Distributionally robust location–allocation models of distribution centers for fresh products with uncertain demands

Abstract

This paper studies the location–allocation problem of distribution centers (DCs) for fresh products, in which it requires to determine the number and locations of DCs and design the allocation scheme for fresh products. The main challenge in optimizing this problem is to handle the uncertain demands with only partially known probability distribution information. To address this challenge, this paper first characterizes the ambiguous probability distributions of fresh products demands by an ambiguity set. Then, from different perspectives, this paper proposes two distributionally robust (DR) location–allocation models to find the optimal decisions that perform best in view of the worst-case distribution within the ambiguity set. The first model is with ambiguous expectation, which is transformed into a mixed-integer linear programming (MILP) model via employing the linear decision rule technique. The second model is with ambiguous chance constraints. This model is a semi-infinite chance constraint programming problem, which is transformed into a mixed-integer second-order cone programming (MISOCP) model by deriving safe approximations of the ambiguous chance constraints. To verify the feasibility and effectiveness of the proposed models, a case study about Hema fresh chain stores in Beijing is addressed. The experimental results demonstrate that the optimal decision provided by the proposed optimization methods can immunize against ambiguous probability distributions of demands with a small cost price.