# Exploiting the Chain Convenience Store Supplier Selection Based on ANP-MOP Model

Authors: Yaqin Ou; Bo Liu
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

The purchase cost of chain convenience stores accounts for a large proportion of the total cost. Enterprises are facing the problem of how to reasonably reduce the purchase cost while ensuring the quality of service. This paper first considers the uniqueness of chain convenience stores, draws on existing research results, and establishes an evaluation index system for chain convenience store suppliers through field research. Then, we use the principal component analysis method of selection to determine the weight of each index and make a preliminary ranking of the importance of chain convenience store suppliers. Secondly, according to the relevant weights determined by the network hierarchy method, the collected data are substituted into the multiobjective mathematical programming model to analyze the distribution of supplier procurement and calculate the procurement cost. The level of procurement expenditures accounted for by suppliers confirms the importance of suppliers. The results show that through the evaluation and ranking of suppliers and the effective management of suppliers according to the ranking results, not only the goal of cost minimization is achieved but also the reasonable service level is guaranteed, which is scientific.


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## Body

## 1. Introduction

The beginning of the entire supply chain management is the selection of suppliers. Among all types of enterprises, the purchase cost of chain retail accounts for the largest total cost. The current research on supplier evaluation and selection in chain retail is not thorough enough. Especially in chain retail, the research on supplier selection based on the two major factors of procurement cost and service level, procurement allocation, and follow-up management is very much lacking [1–3].Guo used AHP to conduct preliminary supplier selection and comprehensive supplier selection and determined its primary and alternative suppliers [4]. Liao and Zhang adopted the AHP-TOPSIS composite method to determine the weight of each index, thus constructing a standardized model for evaluating and selecting green suppliers for papermaking enterprises. And through the application of empirical examples, the feasibility of the way is verified, and an effective method is provided for papermaking enterprises to choose green suppliers [5]. Zhou and Liao used the analytic hierarchy process (AHP) to calculate the weight of a total of 14 indicators in 5 categories, including green environmental indicators, and built an objective and operable supplier evaluation process [6]. Song used the AHP and took candy products as an example to conduct an empirical analysis of the supplier evaluation index system [7]. From the current research on the evaluation of supplier selection by scholars, most scholars still use AHP to construct the supplier index system; still, AHP cannot fully consider the interrelationship between the various index systems. More importantly, most of the scholars' evaluation and selection of suppliers is aimed at manufacturing companies, ignoring the high proportion of chain retail purchase costs in total costs [8–12].From the existing supply chain management research, according to the current supply chain management research, there is not much research on the selection management of chain retail suppliers whose procurement costs account for the total costs. Therefore, it is necessary to further explore the evaluation and selection of chain retail suppliers. This paper takes chain convenience stores in chain retail as an example to examine the evaluation choices of chain convenience store suppliers. The content of this paper is arranged as follows. In Section2, ANP is described in detail and is used to construct, select, and determine the weight of the supplier’s index system. In Section 3, firstly, MOP model is constructed based on ANP model; secondly, taking Rosen, the leader in chain convenience stores, as an example, the collected relevant data which are substituted into the MOP to determine the weight of its supplier evaluation index system and the allocation of procurement volume. The empirical results analysis is presented in Section 4, and a summary of this paper is given in Section 5.


## 2. ANP Model Construction

### 2.1. ANP Model Construction and Index Optimization

The elementsp1,p2,…,pnare in the ANP control layer, and the elements c1,c2,…,cn are in network layer, where c1 has elements ei1,ei2,…,ein, where i=1,2,…,N. The criterion is the control layer pss=1,2,…,m, and the secondary criterion is the element ejll=1,2,…,nj. The elements in the element group ci are compared according to their influence on ejl, and the judgment matrix [13, 14] is constructed under the criterion ps, as shown in Table 1.Table 1
Judgment matrix between each element.
eijei1,ei2,…,einjNormalized feature vectorei1ei2⋮einiwi1jiwi2ji⋮winiji(1)Wij=wi1j1wi1j2…wi1jniwi2j1wi2j2…wi2jni⋮winjj1winjj2…winjjni,(2)C1C2CNe11…e1n1e21…e2n2eN1…eNnnW=e11C1…e1n1e21C2…e2n2eN1CN…eNnnW11W12…W1NW21W22…W2N⋮⋮⋮WN1WN2…WNN.The weight vector is obtained by the characteristic-root method. Repeat the above steps to obtain the matrix record as shown in formula (1):The column vector of here is the sorting vector of the influence degree of the element in the element. If the middle element is not affected by the middle element, then = 0. Repeat the above steps fori = 1, 2, ..., N, j = 1, 2, ..., N. Finally, the supermatrix under the criterion can be obtained as equation (2). There are m of these supermatrices, and they are all non-negative matrices.


