We consider the problem of optimal design and location of a set of facilities. The goal is to optimally allocate the available budget to maximize customer demand (alternatively, the program can be stated as net revenue optimization). Customer demand is assumed to be concave in the attractiveness of the facilities, where the latter is a function of both, the convenience (proximity) and the design of the facilities. Available budget can be spent on both, locating new facilities or improving the design of the existing ones.
The resulting problem is formulated as a non-linear integer program and solved in several steps. First we address optimal design of a single facility and develop closed-form solutions for this problem. Then, we show how the results can be used to reduce the dimensionality of the original problem. Finally, we apply “double TLA” technique to obtain a linearized version with a provable error bound. Computational results are presented to show the effectiveness of each step in this procedure.