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 line...

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Bibliographic Details
Published in:Journal of global optimization 2012-11, Vol.54 (3), p.551-581
Main Authors: Ağralı, Semra, Geunes, Joseph, Taşkın, Z. Caner
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Computer Science
Costs
Customer services
Decomposition
Industrial engineering
Integer programming
Location analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Studies
Suppliers
Supply chains
Transportation problem (Operations research)
Variables
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Summary: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.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-011-9777-z