Primal-dual variable neighborhood search for the simple plant-location problem

The variable neighborhood search metaheuristic is applied to the primal simple plant–location problem and to a reduced dual obtained by exploiting the complementary slackness conditions. This leads to (i) heuristic resolution of (metric) instances with uniform fixed costs, up to n=15,000 users, and m=n potential locations for facilities with an error not exceeding 0.04%; (ii) exact solution of such instances with up to m=n=7,000; and (iii) exact solutions of instances with variable fixed costs and up to m=n=15,000.