CN110852667B - Two-stage scheduling method for multi-period multi-product evanescent product supply chain network design - Google Patents
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Abstract
The invention relates to the technical field of evanescent article supply chain networks, in particular to a two-stage scheduling method for multi-period multi-product evanescent article supply chain network design. The method comprises the steps of site selection model making, configuration model making on the basis of the site selection model and loop feedback program building according to the site selection model and the configuration model. Aiming at the problem of network design of a multi-period multi-product evanescent product supply chain, a two-stage scheduling solving method is provided, and in the first stage, a facility site selection model in the whole supply chain network is established in a strategic decision level. And in the second stage, tactical configuration decision of a material configuration level is carried out so as to build a configuration model, and an addressing model and the configuration model are integrated into a model for solving addressing and configuration problems of suppliers, a mixed production inspection center, a mixed storage and recovery center, a disposal and recovery recycling center and retailers.
Description
Technical Field
The invention relates to the technical field of evanescent article supply chain networks, in particular to a two-stage scheduling method for multi-period multi-product evanescent article supply chain network design.
Background
The evanescent products have the characteristics of short storage period, strong timeliness and the like, and the shortage or overstocking of the commodities in real life can cause a large amount of economic loss. The invention aims to construct an optimization model for integrating multi-cycle, multi-product and capacity-limited supply chain network design problems aiming at a vanishing product supply chain network so as to meet the requirements of customers on the premise of maximizing the total profits of the network, thereby reducing the economic loss caused by shortage or stock backlog.
Disclosure of Invention
The present invention is directed to a two-stage scheduling method for multi-cycle multi-product evanescent product supply chain network design, which solves one or more of the above-mentioned drawbacks of the prior art.
In order to achieve the above object, the present invention provides a two-stage scheduling method for multi-cycle multi-product evanescent product supply chain network design, comprising the following steps:
s1, establishing location selection models of relevant suppliers, disposal centers, recycling centers and hybrid storage and recovery centers;
s2, in the site selection model, the maximum number of relevant suppliers, mixed storage recycling centers and disposal and reuse centers can be obtained based on the initial value of the site selection model, and a configuration model is formulated according to the maximum number;
and S3, constructing a circular feedback program according to the addressing model and the configuration model.
Preferably, the step of establishing the addressing model is as follows:
s11, calculating the total fixed cost of the relevant addressing model, wherein the formula is as follows:
min∑ i GS i ×XS i +∑ m GD m ×XD m +∑ n GR n ×XR n +∑ k GW k ×XW k
s12, establishing related constraint of facility number;
s13, establishing related constraints of facility capacity, wherein the formula is as follows:
preferably, the constraints on the number of facilities include a maximum number of suppliers available for selection, a maximum number of disposal centers available for selection, a maximum number of reuse centers available for selection, and a maximum number of hybrid storage and recovery centers available for selection;
the maximum number of suppliers is formulated as:
∑ i XS i ≤SM
the maximum number formula of the alternative treatment centers is:
∑ m XD m ≤DM
the maximum number of alternative reuse centers is formulated as:
∑ n XR n ≤RM
the maximum quantity formula of the optional hybrid storage and recovery centers is as follows:
preferably, the step of making the configuration model is as follows:
s21, setting an objective function in the configuration model:
s22, establishing constraint conditions of each facility capacity;
s23, establishing relevant constraints related to the capacity of the hybrid storage and recovery center;
s24, establishing balance constraint between a supplier and a mixed production inspection center;
s25, establishing a constraint relation between the supply quantity and the inventory;
s26, establishing a constraint relation between the hybrid storage and recovery center and the retailer;
s27, establishing relevant constraints for disposing the returned products;
and S28, setting the constraint conditions of the variables in the model.
Preferably, the constraint condition for establishing the capacity of each facility comprises the following postures:
posture one: to represent the raw material capability that a supplier can supply at various times, the following constraints are established:
and (5) posture II: to determine the capacity of the hybrid production inspection center at each time period, the following constraints are established:
posture three: to determine the processing power of each epoch handling center, the following constraints are established:
and (4) posture IV: to determine the capacity of the reuse center for each epoch, the following constraints are established:
preferably, the constraints on the facility capacity include the raw material capacity that can be supplied by the supplier at each time period, the capacity that can be supplied by the mix production verification center at each time period, the processing capacity of the disposal center at each time period, and the capacity of the reuse center at each time period.
