A planar single-facility competitive location and design problem under the multi-deterministic choice rule

A new customer choice rule, which may model in some cases the actual patronising behaviour of customers towards the facilities closer to reality than other existing rules, is proposed. According to the new rule, customers split their demand among the firms in the market by patronising only one facility from each firm, the one with the highest utility, and the demand is split among those facilities proportionally to their attraction. The influence of the choice rule in the location of facilities is investigated. In particular, a new continuous competitive single-facility location and design problem using this new rule is proposed. Both exact and heuristic methods are proposed to solve it. A comparison with the classical proportional (or Huff) choice rule when solving the location model reveals that both the location and the quality of the new facility to be located may be quite different depending on the patronising behaviour of customers. Most importantly, the profit that the locating chain may lose if a wrong choice is made can be quite high in some instances. HighlightsThe patronising behaviour of costumers towards the facilities is investigated.A new rule is proposed: customers split their demand by patronising only one facility from each firm.The demand is split among the selected facilities proportionally to their attraction.Exact and heuristic methods are proposed to solve a new continuous competitive location and design problem.The profit that the locating chain may lose if a wrong customer choice rule is used may be high.

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