Bottleneck capacity expansion problems with general budget constraints

This paper presents a unified approach for bottleneck capacity expansion pr oblems. 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 (c) over cap (e) for all e is an element of E. Moreover, we a re given monotone increasing cost functions f(e) for increasing the capacit y of the elements e is an element of E as well as a budget B. The task is t o determine new capacities c(e) greater than or equal to (c) over cap (e) s uch that the objective function given by max(F is an element ofF) min(e is an element ofF) c(e) is maximized under the side constraint that the overal l expansion cost does not exceed the budget B. We introduce an algebraic mo del for defining the overall expansion cost and for formulating the budget constraint. This models allows to capture various types of budget constrain ts in one general model. Moreover, we discuss solution approaches for the g eneral 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 imp rove a recent result of Zhang et al. [15].