A cover-based competitive location model

In this paper we propose a new approach to estimating market share captured by competing facilities. The approach is based on cover location models. Each competing facility has a ‘sphere of influence’ determined by its attractiveness level. More attractive facilities have a larger radius of the sphere of influence. The buying power of a customer within the sphere of influence of several facilities is equally divided among the competing facilities. The buying power of a customer within the sphere of influence of no facility is lost. Assuming the presence of competition in the area, the objective is to add a number of new facilities to a chain of existing facilities in such a way that the increase of market share captured by the chain is maximized. The model is formulated and analysed. Optimal and heuristic solution algorithms are designed. Computational experiments demonstrate the effectiveness of the proposed algorithms.