Preferably, the steps of constructing the loop feedback program are as follows:
s31, solving an addressing model based on a depth-first branch-and-bound method;
s32, constructing a configuration model based on the positions of all facilities in the initial solution of the addressing model and the quantity of the facilities in the model;
s33, judging whether a decision variable in the configuration model is equal to zero or not, if the decision variable is not zero, jumping out of the loop, and if the decision variable is equal to zero, performing the next step;
s34, respectively reducing the configuration models in the step S32 by one unit, re-solving the new addressing problem, and re-designing the configuration problem based on the new addressing problem to obtain a group of new configuration models;
s35, judging whether the maximum value in the new configuration problem is equal to zero, if yes, returning to the step S34 to continue iteration, and if not, turning to the next step;
s36, judging whether the minimum value in the new configuration problem is equal to zero, if so, selecting the maximum overall target value in the iteration; if not, then the maximum overall objective function in the addressing problem in this and the previous iteration is selected and the loop is skipped.
Compared with the prior art, the invention has the beneficial effects that:
1. in the two-stage scheduling method for the multi-period multi-product evanescent article supply chain network design, a two-stage scheduling solving method is provided for evanescent article supply chain network designs with short-life evanescent articles, multi-period multi-products and multi-level evanescent articles, and a facility location model in the whole supply chain network is established in the first stage at a strategic decision level. And in the second stage, tactical configuration decision of a material configuration level is carried out so as to build a configuration model, and an addressing model and the configuration model are integrated into a model for solving addressing and configuration problems of suppliers, a mixed production inspection center, a mixed storage and recovery center, a disposal and recovery recycling center and retailers.
2. In the two-stage scheduling method for multi-period multi-product evanescent article supply chain network design, the proposed model solves the problem of site selection and configuration, and aims to make strategic and tactical decisions on the problem of evanescent article supply chain network design, decompose the problem into a site selection model and a configuration model, design a cyclic feedback program, and use bidirectional necessary feedback from the configuration model to the site selection model, thereby obtaining a more reliable optimal solution.
3. In the two-stage scheduling method for the multi-cycle multi-product evanescent product supply chain network design, an accurate algorithm is applied in the solving process, and an intelligent algorithm integrating tabu search and differencing avoids the situation that the obtained solution is only local optimal and not global optimal.
Drawings
FIG. 1 is an overall flow chart of the present invention;
FIG. 2 is a diagram of an address-configuration model of the present invention;
fig. 3 is a flow chart of a corresponding loop feedback procedure of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
Referring to fig. 1-3, the present invention provides a technical solution:
the invention provides a two-stage scheduling method for multi-period multi-product evanescent product supply chain network design, which comprises the following steps:
s1, establishing location models of relevant suppliers, disposal centers, recycling centers and mixed storage and recovery centers;
s2, in the site selection model, the maximum number of relevant suppliers, mixed storage recycling centers and disposal and reuse centers can be obtained based on the initial value of the site selection model, and a configuration model is formulated according to the maximum number;
and S3, constructing a circular feedback program according to the addressing model and the configuration model.
The steps of establishing the addressing model are as follows:
s11, calculating the total fixed cost of the relevant address selection model;
s12, establishing related constraint of facility number;
and S13, establishing related constraints of facility capacity.
The relevant constraints on the number of facilities include the maximum number of suppliers available for selection, the maximum number of disposal centers available for selection, the maximum number of recycling centers available for selection, and the maximum number of hybrid storage and recovery centers available for selection.
In this embodiment, in calculating the total fixed cost of the relevant site selection model, first, the minimum value of the total fixed cost costs of the selected supplier, disposal center, recycling center, and built hybrid warehouse recycling center is set in the objective function as:
min∑ i GS i ×XS i +∑ m GD m ×XD m +∑ n GR n ×XR n +∑ k GW k ×XW k (1)
wherein the first, second and third terms of the objective function represent the total fixed costs of the supplier, the disposal center and the recycling center, respectively, and the fourth term represents the total fixed cost of the hybrid storage and retrieval center. Wherein GS i Represents the fixed cost of supplier i, and its associated binary decision variable XS i Indicating that if the selected supplier is i, its value equals 1, otherwise it is 0, (the relevant parameters in the second, third, fourth term, and so on, where k denotes the selected hybrid warehouse recycling center, n denotes the selected recycling center, m denotes the selected disposal center.)
