In this paper, a two-stage stochastic facility location problem integrated with inven- tory and recourse decisions is studied and solved. This problem is inspired by an industrial supply chain design problem of a large retail chain with slow-moving prod- ucts. Uncertainty is expressed by a discrete and finite set of scenarios. Recourse actions can be taken after the realization of random demands. Location, inventory, transportation, and recourse decisions are integrated into a mixed-integer program with an objective minimizing the expected total cost. A dual heuristic procedure is studied and embedded into the sample average approximation (SAA) method. The computation experiments demonstrate that our combined SAA with dual heuristic algorithm has a similar performance on solution quality and a much shorter compu- tational time. / Thesis / Master of Applied Science (MASc)

In this study, the design of a three-level distribution system is considered in which a single supplier ships a number of items to the retailers via a set of distribution centers (DC) and stochastic demand is observed at the retailers. The problem is to specify the number and location of the DCs, and the assignment of the retailers to the DCs in such a way that total facility, transportation, safety stock, and joint ordering and average inventory costs are minimized, and customer service requirements are satisfied. Single source constraints are imposed on the assignment of the retailers to the DCs. The integrated location/inventory model incorporates the inventory management decisions into the strategic location/allocation decisions by considering the benefits of risk pooling and the savings that result in the joint replenishment of a group of items. We develop two heuristic methods to solve the non-linear integer-programming model in an integrated way: (1) Improvement type heuristic, (2) Constructive type heuristic. The heuristic algorithms are tested on a number of problem instances with 81 demand points (retailers) and 4 different types of items. Both of the heuristics are able to generate solutions in very reasonable times. The results are compared to the results of the p-median problem and found that the total cost and the number of DCs can be lowered using our integrated model instead of the p-median problem. Finally, sensitivity analysis is performed with respect to the changes in inventory, transportation, and ordering cost parameters, and variability of the demand.