MOPGP’06: 7th Int. Conf. on Multi-Objective Programming and Goal Programming Tours, France, June 12-14, 2006 An interactive procedure to tackle uncertainty in MOLP with interval coefficients Carla Oliveira * Carlos Henggeler Antunes § *INESC Coimbra, Rua Antero de Quental, 199, Coimbra, Portugal coliv@inescc.pt § Universidade de Coimbra, Dep. Engenharia Electrotécnica e de Computadores, Polo II, 3030-030 COIMBRA, Portugal cantunes@inescc.pt 1 Introduction In most real-world situations, problems are characterized by multiple, conflicting and incommensurate axes of evaluation. Moreover, in most real-world problems the available data is inexistent or scarce, difficult to obtain or estimate, the system is subject to changes, etc. Therefore, mathematical programming models for decision support must bear, besides multiple and conflicting objective functions, the uncertainty associated with the model coefficients. There are several approaches to tackle uncertainty in mathematical programming models. In this context, interval programming possesses some interesting characteristics because it does not require the specification or the assumption of probabilistic distributions or possibilistic distributions. The interval programming approach assumes that the ranges of variation of some (or all) coefficients which allow specifying a model are known. Interval programming methods have been used to tackle specific issues in multiple objective linear programming (MOLP): some deal with uncertainty in the objective functions, others handle uncertainty both in the objective functions and in the RHS of the constraints and others deal with uncertainty in all the coefficients of the model (see an illustrated overview of these methods in [5]). In this paper we propose an approach for MOLP problems with interval coefficients that deals with the uncertainty in all the coefficients of the model. 2 Interactive Method Let the MOLP problem with interval coefficients be given by: