Linear programming is a fundamental planning tool. It is often difficult to precisely estimate or forecast certain critical data elements of the linear program. In such cases, it is necessary to address the impact of uncertainty during the planning process. We discuss a variety of LP-based models that can be used for planning under uncertainty. In all cases, we begin with a de-terministic LP mo...

We present a new multiple criteria sorting method that aims at assigning actions evaluated on multiple criteria to p pre-defined ordered classes. The preference information supplied by the decision maker (DM) is a set of assignment examples concerning reference actions. Each assignment example specifies a desired assignment for a reference action to one or several contiguous classes. The assign...

The Quadratic Assignment Problem (QAP) is the problem of making exclusive assignments of n indivisible entities to n other indivisible entities in such a way that a total quadratic interaction cost is minimized. The problem can be interpreted from a wide variety of perspectives. The perspective adopted in this paper is that of the generic facilities location/layout context, as in the seminal wo...

We present an integer linear formulation that uses the so-called “distance variables” to solve the quadratic assignment problem (QAP). The model involves O(n) variables. Valid equalities and inequalities are additionally proposed. We further improved the model by using metric properties as well as an algebraic characterization of the Manhattan distance matrices that Mittelman and Peng [28] rece...

This paper proposes a column generation based heuristic suitable for large and hard instances of the generalized assignment problem. First, just to be able to obtain the convergence of the column generation is reasonable times, it uses a sophisticated “triple” dual stabilization, combining piecewise linear penalty functions, Wentges’ dual smoothing and sub-gradient directional smoothing. In ord...