deletion algorithm is to be directed to supply quotient sheaf, production quotient sheaf, distributor level respectively according to precondition Judged, if this layer of manufacturer's ability is not able to satisfy all customer order demands, the candidate solution be it is invalid, delete this Trivial solution；The input data of the algorithm is S ', P ', D ', and output data is S ", P ", D ", and the S ", P ", D " respectively indicate deletion Supply quotient set, production quotient set, distribution quotient set after infeasible solution；

Step 2.4: the filter algorithm based on objective function approximation obtains the totle drilling cost of supply chain network；

The filter algorithm based on objective function approximation is filtered remaining candidate according to obtained in step 2.3 Solution, to each candidate solution calculating target function approximation, selection target function approximation is the smallest to be deconstructed into final supply chain Network；It reapplies branch and bound method and obtains the freight volume between adjacent two layers vertex, freight volume is brought into objective function and is acquired Totle drilling cost.

Specific step is as follows for the step 2.1:

Step 2.1.1: evaluation index when listing supplier, manufacturer, retail trader respectively preferentially；To each index, press It is different according to its shared specific gravity in the value of objective function, assign different weights；

Step 2.1.1.1: the vendors' evaluating index includes each cost of raw, each raw material carbon emission pair The cost answered, the corresponding cost of each raw material water consumption are transported from supplier to the cost of manufacturer；The specific method is as follows:

Enable PN_nIndicate the order total amount of product n, MN_mRepresent the total demand of raw material m；Formula is as follows:

Each cost of raw:

(∑_i∈ICSM_im/|I|)×MN_m (21)

The corresponding cost of each raw material carbon emission:

a×(∑_i∈IESM_im/|I|)×MN_m (22)

The corresponding cost of each raw material water consumption:

a×(∑_i∈IWSM_im/|I|)×MN_m (23)

It transports from supplier to the cost of manufacturer:

Select a kind of cost of raw material as with reference to cost, weight is set as 1；The weight of other indices is according to it The ratio of corresponding cost and reference cost determines；

The weight for enabling the first cost of raw material is 1, i.e. m=1；The cost weight WSC of raw material m_m, raw material m carbon Discharge weight WSE_m, raw material m water consumption weight WSW_m, it is as follows with the calculation formula of manufacturer's distance weighting WSP:

Step 2.1.1.2: the evaluation index of the manufacturer includes the cost of each production of manufacturer, each production The corresponding cost of carbon emission, the corresponding cost of each production water consumption, operation cost, from supplier transport to manufacturer at Originally, transport from manufacturer to retail trader's cost；

Each index average value is taken, it is calculated separately and is produced from supplier's transporting raw materials to manufacturer, production product and transport Cost caused by product to retail trader's stage；The weight for enabling one of production cost is 1, the weights of other indexs according to Its corresponding cost is determined with the ratio referring to cost；

The cost of each production:

(∑_j∈JCPP_jn/|J|)×PN_n (29)

The corresponding cost of each production carbon emission:

a×(∑_j∈JEPP_jn/|J|)×PN_n (30)

The corresponding cost of each production water consumption:

b×(∑_j∈JWPP_jn/|J|)×PN_n (31)

Operation cost:

It transports from supplier to manufacturer's cost:

It transports from manufacturer to retail trader's cost:

The weight for enabling the first production cost is 1, i.e. n=1；The production cost weight WPC of product n_n, product n Produce carbon emission weight WPE_n, product n production water consumption weight WPW_n, operation cost weight WPM, with supplier's distance weighting It is WPS, as follows with the calculation formula of retail trader distance weighting WPD:

Step 2.1.1.3: the evaluation index of retail trader include: operation cost, the cost transported from manufacturer to retail trader, It transports from retail trader to the cost of client；

Each index average value is taken, it is calculated separately from manufacturer and transports product to retail trader again to caused by client's stage Cost is averaged and is calculated；The weight for enabling operation cost is 1, and the weight of other indexs is according to its corresponding cost and reference The ratio of cost determines；

Operation cost:

It transports from manufacturer to the cost of retail trader:

It transports from retail trader to the cost of client:

Enabling the weight WDM of operation cost is 1, and the calculating with manufacturer's distance weighting WDP and client's distance weighting WDC is public Formula is as follows:

WDM=1 (44)

Step 2.1.2: comprehensive score is carried out to manufacturer respectively；

Each evaluation index same level manufacturer is compared respectively, with 0-1 matrix storage comparative result, ranks are indicated Manufacturer, matrix element indicate that row whether better than column, is that element value takes 1, otherwise takes 0；According still further to the weight of each index, to 0-1 Matrix is weighted addition, obtains score matrix, sums to the matrix by rows, obtains the comprehensive score of the manufacturer；Specific steps It is as follows:

Step 2.1.2.1: the comprehensive score of supplier；

Each cost of raw material compares matrix:

A_m=[α_oq]_I×I (47)

Wherein, α_oqRepresent matrix A_mIn element；o,q∈I,CSM_omIt represents from supplier o and purchases a unit raw material m's Cost；CSM_qmRepresent the cost that a unit raw material m is purchased from supplier q；

Each raw material carbon emission compares matrix:

B_m=[β_oq]_I×I (48)

Wherein, β_oqRepresent matrix B_mIn element；ESM_omIt represents supplier o and produces carbon caused by a unit raw material m Discharge amount；ESM_qmIt represents supplier q and produces carbon emission amount caused by a unit raw material m；

Each raw material water consumption compares matrix:

Q_m=[ρ_oq]_I×I (49)

Wherein, ρ_oqMatrix Q_mIn element；WSM_omIt represents supplier o and produces water consumed by a unit raw material m； WSM_qmIt represents supplier q and produces water consumed by a unit raw material m；

With each manufacturer's distance versus matrix:

W_j=[μ_oq]_I×I (50)

