Raymond Nadeau

A multicriterion view of optimal resource allocation in job-shop production

Abstract This paper describes the use of the Kanban method for the control of production in a job-shop in order to reduce makespan, reduce work-in-progress, improve machine utilisation, and to control the number of machine setups. A knowledge base has been constructed from a large number of simulations and allows the analysis of the behaviour of the production system under different conditions. The choice of appropriate values for the parameters that control production is made via a multi-criteria outranking method based on stochastic dominance.

PROMISE/scenarios: An interactive method for multiobjective stochastic linear programming under partial uncertainty

Abstract In many real contexts where the multiobjective stochastic linear programming can be used as a modelling approach, the decision maker is in general placed in a situation of incomplete information concerning the uncertain parameters of the problem. A good way to express that incomplete information consists in resorting to the idea of scenarios relatively to the objectives and constraints of the stochastic program. While the authors who have suggested methods based on scenarios suppose that the probabilities of those scenarios are known, in this paper we propose a scenarios approach where the probabilities of scenarios is only incompletely specified according to a ranking. That interactive method, called PROMISE/scenarios, is presented and is illustrated by a didactic example.

An Interactive Method To Multiobjective Linear Programming Problems With Interval Coefficients

AbstractIn the context of multiobjective linear programming (MOLP) problems where there is indetermination around some parameters, we suppose that the decision maker knows only the limits of variation of these parameters and eventually one of their central values. For such situations, we have proposed (cf. Urli and Nadeau, 1990) a general methodology wich enables us to transform the non deterministic MOLP problem into a deterministic one and after to solve the latter program by an interactive approach derived from the STEM method. In the present paper we develop a particular method based on that general methodology and we illustrate it by a didactic example.

ELECCALC—an interactive software for modelling the decision maker's preferences

Abstract In general, it is difficult to articulate the decision-makers (DM) preference structure, specially in taking into account several criteria. Most synthetical approaches (single synthetical criterion approach, synthetical outranking approach,…) are based on some a priori information. In this paper, we attempt to analyze such a structure through a descriptive approach. The idea is to explain the global preferences revealed by the DM from pairwise comparisons of reference alternatives. A disaggregation — aggregation interactive procedure like in PREFCALC is used in ELECCALC, which enables a DM to assess the parameters of ELECTRE II.

Multiobjective Stochastic Linear Programming with Incomplete Information: A General Methodology

Numerous multiobjective linear programming methods have been proposed in the last two decades for contexts where the parameters are deterministic. In many real situations, however, parameters of a stochastic nature arise and the analyst is, as a result, confronted with a stochastic multiobjective linear programming problem. Recently, some methods have been developed to deal with this kind of problems; in most of them, the decision maker is supposed to be placed in a risky situation, i.e. a situation where he can associate probability distributions to the stochastic parameters. In many cases, we believe that it would be more realistic to suppose that the decision maker is in a situation of partial uncertainty, i.e. a situation where he possesses only an incomplete information about the stochastic parameters; for example, he could be able to precise only the bounds of variation of the parameters and eventually, their central values. For such situations, we propose a general multiobjective stochastic linear programming methodology which includes many modes of transformation of the stochastic objectives and constraints in order to obtain an equivalent multiobjective deterministic linear programming problem. Finally, this deterministic equivalent program is solved by an interactive method derived from STEM. Our methodology will be illustrated through a didactical example.

Distributional efficiency in multiobjective stochastic linear programming

Several concepts of distributional efficiency are proposed for the Multiobjective Stochastic Linear Programming (MSLP) problem, in contexts where the probability distribution of random parameters is known and the decision maker (DM) has an unknown multi-attribute utility function belonging to a given glass U. We present a general efficient set, the U-admissible solutions, and two subsets, the U-unanimous and U-advocated solutions, the latter being particularly relevant to the case of a single DM. We show how advocated solutions can be generated and/or tested when U is the class of non-decreasing additive concave functions.

Restricted Bayes Strategies for Programs with Simple Recourse

When using linear stochastic programs one generally assumes that the joint probability distribution of the random variables involved is known. However, in practice, for example in manpower planning problems, the knowledge of this distribution is incomplete. Consequently this paper presents a linear stochastic program with partial information, where the confidence in this joint probability distribution is expressed by a parameter varying from 0 to 1. Explicit solutions are given for programs with simple recourse.

Distributional Unanimity in Multiobjective Stochastic Linear Programming

Several notions of efficiency are conceivable for the multiobjective stochastic linear programming problem. In this paper, assuming that the problem’s randomness can be described by discrete scenarios with known probabilities and that decision makers’ preferences, although unknown, can be represented by a class of utility functions, we examine a set of strongly efficient solutions, the unanimous solutions. We state inclusion relations between this and other classes of efficient solutions (admissible and advocated solutions) previously studied. Under plausible assumptions about decision makers’ risk attitudes, we examine how candidates for unanimity can be generated and then tested.

Dominance and Efficiency in Multiobjective Stochastic Linear Programming

In contrast to deterministic multiobjective problems, where the notion of Pareto-efficiency is well accepted, several notions of efficiency are conceivable for the Multiobjective Stochastic Linear Programming problem. Their relevance depends on the available state of information about the decision situation, regarding particularly the Decision Maker’s preference structure and probabilistic anticipations. We investigate efficient sets arising naturally from some extreme reference cases of states of information. We study these sets from the point of view of their relative inclusions and provide some indications as to their computability.

PROMISE: A DSS for multiple objective stochastic linear programming problems

Most of the multiple objective linear programming (MOLP) methods which have been proposed in the last fifteen years suppose deterministic contexts, but because many real problems imply uncertainty, some methods have been recently developed to deal with MOLP problems in stochastic contexts. In order to help the decision maker (DM) who is placed before such stochastic MOLP problems, we have built a Decision Support System called PROMISE. On the one hand, our DSS enables the DM to identify many current stochastic contexts: risky situations and also situations of partial uncertainty. On the other hand, according to the nature of the uncertainty, our DSS enables the DM to choose the most appropriate interactive stochastic MOLP method among the available methods, if such a method exists, and to solve his problem via the chosen method.