The capacity expansion problem in the service industry

Consider the problem of determining capacity expansions within a service industry composed of a chain of existing and new facilities, e.g. restaurants, hotels and gas-stations. The desired solution is a schedule of capacity expansions, each consisting of size, location and timing, in order to maximize profit when only limited funds are available. This paper includes two models. The first is a linear programming model suitable for organizations which rent or lease their facilities. The second is a mixed integer programming model where a fixed cost is paid anytime capacity is expanded. For the linear programming model the authors show how to represent the problem as a generalized network with gains problem and, in a case of non-decreasing demands, as a linear multiple-choice knapsack problem. For the mixed integer programming model they develop a heuristic having complexity O(nlogn) which makes it appropriate for large scale problems.