Wherein, μ_oqRepresent matrix W_jIn element；DSP_ojRepresent the distance between supplier o and manufacturer j；DSP_qjGeneration The distance between table supplier o and manufacturer j；

Addition is weighted according to the weight being calculated in step 2.1.1.1 to above-mentioned comparison matrix, obtains supplier Comparison score matrix between two-by-two:

The comprehensive score formula of supplier is obtained by row summation to matrix T1 again:

The comprehensive score set TS1 of all suppliers is obtained by above-mentioned formula；

Step 2.1.2.2: the comprehensive score of manufacturer；

Each production Cost comparisons matrix:

E_n=[e_uv]_|J|×|J| (53)

Wherein, e_uvRepresent matrix E_nIn element；u,v∈J；CPP_unRepresent manufacturer u produce a unit product n at This；CPP_vnRepresent the cost that manufacturer v produces a unit product n；

Each production carbon emission compares matrix:

F_n=[f_uv]_|J|×|J| (54)

Wherein, f_uvRepresent matrix F_nIn element；EPP_unIt represents manufacturer u and produces the row of carbon caused by a unit product n High-volume；EPP_vnIt represents manufacturer v and produces carbon emission amount caused by a unit product n；

Each production water consumption compares matrix:

G_n=[g_uv]_|J|×|J| (55)

Wherein, g_uvRepresent matrix G_nIn element；WPP_unIt represents manufacturer u and produces water consumed by a unit product n； WPP_vnIt represents manufacturer v and produces water consumed by a unit product n；

Operation cost compares matrix:

H=[h_uv]_|J|×|J| (56)

Wherein, h_uvRepresent the element in matrix H；CMP_uRepresent operation cost in manufacturer's u period；CMP_vRepresent manufacturer Operation cost in the v period；

With the set S distance versus matrix of supplier:

O_i′=[δ_uv]_|J|×|J| (57)

Wherein, δ_uvRepresent matrix O_i′In element；S represents the set of the supplier obtained using top k algorithm；I '= 1,2,…,η；DSP_i′uRepresent the distance between supplier i ' and manufacturer u；DSP_i′vIt represents between supplier i ' and manufacturer v Distance；

With each retail trader's distance versus matrix:

U_k=[ε_uv]_|J|×|J| (58)

Wherein, ε_uvRepresent matrix U_kIn element；DPD_ukThe distance between manufacturer u and retail trader k；DPD_vkManufacturer v The distance between retail trader k；

Addition is weighted according to the weight being calculated in step 2.1.1.2 to above-mentioned comparison matrix, obtains manufacturer Comparison score matrix between two-by-two:

The comprehensive score formula of manufacturer is obtained by row summation to matrix T2 again:

The comprehensive score set TS2 of all manufacturers is obtained by above-mentioned formula；

Step 2.1.2.3: the comprehensive score of retail trader；

Operation cost compares matrix:

L '=[θ_wy]_|K|×|K| (61)

Wherein, θ_wyRepresent matrix L ' in element；w,y∈K；CMD_wRepresent operation cost in the retail trader w period；CMD_yGeneration Operation cost in the table retail trader y period；

With the set P distance versus matrix of manufacturer:

Wherein, x_wyRepresent matrix X_j′In element；P represents the production quotient set obtained using top k algorithm；J '=1, 2,…,η；DPD_j′wRepresent the distance between manufacturer j ' and retail trader w；DPD_j′yIt represents between manufacturer j ' and retail trader y Distance；

With each client's distance versus matrix:

V_l=[z_wy]_|K|×|K| (63)

Wherein, z_wyRepresent matrix V_lIn element；DDC_wlRepresent the distance between retail trader w and client l；DDC_ylIt represents The distance between retail trader y and client l；

Addition is weighted according to the weight being calculated in step 2.1.1.3 to above-mentioned comparison matrix, obtains retail trader Comparison score matrix between two-by-two:

The comprehensive score formula of retail trader is obtained by row summation to matrix T3 again:

The comprehensive score set TS3 of all retail traders is obtained by above-mentioned formula；

Step 2.1.3: the comprehensive score obtained according to step 2.1.2, the top k algorithm based on quicksort are integrated Score high preceding η supply quotient set S, production quotient set P, distribution quotient set D；Specific step is as follows:

Step 2.1.3.1: a base value is found in supplier comprehensive score set TS1；The base value chooses number The value of the last one element in group；

Step 2.1.3.2: element bigger than base value in the set is placed in its left side, the member smaller than base value by subregion Element is placed in its right side；

Step 2.1.3.3: judging left siding-to-siding block length, is such as equal to η, program determination, η element before exporting；As left section is long Degree is greater than η, then repeats step 2.3.1.1 and step 2.3.1.2 to left section, until program determination；As left siding-to-siding block length is less than η then repeats step 2.3.1.1 and step 2.3.1.2 to right section, until program determination；

Step 2.1.3.4: the η element that step 2.1.3.3 is exported is denoted as supply quotient set S；

Step 2.1.3.5: a base value is found in manufacturer's comprehensive score set TS2；Execute step 2.1.3.2 and Step 2.1.3.3, η element before exporting are denoted as production quotient set P；

Step 2.1.3.6: a base value is found in retail trader comprehensive score set TS3；Execute step 2.1.3.2 and Step 2.1.3.3, η element before exporting are denoted as distribution quotient set D.

Specific step is as follows for the step 2.2:

Step 2.2.1: construction setC '={ C }, In 2^S、2^P、2^DThe respectively power set of set S, P, D；

Step 2.2.2: obtaining set S ', P ', D ' according to bit arithmetic, wherein | S ' |=2^I- 1, | P ' |=2^J- 1, | D ' |= 2^K- 1, | C ' |=1, to obtain candidate disaggregation CS:

CS=(2^I-1)×(2^J-1)×(2^K-1) (66)

Specific step is as follows for the step 2.3:

Step 2.3.1: supply quotient sheaf: for the supplier S in S '_iIfThen by S_iIt is added to set S "；

Step 2.3.2: production quotient sheaf: for the manufacturer P in P '_iIfThen By P_iIt is added to set P "；

Step 2.3.3: distributor level: for the manufacturer D in D '_iIf Then by D_iIt is added to set D ".

