Abstract:

Food security bears on the national economy and the people's livelihood， and is an important foundation for national security. The construction of thepost-harvest grain service center is a powerful means to reduce post-harvest grain loss， which is of great significance to guarantee national food security.In this paper， the location problem of post-harvest grain service centers is studied. Based on the reality and the emphasis of this study， the following assumptions are made： （a）The post-harvest grain service center has two kinds of service capabilities， i.e.， cleaning&drying and storage； （b）All raw grain should be transported from the producing area to the service centers for “cleaning&drying” first， while the following "storage" service is optional， and the grain that does not receive “storage” service needs to be transported back to its origin； （c）Transportation of grain between service centers is not considered； （d）Grain yields obey some normal distribution. Before grain yieldsare determined， the following decisions should be made： （a） The number， location， and scale of service centers to be built； （b）The allocation of two service capabilities in each service center. After grain yields have been determined， grain logistics decisions between the producing areas and the service centers need to be made.Considering the two-stage decision characteristic and the assumption of the randomness of grain yields， a two-stage stochastic programming model is established to represent this problem. Based on the structural characteristics of the model， the Benders decomposition algorithm（BD） is used to solve it. Moreover， the multi-cut method， two sets of valid inequalities， and a lower bound lifting strategy are applied to accelerate the algorithm.In the test on random instances， the effectiveness of the algorithm acceleration methods and the advantages of the accelerated BD compared with the general solver Gurobi in solution accuracy are first verified. Then， the value of the stochastic solution （VSS） is calculated and it is obtained that the stochastic solutions considering the randomness of grain yields can bring an average cost saving of 0.8% compared with the deterministic solutions. In the real case study， based on the grain yield data of 84 county-level regions in Hubei Province， the optimal geographical distribution， construction scale， and capacity allocation scheme of grain post-production service centers in Hubei Province are obtained using the proposed model and algorithm， which verifies the model and algorithm for real problems.This is the first study on the location problem of post-harvest grain service centers. It enriches the existing literature onthe location-allocation problem by considering the capacity allocation decision in the model. The model is widely applicable to location problems of centers with multiple capabilities.

Key words: post-harvest grain service center, multi-functional characteristic, location-allocation, two-stage stochastic programming, Benders decomposition algorithm