Location of a new facility on a linear market in the presence of weights

In this paper, the authors study the trading areas of n facilities with unequal weights located on a finite linear market. Customers are uniformly distributed on the market. Their attraction to a facility is directly proportional to the weight of the facility and inversely proportional to the distance separating them from the facility. The problem considered is that of determining which location will maximize the trading area of a new facility entering the market. A procedure which solves this problem in O(n²) time is presented and illustrated by means of a simple example.