The specific steps of objective function approximation are solved in the step 2.4 are as follows:

The cost CSM of each raw material of supplier in remaining candidate solution_m, carbon emission ESM_m, water consumption WSM_mCalculation formula such as Under:

The cost CPP of each production of manufacturer in remaining candidate solution_n, carbon emission EPP_n, water consumption WPP_nCalculation formula It is as follows:

Distance Dis, the Dis in remaining candidate solution between manufacturer include that supplier transports to manufacturer, manufacturer's transport It transports to retail trader, retail trader to lorry quantity TSP, TPD, TDC of client, calculation formula is as follows:

Objective function approximation Obj_apprFormula are as follows:

The beneficial effects of adopting the technical scheme are that a kind of solution greening supply chain association provided by the invention With the method for design problem；This method using cost, carbon emission, water consumption as optimization aim, establish integrated manufacturer's selection and The supply chain mathematical model of the quaternary structure of Transportation Planning.Meanwhile an effective method for solving is proposed, former problem is divided into Partner selection subproblem and Transportation Planning subproblem, the method approached using multistep are latent by the way that multiple strobe utilities removals are arranged Infeasible solution, and calculate an approximate objective function value further to be selected.Finally, selection has minimum close Like the candidate solution of value, the freight volume between connection vertex is determined using branch and bound method, and calculates final goal functional value. Experiments verify that the algorithm can provide the solution of high-quality and high-efficiency for complicated supply chain.

Detailed description of the invention

Fig. 1 is the method flow diagram provided in an embodiment of the present invention for solving greening supply chain collaborative design problem；

Fig. 2 is supply chain network structure chart provided in an embodiment of the present invention；

Fig. 3 is compound out of kilter method main thought figure provided in an embodiment of the present invention；

Specific embodiment

With reference to the accompanying drawings and examples, specific embodiments of the present invention will be described in further detail.Implement below Example is not intended to limit the scope of the invention for illustrating the present invention.

The method of the present embodiment is as described below.

As shown in Fig. 2, using digraph G=<V, one level Four greening supply chain network of E>simulation, each vertex v * ∈ V A potential supply chain partner (such as supplier) is represented, vertex set is made of four kinds of different types of affiliates: supply Quotient, manufacturer, retail trader and client, each edge in Fig. 2 represent the quantity of transporting raw materials or product between vertex, and only The vertex of two adjacent layers can connect (such as supply quotient sheaf and production quotient sheaf).Its target is to select to close from corresponding level The manufacturer of suitable quantity, to meet the order of each client and be no more than the energy power limit of each manufacturer, and determining transport quantity (vi, vj)。

In order to which supply-chain integration is included in environment influence, this method considers production other than considering cost The carbon emission that is generated in transportational process, water consumption founding mathematical models.In addition, product or raw material are usual in practical logistics It is transported from a website to another website by certain means of transportation.Therefore, according to the quantity of means of transport rather than product Or the quantity calculating total transport cost of raw material is more accurate.So this method passes through constraint condition for product or the number of raw material Amount is converted to corresponding means of transport quantity, and ensures high charging ratio.Then, total transport is calculated based on the quantity of means of transport Cost, this is entirely different with previous method.

A method of greening supply chain collaborative design problem being solved, as shown in Figure 1, including the following steps:

Wherein, i represents vendor number, i ∈ I；J represents manufacturer's number, j ∈ J；K represents retail trader's number, k ∈ K；l Represent customer number, l ∈ L；M represents raw material number, m ∈ M；N representative products number, n ∈ N；CSM_imRepresentative is adopted from supplier i Purchase the cost of a unit raw material m；CPP_jnRepresent the cost that manufacturer j produces a unit product n；ESM_imIt is raw to represent supplier i Produce carbon emission amount caused by a unit raw material m；EPP_jnIt represents manufacturer j and produces carbon emission caused by a unit product n Amount；WSM_imIt represents supplier i and produces water consumed by a unit raw material m；WPP_jnIt represents manufacturer j and produces unit production Water consumed by product n；DSP_ijRepresent the distance between supplier i and manufacturer j；DPD_jkRepresent manufacturer j and retail trader k The distance between；DDC_klRepresent the distance between retail trader k and client l；CMP_jRepresent operation cost in manufacturer's j period； CMD_kRepresent operation cost in the retail trader k period；CT_SpRepresent the cost of 1 kilometer of Freight Transport；ET_spRepresent a lorry Carbon emission caused by 1 kilometer of transport；A, b respectively represent conversion weight when carbon emission, water consumption to be converted to cost；sp_j It indicates whether to select manufacturer j as supply chain cooperation manufacturer, 1 represents selection, and 0 representative does not select；sd_kIndicate whether selection point It sells quotient k and represents selection as supply chain cooperation manufacturer, 1,0 representative does not select；aspm_ijmIt transports from supplier i to manufacturer j's The quantity of raw material m；apdp_jknIt transports from manufacturer j to the quantity of the product n of retail trader k；aSP_ijFormer material is transported from supplier i Expect to the lorry quantity of manufacturer j；aPD_jkThe lorry quantity of product to retail trader k is transported from manufacturer j；aDC_klFrom retail trader k Transport the lorry quantity of product to client l；

Cost in the model include cost of raw, production cost, supplier to manufacturer transport at Sheet, the transportation cost of manufacturer to retail trader, retail trader to client transportation cost；Carbon emission includes that raw material production process produces The discharge that raw discharge, production discharge and cargo transport generates in the process；Water consumption include raw material production consumption and Production consumption.

