350 European Journal of Operational Research31 (1987) 350-357 North-Holland MOLP with an interactive assessment of a piecewise linear utility function Eric JACQUET-LAGRI~ZE and Rachid MEZIANI Universitd Paris-Dauphine LAMSADE, Place du Mal de Lattre de Tassigny, 75016 Paris, France Roman SLOWINSKI Institute of Control Engineering, Technical University of Poznan, Poland Abstract: The paper presents a methodology for Multi-Objective Linear Programming (MOLP) problems. It relies on three steps: (1) Generation of a subset of feasible efficient solutions (from 10 to 50) as representative as possible of the efficient set. (2) Assessment of an additive utility function using an interactive method (PREFCALC). (3) Optimization of the additive utility function on the original set of feasible alternatives. Following this methodology enables the user to find compromise solutions which can be different from the vertices. It is particularly adapted for large scale linear programs where traditional multiobjective methods would be too costly to use, since the interactive phase is limited to step 2, using PREFCALC on a micro-computer. A micro-computer version of the method (PREFCHAT) is available. Keywords: Multiple criteria linear programming, interactive method, utility function, decision making 1. Outline of the method This paper presents a new method to support Decision Makers (DMs) in solving Multi-Objec- tive Linear Programming (MOLP) problems: max g,(x) = E c jxj j=l gK(x) = ~., crjxj j=l s.t. ~aijx j<~bi, i=l ..... m, j=l xj>~0, j=l ..... n. Why a new method ? Many have been pro- posed, most of them are interactive, many are operational under the form of computer programs (see for instance Slowinski [13], Vincke [15]). Most of the previous methods, when they are interactive, use the concept of 'local preferences'. As a consequence, one has to solve one or more optimizations of the initial linear program at each iteration. This can be costly and time consuming, preventing quick answers in the process, and mak- ing the method less interactive. The method proposed here relies on a com- pletely different principle. It consists of three steps. (1) Generation of a subset of efficient solutions Preferences do not always pre-exist. It is there- fore important to show some feasible alternatives to the DM and their values on the criteria in order to enable him to react entering so in a learning process of his preferences. In order to show him interesting solutions, we suggest to generate a few efficient solutions. This technical step is not inter- active and does not require the presence of the DM. Received June 1985 0377-2217/87/$3.50 © 1987, Elsevier SciencePublishers B.V. (North-Holland)