An Efficient and Simple Approach to Solve a Distribution Problem

We consider a distribution problem in a supply chain consisting of multiple plants, multiple regional warehouses, and multiple customers. We focus on the problem of selecting a given number of warehouses among a set of candidate ones, assigning each customer to one or more of the selected warehouses while minimizing costs. We present a mixed integer formulation of the problem of minimizing the sum of the total transportation costs and of the fixed cost associated with the opening of the selected warehouses. We develop a heuristic and a metaheuristic algorithm to solve it. The problem was motivated by the request of a company in the US which was interested both in determining the optimal solution of the problem using available optimization solvers, and in the design and implementation of a simple heuristic able to find good solutions (not farther than 1% from the optimum) in a short time. A series of computational experiments on randomly generated test problems is carried out. Our results show that the proposed solution approaches are a valuable tool to meet the needs of the company.