### 2.2. Construction and Optimization of Evaluation Index System

On the basis of summarizing the research of scholars, a questionnaire was designed in combination with the characteristics of chain convenience stores; after distribution, recovery, and calculation, the evaluation index system of chain convenience store procurement suppliers was initially constructed [9–13] (as shown in Table 2).Table 2
Evaluation index system for purchasing suppliers of chain convenience store.
Target layerCriterion layerIndex layerIndicator typeSupplier selection evaluationTechnical skills B1Logistics facilities and equipment C1QualitativeInformation team processing ability C2QualitativeProportion of supply chain management professionals C3QualitativeScheme design ability C4QualitativeProcess integration capability C5QualitativeTeamwork ability B2Supply capacity C6QualitativeReliability C7QualitativeAfter-sales service C8QualitativeDelivery accuracy C9QuantitativeQuick response ability C10QualitativeInternal competitiveness B3Operating resources C11QualitativeR & D capabilities C12QualitativeProduction management ability C13QualitativeOrganizational effectiveness analysis C14QualitativeOperational capability C15QualitativeExternal competitiveness B4Market environment and competition C16QualitativeCustomer needs and feedback C17QualitativeEconomic environment C18QualitativeSocial environment C19QualitativePrice factor B5Transportation cost C20QuantitativeProduct cost C21QuantitativeStorage cost C22QuantitativeQuality cost C23QuantitativeOut-of-stock cost C24QuantitativeIn response to the initially constructed indicator system, a questionnaire on the importance of indicators was designed and distributed to multiple experts to score them. Then, the questionnaire was returned to the minimum and maximum statistics of all indicators, and mean and standard deviation were calculated. By comparing and analyzing the results, the criterion layer and the index layer are selected to obtain a new and more realistic index system [14–17], and then the data on the importance of the criterion layer and the index layer are sorted out.Table3 shows the mean and standard deviation of the importance scores of the five categories of indicators by respondents. It can be seen from the table that the mean (8.13) of the price factor is the largest, which is almost close to the maximum value of 9.00, which also shows that price is the most crucial consideration. Secondly, the larger mean is cooperation ability (7.31), which shows that the cooperation ability is also vital. The mean of technical ability (7.11) and the mean of cooperation ability (7.31) are very close in size, so they are even more important. However, the internal competitiveness (3.11) and external competitiveness (4.07) have a smaller mean.Table 3
Descriptive statistical analysis of criterion-level indicators.
Technical skillsTeamwork abilityInternal competitivenessExternal competitivenessPrice factorNumber100100100100100Minimum45237Maximum99589Mean (mean)7.117.313.114.078.13Standard deviation0.8770.8030.8101.1430.802The standard deviation of price factor, cooperation ability, and internal competitiveness is relatively small. It can be seen that the respondents have basically no objection to the importance of these three indicators, while the standard deviation of external competitiveness and technical ability is relatively large, indicating that interviewers have a specific difference in their opinions on the importance of these two indicators.In the same way, the subdivision secondary indicators of other standard levels are shown in Table4.Table 4
The optimized index system.
TargetCriterion layerIndex layerIndicator typeData sourcesSupplier selection evaluationTechnical skillsLogistics facilities and equipmentQualitativeScoring by expertsProportion of supply chain managementQuantitativeFormula calculationProcess integration capabilityQualitativeScoring by expertsTeamwork abilitySupply capacityQualitativeScoring by expertsReliabilityQualitativeScoring by expertsDelivery accuracyQuantitativeFormula calculationInternal competitivenessOperating resourcesQualitativeScoring by expertsProduction management abilityQualitativeScoring by expertsExternal competitivenessOrganizational effectiveness analysisQualitativeScoring by expertsCustomer needs and feedbackQualitativeScoring by expertsPrice factorTransportation costQuantitativeFormula calculationStorage costQuantitativeFormula calculationQuality costQuantitativeFormula calculationOut-of-stock costQuantitativeFormula calculation


### 2.3. Establishment of the Index Weights for Supplier Evaluation Index System

The following only lists the evaluation data of one group of five groups of experts on the pairwise comparison matrix of the criterion-level indicators. The evaluation data of all indicators are directly input into the software for calculation [18–21]. The calculation results are shown in Table 5. The indicators of the standard level in the software are technical capabilities B1, cooperation capabilities B2, external competitiveness B3, internal competitiveness B4, and price factors B5.Expert Group 1:wi=0.252,0.173,0.143,0.076,0.356Expert Group 2:wi=0.220,0.228,0.099,0.065,0.388Expert Group 3:wi=0.187,0.348,0.063,0.107,0.295Expert Group 4:wi=0.241,0.199,0.118,0.072,0.370Expert Group 5:wi=0.241,0.115,0.076,0.199,0.369Table 5
Pairwise comparison matrix of expert group 1’s evaluation of criterion-level indicators.
BiB1B2B3B4B5WiB113221/20.252B21/31131/20.173B31/21121/30.143B41/21/31/211/40.076B5223410.356Note: the eigenvalue of the matrix is 5.200; the matrix consistency is 0.045 which is less than 0.1. Expert Group 1: = (0.252,0.173,0.143,0.076,0.356). Expert Group 2: = (0.220,0.228,0.099,0.065,0.388). Expert Group 3: = (0.187,0.348,0.063,0.107,0.295). Expert Group 4: = (0.241,0.199,0.118,0.072,0.370). Expert Group 5: = (0.241,0.115,0.076,0.199,0.369).Using the geometric mean, the final weight of the B-level indicators can be determined as(3)uj=∏i=1mwi1m,uB=0.231,0.210,0.105,0.100,0.354.The same method is used to calculate the weighted hypermatrix of all indicators. From the limit matrix, all indicator weights between indicators can be obtained as shown in Table6 and Figure 1.Table 6
Index weights of the index layer.
NameWeighted valueLimit valueLogistics facilities and equipment0.306470.04045Proportion of supply chain management0.287520.04076Process integration capability0.406010.04385Supply capacity0.353250.05102Reliability0.225430.05023Delivery accuracy0.421320.06102Operating resources0.541240.00731Production management ability0.458760.03621Organizational effectiveness analysis0.446760.00821Customer needs and feedback0.553240.03205Transportation cost0.224320.13385Storage cost0.334920.24137Quality cost0.219750.11265Out-of-stock cost0.221010.14102Figure 1
Index weight distribution chart of the index layer.The top seven indicators are product cost, out-of-stock cost, transportation cost, quality cost, delivery accuracy, supply capacity, and reliability.


