Showing papers in "Rairo-operations Research in 2001"

Solving the simple plant location problem by genetic algorithm

Abstract: The simple plant location problem (SPLP) is considered and a genetic algorithm is proposed to solve this problem. By using the developed algorithm it is possible to solve SPLP with more than 1000 facility sites and customers. Computational results are presented and compared to dual based algorithms.

Multicriteria scheduling problems: a survey

Abstract: This paper presents a state-of-the-art survey on multicriteria scheduling and introduces a definition of a multicriteria scheduling problem. It provides a framework that allows to tackle multicriteria scheduling problems, according to Decision Aid concepts. This problem is decomposed into three different problems. The first problem is about obtaining a model. The second one is how to take criteria into account and the third one is about solving a scheduling problem. An extension to an existing notation for scheduling problems is proposed for multicriteria scheduling problems. Then, basic results from the literature on multicriteria optimization are presented. These results are used to build the final scheduling problem to solve. Finally a survey is presented for one-machine, parallel machines and flowshop multicriteria scheduling problems.

The triangles method to build X-trees from incomplete distance matrices

Abstract: On decrit une methode pour la reconstruction des X-arbres (arbres values admettant X comme ensemble de feuilles) a partir de tableaux de distances incomplets (ou certaines valeurs sont incertaines ou inconnues). Elle permet de construire un arbre non oriente a partir de 2n - 3 valeurs de distance entre les n elements de X, sous des conditions qui sont explicitees. Cette construction est basee sur une relation entre X-arbres et 2-arbres values generalises d'ensemble de sommets X.

Une approche hybride pour le sac à dos multidimensionnel en variables 0–1

Abstract: We present, in this article, a hybrid approach for solving the 0–1 multidimensional knapsack problem (MKP). This approach combines linear programming and Tabu search. The resulting algorithm improves on the best result on many well-known hard benchmarks.

Sur l’équilibre fort selon Berge

Abstract: In this paper we study the main properties of the strong Berge equilibrium, then we prove a theorem of its existence based on the Ky Fan inequality and finally, we provide an algorithm for its determination.

Complexity of partial inverse assignment problem and partial inverse cut problem

Abstract: For a given partial solution, the partial inverse problem is to modify the coecients such that there is a full solution containing the partial solution, while the full solution becomes optimal under new coecients, and the total modication is minimum. In this paper, we show that the partial inverse assignment problem and the partial in- verse minimum cut problem are NP-hard if there are bound constraints on the changes of coecients.

Bottleneck Capacity Expansion Problems with General Budget Constraints

Abstract: This paper presents a unied approach for bottleneck capacity expansion problems. In the bottleneck capacity expansion problem, BCEP, we are given a nite ground set E, a familyF of fea- sible subsets of E and a nonnegative real capacity ce for all e 2 E. Moreover, we are given monotone increasing cost functions fe for in- creasing the capacity of the elements e2 E as well as a budget B.T he task is to determine new capacities ce ce such that the objective func- tion given by maxF2F mine2F ce is maximized under the side constraint that the overall expansion cost does not exceed the budget B.W e in- troduce an algebraic model for dening the overall expansion cost and for formulating the budget constraint. This models allows to capture various types of budget constraints in one general model. Moreover, we discuss solution approaches for the general bottleneck capacity expan- sion problem. For an important subclass of bottleneck capacity expan- sion problems we propose algorithms which perform a strongly poly- nomial number of steps. In this manner we generalize and improve a recent result of Zhang et al. (15).

On Minimizing Total Tardiness in a Serial Batching Problem

Abstract: We study the problem of scheduling jobs on a serial batching machine to minimize total tardiness. Jobs of the same batch start and are completed simultaneously and the length of a batch equals the sum of the processing times of its jobs. When a new batch starts, a constant setup time s occurs. This problem 1| s-batch | ∑ T i is known to be NP-Hard in the ordinary sense. In this paper we show that it is solvable in pseudopolynomial time by dynamic programming.