Further, in establishing the relevant constraint on the number of facilities, the following constraint is established for limiting the number of suppliers to choose from, wherein the SM table indicates the maximum number of suppliers to choose from:
∑ i XS i ≤SM (2)
the following constraints are established for limiting the number of alternative treatment centres, where DM represents the maximum number of alternative treatment centres:
∑ m XD m ≤DM (3)
the following constraints are established for limiting the number of alternative reuse centers, where RM represents the maximum number of alternative reuse centers:
∑ n XR n ≤RM (4)
in particular, in establishing the relevant constraints on facility capacity, in order to indicate that the supplier's ability to supply raw materials is limited (and not unlimited), the relevant constraints are set up:
wherein,
representing the ratio of conversion of raw material r from a supplier to product c,
indicating the number of products c produced by the hybrid storage and recovery center,
indicating the ability of the supplier i to supply raw material r, i.e. the amount of raw material. And is thus constrained.
Wherein, V c Which represents the volume of the product c,
representing the capacity of the hybrid production verification center j to produce product c,
representing the warehouse capacity of the hybrid warehouse k, multiplying the total volume of the products by the number of products c, and constraining the product volume by the total volume of the warehouse, so as to obtain the maximum amount of products, i.e. embodying the capacity occupied by all the products entering the hybrid warehouse recovery center within the limits of the warehouse capacity.
Wherein,
the recovery ability of n, r1, representing the center of reuse c Representing the return rate of product c from the retailer to the hybrid storage and retrieval center; r2 c Indicating the recovery of the returned product, thereby ensuring that the maximum value of the returned product delivered from the hybrid storage recovery center to the recycling center is less than the capacity of the recycling center.
Wherein,
representing the processing capacity of the handling center m to process expired products c. The number of products returned in the produced products and transported back to the disposal center is less than the number of products that the disposal center is capable of handling.
This constraint is a binary constraint on the relevant variables. Namely: XS (Cross site) i If the selected supplier is i, the selected supplier is 1, otherwise the selected supplier is 0; XW k If the used mixed storage and recovery center is k, the value is 1, otherwise, the value is 0; XD m If the selected treatment center is m, the treatment center is 1, otherwise, the treatment center is 0; XR (X ray diffraction) n And if the selected reuse center is n, it is 1, otherwise it is 0.
It is worth mentioning that a configuration model of the correlation function is established, and according to the above assumptions, a configuration model is established that recycles from raw materials to products throughout the supply chain network. Wherein: i is a supplier, j is a mixed production inspection center, k is a mixed storage and recovery center, n is a recycling center, m is a disposal center, and 1 is a retailer; 0 represents raw materials shipped from a supplier to a mix production inspection center; p represents the product shipped from the mixed production and inspection center to the mixed production and inspection center, RPT + RP represents the sum of the product returned from the mixed production and inspection center to the mixed production and inspection center and the product returned from the retailer to the mixed production and inspection center again; q represents products shipped from the hybrid warehouses to the retailer, RQ represents products returned from the retailer to the hybrid warehouses; RR denotes a product transported from the hybrid production inspection center to the recycling center; RD denotes a product transported from a hybrid production inspection center to a disposal center.
In this embodiment, the step of formulating the configuration model is as follows:
s21, setting an objective function in the configuration model:
s22, establishing constraint conditions of each facility capacity;
s23, establishing relevant constraints related to the capacity of the hybrid storage and recovery center;
s24, establishing balance constraint between the insurance supplier and the mixed production inspection center;
s25, establishing a constraint relation between the supply quantity and the inventory;
s26, establishing a constraint relation between the hybrid warehouse recovery center and the retailer;
s27, establishing relevant constraints for disposing the returned products;
and S28, setting the constraint conditions of the variables in the model.
Constraints on facility capacity include the raw material capacity that a supplier can supply at each time period, the capacity that a mix production and inspection center can supply at each time period, the processing capacity of a disposal center at each time period, and the capacity of a reuse center at each time period.
Wherein the objective function is:
the objective function is to take the maximum profit, i.e., the total revenue minus the total cost, where the total revenue includes: income of products produced and sold (F) R1 )：
F R1 ＝max∑ t ∑ k ∑ l ∑ c F R V ct ×Z klct (wherein Z is klct Representing the number of products c delivered to the retailer 1 by the hybrid warehouse recovery center k during time t), and the revenue recovered and sold to the recycling center (F) R2 )：F R2 ＝∑ t ∑ c ∑ n ∑ j RR jnct ×F R V Rnct (wherein RR jnct Indicating t periods from mixed productionThe number of products c delivered by inspection center j to recycling center n).