## 2.1. ANP Model Construction and Index Optimization

The elementsp1,p2,…,pnare in the ANP control layer, and the elements c1,c2,…,cn are in network layer, where c1 has elements ei1,ei2,…,ein, where i=1,2,…,N. The criterion is the control layer pss=1,2,…,m, and the secondary criterion is the element ejll=1,2,…,nj. The elements in the element group ci are compared according to their influence on ejl, and the judgment matrix [13, 14] is constructed under the criterion ps, as shown in Table 1.Table 1
Judgment matrix between each element.
eijei1,ei2,…,einjNormalized feature vectorei1ei2⋮einiwi1jiwi2ji⋮winiji(1)Wij=wi1j1wi1j2…wi1jniwi2j1wi2j2…wi2jni⋮winjj1winjj2…winjjni,(2)C1C2CNe11…e1n1e21…e2n2eN1…eNnnW=e11C1…e1n1e21C2…e2n2eN1CN…eNnnW11W12…W1NW21W22…W2N⋮⋮⋮WN1WN2…WNN.The weight vector is obtained by the characteristic-root method. Repeat the above steps to obtain the matrix record as shown in formula (1):The column vector of here is the sorting vector of the influence degree of the element in the element. If the middle element is not affected by the middle element, then = 0. Repeat the above steps fori = 1, 2, ..., N, j = 1, 2, ..., N. Finally, the supermatrix under the criterion can be obtained as equation (2). There are m of these supermatrices, and they are all non-negative matrices.


## 2.2. Construction and Optimization of Evaluation Index System

On the basis of summarizing the research of scholars, a questionnaire was designed in combination with the characteristics of chain convenience stores; after distribution, recovery, and calculation, the evaluation index system of chain convenience store procurement suppliers was initially constructed [9–13] (as shown in Table 2).Table 2
Evaluation index system for purchasing suppliers of chain convenience store.
Target layerCriterion layerIndex layerIndicator typeSupplier selection evaluationTechnical skills B1Logistics facilities and equipment C1QualitativeInformation team processing ability C2QualitativeProportion of supply chain management professionals C3QualitativeScheme design ability C4QualitativeProcess integration capability C5QualitativeTeamwork ability B2Supply capacity C6QualitativeReliability C7QualitativeAfter-sales service C8QualitativeDelivery accuracy C9QuantitativeQuick response ability C10QualitativeInternal competitiveness B3Operating resources C11QualitativeR & D capabilities C12QualitativeProduction management ability C13QualitativeOrganizational effectiveness analysis C14QualitativeOperational capability C15QualitativeExternal competitiveness B4Market environment and competition C16QualitativeCustomer needs and feedback C17QualitativeEconomic environment C18QualitativeSocial environment C19QualitativePrice factor B5Transportation cost C20QuantitativeProduct cost C21QuantitativeStorage cost C22QuantitativeQuality cost C23QuantitativeOut-of-stock cost C24QuantitativeIn response to the initially constructed indicator system, a questionnaire on the importance of indicators was designed and distributed to multiple experts to score them. Then, the questionnaire was returned to the minimum and maximum statistics of all indicators, and mean and standard deviation were calculated. By comparing and analyzing the results, the criterion layer and the index layer are selected to obtain a new and more realistic index system [14–17], and then the data on the importance of the criterion layer and the index layer are sorted out.Table3 shows the mean and standard deviation of the importance scores of the five categories of indicators by respondents. It can be seen from the table that the mean (8.13) of the price factor is the largest, which is almost close to the maximum value of 9.00, which also shows that price is the most crucial consideration. Secondly, the larger mean is cooperation ability (7.31), which shows that the cooperation ability is also vital. The mean of technical ability (7.11) and the mean of cooperation ability (7.31) are very close in size, so they are even more important. However, the internal competitiveness (3.11) and external competitiveness (4.07) have a smaller mean.Table 3
Descriptive statistical analysis of criterion-level indicators.
Technical skillsTeamwork abilityInternal competitivenessExternal competitivenessPrice factorNumber100100100100100Minimum45237Maximum99589Mean (mean)7.117.313.114.078.13Standard deviation0.8770.8030.8101.1430.802The standard deviation of price factor, cooperation ability, and internal competitiveness is relatively small. It can be seen that the respondents have basically no objection to the importance of these three indicators, while the standard deviation of external competitiveness and technical ability is relatively large, indicating that interviewers have a specific difference in their opinions on the importance of these two indicators.In the same way, the subdivision secondary indicators of other standard levels are shown in Table4.Table 4
The optimized index system.
TargetCriterion layerIndex layerIndicator typeData sourcesSupplier selection evaluationTechnical skillsLogistics facilities and equipmentQualitativeScoring by expertsProportion of supply chain managementQuantitativeFormula calculationProcess integration capabilityQualitativeScoring by expertsTeamwork abilitySupply capacityQualitativeScoring by expertsReliabilityQualitativeScoring by expertsDelivery accuracyQuantitativeFormula calculationInternal competitivenessOperating resourcesQualitativeScoring by expertsProduction management abilityQualitativeScoring by expertsExternal competitivenessOrganizational effectiveness analysisQualitativeScoring by expertsCustomer needs and feedbackQualitativeScoring by expertsPrice factorTransportation costQuantitativeFormula calculationStorage costQuantitativeFormula calculationQuality costQuantitativeFormula calculationOut-of-stock costQuantitativeFormula calculation


