Bottleneck Capacity Expansion Problems with General Budget Constraints

Abstract

This paper presents a unied approach for bottleneck capacity expansion problems. In the bottleneck capacity expansion problem, BCEP, we are given a nite ground set E, a familyF of fea- sible subsets of E and a nonnegative real capacity ce for all e 2 E. Moreover, we are given monotone increasing cost functions fe for in- creasing the capacity of the elements e2 E as well as a budget B.T he task is to determine new capacities ce ce such that the objective func- tion given by maxF2F mine2F ce is maximized under the side constraint that the overall expansion cost does not exceed the budget B.W e in- troduce an algebraic model for dening the overall expansion cost and for formulating the budget constraint. This models allows to capture various types of budget constraints in one general model. Moreover, we discuss solution approaches for the general bottleneck capacity expan- sion problem. For an important subclass of bottleneck capacity expan- sion problems we propose algorithms which perform a strongly poly- nomial number of steps. In this manner we generalize and improve a recent result of Zhang et al. (15).