Qualifications include precondition and constraint condition；

The constraint condition are as follows:

Constraint between lorry quantity and raw material, product quantity:

Wherein,ATM_mThe maximum of raw material m can be delivered by representing a lorry Quantity；ATP_nThe maximum quantity of product n can be delivered by representing a lorry；adcp_klnRepresentative is transported from retail trader k to client l's The quantity of product n；

The order demand of client must satisfy constraint:

Retail trader inventory constraint:

Manufacturer produces force constraint:

Supplier is for stress constraint:

Retail trader's amount of stocking up, shipment amount are consistent:

Wherein,

∑_i∈Iaspm_ijm=MPR_mn×∑_k∈Kapdp_jkn (10)

Nonnegative integer and binary system constraint:

sp_j∈{0,1}(17)

sd_k∈{0,1}(18)

Wherein,

For GSCND, a kind of direct method is exactly to enumerate the combination of all candidate buddies, deletes infeasible combination, Then the freight volume between two vertex is calculated, final choice has the combination of minimum target functional value as optimal solution party Case.However, it is unpractical for calculating all combinations.Therefore, method proposes a kind of effective approximation methods --- and it is compound to select Excellent algorithm, by reducing solution space gradually come the optimal solution of approximation problem.Firstly, to supply quotient sheaf, raw vendor level and retail trader The alternative manufacturer of layer carries out comprehensive assessment, and there is the manufacturer of preferably assessment score to enter and calculate in next step.Then, it enumerates by this The all possible combinations that a little manufacturers are constituted as candidate disaggregation, (i.e. can not by the candidate solution that deletion is not able to satisfy customer order wherein Row solution), an objective function approximation is calculated to remaining each candidate solution, the smallest candidate solution of selection target function approximation is made For final supply chain network structure.Finally, calculating the freight volume between every two vertex using branch and bound method, this is obtained The approximate solution of problem.The subalgorithm applied in the overall structure of this method and each step is as shown in Figure 3；

Specific step is as follows:

Step 2.1.1: evaluation index when listing supplier, manufacturer, retail trader respectively preferentially；To each index, press It is different according to its shared specific gravity in target function value, assign different weights；

Enable PN_nIndicate the order total amount of product n, MN_mRepresent the total demand of raw material m.Then have:

Each cost of raw:

The corresponding cost of each raw material carbon emission:

The corresponding cost of each raw material water consumption:

It transports from supplier to the cost of manufacturer:

The weight for enabling the first cost of raw material (m=1) is 1；The cost weight WSC of raw material m_m, raw material m carbon row Delegate power weight WSE_m, raw material m water consumption weight WSW_m, it is as follows with the calculation formula of manufacturer's distance weighting WSP.

Each index average value is taken, it is calculated separately and is produced from supplier's transporting raw materials to manufacturer, production product and transport Cost caused by product to retail trader's stage.The weight for enabling one of production cost is 1, the weights of other indexs according to Its corresponding cost is determined with the ratio referring to cost；

The cost of each production:

(∑_j∈JCPP_jn/|J|)×PN_n (29)

The corresponding cost of each production carbon emission:

a×(∑_j∈JEPP_jn/|J|)×PN_n (30)

The corresponding cost of each production water consumption:

b×(∑_j∈JWPP_jn/|J|)×PN_n (31)

Operation cost:

It transports from supplier to manufacturer's cost:

It transports from manufacturer to retail trader's cost:

The weight for enabling the first production cost (n=1) is 1.The production cost weight WPC of product n_n, product n life Produce carbon emission weight WPE_n, product n production water consumption weight WPW_n, operation cost weight WPM, with supplier's distance weighting It is WPS, as follows with the calculation formula of retail trader distance weighting WPD.

Each index average value is taken, it is calculated separately from manufacturer and transports product to retail trader again to caused by client's stage Cost is averaged and is calculated.The weight for enabling operation cost is 1, and the weight of other indexs is according to its corresponding cost and reference The ratio of cost determines；

Operation cost:

It transports from manufacturer to the cost of retail trader:

It transports from retail trader to the cost of client:

Enabling the weight WDM of operation cost is 1, and the calculating with manufacturer's distance weighting WDP and client's distance weighting WDC is public Formula is as follows.

WDM=1 (44)

Step 2.1.2: comprehensive score is carried out to manufacturer；

To each evaluation index same level, manufacturer compares two-by-two, and with 0-1 matrix storage comparative result；The equal table of ranks Show manufacturer, matrix element indicates that row represents manufacturer and whether is better than column and represents manufacturer, is that element value takes 1, otherwise takes 0；According still further to every The weight of a index is weighted addition to 0-1 matrix, and Comparison score matrix between obtaining manufacturer two-by-two asks the matrix by rows With obtain the total score of each manufacturer；Specific step is as follows:

Step 2.1.2.1: the comprehensive score of supplier；

Each cost of raw material compares matrix:

A_m=[α_oq]_I×I (47)

Each raw material carbon emission compares matrix:

B_m=[β_oq]_I×I (48)

Each raw material water consumption compares matrix:

Q_m=[ρ oq]_I×I (49)

With each manufacturer's distance versus matrix:

W_j=[μ_oq]_I×I (50)

Step 2.1.2.2: the comprehensive score of manufacturer；

Each production Cost comparisons matrix:

E_n=[e_uv]_|J|×|J| (53)

Each production carbon emission compares matrix:

F_n=[f_uv]_|J|×|J| (54)

Each production water consumption compares matrix:

G_n=[g_uv]_|J|×|J| (55)

Operation cost compares matrix:

H=[h_uv]_|J|×|J| (56)

With the set S distance versus matrix of supplier:

O_i′=[δ_uv]_|J|×|J| (57)

Wherein, δ_uvRepresent matrix O_i′In element；S represents the set of the supplier obtained using top k algorithm；I '= 1,2,…,η；DSO_i′uRepresent the distance between supplier i ' and manufacturer u；DSP_i′vIt represents between supplier i ' and manufacturer v Distance；