The total cost function comprises:
cost of demand due to lack of stock, F c1 ＝∑ t ∑ c ∑ l F lct ×UD lct In the formula F lct Indicating that product c meets retailer 1 demand cost for time t and UD lct Indicating the number of products c satisfying retailer 1 during time t.
Total fixed cost, F c2 ＝∑ t ∑ r ∑ i ∑ j XO ijrt ×GO rit In the formula XO ijrt Judging whether the mixed production inspection center orders raw materials r, GO from a supplier i in a t period for the binary variable rit Representing a fixed cost of ordering raw material r from supplier i during time t.
The cost of the purchase is reduced by the purchase cost,
in the formula
Represents the cost of purchasing raw material r from supplier i during time t, O ijrt Indicating the quantity of raw material r being shipped from supplier i to the mix production verification center j during time t.
The production cost is low, and the production cost is low,
in the formula
Unit production cost, P, of product c produced by Table mix production inspection center j during time t jkct Indicating the number of products c produced by the mix production verification center j and transported to the mix warehouse recovery center during time t.
The cost is kept, and the cost is saved,
in the formula
Represents the unit holding cost S of the product c in the period t by the mixed warehouse recovery center k kcnt Indicating the number of products c still in the blend warehouse recovery center k at the end of time t.
Cost of expiry, F c6 ＝∑ t＞3 ∑ c ∑ l ∑ k rv c，t-3 ×RQ lkct In the formula rv c，t-3 Indicating the unit cost, RQ, of expired products lkct Indicating the amount of product c returned from retailer 1 to the hybrid warehouse recovery center k during time t.
The cost of the inspection is tested, and the cost is tested,
in the formula
Represents the inspection unit inspection cost, RP, of the mixed warehouse inspection center j for the product c in the period t kjct Indicates the number of products c returned from the mixed warehouse recovery center k to the mixed production inspection center j, RPT, during the period t kjct Representing the number of products c returned from retailer 1 to the hybrid storage and retrieval center k and then shipped to the hybrid production verification center j during period t.
The cost of the disposal is high,
in the formula
Represents the disposal cost, RD, of the disposal center m for the product c during the period t jmct Representing the number of products c transported from the mixed production inspection center j to the disposal center m during the time period t.
Forward transport cost, F c9 ＝∑ t ∑ r ∑ j ∑ i F TC SP ijrt ×A ijrt +∑ t ∑ j ∑ c Σ k (F TC PW jkct ×B jkct )+∑ t ∑ c ∑ l ∑ k F TC WR klct ×Q klct In the formula F TC SP ijrt Represents the transportation cost, A, of raw material r transported from supplier i to the mixed production inspection center j during the period t ijrt Denotes the quantity of transported raw material r, F TC PW jkct Represents the unit transportation cost of the product c from the mixed production inspection center j to the mixed storage recovery k in the period t, B jkct Indicating the quantity of product c transported to the hybrid storage and recovery center, F TC WR klct Representing the number of products c transported from the hybrid storage recovery center k to the retailer 1 during the time period t.
Reverse transportation cost, F c10 ＝∑ t ∑ c ∑ l ∑ k F TC WR klct ×RQ klct +∑ t ∑ c ∑ m ∑ j F TC PD jmct ×RD jmct +∑ t ∑ j ∑ c ∑ k (F TC PW jkct ×(RBT kjct +RB kjct ))
In the formula F TC PD jmct Represents the unit transportation cost, RD, of the product c from the mixed production inspection center j to the disposal center m during the period t jmct Representing the number of products c transported from the mixed production inspection center j to the disposal center m during the period t, other transportation costs being the same as in the forward transportation costs.