## 2.3. Establishment of the Index Weights for Supplier Evaluation Index System

The following only lists the evaluation data of one group of five groups of experts on the pairwise comparison matrix of the criterion-level indicators. The evaluation data of all indicators are directly input into the software for calculation [18–21]. The calculation results are shown in Table 5. The indicators of the standard level in the software are technical capabilities B1, cooperation capabilities B2, external competitiveness B3, internal competitiveness B4, and price factors B5.Expert Group 1:wi=0.252,0.173,0.143,0.076,0.356Expert Group 2:wi=0.220,0.228,0.099,0.065,0.388Expert Group 3:wi=0.187,0.348,0.063,0.107,0.295Expert Group 4:wi=0.241,0.199,0.118,0.072,0.370Expert Group 5:wi=0.241,0.115,0.076,0.199,0.369Table 5
Pairwise comparison matrix of expert group 1’s evaluation of criterion-level indicators.
BiB1B2B3B4B5WiB113221/20.252B21/31131/20.173B31/21121/30.143B41/21/31/211/40.076B5223410.356Note: the eigenvalue of the matrix is 5.200; the matrix consistency is 0.045 which is less than 0.1. Expert Group 1: = (0.252,0.173,0.143,0.076,0.356). Expert Group 2: = (0.220,0.228,0.099,0.065,0.388). Expert Group 3: = (0.187,0.348,0.063,0.107,0.295). Expert Group 4: = (0.241,0.199,0.118,0.072,0.370). Expert Group 5: = (0.241,0.115,0.076,0.199,0.369).Using the geometric mean, the final weight of the B-level indicators can be determined as(3)uj=∏i=1mwi1m,uB=0.231,0.210,0.105,0.100,0.354.The same method is used to calculate the weighted hypermatrix of all indicators. From the limit matrix, all indicator weights between indicators can be obtained as shown in Table6 and Figure 1.Table 6
Index weights of the index layer.
NameWeighted valueLimit valueLogistics facilities and equipment0.306470.04045Proportion of supply chain management0.287520.04076Process integration capability0.406010.04385Supply capacity0.353250.05102Reliability0.225430.05023Delivery accuracy0.421320.06102Operating resources0.541240.00731Production management ability0.458760.03621Organizational effectiveness analysis0.446760.00821Customer needs and feedback0.553240.03205Transportation cost0.224320.13385Storage cost0.334920.24137Quality cost0.219750.11265Out-of-stock cost0.221010.14102Figure 1
Index weight distribution chart of the index layer.The top seven indicators are product cost, out-of-stock cost, transportation cost, quality cost, delivery accuracy, supply capacity, and reliability.


## 3. MOP Model Construction

We establish a specific model for chain convenience store purchasing supplier selection and purchasing volume allocation.


### 3.1. Meaning of Symbols

The mathematical symbols of the following model are defined as follows:(1)
Two types of decision variables:One is the allocation ratioxij0<xij<1 of the purchased quantity when purchasing goods from each candidate supplier gi; the other is the variable yij=1 that indicates whether the company purchases product j from a supplier gi, if the company purchases product j from that supplier, then yij=1, otherwise yij=0, where i is the serial number of the supplier, i = 1,2, ..., m, j is the serial number of the purchased product, j=1,2,…,n.(2)
Parameter description:cj: the total amount of the company’s purchase of product j during the planning period; uij: the minimum purchase cost required for the product j purchased by the supplier gi; kij: the maximum supply of product j provided by the supplier gi; ni: the company can choose the number of suppliers; n: the number of products that the company intends to purchase; qij: the importance factor of the products provided by the supplier gi; jij the product cost of buying j products from the supplier gi; ji: the company expects to limit the maximum cost of the supplier's product j. tij: the out-of-stock cost when the gi supplier provides the j product; tj: the maximum out-of-stock cost when the company limits the gi supplier to provide the j product; dij: the transportation of the j product purchased from the gi supplier cost; dj: the highest transportation cost of the company's purchase of j product limited by the gi supplier; lij: the quality cost of the j product purchased by the gi supplier; lj: the highest quality cost of the company's limited gi supplier j product; rij: gi supplier j product delivery accuracy rate; rj: represents the lowest delivery accuracy rate that the company expects supplier j's product; eij: gi supplier j's product supply capacity; ej: the company expects the minimum supply capacity of gi supplier; nij: the reliability of the product provided by the supplier gi; nj: indicates the lowest limit of the reliability of the product expected by the supplier gi to provide j; pij: the proportion of the purchase cost of the gi supplier’s purchase of j products.


### 3.2. Model Establishment

According to the concept and symbolic assumptions of cooperation with essential suppliers, the following MOP models for supplier selection can be established:(1)
Objective function:(4)maxZ1=−∑i=1m∑j=1npijxij,(5)maxZ2=∑i=1m∑j=1nqijxij.(2)
Constraints:St:(6)uij≤cjxij≤kij,(7)∑i=1m∑j=1nfijxij≤fj,(8)∑i=1m∑j=1ntijxij≤tj,(9)∑i=1m∑j=1ndijxij≤dj,(10)∑i=1m∑j=1nlijxij≤lj,(11)∑i=1m∑j=1nrijxij≤rj,(12)∑i=1m∑j=1neijxij≤ej,(13)∑i=1m∑j=1nrijxij≤rj,(14)∑i=1mxij=1,(15)xijyij−1=0,(16)xij∈0,1,(17)yij∈0,1.(3)
Formula meaning:Formula (4): represents the lowest purchasing cost.Formula (5): represents the amount of priority to purchase from gi suppliers when purchasing product j.Formula (6): the upper and lower limits of the ability of supplier gi to provide products.Formula (7): the product cost constraint when supplier gi purchases product j.Formula (8): the constraint of the out-of-stock cost when supplier gi purchases product j.Formula (9): the transportation cost constraint when supplier gi purchases product j.Equation (10): constraint of quality cost when gi supplier purchases product j.Equation (11): constraint on the delivery accuracy of product j of gi supplier.Formula (12): requirements for the supply capacity of gi supplier j's products.Formula (13): gi supplier provides product j reliability requirements.Equation (14): when purchasing product j from the gi supplier, yij must be 1.


