A general purpose exact solution method for mixed integer concave minimization problems

In this article, we discuss an exact algorithm for solving mixed integer concave minimization problems. A piecewise inner-approximation of the function is achieved using auxiliary linear program that leads to a bilevel program, which provides lower bound original problem. The reduced single level formulation with help Karush–Kuhn–Tucker (KKT) conditions. Incorporating KKT conditions lead complementary slackness are linearized BigM, identify tight value general Multiple programs, when solved over iterations, guarantee convergence optimum Though and can be applied any optimization problem function(s), in paper, solve two common classes operations supply chain problems; namely, knapsack problem, production-transportation computational experiments indicate our proposed approach outperforms customized methods have been used literature problems by order magnitude most test cases.