An outer-approximation algorithm for a class of mixed-integer nonlinear programs
Mathematical Programming: Series A and B
Inexact Cuts in Benders Decomposition
SIAM Journal on Optimization
Capacity and flow assignment of data networks by generalized Benders decomposition
Journal of Global Optimization
A Joint Location-Inventory Model
Transportation Science
Stochastic Transportation-Inventory Network Design Problem
Operations Research
Trade-offs Between Customer Service and Cost in Integrated Supply Chain Design
Manufacturing & Service Operations Management
Facility Location Modeling and Inventory Management with Multisourcing
Transportation Science
Generalized Benders' Decomposition for topology optimization problems
Journal of Global Optimization
Expert Systems with Applications: An International Journal
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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.