A facility location model with safety stock costs: analysis of the cost of single-sourcing requirements
We consider a supply chain setting where multiple uncapacitated facilities serve a set of customers with a single product. The majority of literature on such problems requires assigning all of any given customer’s demand to a single facility. While this single-sourcing strategy is optimal under linear (or concave) cost structures, it will often be suboptimal under the nonlinear costs that arise in the presence of safety stock costs. Our primary goal is to characterize the incremental costs that result from a single-sourcing strategy. We propose a general model that uses a cardinality constraint on the number of supply facilities that may serve a customer. The result is a complex mixed-integer nonlinear programming problem. We provide a generalized Benders decomposition algorithm for the case in which a customer’s demand may be split among an arbitrary number of supply facilities. The Benders subproblem takes the form of an uncapacitated, nonlinear transportation problem, a relevant and interesting problem in its own right. We provide analysis and insight on this subproblem, which allows us to devise a hybrid algorithm based on an outer approximation of this subproblem to accelerate the generalized Benders decomposition algorithm. We also provide computational results for the general model that permit characterizing the costs that arise from a single-sourcing strategy. Copyright Springer Science+Business Media, LLC. 2012
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Volume (Year): 54 (2012)
Issue (Month): 3 (November)
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- Nozick, Linda K. & Turnquist, Mark A., 2001. "A two-echelon inventory allocation and distribution center location analysis," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 37(6), pages 425-441, December.
- Eduardo Muñoz & Mathias Stolpe, 2011. "Generalized Benders’ Decomposition for topology optimization problems," Journal of Global Optimization, Springer, vol. 51(1), pages 149-183, September.
- Nozick, Linda K. & Turnquist, Mark A., 1998. "Integrating inventory impacts into a fixed-charge model for locating distribution centers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 34(3), pages 173-186, September.
- Cote, Gilles & Laughton, Michael A., 1984. "Large-scale mixed integer programming: Benders-type heuristics," European Journal of Operational Research, Elsevier, vol. 16(3), pages 327-333, June.
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