Discrete facility location with nonlinear diseconomies in fixed costs

A discrete facility location problem is formulated where the total fixed cost for establishing the facilities includes a component that is a nonlinear function of the number of facilities being established. Some theoretical properties of the solution are derived when this fixed cost is a convex nondecreasing function of the number of facilities. Based on these properties an efficient bisection heuristic is developed, where at each iteration, the classical ‘uncapacitated facility location’ and/or ‘m-median’ subproblems are solved using available efficient heuristics.