With each retail trader's distance versus matrix:

U_k=[ε_uv]_|J|×|J| (58)

Step 2.1.2.3: the comprehensive score of retail trader；

Operation cost compares matrix:

L '=[θ_wy]_|K|×|K| (51)

With the set P distance versus matrix of manufacturer:

With each client's distance versus matrix:

V_l=[z_wy]_|K|×|K| (63)

Specific step is as follows:

CS=(2^I-1)×(2^J-1)×(2^K-1) (66)

The infeasible solution deletion algorithm is to be directed to supply quotient sheaf, production quotient sheaf, distributor level respectively according to precondition Judged, if this layer of manufacturer's ability is not able to satisfy all customer order demands, the candidate solution be it is invalid, delete this Trivial solution；The input data of the algorithm is S ', P ', D ', and output data is S ", P ", D ", and the S ", P ", D " respectively indicate deletion Supply quotient set, production quotient set, distribution quotient set after infeasible solution；Algorithm flow is as follows:

For the GSCND of the medium and above scale, candidate solution quantity be it is very huge, to be found from numerous candidate solutions Optimal solution, it is clear that solution efficiency is very low.Therefore, it method proposes a kind of filter method based on each manufacturer's capacity consistency, deletes Remove a large amount of infeasible candidate solution.According to the two important premises proposed in precondition, it may be assumed that the order of all clients must Must all it meet；There are certain capacity consistency in each supplier, manufacturer, retail trader.

Therefore, can be judged respectively for supply quotient sheaf, production quotient sheaf, distributor level, if this layer of manufacturer's ability It is not able to satisfy all customer order demands, then the candidate solution is invalid.For example, candidate solution S1 S3 | P1 P2 | D1 | C1 C2, If the sum of S1 S3 raw material supply ability is not able to satisfy all customer orders, the candidate solution that all supply quotient sheafs are S1 S3 It is all invalid.Similarly, for producing quotient sheaf, if the sum of the production capacity of P1 P2 is not able to satisfy customer order, all lifes Business men layer is that the candidate solution of P1 P2 is all invalid.And, the stock ability of each retail trader must similarly, for distributor level Customer order must be met.

Based on the thinking, method proposes supplier, manufacturer, three layers of retail trader filter algorithm, wherein inputting number All suppliers for being enumerated according to S ', P ', D ' expression, manufacturer, retail trader's combination set, S ", P ", D " are returning for algorithm Value is returned, indicates filtered manufacturer's composite set.In this way, numerous invalid candidate solutions can be deleted, solution space is reduced.

Step 2.3.3: distributor level: for the manufacturer D in D '_iIf Then by D_iIt is added to set D "；

Solve the specific steps of objective function approximation are as follows:

Each cost of raw material CSM of supplier in remaining candidate solution_m, carbon emission ESM_m, water consumption WSM_mCalculation formula such as Under:

Each production cost CPP of manufacturer in remaining candidate solution_n, carbon emission EPP_n, water consumption WPP_nCalculation formula It is as follows:

Objective function approximation Obj_apprFormula are as follows:

All codes are all made of java realization in the present embodiment, and specific experiment environment configurations are as shown in table 1:

The configuration of 1 experimental situation of table

In the present embodiment | S |=| P |=| D |=| C |=50, preferentially number η takes 5 for manufacturer, obtains supplier through this method 5 manufacturer of top after layer, production quotient sheaf, distributor level synthesis point, as shown in table 2, transporting raw materials or product quantity between manufacturer As shown in table 3, the lorry quantity of transporting raw materials or product is as shown in table 4 between manufacturer；

2 manufacturer of table preferentially result

Transporting raw materials or product quantity between 3 manufacturer of table

	P18	D44
			S27	3200	---
S35	384376	---
			P18	---	387576

The lorry quantity of transporting raw materials or product between 4 manufacturer of table

	P18	D44
			S27	4	---
S35	481	---
			P18	---	776

(25-1) can be enumerated by this 15 manufacturers³=29791 candidate solutions, wherein infeasible by deleting 4561 Xie Hou, remaining 25230 candidate solutions, successively calculates the objective function approximation of each candidate solution, obtains objective function approximation The smallest manufacturer's group is combined into S27S35P18D44, carries out model solution again to the supply chain, and obtaining target function value is 4441113.S27S35P18D47 is combined into using optimal manufacturer's group that CPLEX optimization software obtains, target function value is 4425888, it can be seen that the accuracy rate for choosing optimal manufacturer is 75%, and relative error is about 0.34%.

It is provided with ten groups of experiments in feasibility the present embodiment in order to verify this method, is compared with CPLEX optimization software, Each alternative Number of firms is linearly increasing, and every group of experiment generates 3 test cases at random, has recorded optimal solution, approximate solution, phase respectively To error and problem solving time.Executing the time is more than 30 minutes, is considered as calculating time-out.Test result is as shown in table 5:

5 test result of table

The test case below of problem scale 50/50/50/50 known to above-mentioned experimental data, relative error do not surpass 1% is crossed, the test case that problem scale is 60/60/60/60 to 70/70/70/70, relative error is no more than 2%.It can see Out, for relative error with the increase of problem scale, error has certain increase tendency, but increasess slowly, in acceptable range Within；

CPLEX optimization software has certain advantage when solving small-scale problem, but when problem scale reaches 70/70/70/ When 70, the calculating time is sharply increased, and the solution of problem can not be obtained within the acceptable time.And this method can be solved and be asked Topic scale solves the time at 10 minutes or so to 100/100/100/100, when problem scale reach 70/70/70/70 with Under test case, runing time is no more than 3 minutes.Problem scale is more than 70/70/70/70, runing time increasing degree Superiority more gentle, which reflects it on Large-scale Optimization Problems has good degree of approximation and solving speed.

