Distribution Planning with Consolidation - A Two-Stage Stochastic Programming Approach

Abstract

The distribution planning problem with consolidation center(s) addresses the coordination of distribution activities between a set of suppliers and a set of customers, through the use of intermediate facilities in order to achieve savings in transportation cost. We study the problem from the perspective of a third-party logistics provider (3PL) that is coordinating shipments between suppliers and customers. Given customer demand of products from different suppliers, the goal is to consolidate the shipments in fewer high volume loads, from suppliers to the consolidation center(s) and from the consolidation center(s) to customer. We assume that suppliers have a finite set of transportation options, each with a given capacity and time of arrival at the consolidation center(s). Similarly, customers have a set of transportation options, each with a given capacity and dispatch time from the consolidation center(s). The 3PL wants to determine the optimal transportation options, or shipment schedule, and the allocation of shipments to transportation options from suppliers to consolidation center(s), and from consolidation center(s) to customers, that minimize the total transportation cost and holding cost at the consolidation center.

The literature studies many variations of this problem, which assume deterministic demand. This thesis extends the problem for stochastic demand and formulates it as a two-stage stochastic programming model. We model the case where the choice of transportation options is a \textit{contractual} decision, and a 3PL needs to decide on which options to reserve for a given planning period subject to stochastic customer demand. Therefore, the choices of transportation options are the stage one variables in the two-stage stochastic program. The second stage variables, which are decisions that are made after the uncertainty conditions become known, represent the allocation of orders to reserved transportation options as well as shipping orders through a spot-market carrier, at a greater transportation cost. Because of the high computational demand of the model, the integer L-shaped method is applied to decompose the problem. To increase the efficiency of the algorithm, we experiment with three valid cuts with the goal of generating stronger cuts than the L-cut. We also apply three algorithm enhancement techniques to speed up the convergence of the algorithm. Numerical results show that the performance of our proposed methodology and valid cuts is comparable to that of CPLEX. We suggest promising areas for future work to further improve the computational efficiency of our decomposition algorithm.