By Felli V., Schneider S.
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Extra resources for A note on regularity of solutions to degenerate elliptic equations of Caffarelli-Kohn-Nirenberg type
181, 598–619 (2007) 2. R. Aboolian, O. Berman, D. Krass, Competitive facility location and design problem. Eur. J. Oper. Res. 182, 40–62 (2007) 3. E. Alekseeva, N. Kocheva, Y. Kotcetov, A. rjp/-centroid problem, in Evolutionary Computation in Combinatorial Optimization, ed. by P. Cowling, P. Merz. Lecture Notes in Computer Science, vol. 6022 (Springer, Berlin, 2010), pp. 11–22 4. S. D. M. Shetty, Nonlinear Programming: Theory and Algorithms (Wiley, New York, 1993) 5. L. Beresnev, Upper bounds for objective function of discrete competitive facility location problems.
For simplicity it is assumed that production cost is zero. Due to homogeneity assumption customers always buy from the competitor who charges the lowest price, and do not have any other preferences concerning their suppliers. e. 94) where zij binary variable indicating whether leader serves market j from location i. xij binary variable indicating whether follower serves market j from location i. vi binary variable, takes value 1 if leader opens a facility at location i. yi binary variable, takes value 1 if follower opens a facility at location i.
Another subject that is addressed by several authors is the existence or (not) of a set of locations and pricing or production quantities that will ensure a Nash equilibrium, that is, a position where neither firms have incentives to move. 1 Stability in Location Decisions In 1987, Dobson and Karmarkar  stated the notion of stability in the facility location decision. A set of facilities is considered stable if each facility is economically viable and no competitor can successfully open any facilities.
A note on regularity of solutions to degenerate elliptic equations of Caffarelli-Kohn-Nirenberg type by Felli V., Schneider S.