Technical Note: Solving the Problems of Extremum and Sorting with a Mixed Integer Linear Programming Model

To our knowledge our proposal is the first work in the literature that solves the problems of maximum, minimum and sorting a set of variables with a Mixed Integer Linear Program (MILP). Although these problems are very nonlinear, the MILP model that solves them is surprisingly not very complex. We present the formal description of our MILP model and then we implement it with the GAMS software. Then we present some numerical examples based on this latter implementations that show that although relatively simple our MILP model consumes a lot of computational resources. Finally we point out to some directions of improvement of our MILP model.