Competitive facilities: Market share and location with random utility

A new approach is proposed for calculating the expected market share. It is assumed that consumers patronize a facility according to a utility function, selecting the facility with the highest utility value. However, consumers' ratings of the utility components are stochastic by some random distribution. Therefore, the buying power of customers located at the same point is divided among several facilities. A probability that a consumer patronizes a certain facility can be calculated. Consequently, the expected market share by competing facilities can be estimated. This calculation is more than 1,000 times faster than repeating a simulation enough times to achieve a reasonable accuracy. The distance decay calculated using the new approach is approximately exponential. A procedure for finding the optimal location anywhere in the plane for a new facility that maximizes the market share is also introduced.