## 3.1. Meaning of Symbols

The mathematical symbols of the following model are defined as follows:(1)
Two types of decision variables:One is the allocation ratioxij0<xij<1 of the purchased quantity when purchasing goods from each candidate supplier gi; the other is the variable yij=1 that indicates whether the company purchases product j from a supplier gi, if the company purchases product j from that supplier, then yij=1, otherwise yij=0, where i is the serial number of the supplier, i = 1,2, ..., m, j is the serial number of the purchased product, j=1,2,…,n.(2)
Parameter description:cj: the total amount of the company’s purchase of product j during the planning period; uij: the minimum purchase cost required for the product j purchased by the supplier gi; kij: the maximum supply of product j provided by the supplier gi; ni: the company can choose the number of suppliers; n: the number of products that the company intends to purchase; qij: the importance factor of the products provided by the supplier gi; jij the product cost of buying j products from the supplier gi; ji: the company expects to limit the maximum cost of the supplier's product j. tij: the out-of-stock cost when the gi supplier provides the j product; tj: the maximum out-of-stock cost when the company limits the gi supplier to provide the j product; dij: the transportation of the j product purchased from the gi supplier cost; dj: the highest transportation cost of the company's purchase of j product limited by the gi supplier; lij: the quality cost of the j product purchased by the gi supplier; lj: the highest quality cost of the company's limited gi supplier j product; rij: gi supplier j product delivery accuracy rate; rj: represents the lowest delivery accuracy rate that the company expects supplier j's product; eij: gi supplier j's product supply capacity; ej: the company expects the minimum supply capacity of gi supplier; nij: the reliability of the product provided by the supplier gi; nj: indicates the lowest limit of the reliability of the product expected by the supplier gi to provide j; pij: the proportion of the purchase cost of the gi supplier’s purchase of j products.


## 3.2. Model Establishment

According to the concept and symbolic assumptions of cooperation with essential suppliers, the following MOP models for supplier selection can be established:(1)
Objective function:(4)maxZ1=−∑i=1m∑j=1npijxij,(5)maxZ2=∑i=1m∑j=1nqijxij.(2)
Constraints:St:(6)uij≤cjxij≤kij,(7)∑i=1m∑j=1nfijxij≤fj,(8)∑i=1m∑j=1ntijxij≤tj,(9)∑i=1m∑j=1ndijxij≤dj,(10)∑i=1m∑j=1nlijxij≤lj,(11)∑i=1m∑j=1nrijxij≤rj,(12)∑i=1m∑j=1neijxij≤ej,(13)∑i=1m∑j=1nrijxij≤rj,(14)∑i=1mxij=1,(15)xijyij−1=0,(16)xij∈0,1,(17)yij∈0,1.(3)
Formula meaning:Formula (4): represents the lowest purchasing cost.Formula (5): represents the amount of priority to purchase from gi suppliers when purchasing product j.Formula (6): the upper and lower limits of the ability of supplier gi to provide products.Formula (7): the product cost constraint when supplier gi purchases product j.Formula (8): the constraint of the out-of-stock cost when supplier gi purchases product j.Formula (9): the transportation cost constraint when supplier gi purchases product j.Equation (10): constraint of quality cost when gi supplier purchases product j.Equation (11): constraint on the delivery accuracy of product j of gi supplier.Formula (12): requirements for the supply capacity of gi supplier j's products.Formula (13): gi supplier provides product j reliability requirements.Equation (14): when purchasing product j from the gi supplier, yij must be 1.


## 4. Lawson Convenience Store Supplier Evaluation Selection

### 4.1. The Weight of Index System Determined Based on ANP Model

According to the indicator system constructed in the previous paper and the determination of related weights, the relevant data are substituted for the evaluation and selection of Lawson convenience store suppliers [22–26], and now 5 suppliers =g1,g2,g3,g4,g5 are screened and one is selected as a partner of the company; a tripartite group p1,p2,p3,p4,p5 is formed by a team of senior purchasers, a team of logistics managers, and a team of experts in related industries. The expert group decided to select the top seven indicators to evaluate the five suppliers. The weights of the tripartite experts in the decision-making are: senior purchaser team ϖ=0.5, logistics manager team ϖ=0.3, and related industry expert teamϖ=0.2. In the evaluation index, the evaluation data of five quantitative indicators come from 5 procurement suppliers, where product cost, out-of-stock cost, quality cost, and transportation cost are the ratios of the average cost of the four products to the related expenses in the same industry, which are shown in Table 7 and Figure 2.Table 7
Five quantitative indicators of five suppliers.
g1g2g3g4g5Storage cost65%60%70%58%76%Out-of-stock cost60%64%65%70%66%Transportation cost60%58%60%68%59%Quality cost59%67%72%55%75%Delivery accuracy97%96%92%92%91%Figure 2
Distribution map of five quantitative indicators of five suppliers.The tripartite experts score the supplier’s performance under the qualitative indicators and the data of all qualitative indicators. The scoring adopts a nine-point system. The supplier’s performance is represented by 9-1 from high to bottom. 9 points means very good, and 1 point represents extremely poor performance. The larger the score, the better the performance.The three-party experts' specific scores on the 5 candidates for selection and the final scores after calculation are shown in Table8 and Figure 3.Table 8
Specific scoring results of 5 candidate suppliers.
g1g2g3g4g5Storage cost87.76.33.86.5Out-of-stock cost7.76.854.57.1Transportation cost7.386.46.57Quality cost6.75.966.76.7Delivery accuracy6.67.35.76.26.5Supply capacity8.57.25.56.46.5Reliability7.16.86.45.77.1Figure 3
Distribution of specific scoring results of 5 candidate suppliers.The first step is to determine the weights. In the previous paper, the results of ANP have been obtained and the weights of the seven evaluation indicators are(18)W=0.24137,0.14102,0.13385,0.11265,0.06102,0.05102,0.05023.The second step is to construct an evaluation matrix of five procurement suppliers under seven evaluation indicators in the software.The third step is to define the attributes of the index evaluation. For each evaluation index, define its evaluation attribute and construct the evaluation attribute matrix for pairwise comparison.The fourth step is to sort the suppliers, input the final score value of each supplier, and further comprehensively calculate the corresponding ranking result:g1>g2>g5>g3>g4, and you can get 5 purchases. The supplier’s importance coefficient is q = (0.23310, 0.23193, 0.18241,0.17214, 0.21423).