Finally, it should be noted that the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although Present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: it still may be used To modify to technical solution documented by previous embodiment, or some or all of the technical features are equal Replacement；And these are modified or replaceed, the scope of the claims in the present invention that it does not separate the essence of the corresponding technical solution.

Claims

1. a kind of method for solving greening supply chain collaborative design problem, characterized by the following steps:

Step 1: the quantity of product or raw material being converted into corresponding means of transport quantity, is made with cost, carbon emission, water consumption For optimization aim, the supply chain mathematical model of the quaternary structure of integrated manufacturer's selection and Transportation Planning is established；The mathematical model Including objective function and qualifications, the formula of the objective function is as follows:

Wherein, i represents vendor number, i ∈ I；J represents manufacturer's number, j ∈ J；K represents retail trader's number, k ∈ K；L is represented Customer number, l ∈ L；M represents raw material number, m ∈ M；N representative products number, n ∈ N；CSM_imIt represents from supplier i buying one The cost of unit raw material m；CPP_jnRepresent the cost that manufacturer j produces a unit product n；ESM_imRepresent supplier i production one Carbon emission amount caused by unit raw material m；EPP_jnIt represents manufacturer j and produces carbon emission amount caused by a unit product n； WSM_imIt represents supplier i and produces water consumed by a unit raw material m；WPP_jnIt represents manufacturer j and produces a unit product n Consumed water；DSP_ijRepresent the distance between supplier i and manufacturer j；DPD_jkIt represents between manufacturer j and retail trader k Distance；DDC_klRepresent the distance between retail trader k and client l；CMP_jRepresent operation cost in manufacturer's j period；CMD_kGeneration Operation cost in the table retail trader k period；CTsp represents the cost of 1 kilometer of Freight Transport；ETsp represents a Freight Transport 1 Carbon emission caused by kilometer；A, b respectively represent conversion weight when carbon emission, water consumption to be converted to cost；sp_jExpression is No to select manufacturer j as supply chain cooperation manufacturer, 1 represents selection, and 0 representative does not select；sd_kIndicate whether selective distribution quotient k Selection is represented as supply chain cooperation manufacturer, 1,0 representative does not select；aspm_ijmIt transports from supplier i to the raw material of manufacturer j The quantity of m；apdp_jknIt transports from manufacturer j to the quantity of the product n of retail trader k；aSP_ijFrom supplier's i transporting raw materials to life The lorry quantity of business men j；aPD_jkThe lorry quantity of product to retail trader k is transported from manufacturer j；aDC_klIt transports and produces from retail trader k Product to client l lorry quantity；

The qualifications include precondition and constraint condition；

The precondition are as follows: the order of all clients must all meet；Supplier constrains with the supply upper limit, manufacturer With production upper limit constraint, retail trader has storage upper limit constraint；Each manufacturer, operation cost is fixed in retail trader's period；No Same raw material or product can be merged into same lorry；

The constraint condition are as follows:

Constraint between lorry quantity and raw material, product quantity:

Wherein,ATM_mThe maximum number of raw material m can be delivered by representing a lorry Amount；ATP_nThe maximum quantity of product n can be delivered by representing a lorry；adcp_klnRepresentative is transported from retail trader k to the production of client l The quantity of product n；

The order demand of client must satisfy constraint:

Retail trader inventory constraint:

Manufacturer produces force constraint:

Supplier is for stress constraint:

Retail trader's amount of stocking up, shipment amount are consistent:

Wherein,

∑_i∈Iaspm_ijm=MPR_mn×∑_k∈Kapdp_jkn (10)

Wherein,MPR_mnRepresent the quantitative relation ratio between raw material m and product n；

Nonnegative integer and binary system constraint:

sp_j∈{0,1} (17)

sd_k∈{0,1} (18)

Wherein,

Step 2: the transport between optimal supply chain network structure and the structure every two vertex is obtained according to compound out of kilter method Amount, obtains totle drilling cost according to objective function；

The compound out of kilter method is to carry out synthesis by the alternative manufacturer to supply quotient sheaf, raw vendor level and distributor level to comment Estimate, obtains the manufacturer with preferably assessment score；The manufacturer includes supply quotient sheaf, production quotient sheaf, distributor level；Enumerate by The all possible combinations that these manufacturers are constituted delete the candidate solution for not being able to satisfy customer order wherein as candidate disaggregation；And it is right Remaining each candidate solution calculating target function approximation, the smallest candidate solution of selection target function approximation is as final supply Chain network structure reapplies branch and bound method to calculate the freight volume between every two vertex, freight volume is brought into target letter Totle drilling cost is acquired in number.

2. a kind of method for solving greening supply chain collaborative design problem according to claim 1, it is characterised in that: described Specific step is as follows for step 2:

Step 2.1: the high supply quotient set S of comprehensive score, production quotient set P, distribution quotient set are obtained according to partner's out of kilter method Close D；

Partner's out of kilter method is assessment score to be calculated for candidate manufacturer, and obtain the comprehensive of each candidate manufacturer using weighting adduction Close scoring；Using the top k algorithm based on quicksort, select respectively the high preceding η supplier of comprehensive score, raw manufacturer and Retail trader obtains supply quotient set S, production quotient set P, distribution quotient set D；

The infeasible solution deletion algorithm is to be directed to supply quotient sheaf, production quotient sheaf, distributor level respectively according to precondition to carry out Judgement, if this layer of manufacturer's ability is not able to satisfy all customer order demands, the candidate solution be it is invalid, it is invalid to delete this Solution；The input data of the algorithm is S ', P ', D ', and output data is S ", P ", D ", the S ", P ", D " respectively indicates deletion can not Supply quotient set, production quotient set, distribution quotient set after row solution；

The filter algorithm based on objective function approximation is the filtered residue candidate solution according to obtained in step 2.3, To each candidate solution calculating target function approximation, selection target function approximation is the smallest to be deconstructed into final supply chains system Network；It reapplies branch and bound method and obtains the freight volume between adjacent two layers vertex, freight volume is brought into and is acquired in objective function Totle drilling cost.