Further, establishing the constraint conditions of the capacity of each facility specifically comprises:
to represent the raw material capability that a supplier can supply at various times, the following constraints are established:
to determine the capacity of the hybrid production verification center at each time period, the following constraints are established:
to determine the processing power of the various epoch handling centers, the following constraints are established:
to determine the capacity of the reuse center for each epoch, the following constraints are established:
specifically, in establishing the relevant constraints regarding the capacity of the hybrid warehouses, the relevant constraints of 14 to 17 (first, second, third and fourth periods, respectively, and above) are established to ensure that the sum of the amount of products entering each hybrid warehouses and the total amount of products stored in the hybrid warehouses at the previous period is less than the capacity of the hybrid warehouses:
since the product's expiration is returned from the hybrid storage and recovery center to the hybrid production verification center, the amount of returned product is 0 since there was no product expiration for the first three periods, so the following constraints are established:
based on the first-in-first-out (FIFO) principle, the relative equation is established for the number of products in the hybrid warehouse recovery center in the first three periods:
according to the assumptions mentioned in the first three periods there is no return of product and therefore: in a first period, t 1, the number of products stored in the hybrid storage and recovery center:
the number of products produced during the first period that remain in the hybrid storage and recovery center at the end of the second period:
the quantity of product present in the hybrid bin recovery center during the second period:
the product produced in the first period, which is still in the hybrid storage and recovery center at the end of the third period:
the product produced in the second period, which was still in the hybrid warehouse recovery center at the end of the third period:
at the end of the third period there is product in the warehouse recovery center mixed:
processing starts from the fourth period, and by the next period, the number of products returned from the hybrid storage and recovery center to the hybrid production and inspection center (due to expiration) establishes the following constraints:
return value S in this constraint kc，t-3，t-1 (products produced during time (t-3) at the end of time (t-1)) if the difference between the contents of the hybrid recycler and the quantity of products transported from the hybrid recycler to the retailer is positive, then it is indicated that the products produced during the first three phases are redundant and not sent to the retailer. These products are therefore sent back to the mix production verification centre.
Establishing a correlation equation for the quantity of product present in the hybrid storage and retrieval center after the fourth period based on a first-in-first-out principle, the quantity of product already present in the hybrid storage and retrieval center for two periods during the fourth period and thereafter:
after the fourth time period, there is a time period of product count in the hybrid warehouse recovery center:
the number of all products present in the hybrid warehouse recovery center at the fourth and later date:
further, a balance constraint between the supplier and the hybrid production verification center is established:
to ensure the balance constraint between the supplier and the mix production verification center, and the stock of raw materials of the mix production verification center, a relevant constraint is established, i.e., the number of raw materials present in the mix production verification center when t is 1:
in the second and later periods (t ≧ 2), the sum of the amounts of raw materials in the mix production inspection center and raw materials remaining in the previous period:
establishing constraints relating the quantity of raw materials shipped from a supplier to a hybrid production verification center at various times to the quantity of orders to date for the supplier of the raw materials provided (i.e., order costs):
furthermore, to ensure that the supply is less than inventory, i.e., the number of products shipped from each hybrid storage and recovery center to the retailer must be less than or equal to inventory, and after the first period, the relevant constraints are established taking into account the relationship between the number of products in the respective period and the number in the preceding period:
in the first period (t ═ 1), the number of products shipped to the retailer is less than the number of products shipped from the production verification center to the mixed production collection warehouse, for which the relevant constraints are established:
in the second period (t ═ 2), the number of products shipped to the retailer is less than the number of products shipped from the production verification center to the mixed production collection warehouse and the number of products stored in the mixed storage recovery center that were added during the first period, for which the relevant constraints are established:
in the third period (t ═ 3), the number of products shipped to the retailer is less than the number of products shipped from the production checking center to the mixed production collection warehouse and the number of products in the mixed storage recovery center that were added in the first two periods, and the relevant constraints are established for this purpose:
after the fourth period (t ≧ 4), the number of products shipped to the retailer is less than the number of products shipped from the production verification center to the commingled production collection warehouse and the number of products stocked in the commingled warehouse recovery center in the first three periods, for which the relevant constraints are established:
when considering the relationship between the retailer and the hybrid storage and recovery center, if the time of product transport to the retailer is greater than the product shelf life, the retailer is out of model coverage and therefore not considered. If the retailer is within range, the retailer is available, so the relevant constraints are established:
in addition, to ensure that each retailer is supplied by at most one hybrid warehouse recycling center, the relevant constraints are established:
to ensure that each retailer, when within the coverage area of the hybrid storage and retrieval center, sells products that are inventory items in the warehouse, or that are contemporaneously manufactured products, relevant constraints are established:
to ensure that the retailer receives products at each time period that are less than or equal to their demand, does not accept products that are greater than their demand, and that the retailer outside the warehouse footprint does not accept supplies, the following relevant constraints are established:
to represent the quantity of product returned from the retailer to the hybrid warehouse recovery center, the relevant constraints are established:
to indicate that there were no items returned from the retailer to the hybrid warehouse recovery center in the first three phases, the relevant constraints are established:
further, to indicate that the product returned from the retailer to the hybrid storage and retrieval center is transported directly from the hybrid storage and retrieval center to the hybrid production inspection center, the relevant conditions are established:
the quantity of returned products transported from the mixed production inspection center to the disposal center is equal to (1-r 2) of returned products returned from the mixed storage and recovery center and the retailer c ) Percent, establishing relevant conditions:
to represent the number of returned products from shipment to the recovery center, the following constraints are established:
for non-negative settings of the relevant variables, and integer and binary limits, the relevant constraints are established:
in this embodiment, the steps of constructing the loop feedback program are as follows:
s31, solving an addressing model based on a depth-first branch-and-bound method;
s32, constructing a configuration model based on the positions of all facilities in the initial solution of the addressing model and the quantity of the facilities in the model;
s33, judging whether a decision variable in the configuration model is equal to zero or not, if the decision variable is not zero, jumping out of the loop, and if the decision variable is equal to zero, performing the next step;
s34, respectively reducing the configuration models in the step S32 by one unit, re-solving a new addressing problem, and then re-designing the configuration problem based on the new addressing problem to obtain a group of new configuration models;
s35, judging whether the maximum value in the new configuration problem is equal to zero, if yes, returning to the step S34 to continue iteration, and if not, turning to the next step;
s36, judging whether the minimum value in the new configuration problem is equal to zero, if so, selecting the maximum overall target value in the iteration; if not, the maximum overall objective function in the addressing problem in this and the previous iteration is selected and the loop is left out.