### 4.2. Purchase Volume Allocated Based on MOP

#### 4.2.1. Data Collection

There are too many types of chain convenience stores. Here, 4 of them are selected as an example [27]. Substitute the 5 buyers qualified in the preliminary selection and sorted into the model and calculate and evaluate further. The parameter values and evaluation information of each supplier's supply capacity and level and the parameter values required by retail enterprises for the supplier's supply capacity and level are shown in Tables 9 and 10 .Table 9
Parameter values and evaluation information for marking the supply capacity and level of each supplier.
Product serial numberSupplierpij (%)qij (%)kij (ten thousand yuan)uij (ten thousand yuan)fij (ten thousand yuan)tij (ten thousand yuan)dij (ten thousand yuan)lij (ten thousand yuan)rij (%)eijnij111223.3159610.20.1906721123.213740.50.10.19588231522.3108510.20.12907751422.511840.50.10.159076321318.912530.50.10.1958731219.28530.50.10.129066411121.58630.50.10.05907641220.25420.50.10.059565Table 10
The requirements of a retail company on the supply capacity of its suppliers.
Purchase products (ten thousand yuan)cjfjtjdjrjejljnj12071.20.59580.5821250.80.49290.39315610.49590.2941050.70.39580.38


#### 4.2.2. Data Processing

According to the symbols established in formulas (4) to (17) and the supplier's importance coefficient established in the previous article, the MOP model that can be established is as follows:(19)maxz1=0.12x11+0.11x21+0.15x32+0.14x52+0.13x23+0.12x33+0.11x14+0.12x44maxz2=0.233x11+0.232x21+0.18x32+0.214x52+0.232x23+0.182x33+0.233x14+0.138x44s.t.9≤20x11≤15,7≤20x21≤13,x32≤10,8≤x52≤115≤15x23≤12,5≤20x21≤13,6≤10x14≤8,4≤10x44≤56x11+4x21≤7,5x32+4x52≤5,3x23+3x33≤6,3x14+2x44≤5x11+0.5x21≤1.2,x32+0.5x52≤0.8,0.5x32+0.5x33≤1,0.5x14+0.5x44≤0.70.2x11+0.1x21≤0.5,0.2x32+0.1x52≤0.4,0.1x32+0.1x33≤0.4,0.1x14+0.1x44≤0.30.9x11+0.95x21≥0.95,7x32+7x52≥9,8x32+6x33≥9.7x14+6x44≥87x11+8x21≥8,7x32+6x52≥9,7x32+6x33≥9.6x14+7x44≥8x11+x21=1,x32+x52=1,x23+x33=1,x14+x44=1x11×y11−1=0,x21×y21−1=0,x32×y32−1=0,x52×y52−1=0x23×y23−1=0,x33×y33−1=0,x14×y14−1=0,x44×y4−1=00≤xij≤1,0≤yij≤1i=1.2,…,5,j=1.2,…,4.


#### 4.2.3. Solution

According to the algorithm introduced in the previous paper, we can solve(20)z1∗=49.1%,x11=0.427,x21=0.573,x32=0.516,x52=0.484x23=0.785,x33=0.215,x14=0.548,x44=0.452y11=1,y21=1,y32=1,y52=1,y23=1,y33=1,y14=1,y44=1,and adopt λ=0.05. Then, the above model can be further transformed into the following form:(21)maxz2=0.233x11+0.232x21+0.182x32+0.214x52+0.232x23+0.182x33+0.233x14+0.138x44.The constraint condition is added on the original basis, namely:(22)0.12x11+0.11x21+0.15x32+0.14x52+0.13x23+0.12x33+0.11x14+0.12x44≤1−λ×49.1%.The solution of the single objective mathematical programming model is(23)x11=0.712,x21=0.288,x32=0.195,x52=0.805,x23=0.751,x33=0.249,x14=0.378,x44=0.622,y11=1,y21=1,y32=1,y52=1,y23=1,y33=1,y14=1,y44=1.


## 4.1. The Weight of Index System Determined Based on ANP Model

According to the indicator system constructed in the previous paper and the determination of related weights, the relevant data are substituted for the evaluation and selection of Lawson convenience store suppliers [22–26], and now 5 suppliers =g1,g2,g3,g4,g5 are screened and one is selected as a partner of the company; a tripartite group p1,p2,p3,p4,p5 is formed by a team of senior purchasers, a team of logistics managers, and a team of experts in related industries. The expert group decided to select the top seven indicators to evaluate the five suppliers. The weights of the tripartite experts in the decision-making are: senior purchaser team ϖ=0.5, logistics manager team ϖ=0.3, and related industry expert teamϖ=0.2. In the evaluation index, the evaluation data of five quantitative indicators come from 5 procurement suppliers, where product cost, out-of-stock cost, quality cost, and transportation cost are the ratios of the average cost of the four products to the related expenses in the same industry, which are shown in Table 7 and Figure 2.Table 7
Five quantitative indicators of five suppliers.
g1g2g3g4g5Storage cost65%60%70%58%76%Out-of-stock cost60%64%65%70%66%Transportation cost60%58%60%68%59%Quality cost59%67%72%55%75%Delivery accuracy97%96%92%92%91%Figure 2
Distribution map of five quantitative indicators of five suppliers.The tripartite experts score the supplier’s performance under the qualitative indicators and the data of all qualitative indicators. The scoring adopts a nine-point system. The supplier’s performance is represented by 9-1 from high to bottom. 9 points means very good, and 1 point represents extremely poor performance. The larger the score, the better the performance.The three-party experts' specific scores on the 5 candidates for selection and the final scores after calculation are shown in Table8 and Figure 3.Table 8
Specific scoring results of 5 candidate suppliers.
g1g2g3g4g5Storage cost87.76.33.86.5Out-of-stock cost7.76.854.57.1Transportation cost7.386.46.57Quality cost6.75.966.76.7Delivery accuracy6.67.35.76.26.5Supply capacity8.57.25.56.46.5Reliability7.16.86.45.77.1Figure 3
Distribution of specific scoring results of 5 candidate suppliers.The first step is to determine the weights. In the previous paper, the results of ANP have been obtained and the weights of the seven evaluation indicators are(18)W=0.24137,0.14102,0.13385,0.11265,0.06102,0.05102,0.05023.The second step is to construct an evaluation matrix of five procurement suppliers under seven evaluation indicators in the software.The third step is to define the attributes of the index evaluation. For each evaluation index, define its evaluation attribute and construct the evaluation attribute matrix for pairwise comparison.The fourth step is to sort the suppliers, input the final score value of each supplier, and further comprehensively calculate the corresponding ranking result:g1>g2>g5>g3>g4, and you can get 5 purchases. The supplier’s importance coefficient is q = (0.23310, 0.23193, 0.18241,0.17214, 0.21423).