3. a kind of method for solving greening supply chain collaborative design problem according to claim 3, it is characterised in that: described Specific step is as follows for step 2.1:

Step 2.1.1: evaluation index when listing supplier, manufacturer, retail trader respectively preferentially；To each index, according to it Shared specific gravity is different in the value of objective function, assigns different weights；

Step 2.1.1.1: the vendors' evaluating index includes that each cost of raw, each raw material carbon emission are corresponding Cost, the corresponding cost of each raw material water consumption are transported from supplier to the cost of manufacturer；The specific method is as follows:

Each cost of raw:

(∑_i∈ICSM_im/|I|)×MN_m (21)

The corresponding cost of each raw material carbon emission:

a×(∑_i∈IESM_im/|I|)×MN_m (22)

The corresponding cost of each raw material water consumption:

a×(∑_i∈IWSM_im/|I|)×MN_m (23)

It transports from supplier to the cost of manufacturer:

Select a kind of cost of raw material as with reference to cost, weight is set as 1；The weight of other indices is according to its correspondence The ratio of cost and reference cost determines；

The weight for enabling the first cost of raw material is 1, i.e. m=1；The cost weight WSC of raw material m_m, raw material m carbon emission power Weight WSE_m, raw material m water consumption weight WSW_m, it is as follows with the calculation formula of manufacturer's distance weighting WSP:

Step 2.1.1.2: the evaluation index of the manufacturer includes the cost of each production of manufacturer, each production carbon row Put corresponding cost, the corresponding cost of each production water consumption, operation cost, from supplier transport to manufacturer's cost, from Manufacturer transports to retail trader's cost；

Take each index average value, calculate separately its from supplier's transporting raw materials to manufacturer, production product and transport product to Cost caused by retail trader's stage；The weight for enabling one of production cost is 1, and the weight of other indexs is right according to its Cost is answered to determine with the ratio referring to cost；

The cost of each production:

(∑_j∈JCPP_jn/|J|)×PN_n (29)

The corresponding cost of each production carbon emission:

a×(∑_j∈JEPP_jn/|J|)×PN_n (30)

The corresponding cost of each production water consumption:

b×(∑_j∈JWPP_jn/|J|)×PN_n (31)

Operation cost:

It transports from supplier to manufacturer's cost:

It transports from manufacturer to retail trader's cost:

The weight for enabling the first production cost is 1, i.e. n=1；The production cost weight WPC of product n_n, product n production carbon Discharge weight WPE_n, product n production water consumption weight WPW_n, operation cost weight WPM, with supplier's distance weighting WPS, with The calculation formula of retail trader distance weighting WPD is as follows:

Step 2.1.1.3: the evaluation index of retail trader include: operation cost, the cost transported from manufacturer to retail trader, from point Pin quotient transports to the cost of client；

Take each index average value, calculate separately its from manufacturer transport product to retail trader again to caused by client's stage at This, is averaged and is calculated；The weight for enabling operation cost is 1, the weights of other indexs according to its corresponding cost and referring at This ratio determines；

Operation cost:

It transports from manufacturer to the cost of retail trader:

It transports from retail trader to the cost of client:

Enabling the weight WDM of operation cost is 1, such as with manufacturer's distance weighting WDP, with the calculation formula of client's distance weighting WDC Under:

WDM=1 (44)

Step 2.1.2: comprehensive score is carried out to manufacturer respectively；

Each evaluation index same level manufacturer is compared respectively, with 0-1 matrix storage comparative result, ranks indicate factory Quotient, matrix element indicate that row whether better than column, is that element value takes 1, otherwise takes 0；According still further to the weight of each index, to 0-1 square Battle array is weighted addition, obtains score matrix, sums to the matrix by rows, obtains the comprehensive score of the manufacturer；Specific steps are such as Under:

Step 2.1.2.1: the comprehensive score of supplier；

Each cost of raw material compares matrix:

A_m=[α_oq]_I×I (47)

Wherein, α_oqRepresent matrix A_mIn element；o,q∈I,CSM_omRepresent from supplier o purchase a unit raw material m at This；CSM_qmRepresent the cost that a unit raw material m is purchased from supplier q；

Each raw material carbon emission compares matrix:

B_m=[β_oq]_I×I (48)

Wherein, β_oqRepresent matrix B_mIn element；ESM_omIt represents supplier o and produces carbon emission caused by a unit raw material m Amount；ESM_qmIt represents supplier q and produces carbon emission amount caused by a unit raw material m；

Each raw material water consumption compares matrix:

Q_m=[ρ_oq]_I×I (49)

Wherein, ρ_oqMatrix Q_mIn element；WSM_omIt represents supplier o and produces water consumed by a unit raw material m；WSM_qmGeneration Table supplier q produces water consumed by a unit raw material m；

With each manufacturer's distance versus matrix:

W_j=[μ_oq]_I×I (50)

Wherein, μ_oqRepresent matrix W_jIn element；DSP_ojRepresent the distance between supplier o and manufacturer j；DSP_qjRepresent supply The distance between quotient o and manufacturer j；

Addition is weighted according to the weight being calculated in step 2.1.1.1 to above-mentioned comparison matrix, obtains supplier two-by-two Between Comparison score matrix:

Step 2.1.2.2: the comprehensive score of manufacturer；

Each production Cost comparisons matrix:

E_n=[e_uv]_|J|×|J| (53)

Wherein,_uvRepresent matrix E_nIn element；u,v∈J；CPP_unRepresent the cost that manufacturer u produces a unit product n；CPP_vn Represent the cost that manufacturer v produces a unit product n；

Each production carbon emission compares matrix:

