Design of robust distribution network under demand uncertainty: A case study in the pulp and paper

Abstract

The design of a supply chain network helps companies in dealing with variability and uncertain evolution of demand over time. An efficient supply chain network may contribute to fulfill the customers’ demands in a quick and least cost manner. Therefore, it is important to solve the problem dealt with in this article concerning the design of the distribution network under demand uncertainty. The problem is to determine which warehouses to open and how much space to rent (outsource) in warehouses owned by third-party logistics providers. This paper presents the development and application of the robust optimization methodology to distribution network design problem under demand uncertainty. The proposed method allows the designer to find a network configuration having a total cost that is robust to typical changes in the geographical distribution of the demand. The Algorithm is an iterative process based on Benders decomposition. At each iteration, the following two steps are performed. In the first step, the global design problem (master problem) is solved to decide on the best use of warehouses according to the information provided by the previous iterations. For a given warehouse configuration and under some restrictions on demand variations, the second step determines the demand that incurred the largest transportation cost, granted that the transportation cost is optimal. These steps are repeated until finding the warehouses configuration that gives the smallest worst-case transportation cost. At each iteration the worst-case transportation cost sub-problem provides new information to the global design problem, such that the latter can improve its robustness. We report numerical results for real size network problems. The main results show that a high level of robustness of the distribution network can be achieved at a relatively low cost.