## 4.2. Purchase Volume Allocated Based on MOP

### 4.2.1. Data Collection

There are too many types of chain convenience stores. Here, 4 of them are selected as an example [27]. Substitute the 5 buyers qualified in the preliminary selection and sorted into the model and calculate and evaluate further. The parameter values and evaluation information of each supplier's supply capacity and level and the parameter values required by retail enterprises for the supplier's supply capacity and level are shown in Tables 9 and 10 .Table 9
Parameter values and evaluation information for marking the supply capacity and level of each supplier.
Product serial numberSupplierpij (%)qij (%)kij (ten thousand yuan)uij (ten thousand yuan)fij (ten thousand yuan)tij (ten thousand yuan)dij (ten thousand yuan)lij (ten thousand yuan)rij (%)eijnij111223.3159610.20.1906721123.213740.50.10.19588231522.3108510.20.12907751422.511840.50.10.159076321318.912530.50.10.1958731219.28530.50.10.129066411121.58630.50.10.05907641220.25420.50.10.059565Table 10
The requirements of a retail company on the supply capacity of its suppliers.
Purchase products (ten thousand yuan)cjfjtjdjrjejljnj12071.20.59580.5821250.80.49290.39315610.49590.2941050.70.39580.38


### 4.2.2. Data Processing

According to the symbols established in formulas (4) to (17) and the supplier's importance coefficient established in the previous article, the MOP model that can be established is as follows:(19)maxz1=0.12x11+0.11x21+0.15x32+0.14x52+0.13x23+0.12x33+0.11x14+0.12x44maxz2=0.233x11+0.232x21+0.18x32+0.214x52+0.232x23+0.182x33+0.233x14+0.138x44s.t.9≤20x11≤15,7≤20x21≤13,x32≤10,8≤x52≤115≤15x23≤12,5≤20x21≤13,6≤10x14≤8,4≤10x44≤56x11+4x21≤7,5x32+4x52≤5,3x23+3x33≤6,3x14+2x44≤5x11+0.5x21≤1.2,x32+0.5x52≤0.8,0.5x32+0.5x33≤1,0.5x14+0.5x44≤0.70.2x11+0.1x21≤0.5,0.2x32+0.1x52≤0.4,0.1x32+0.1x33≤0.4,0.1x14+0.1x44≤0.30.9x11+0.95x21≥0.95,7x32+7x52≥9,8x32+6x33≥9.7x14+6x44≥87x11+8x21≥8,7x32+6x52≥9,7x32+6x33≥9.6x14+7x44≥8x11+x21=1,x32+x52=1,x23+x33=1,x14+x44=1x11×y11−1=0,x21×y21−1=0,x32×y32−1=0,x52×y52−1=0x23×y23−1=0,x33×y33−1=0,x14×y14−1=0,x44×y4−1=00≤xij≤1,0≤yij≤1i=1.2,…,5,j=1.2,…,4.


### 4.2.3. Solution

According to the algorithm introduced in the previous paper, we can solve(20)z1∗=49.1%,x11=0.427,x21=0.573,x32=0.516,x52=0.484x23=0.785,x33=0.215,x14=0.548,x44=0.452y11=1,y21=1,y32=1,y52=1,y23=1,y33=1,y14=1,y44=1,and adopt λ=0.05. Then, the above model can be further transformed into the following form:(21)maxz2=0.233x11+0.232x21+0.182x32+0.214x52+0.232x23+0.182x33+0.233x14+0.138x44.The constraint condition is added on the original basis, namely:(22)0.12x11+0.11x21+0.15x32+0.14x52+0.13x23+0.12x33+0.11x14+0.12x44≤1−λ×49.1%.The solution of the single objective mathematical programming model is(23)x11=0.712,x21=0.288,x32=0.195,x52=0.805,x23=0.751,x33=0.249,x14=0.378,x44=0.622,y11=1,y21=1,y32=1,y52=1,y23=1,y33=1,y14=1,y44=1.


