Reconciling Franchisor and Franchisee: A Planar Biobjective Competitive Location and Design Model

This paper deals with a hard nonlinear biobjective optimization problem: finding the optimal location and design for a new franchised facility within a region where facilities (both of the franchise and not) already exist and compete for the market. The franchisor and the new franchisee both want to maximise their own profit in the market, but these two objectives are in conflict. Customers patronize all the facilities, old and new, proportionally to their attraction to them. Both resulting objective functions are neither convex nor concave. An interval branch and bound method is proposed to obtain an outer approximation of the whole set of efficient solutions. Computational experiments highlight the different kinds of information provided by this method and by a variation of the lexicographic method.

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