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

Competitive location: a state-of-art review

“…The authors researched the behavior of optimal solutions under different environments and changes in the basic model parameters using random problems and a robust evolutionary algorithm for solving this problem in another work (Redondo et al, 2009c). Fernandez et al (2006) presented a hard nonlinear bi-objective optimization problem: detecting the optimal location and design for a new franchised facility within a region where facilities (both of the franchise and not) already exist. The franchisor and the new franchisee both wish to maximize their own profits on the market, but these two objectives are in conflict.…”

Obtaining the efficient set of nonlinear biobjective optimization problems via interval branch-and-bound methods

“…Thus, it reduces the computation of S E to the solution of a finite number of constraint problems. The computational studies presented in [13] show that CLM clearly outperforms the iB&B method given in [15].…”

“…The methods proposed in the literature with that purpose are specialized either for particular problems (for instance, in [37] it is shown how to obtain the whole efficient set of some location problems) or for a particular class of multiobjective problems (for instance, the multiobjective simplex methods for the linear case [18]). To the extent of our knowledge, only two general methods (see [13,15]) have been proposed in the literature with that purpose for the general nonlinear biobjective problem (1). The reason for this lack of methods is that even obtaining a single efficient point of a nonlinear biobjective problem can be a difficult task.…”

“…Something similar can be done in the decision space, by drawing the superset in a color scale depending on the objective value of one of the objectives. The rudimentary interval B&B method in [15], iB&B in what follows, deals with the multiple objectives directly. It starts with an initial box containing the feasible set.…”

“…In the following section we review the basic iB&B algorithm given in [15], as well as the tools used to derive it. It is in Sect.…”