Facility location under zone pricing

Zone pricing consists in determining simultaneously several delivered prices together with the zones where these prices apply. A model and algorithm are proposed to determine optimal facility locations, prices, tariff-zones, and market areas in order to maximize the firm's profit under zone pricing. The resulting nonlinear mixed-integer program is tackled by projecting the objective function on the price space, solving repeatedly uncapacitated facility location problems for fixed values of the prices. The implicit profit function so defined is optimized by branch-and-bound. Computational results are reported.