Competitive facility location with random attractiveness

Customers' perception of a particular facility's attractiveness is likely to be heterogeneous. However, existing competitive facility location models assume that facilities' attractiveness levels are fixed. We extend the gravity model assuming randomly distributed facilities' attractiveness. We propose two effective solution methods. One is based on discretizing the attractiveness level distribution. The second is based on the concept of an “effective” attractiveness. Effective attractiveness is the level of fixed attractiveness whose calculated optimal market share approximately equals the expected optimal market share under random attractiveness. We show how effective attractiveness is calculated.