Heuristic algorithm for solving large location-inventory problemswith demand uncertainty.

In this paper, we analyze a location-inventory problem for the design of large supply chain networks with uncertain demand. We give a continuous non-linear formulation that integrates location, allocation and inventory decisions, and includes the costs of transportation, cycle inventory, safety stock, ordering and facility opening. Then, relying on the fact that the model becomes linear when fixing some variables, we propose a heuristic algorithm that solves the resulting linear program and uses the solution to improve the variables estimations for the next iteration. In order to show the efficiency of the algorithm, we compare our results with the conic quadratic formulation of the problem. Computational experiments show that the heuristic algorithm can be efficiently used to find fast and close to optimal solutions for large supply chain networks. Finally, we provide managerial insights regarding the ways demand uncertainty and risk pooling affect the design of a supply chain