Extension of Reverse Elimination Method Through a Dynamic Management of the Tabu List

Abstract: The Reverse Elimination Method (REM) is a dynamic strategy for managing the tabu list. It is based on logical interdependencies between the solutions encountered during recent iterations of the search. REM provides both a necessary and sufficient condition to prevent cycling. The purpose of this paper is first to incorporate in REM a chronological order rule when cycling is unavoidable, thereby assuring the finite convergence of Tabu Search. Secondly, we correct a generalization of REM, the so-called REM-t method proposed by Glover (1990) where t is an integer parameter which controls the number of tabu attributes. A suitable adjustment of this parameter t can be designed in order to create a balance between diversification and intensification. In this paper, new dynamic rules for controlling the adjustment of the parameter t, are proposed. Finally, to illustrate the differences between the variants proposed for managing the tabu list, we test some of them on the 0-1 multidimensional knapsack problem.

Resource allocation in a mobile telephone network: A constructive repair algorithm

Abstract: Afin de couvrir les besoins lies au developpement de son reseau, un operateur francais de telephonie mobile doit periodiquement planifier l'achat et l'installation de nouveaux materiels, tout en respectant un ensemble de contraintes (contraintes obligatoires ou preferences hierarchisees). Cet article presente la methode, baptisee constructive repair, utilisee pour resoudre ce probleme dans les delais impartis (1 min de temps de calcul). Cette methode repare le planning durant sa construction. Une suite de procedures de reparation est definie: si une reparation donnee ne peut aboutir sur une solution partielle, une reparation plus forte (relâchant eventuellement des contraintes plus importantes) est appelee. Nous avons teste notre methode sur dix problemes (aussi bien reels que specifiquement concus a la main pour ces tests). Nos solutions sont toutes au moins aussi bonnes que celles imaginees par l'ingenieur responsable de la planification.

A New Relaxation in Conic Form for the Euclidean Steiner Problem in ℜ

Abstract: In this paper, we present a new mathematical programming formulation for the Euclidean Steiner Tree Problem (ESTP) in ℜ. We relax the integrality constrains on this formulation and transform the resulting relaxation, which is convex, but not everywhere differentiable, into a standard convex programming problem in conic form. We consider then an efficient computation of an ϵ -optimal solution for this latter problem using interior-point algorithm.

Separable convexification and DCA techniques for capacity and flow assignment problems

Abstract: On etudie ici une version continue du probleme de dimensionnement et routage dans un reseau de communications, dans lequel les couts de conception sont combines aux mesures de delai moyen d'acheminement, engendrant un probleme de multiflots avec une fonction objectif non convexe. On propose un encadrement de la valeur optimale par convexification separable sur les arcs, d'une part, et par calcul d'optima locaux issus d'un modele DC (difference de fonctions convexes) des fonctions de cout. Cette derniere technique permet de reduire la distance a la valeur optimale et on illustre son efficacite sur des problemes d'expansion de capacites.

Fast simulation for road traffic network

Abstract: Dans cet article, nous presentons une methode pour realiser des simulations rapides de grands systemes Markoviens. Cette methode est basee sur l'utilisation de trois concepts: l'uniformisation de chaine de Markov, une dynamique liee aux evenements et la modularite. Une application de trafic urbain illustre les performances de notre approche.

Minimizing the earliness and tardiness cost of a sequence of tasks on a single machine

Abstract: Assume that n tasks must be processed by one machine in a fixed sequence. The processing time, the preferred starting time and the earliness and tardiness costs per time unit are known for each task. The problem is to allocate each task a starting time such that the total cost incurred by the early and tardy tasks is minimum. Garey et al. have proposed a nice $O(n \log n)$ algorithm for the special case of symmetric and task-independent costs. In this paper we first extend that algorithm to the case of asymmetric and task-independent cost without increasing its worst-case complexity. For the general case of asymmetric and task-dependent costs, we propose an $O(n^3 \log n)$ algorithm based on a strong dominance property that yields to model the scheduling problem as a minimum cost path in a valued directed acyclic graph.

A modified algorithm for the strict feasibility problem

Abstract: In this note, we present a slight modification of an algorithm for the strict feasibility problem. This modification reduces the number of iterations.

Single machine preemptive scheduling to minimize the weighted number of late jobs with deadlines and nested release/due date intervals

Abstract: This paper is devoted to the following version of the single machine preemptive scheduling problem of minimizing the weighted number of late jobs. A processing time, a release date, a due date and a weight of each job are given. Certain jobs are specified to be completed in time, i.e. , their due dates are assigned to be deadlines, while the other jobs are allowed to be completed after their due dates. The release/due date intervals are nested, i.e. , no two of them overlap (either they have at most one common point or one covers the other). Necessary and sufficient conditions for the completion of all jobs in time are considered, and an O(n logn ) algorithm (where n is the number of jobs) is proposed for solving the problem of minimizing the weighted number of late jobs in case of oppositely ordered processing times and weights.

