A Mixed-Integer Linear Programming model is proposed to determine the optimal number, location and capacity of the warehouses required to support a 5-year forecast for a business with seasonal demand. Discrete transportation costs, dynamic warehouse contracting, and handling of safety stock are the three main features that make the problem different from the previous reported work in the facility location problem. The most effective modeling alternative for each of these complicating issues was identified. To solve large-scale problems, tightening constraints, approximating reformulations and multistage heuristics are proposed. Solution algorithms that exploit the problem structure were developed. A 2-stage heuristic based on products grouping is able to obtain the optimal solution in 95% of the instances tested. A 3-stage heuristic, using a single mode model as intermediate step, was found to be better suited for very large-scale problems yielding only a 1% deviation from the optimal solution. To take advantage of the feasible solution found using the developed heuristics, decomposition strategies are explored to yield proven optimal solutions.
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Bravo, Juan José, and Carlos Julio Vidal. "Freight transportation function in supply chain optimization models: A critical review of recent trends." Expert Systems with Applications 40.17 (2013): 6742-6757.
Daskin, Mark S., Collette R. Coullard, and Zuo-Jun Max Shen. "An inventory-location model: Formulation, solution algorithm and computational results." Annals of operations research 110.1-4 (2002): 83-106.