Liu YANG, Bing ZHAO, Pinyuan ZHAO, Bingqing ZHANG, Xuejie BAI

Hebei Agricultural University, Baoding 071001, China

Abstract In view of the uncertainty in the location selection of logistics distribution center for the fresh agricultural products, the present study established a robust model based on the maximization of principal component score taking budget cost parameters as an example. In the process of model solving, the interval form of the uncertain set was used to clarify the constraint conditions, to transform into a certain 0-1 integer linear programming model, so as to solve with the aid of LINGO software. Finally, through studying the location selection of logistics distribution center for fresh agricultural products in the Beijing-Tianjin-Hebei region, it analyzed the application of the robust model and tested the validity of the model.

Key words Fresh agricultural products, Logistics distribution, Center location, Robust model

1 Introduction

Fresh agricultural products are gradually favored by more and more consumers. How to efficiently and quickly bring fresh agricultural products from the market to the hands of consumers has attracted more and more attention. In this situation, it is particularly important to optimize the location of logistics distribution center for fresh agricultural products. On the basis of two-dimensional language information and modified algorithm, Lietal.[1]summarized the location of logistics distribution center as a multi-attribute group decision-making problem. M. Yangetal.[2]proposed a distributed robust optimization method to deal with the demand uncertainty, refine the bounded disturbance set, and develop a computable safe approximation of the chance constraint. On the basis of the deterministic model, Zhong Weiyaetal.[3]established an interval two-stage robust optimization model and used robust ideas to solve corresponding problems. Based on theories such as ranking method and gray relational analysis, Song Zhilanetal.[4]used fuzzy thinking to obtain the optimal location through the degree of approximation. Xu Xiangjinetal.[5]established a location selection model with the goal of the lowest total cost of social fresh agricultural products. In this study, we intended to establish a robust model based on maximizing the principal component score. In view of the uncertainty of the model parameters, using the interval form of the uncertainty set, we transformed the robust model into a certain 0-1 integer linear programming problem, which can be solved by the branch and bound method. Finally, we explained the rationality of the model through specific cases.

2 Robust model for location selection under uncertain information

(1)

In the model, the objective function is the maximum score of each candidate city; the first constraint is that the capital invested to build a factory is not higher than the cost of building a factory; the second constraint is that the return on factory construction should not be less than the return on investment. The robust model itself is a semi-infinite problem, which is difficult to solve directly, so we need to transform it into a linear program, that is, a robust counterpart model.

Then the uncertain problem is transformed into a definite problem processing, similarly, we can transform the second constraint in model (1) into:

In summary, the robust counterpart model is as follows:

(2)

After model transformation, we transformed a robust model under uncertain information into a 0-1 integer linear programming model, and then used LINGO software to solve it.

3 Case study

3.1 Case descriptionAccording to the GDP of each city in the Beijing-Tianjin-Hebei region in 2019, we selected 6 cities as alternative location. Based on the scores of principal component analysis, we analyzed the relevant indicator data of these 6 cities, established a robust model, and finally selected 3 fresh agricultural product logistics distribution centers, which cover the Beijing-Tianjin-Hebei region well and are favorable for construction of the logistics distribution network system for fresh agricultural products in the Beijing-Tianjin-Hebei region.

By consulting relevant materials, we determined that the main factors influencing the location of the fresh agricultural product logistics distribution center in the Beijing-Tianjin-Hebei region include supply, demand, logistics and environmental conditions. According to the nature of each factor, we further subdivided these factors and obtained a total of 14 secondary indicators. The indicator system for determining the location of the logistics distribution center is shown in Table 1.

Through consulting theStatisticalYearbooksofBeijing,TianjinandHebeiProvincesin 2018, we can get data on relevant indicators. Based on the principal component analysis method, with the aid of SPSS software, we made a quantitative analysis on the main factors affecting the location of the fresh agricultural product logistics distribution center, and determined the indicator weight, to provide a theoretical basis for the final location. The weight of each indicator is shown in Table 2.

Table 1 Indicator system for location selection of logistics distribution center

Using the weight of each indicator and the expressions about each standardized variable, we obtained the score of each candidate location, as shown in Table 3.

Table 2 Results of indicator weight

Table 3 Score of each candidate location

3.2 Calculation resultsIn the robust counterpart model , the investmentq=(2 500, 1 500, 3 000, 2 000, 5 000, 2 000) (104yuan), the profitp=(3 250, 1 950, 3 900, 2 600, 6 500, 2 600) (104yuan), the number of established logistics distribution centern=3, assumeζ=0.15, the budget costc1=2 295 (104yuan),c2=3 105 (104yuan). Based on principal component analysis, the score of each candidate location in the objective function isW=(-1.296 3, -1. 395 8, 1.477 6, 0.146 0, 2.396 7, -1.328 2). According to the operating results of the LINGO software,x1=0,x2=1,x3=1,x4=0,x5=0,x6=1, indicating that the three fresh agricultural product logistics distribution centers are located in Handan, Tianjin, and Tangshan, as shown in Fig.1.

Fig.1 Distribution of location of logistics distribution center for fresh agricultural products in Beijing-Tianjin-Hebei region

4 Conclusions

Uncertainty is common in real life, so the robust model of location problem under uncertain information has a wide range of applications. In this study, through extending the budget cost parameter from a value to a possible value in an interval, we transformed the robust model is transformed into a definite 0-1 integer linear programming problem for solving. In view of the changes in the market environment and other factors, the model we established is relatively realistic.