Best and Worst Optimum for Linear Programs with Interval Right Hand Sides

Abstract

In optimization, it is used to deal with uncertain and inaccurate factors which make difficult the assignment of a single plausible value to each model parameters. Two approaches are possible: in the first one, a single nominal value is assigned to each parameter, the corresponding optimal solution is computed, then the interval in which each parameter can vary in order to preserve optimality solution is determined; the second approach consists in taking into account in the model to optimize, the possible variations of each parameter. In mathematical programming, the first approach is known as sensitivity analysis (see e.g. [6]). For the second approach, stochastic optimization may be applied for some problems in which parameters value can be described by probability laws (see for example [4]). When it is not possible nor relevant to associate probability laws to parameters, another way amounts to assign a set of possible values to each parameter. Two models may be considered: in the first one, a finite set of values is assigned to each uncertain model coefficient; in the second one, each uncertain model coefficient is associated with an interval number. In this paper, we only consider this second model called interval linear programming.