The necessary feedback from the configuration to the addressing model is obtained by the parameter values of SM, WM, DM, RM. And providing a loop feedback program by utilizing the decision variable values which do not meet the requirements in the configuration model. The optimal values of the SM, WM, DM, RM parameters are selected and the location is guided for updating. The method comprises the following steps:
the method comprises the following steps: solving an addressing model by adopting a depth-first-based branch-bound method according to the initial values of SM, WM, DM and RM;
1.1) find a set of { XS on the root node i ，XW k ，XD m ，XR n A feasible solution of };
1.2) taking the feasible solution as a lower bound, performing pruning search on the binary tree, and pruning a node and all nodes under the node when the value of the node is not superior to that of the node;
1.3) when a node superior to the lower bound is encountered during retrieval, replacing the node as a new lower bound;
1.4) circularly executing the steps 1.1-1.3 until an optimal feasible solution appears, and taking the optimal feasible solution as an initial solution of the addressing model.
Step two: the configuration model is constructed based on the location of each facility in the initial solution of the addressing model and the number of facilities in the model, i.e. { XS } i ，XW k ，XD m ，XR n }；
Step three: determining UD ═ Sigma in configuration model t ∑ c ∑ l UD lct I.e. the number of products c offered to retailer 1 in the warehouse during the time t is the number of retailers fulfilling the retailer's need for product changes) is equal to zero, and if it is not, the loop is skipped, i.e. the initial values of SM, WM, DM, RM and the objective function of the addressing model are all optimal. Thus stopping the cycle. If equal to zero, go to the next step.
Step four: performing iteration: each SM, WM, DM and RM is reduced by one unit, and four new addressing problems are solved again. The configuration problem is then redesigned based on the new addressing problem to get a new set of { XS i ，XW k ，XD m ，XR n }。
Step five: determining sigma of four configuration problems t ∑ c ∑ l UD lct If yes, returning to the fourth step to continue iteration, otherwise, turning to the next step.
Step six: determine sigma of four configuration problems t ∑ c ∑ l UD lct If it is equal to zero, then the maximum overall target value is selected among the four questions in this iteration; if not, the maximum overall objective function in the addressing problem in this and the previous iteration is selected and the loop is left out.
Therefore, the method for designing and scheduling the network of the evanescent product supply chain is realized.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and the preferred embodiments of the present invention are described in the above embodiments and the description, and the present invention is not limited to the embodiments, and various changes and modifications may be made without departing from the spirit and scope of the present invention, and these changes and modifications fall within the scope of the claimed invention. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (6)
1. A two-stage scheduling method for multi-cycle multi-product evanescent product supply chain network design comprises the following steps:
s1, establishing location selection models of relevant suppliers, disposal centers, recycling centers and hybrid storage and recovery centers;
s2, in the site selection model, the maximum number of relevant suppliers, mixed storage recycling centers and disposal and reuse centers can be obtained based on the initial value of the site selection model, and a configuration model is formulated according to the maximum number;
s3, constructing a loop feedback program according to the addressing model and the configuration model;
the steps of the loop feedback program construction are as follows:
s31, solving an addressing model based on a depth-first branch-and-bound method;
s32, constructing a configuration model based on the positions of all facilities in the initial solution of the addressing model and the quantity of the facilities in the model;
s33, judging whether the decision variable in the configuration model is equal to zero, if the decision variable is not zero, jumping out of the loop, and if the decision variable is equal to zero, performing the next step;
s34, respectively reducing the configuration models in the step S32 by one unit, re-solving the new addressing problem, and re-designing the configuration problem based on the new addressing problem to obtain a group of new configuration models;
s35, judging whether the maximum value in the new configuration problem is equal to zero, if yes, returning to the step S34 to continue iteration, and if not, turning to the next step;
s36, judging whether the minimum value in the new configuration problem is equal to zero, if so, selecting the maximum overall target value in the iteration; if not, the maximum overall objective function in the addressing problem in this and the previous iteration is selected and the loop is left out.
