Distribution planning with random demand and recourse in a transshipment network

In this paper we consider a distribution planning problem in a transshipment network under stochastic customer demand, to account for uncertainty faced in real-life applications when planning distribution activities. To date, considerations of randomness in distribution planning networks with intermediate facilities have received very little attention in the literature. We address this gap by modeling uncertainty in a distribution network with an intermediate facility, and providing insight on the benefit of accounting for randomness at the distribution planning phase. The problem is studied from the perspective of a third-party logistics provider (3PL) that is outsourced to handle the logistics needs of its customers; the 3PL uses a consolidation center to achieve transportation cost savings. We formulate a two-stage stochastic programming model with recourse that aims to minimize the sum of transportation cost, expected inventory holding cost and expected outsourcing cost. The recourse variables ensure that the problem is feasible regardless of the realization of demand, by allowing the option of using a spot market carrier if demand exceeds capacity. We propose a flow-based formulation with a nonlinear holding cost component in the objective function. We then develop an alternative linear path-based formulation that models the movement of freight in the network as path variables. We apply Sample Average Approximation (SAA) to solve the problem, and show that it results in reasonable optimality gaps for problem instances of different sizes. We conduct extensive testing to evaluate the benefits of our proposed stochastic model compared to its deterministic counterpart. Our computational experiments provide managerial insight into the robustness and cost-efficiency of the distribution plans of our proposed stochastic model, and the conditions under which our model achieves significant distribution cost savings.