## 4.2.1. Data Collection

There are too many types of chain convenience stores. Here, 4 of them are selected as an example [27]. Substitute the 5 buyers qualified in the preliminary selection and sorted into the model and calculate and evaluate further. The parameter values and evaluation information of each supplier's supply capacity and level and the parameter values required by retail enterprises for the supplier's supply capacity and level are shown in Tables 9 and 10 .Table 9
Parameter values and evaluation information for marking the supply capacity and level of each supplier.
Product serial numberSupplierpij (%)qij (%)kij (ten thousand yuan)uij (ten thousand yuan)fij (ten thousand yuan)tij (ten thousand yuan)dij (ten thousand yuan)lij (ten thousand yuan)rij (%)eijnij111223.3159610.20.1906721123.213740.50.10.19588231522.3108510.20.12907751422.511840.50.10.159076321318.912530.50.10.1958731219.28530.50.10.129066411121.58630.50.10.05907641220.25420.50.10.059565Table 10
The requirements of a retail company on the supply capacity of its suppliers.
Purchase products (ten thousand yuan)cjfjtjdjrjejljnj12071.20.59580.5821250.80.49290.39315610.49590.2941050.70.39580.38


## 4.2.2. Data Processing

According to the symbols established in formulas (4) to (17) and the supplier's importance coefficient established in the previous article, the MOP model that can be established is as follows:(19)maxz1=0.12x11+0.11x21+0.15x32+0.14x52+0.13x23+0.12x33+0.11x14+0.12x44maxz2=0.233x11+0.232x21+0.18x32+0.214x52+0.232x23+0.182x33+0.233x14+0.138x44s.t.9≤20x11≤15,7≤20x21≤13,x32≤10,8≤x52≤115≤15x23≤12,5≤20x21≤13,6≤10x14≤8,4≤10x44≤56x11+4x21≤7,5x32+4x52≤5,3x23+3x33≤6,3x14+2x44≤5x11+0.5x21≤1.2,x32+0.5x52≤0.8,0.5x32+0.5x33≤1,0.5x14+0.5x44≤0.70.2x11+0.1x21≤0.5,0.2x32+0.1x52≤0.4,0.1x32+0.1x33≤0.4,0.1x14+0.1x44≤0.30.9x11+0.95x21≥0.95,7x32+7x52≥9,8x32+6x33≥9.7x14+6x44≥87x11+8x21≥8,7x32+6x52≥9,7x32+6x33≥9.6x14+7x44≥8x11+x21=1,x32+x52=1,x23+x33=1,x14+x44=1x11×y11−1=0,x21×y21−1=0,x32×y32−1=0,x52×y52−1=0x23×y23−1=0,x33×y33−1=0,x14×y14−1=0,x44×y4−1=00≤xij≤1,0≤yij≤1i=1.2,…,5,j=1.2,…,4.


## 4.2.3. Solution

According to the algorithm introduced in the previous paper, we can solve(20)z1∗=49.1%,x11=0.427,x21=0.573,x32=0.516,x52=0.484x23=0.785,x33=0.215,x14=0.548,x44=0.452y11=1,y21=1,y32=1,y52=1,y23=1,y33=1,y14=1,y44=1,and adopt λ=0.05. Then, the above model can be further transformed into the following form:(21)maxz2=0.233x11+0.232x21+0.182x32+0.214x52+0.232x23+0.182x33+0.233x14+0.138x44.The constraint condition is added on the original basis, namely:(22)0.12x11+0.11x21+0.15x32+0.14x52+0.13x23+0.12x33+0.11x14+0.12x44≤1−λ×49.1%.The solution of the single objective mathematical programming model is(23)x11=0.712,x21=0.288,x32=0.195,x52=0.805,x23=0.751,x33=0.249,x14=0.378,x44=0.622,y11=1,y21=1,y32=1,y52=1,y23=1,y33=1,y14=1,y44=1.


## 5. The Data Analysis

From the above calculation results, it can be seen that the best procurement plan for the company when purchasing product 1 is to chooseg1 and g2 suppliers, and the optimal procurement volume is 71.2% for g1 and 28.8% for g2; when the company purchases product 2, the best procurement plan is to choose g3 and g5 suppliers. The best procurement volume is 19.5% for g3 and 80.5% for g5. The best solution for the company to purchase product 3 is to choose g2 and g3 as suppliers, and the optimal purchase quantity is 75.1% for g2 and 24.9% for g3.The best solution for the company to purchase product 4 is to choose g1 and g4 as suppliers, and the optimal purchase quantity is 37.8% for g1 and 62.2% for g4.Based on the above analysis, the total procurement costs of these five suppliers are calculated as follows:M (g1) = 0.712 ∗ 20 + 0.378∗10 = 19.02,M (g2) = 0.288∗20 + 0.751∗15 = 17.025,M (g3) = 0.195∗12 + 0.249∗15 = 6.075,M (g4) = 0.622∗10 = 6.22,M (g5) = 0.805∗12 = 9.66.Through the calculation of the procurement costs of the above suppliers, when the purchase cost is constant, the higher the company's purchase cost for a certain supplier, the more transactions the supplier has with the company, and the more important it is to the company. [28–31], so it can be concluded that the order of the 5 suppliers to be selected is g1>g2>g5>g3>g4. According to the situation of these 5 suppliers, a multiobjective mathematical programming model is established to calculate the distribution of the calculated purchase amount. From the above calculation results, it can be seen that the procurement expenditures of the 5 suppliers are basically in line with the importance of the suppliers in the previous section, and the amount is g, which accounts for 190,200 RMB, 170,250RMB, 60,750 RMB, 62,200RMB, and 96,600 RMB.


## 6. Conclusion

Reasonably reducing the purchase cost while ensuring the level of service quality is always a problem to be solved by chain convenience stores. This paper constructs ANP to select the chain convenience store supplier indicators, takes the Lawson convenience store as an example to collect relevant data, and combines the MOP to choose and rank Lawson chain convenience store suppliers. Then, the reasonable selection of Rosen's suppliers is carried out to determine the procurement allocation of each supplier, to provide a theoretical basis for the later maintenance of suppliers, which is helpful for the supervision and classification management of suppliers, ensuring the supply quality of suppliers, deepening the cooperation with suppliers, controlling the procurement cost, and effectively improving the service level and competitiveness of enterprises. Existing research has neglected the importance of suppliers and later management. This article considers the service level quality while considering the purchase cost, which has certain guiding significance for the development of modern enterprises. At the same time, it also verified that the established model is scientific and practical. With the continuous changes in consumer demand, multiple goals can be incorporated in the future to select and manage the suppliers of chain retail stores.



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*Source: 5582067-2021-05-19.xml*