Bottleneck capacity expansion problems with general budget constraints

Bottleneck capacity expansion problems with general budget constraints

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Article ID: iaor20053009
Country: France
Volume: 35
Issue: 1
Start Page Number: 1
End Page Number: 20
Publication Date: Jan 2001
Journal: RAIRO Operations Research
Authors: , ,
Keywords: capacity expansion
Abstract:

This paper presents a unified approach for bottleneck capacity expansion problems. In the bottleneck capacity expansion problem, BCEP, we are given a finite ground set E, a family ℱ of feasible subsets of E and a nonnegative real capacity ĉe for all eE. Moreover, we are given monotone increasing cost functions fe for increasing the capacity of the elements eE as well as a budget B. The task is to determine new capacities ce≥ĉe such that the objective function given by maxF∈ℱmine∈ℱce is maximized under the side constraint that the overall expansion cost does not exceed the budget B. We introduce an algebraic model for defining the overall expansion cost and for formulating the budget constraint. This model allows to capture various types of budget constraints in one general model. Moreover, we discuss solution approaches for the general bottleneck capacity expansion problem. For an important subclass of bottleneck capacity expansion problems we propose algorithms which perform a strongly polynomial number of steps. In this manner we generalize and improve a recent result of Zhang et al.

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