Tarification par des jeux Coopératifs avec Demandes Élastiques

Abstract: We propose here a pricing Model which is an extension of the Cooperative Game concept and which includes a notion of Elastic Demand. We present some existence results as well as some algorithms. We conclude by discussing this model in the context of some Production and Transportation problems.

Optimal and Near-Optimal (s,S) Inventory Policies for Levy Demand Processes

Abstract: A Levy jump process is a continuous-time, real-valued stochastic process which has independent and stationary increments, with no Brownian component. We study some of the fundamental properties of Levy jump processes and develop (s,S) inventory models for them. Of particular interest to us is the gamma-distributed Levy process, in which the demand that occurs in a fixed period of time has a gamma distribution. We study the relevant properties of these processes, and we develop a quadratically convergent algorithm for finding optimal (s,S) policies. We develop a simpler heuristic policy and derive a bound on its relative cost. For the gamma-distributed Levy process this bound is 7.9% if backordering unfilled demand is at least twice as expensive as holding inventory. Most easily-computed (s,S) inventory policies assume the inventory position to be uniform and assume that there is no overshoot. Our tests indicate that these assumptions are dangerous when the coefficient of variation of the demand that occurs in the reorder interval is less than one. This is often the case for low-demand parts that experience sporadic or spiky demand. As long as the coefficient of variation of the demand that occurs in one reorder interval is at least one, and the service level is reasonably high, all of the polices we tested work very well. However even in this region it is often the case that the standard Hadley–Whitin cost function fails to have a local minimum.

Multiple Routing Strategies in a Labelled Network

Abstract: We present here models and algorithms for the construction of efficient path systems, robust to possible variations of the characteristics of the network. We propose some interpretations of these models and proceed to numerical experimentations of the related algorithms. We conclude with a discussion of the way those concepts may be applied to the design of a Public Transportation System.

Un Algorithme pour la Bipartition d'un Graphe en Sous-graphes de Cardinalité Fixée

Abstract: A branch-and-bound method for solving the min cut with size constraint problem is presented. At each node of the branch-and-bound tree the feasible set is approximated by an ellipsoid and a lower bound is computed by minimizing the quadratic objective function over this ellipsoid. An upper bound is also obtained by a Tabu search method. Numerical results will be presented.

Semi-definite positive programming relaxations for graph Kn-COLORING in frequency assignment

Abstract: Dans cet article, nous decrivons une nouvelle classe de problemes de coloration rencontres en Allocation de Frequences militaire: nous voulons minimiser le nombre de n-uplets distincts utilises pour colorier un ensemble done de n-cliques d'un graphe Pour approcher ces problemes generalement NP-difficiles, nous proposons deux relaxations basees sur les modelisations semi-definies de la coloration de graphes et d'hypergraphes, ainsi qu'une generalisation des travaux de Karger et al a la coloration d'hypergraphes, pour trouver de bonnes solutions faisables par une approche probabiliste

The Lorenz Transform approach to the Optimal Repair-Cost limit remplacement Policy with Imperfect Repair

Abstract: In this paper, we consider a repair-cost limit replacement problem with imperfect repair and develop a graphical method to determine the optimal repair-cost limit which minimizes the expected cost per unit time in the steady-state, using the Lorenz transform of the underlying repair-cost distribution function. The method proposed can be applied to an estimation problem of the optimal repair-cost limit from empirical repair-cost data. Numerical examples are devoted to examine asymptotic properties of the non-parametric estimator for the optimal repair-cost limit.

Efficient and Local Efficient Solutions for Assignment Type Problems

Abstract: In this paper, we analyse the multiobjective problem generated by applying a goal programming approach to deal with linear assignment type problem. We specify sufficient conditions for a solution to be efficient for this problem. The notion of efficiency with respect to a neighborhood is also introduced and characterized through sufficient conditions. Unfortunately, these conditions are not necessary in general.

Finding the Principal Points of a Random Variable

Abstract: The p-principal points of a random variable X with finite second moment are those p points in minimizing the expected squared distance from X to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing procedures in the literature provide just a local optimum. In this paper we show that standard Global Optimization techniques can be applied.