F_n=[f_uv]_|J|×|J| (54)

Wherein, f_uvRepresent matrix F_nIn element；EPP_unIt represents manufacturer u and produces carbon emission amount caused by a unit product n； EPP_vnIt represents manufacturer v and produces carbon emission amount caused by a unit product n；

Each production water consumption compares matrix:

G_n=[g_uv]_|J|×|J| (55)

Wherein, g_uvRepresent matrix G_nIn element；WPP_unIt represents manufacturer u and produces water consumed by a unit product n；WPP_vn It represents manufacturer v and produces water consumed by a unit product n；

Operation cost compares matrix:

H=[h_uv]_|J|×|J| (56)

Wherein, h_uvRepresent the element in matrix H；CMP_uRepresent operation cost in manufacturer's u period；CMP_vRepresent manufacturer's v period Interior operation cost；

With the set S distance versus matrix of supplier:

O_i'=[δ_uv]_|J|×|J| (57)

Wherein, δ_uvRepresent matrix O_i′In element；S represents the set of the supplier obtained using top k algorithm；I '=1, 2,…,η；DSP_i′uRepresent the distance between supplier i ' and manufacturer u；DSP_i′vIt represents between supplier i ' and manufacturer v Distance；

With each retail trader's distance versus matrix:

U_k=[ε_uv]_|J|×|J| (58)

Wherein, ε_uvRepresent matrix U_kIn element；DPD_ukThe distance between manufacturer u and retail trader k；DPD_vkManufacturer v with point Sell the distance between quotient k；

Addition is weighted according to the weight being calculated in step 2.1.1.2 to above-mentioned comparison matrix, obtains manufacturer two-by-two Between Comparison score matrix:

Step 2.1.2.3: the comprehensive score of retail trader；

Operation cost compares matrix:

L '=[θ_wy]_|K|×|K| (61)

Wherein, θ_wyRepresent matrix L ' in element；w,y∈K；CMD_wRepresent operation cost in the retail trader w period；CMD_yIt represents and divides Sell operation cost in the quotient y period；

With the set P distance versus matrix of manufacturer:

Wherein, x_wyRepresent matrix X_j′In element；P represents the production quotient set obtained using top k algorithm；J '=1,2 ..., η；DPD_j′wRepresent the distance between manufacturer j ' and retail trader w；DPD_j′yRepresent the distance between manufacturer j ' and retail trader y；

With each client's distance versus matrix:

V_l=[z_wy]_|K|×|K| (63)

Wherein, z_wyRepresent matrix V_lIn element；DDC_wlRepresent the distance between retail trader w and client l；DDC_ylRepresent retail trader The distance between y and client l；

Addition is weighted according to the weight being calculated in step 2.1.1.3 to above-mentioned comparison matrix, obtains retail trader two-by-two Between Comparison score matrix:

Step 2.1.3: the comprehensive score obtained according to step 2.1.2, the top k algorithm based on quicksort obtain comprehensive score High preceding η supply quotient set S, production quotient set P, distribution quotient set D；Specific step is as follows:

Step 2.1.3.1: a base value is found in supplier comprehensive score set TS1；The base value is chosen in array The value of the last one element；

Step 2.1.3.2: element bigger than base value in the set is placed in its left side by subregion, and the element smaller than base value is set In its right side；

Step 2.1.3.3: judging left siding-to-siding block length, is such as equal to η, program determination, η element before exporting；As left siding-to-siding block length is big In η, then step 2.3.1.1 and step 2.3.1.2 is repeated to left section, until program determination；If left siding-to-siding block length is less than η, then Step 2.3.1.1 and step 2.3.1.2 is repeated to right section, until program determination；

Step 2.1.3.5: a base value is found in manufacturer's comprehensive score set TS2；Execute step 2.1.3.2 and step 2.1.3.3, η element before exporting is denoted as production quotient set P；

Step 2.1.3.6: a base value is found in retail trader comprehensive score set TS3；Execute step 2.1.3.2 and step 2.1.3.3, η element before exporting is denoted as distribution quotient set D.

4. a kind of method for solving greening supply chain collaborative design problem according to claim 3 or 4, it is characterised in that: Specific step is as follows for the step 2.2:

Step 2.2.1: construction setC '={ C }, wherein 2^S、 2^P、2^DThe respectively power set of set S, P, D；

Step 2.2.2: obtaining set S ', P ', D ' according to bit arithmetic, wherein | S ' |=2^I- 1, | P ' |=2^J- 1, | D ' |=2^K-1, | C ' |=1, to obtain candidate disaggregation CS:

CS=(2^I-1)×(2^J-1)×(2^K-1) (66)。

5. a kind of method for solving greening supply chain collaborative design problem according to claim 5, it is characterised in that: described Specific step is as follows for step 2.3:

Step 2.3.1: supply quotient sheaf: for the supplier S in S '_iIf Then by S_iIt is added to set S "；

Step 2.3.2: production quotient sheaf: for the manufacturer P in P '_iIfThen by P_iAdd It is added to set P "；

Step 2.3.3: distributor level: for the manufacturer D in D '_iIfThen will D_iIt is added to set D ".

6. a kind of method for solving greening supply chain collaborative design problem according to claim 6, it is characterised in that: described The specific steps of objective function approximation are solved in step 2.4 are as follows:

The cost CSM of each raw material of supplier in remaining candidate solution_m, carbon emission ESM_m, water consumption WSM_mCalculation formula it is as follows:

The cost CPP of each production of manufacturer in remaining candidate solution_n, carbon emission EPP_n, water consumption WPP_nCalculation formula such as Under:

Distance Dis, the Dis in remaining candidate solution between manufacturer include supplier transport to manufacturer, manufacturer transport to point Pin quotient, retail trader transport to lorry quantity TSP, TPD, TDC of client, and calculation formula is as follows:

Objective function approximation Obj_apprFormula are as follows: