Trading areas of facilities with different sizes

In this paper the authors analyze the problem of finding the trading area for a facility on a linear market. Given the objective of maximizing profit, they first build a model with the facility sizes as variables. Then an algorithm is developed which determines the trading areas of all facilities for a given set of weights. Finally the authors parametrically change the weight of one of the given facilities and study the resulting changes in its trading area and thus find the optimal weight given the profit-maximizing objective.