Abstract-- This paper describes an interactive approach for multiobjective linear programming problems combining the tolerance approach to sensitivity analysis with the reference point methodology. It aims at providing decision makers with a flexible decision aid tool, enabling to perform a progressive search of the set of efficient solutions, and which does not require too much computational effort. The proposed combined approach enables to gather, in an interactive manner, information about the problem and the trade-offs to be made among the objectives in order to obtain a compromise solution, which a final decision can be based on. The main concepts will be geometrically illustrated with a simple example. Index terms-- Multiple objective linear programming, Tolerance approach to sensitivity analysis, Reference point approaches, Interactive decision analysis I. INTRODUCTION Decision making situations inherently involve multiple, often conflicting, and incommensurate aspects of evaluation of the merit of feasible solutions. Besides, the unavoidable influence of distinct sources of uncertainty and vague or unstable decision makers’ (DMs) preference information are generally at stake. Multiple objective models enable DMs rationalizing the comparisons among different alternative solutions, providing them with a better perception of the conflicting aspects under evaluation and the ability to grasp the nature of the trade-offs to be made. In any interactive decision support method the DM's preference structure is then of particular relevance, understood as the construct that the DM leans on for evaluating and selecting a satisfactory plan from the set of efficient solutions. An important issue is the procedure’s capability to generate efficient solutions by using the preference information supplied by the DM to drive the search. Corresponding author. Telf.: +351239851040; fax: +351239824692. E-mail address: arborges@isec.pt (A.R. Borges). Sensitivity analysis in mathematical programming problems is aimed at dealing with the uncertainty and imprecision which are inherent to the models. Traditional sensitivity analysis in linear programming generally computes ranges to indicate how much the specified coefficients can change before the optimal solution (basis) changes. However, the ranges obtained by traditional sensitivity analysis are easily determined only when the coefficients are not allowed to change in a simultaneous manner. Wendell [6, 7] developed the tolerance approach to sensitivity analysis that enables to consider the impact of simultaneous and independent changes of more than one coefficient. If the DM is confident that the coefficient values in a problem will be within the maximum tolerance percentage of their estimated values, then the DM can be sure that the optimal solution (basis) obtained using the estimated coefficient values will remain optimal in his problem. Reference point methods [8, 9] can be used as a tool to compute efficient solutions of a multiobjective programming problem, according to the concept of quasi-satisficing decision proposed by Wierzbicki. It relies on the definition of an achievement scalarizing function that projects reference points onto the efficient solution set. Section II and III present some key concepts of multiobjective linear programming (MOLP), with special emphasis on the reference point approach to compute efficient solutions and the tolerance approach to sensitivity analysis in MOLP, respectively. These are important to introduce the proposed interactive tolerance approach to sensitivity analysis to deal with the uncertainty on the reference values in MOLP problems. This approach is described in detail in section IV. In section V a multiple objective problem, with two objective functions, is studied to illustrate geometrically the interactive approach. Some future research is outlined in section VI. Finally, in section VII some conclusions are drawn. AN INTERACTIVE TOLERANCE APPROACH TO SENSITIVITY ANALYSIS IN MULTIOBJECTIVE LINEAR PROGRAMMING USING REFERENCE POINTS Ana Rosa Borges c) (a, , Carlos Henggeler Antunes c) (b, (a) ISEC, Coimbra Polytechnic Institute, Apartado 10057, 3030-601 Coimbra, Portugal (b) Dep. of Electrical Engineering and Computers, University of Coimbra, 3030-030 Coimbra, Portugal (c) INESC - Rua Antero de Quental 199, 3000-033 Coimbra, Portugal arborges@isec.pt , cantunes@inescc.pt