2. The method of two-stage scheduling of multi-cycle multi-product evanescent product supply chain network design of claim 1, wherein: the steps of establishing the site selection model are as follows:
s11, calculating the total fixed cost of the relevant address selection model, wherein the formula is as follows:
min∑ i GS i ×XS i +∑ m GD m ×XD m +∑ n GR n ×XR n +∑ k GW k ×XW k ，
wherein the first, second and third terms of the objective function represent the total fixed costs of the supplier, disposal center and recycling center, respectively, and the fourth term represents the total fixed cost of the hybrid storage and recovery center, wherein the GS i Represents the fixed cost of supplier i, and its associated binary decision variable XS i Indicating that if the selected supplier is i, its value equals 1, otherwise 0, the relevant parameters in the second, third and fourth terms, and so on, where k denotes the selected hybrid warehouse recycling center, n denotes the selected recycling center, m denotes the selected disposal center;
s12, establishing related constraint of facility number;
s13, establishing related constraints of facility capacity, wherein the formula is as follows:
wherein,
representing the ratio of conversion of raw material r obtained from a supplier into product c,
indicating the number of products c produced by the hybrid storage and recovery center,
represents the ability of the supplier i to supply the raw material r, i.e., the raw material quantity, and is thus constrained.
3. The method of two-stage scheduling of multi-cycle multi-product evanescent product supply chain network design of claim 2, wherein: the constraints on the number of facilities include a maximum number of alternative suppliers, a maximum number of alternative disposal centers, a maximum number of alternative recycling centers, and a maximum number of alternative hybrid storage and recovery centers;
the maximum number of suppliers is formulated as:
∑ i XS i SM, where the SM table represents the maximum number of suppliers that can be selected,
the maximum number of alternative treatment centers is formulated as:
∑ m XD m DM, where DM represents the maximum number of treatment centers available for selection,
the maximum number of alternative reuse centers is formulated as:
∑ n XR n RM, where RM represents the maximum number of reusable centers available for selection,
the maximum quantity formula of the optional hybrid storage and recovery centers is as follows:
wherein,
n represents the recovery ability of the reuse center, r1 e Representing the return rate of product c from the retailer to the hybrid storage and retrieval center; r2 c Indicating the recovery of the returned product, thereby ensuring that the maximum value of the returned product delivered from the hybrid storage recovery center to the recycling center is less than the capacity of the recycling center.
4. The method of two-stage scheduling of multi-cycle multi-product evanescent product supply chain network design of claim 1, wherein: the configuration model making steps are as follows:
s21, setting an objective function in the configuration model:
the objective function is to take the maximum profit, i.e., total revenue minus total cost; wherein the total revenue comprises: income F of products produced and sold R1 ：
F R1 ＝max∑ t ∑ k ∑ l ∑ c F R V ct ×Z klct Wherein Z is klct Representing the number of products c delivered to the retailer l by the hybrid warehouse recovery center k during the period t, and the income F recovered and sold to the recycling center R2 ：F R2 ＝∑ t ∑ c ∑ n ∑ j RR jnct ×F R VR nct Wherein RR jnct Representing the number of products c transported from the hybrid production verification center j to the recycling center n during time t,
the total cost function comprises:
cost of demand due to lack of stock, F c1 ＝∑ t ∑ c ∑ l F lct ×UD lct In the formula F lct Indicating that product c meets retailer l's demand cost during time t and UD lct Indicating that product c meets retailer i for period t,
total fixed cost, F c2 ＝∑ t ∑ r ∑ i ∑ j XO ijrt ×GO rit In the formula XO ijrt Judging whether the mixed production inspection center orders raw materials r, GO from a supplier i in a t period for the binary variable rit Representing a fixed cost of ordering raw material r from supplier i during time t,
the cost of the purchase is reduced by the purchase cost,
in the formula
Represents the cost, O, of purchasing raw material r from supplier i during time t ijrt Indicating the quantity of raw material r being shipped from supplier i to the mix production verification center j during time t,
the production cost is low, and the production cost is low,
in the formula
Represents the unit production cost, P, of the mixed production inspection center j producing the product c in the period t jkct Indicating the number of products c produced by the mix production and inspection center j and transported to the mix warehouse recovery center during time t,
the cost is kept, and the cost is saved,
in the formula
Represents the unit holding cost S of the product c in the period t by the mixed warehouse recovery center k kcnt Indicating the number of products c still in the blend warehouse recovery center k at the end of time t,
cost of expiration, F c6 ＝∑ t＞3 ∑ c ∑ l ∑ k rv c，t-3 ×RQ lkct In the formula rv c，t-3 Indicating the unit cost, RQ, of expired products lkct Indicating the amount of product c returned from retailer i to the hybrid warehouse recovery center k during time t,
the cost of the inspection is tested, and the cost is tested,
in the formula
Represents the inspection unit inspection cost, RP, of the mixed warehouse inspection center j for the product c in the period t kjct Show product c in weeksThe number of returns from the hybrid storage recovery center k to the hybrid production inspection center j during period t, RPT kjct Representing the number of products c returned from retailer l to the hybrid warehouse recovery center k, and then shipped to the hybrid production verification center j in cycle t,
the cost of the disposal is high,
in the formula
Represents the disposal cost, RD, of the disposal center m for the product c during the period t jmct Representing the number of products c transported from the mixed production inspection center j to the disposal center m during the time period t,
forward transport cost, F c9 ＝∑ t ∑ r ∑ j ∑ i F TC SP ijrt ×A ijrt +∑ t ∑ j ∑ c Σ k (F TC PW jkct ×B jkct )+Σ t Σ c Σ l Σ k F TC WR klct ×Q klct In the formula F TC SP ijrt Represents the transportation cost, A, of raw material r transported from supplier i to the mixed production inspection center j during the period t ijrt Denotes the quantity of transported raw material r, F TC PW jkct Represents the unit transportation cost of the product c from the mixed production inspection center j to the mixed storage recovery k in the period t, B jkct Indicating the quantity of product c transported to the hybrid storage and recovery center, F TC WR klct Represents the number of products c transported from the hybrid storage recovery center k to the retailer l over a period t;
reverse transportation cost, F c10 ＝∑ t ∑ c ∑ l ∑ k F TC WR klct ×RQ klct +∑ t ∑ c ∑ m ∑ j F TC PD jmct ×RD jmct +∑ t ∑ j ∑ c ∑ k (F TC PW jkct ×(RBT kjct +RB kjct ))
In the formula F TC PD jmct Represents the unit transportation cost, RD, of the product c from the mixed production inspection center j to the disposal center m during the period t jmct Represents the number of products c transported from the mixed production inspection center j to the disposal center m during the period t, and the other transportation costs are the same as those in the forward transportation costs;
s22, establishing constraint conditions of each facility capacity;
s23, establishing relevant constraints on the capacity of the hybrid warehouse recovery center;
s24, establishing balance constraint between a supplier and a mixed production inspection center;
s25, establishing a constraint relation between the supply quantity and the inventory;
s26, establishing a constraint relation between the hybrid storage and recovery center and the retailer;
s27, establishing relevant constraints for disposing returned products;
and S28, setting the constraint conditions of the variables in the model.
5. The method of two-stage scheduling of multi-cycle multi-product evanescent product supply chain network design of claim 4, wherein: the constraints for establishing the capacity of each facility comprise the following postures:
posture one: to represent the raw material capability that a supplier can supply at various times, the following constraints are established:
and (5) posture II: to determine the capacity of the hybrid production inspection center at each time period, the following constraints are established:
and (3) posture three: to determine the processing power of each epoch handling center, the following constraints are established:
and (4) posture IV: to determine the capacity of the reuse center for each epoch, the following constraints are established:
6. the method of two-stage scheduling of multi-cycle multi-product evanescent product supply chain network design of claim 4, wherein: the constraints on facility capacity include the raw material capacity that the supplier can supply at each time period, the capacity that the hybrid production verification center can supply at each time period, the processing capacity of the disposal center at each time period, and the capacity of the reuse center at each time period.
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