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.

We present a review of the main “global optimization" methods. The paper comprises one introduction and two parts. In the introduction, we recall some generalities about non linear constraint-less optimization and we list some classifications which have been proposed for the global optimization methods. We then describe, in the first part, various “classical" global optimization methods, most of which available long before the appearance of Simulated Annealing (a key event in this field). There exists plenty of papers and books dealing with these methods, and studying in particular their convergence properties. The second part of the paper is devoted to more recent or atypical methods, mostly issued from combinatorial optimization. The three main methods are “metaheuristics": Simulated Annealing (and derived techniques), Tabu Search and Genetic Algorithms; we also describe three other less known methods. For these methods, theoretical studies of convergence are less abundant in the literature, and the use of convergence results is by far more limited in practice. However, the fitting of some of these techniques to continuous variables problems gave very promising results; that question is not discussed in detail in the paper, but useful references allowing to deepen the subject are given.

In this paper, we analyse the multiobjective problem generated byapplying a goal programming approach to deal with linearassignment type problem. We specify sufficient conditions for asolution to be efficient for this problem. The notion ofefficiency with respect to a neighborhood is also introduced andcharacterized through sufficient conditions. Unfortunately, theseconditions are not necessary in general.

The p-principal points of a random variable X with finitesecond momentare those ppoints in ${\mathbb R}$ minimizing the expected squared distance from X tothe closest point.Although the determination of principal points involves in general theresolution of a multiextremal optimization problem, existing procedures inthe literature provide just a local optimum. In this paper we show thatstandard Global Optimization techniques can be applied.

We study a continuous version of the capacity and flow assignment problem(CFA) where the design cost is combined with an average delay measureto yield a non convex objective function coupled with multicommodity flowconstraints. A separable convexification of each arc cost function is proposedto obtain approximate feasible solutions within easily computable gaps fromoptimality. On the other hand, DC (difference of convex functions) programming can be usedto compute accurate upper bounds and reduce the gap.The technique is shown to be effective when topology is assumedfixed and capacity expansion on some arcs is considered.

In this paper we present a method to perform fast simulation oflarge Markovian systems. This method is based on the use of threeconcepts: Markov chain uniformization, event-driven dynamics,and modularity. An application of urban trafficsimulation is presented to illustrate the performance of our approach.

To cope with its development, a French operator of mobile telephone networkmust periodically plan the purchase and the installation of new hardware,in such a way that a hierarchy of constraints (required and preferred)is satisfied.This paper presents the “constructive repair” method we used to solvethis problem within the allowed computing time (1 min). This method repairsthe planning during its construction. A sequence of repair procedures is defined: if a given repair cannot be achieved on a partial solution,a stronger repair (possibly relaxing more important constraints) is called upon.We tested our method on ten (both hand-made and real) problems. All our solutions were at least as good as thoses computed by hand by the engineer in charge with the planning.

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(nlogn) 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(n3 logn) 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.

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.

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.

A method to infer X-trees (valued trees having X as set of leaves) from incomplete distance arrays (where some entries are uncertain or unknown) is described. It allows us to build an unrooted tree using only 2n-3 distance values between the n elements of X, if they fulfill some explicit conditions. This construction is based on the mapping between X-tree and a weighted generalized 2-tree spanning X.

In this paper we will describe a new class of coloring problems, arising from military frequency assignment, where we want tominimize the number of distinct n-uples of colors used to color a givenset of n-complete-subgraphs of a graph. We will propose two relaxations based onSemi-Definite Programming models for graph and hypergraphcoloring, to approximate those (generally) NP-hard problems, as well asa generalization of the works of Karger et al. for hypergraph coloring,to find good feasible solutions with a probabilisticapproach.

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(nlogn) 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.

We study the problem of scheduling jobs on a serial batching machineto minimize total tardiness. Jobs of the same batch start and arecompleted simultaneously and the length of a batch equals the sum ofthe processing times of its jobs. When a new batch starts, a constantsetup time s occurs. This problem 1| s-batch| ∑Ti isknown to be NP-Hard in the ordinary sense. In this paper we show thatit is solvable in pseudopolynomial time by dynamic programming.

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.

For a given partial solution,the partial inverse problem is to modify the coefficientssuch that there is a full solution containing the partial solution, while the full solution becomes optimal under new coefficients, and the total modification is minimum.In this paper, we show that the partial inverseassignment problem and the partial inverse minimum cut problem are NP-hard ifthere are bound constraints on the changes of coefficients.

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.

This paper presents a unified approach forbottleneckcapacity expansion problems. In the bottleneck capacity expansion problem, BCEP, we are given a finite ground set E, a family Fof feasible subsets of E and a nonnegative real capacity ĉefor all e ∈ E. Moreover, we are given monotone increasing cost functions f e for increasing the capacity of the elements e ∈ E as well as a budget B. The task is to determine new capacities ce ≥ ĉe such that the objective function given by maxF∈F mine∈F ce is maximized under the sideconstraint that the overall expansion cost does not exceed the budget B.We introduce an algebraic model for defining the overall expansion cost and for formulating the budget constraint. This models allows to capturevarious types of budget constraints in one general model.Moreover, wediscuss solution approaches for the general bottleneck capacityexpansion problem. For an important subclass of bottleneck capacity expansion problems we propose algorithms which perform a strongly polynomial number ofsteps. In this manner we generalize and improve a recent result ofZhang et al. [15].

A Levy jump process is a continuous-time, real-valued stochasticprocess which has independent and stationary increments, with no Browniancomponent. We study some of the fundamental properties of Levy jumpprocesses and develop (s,S) inventory models for them. Of particularinterest to us is the gamma-distributed Levy process, in which the demandthat occurs in a fixed period of time has a gamma distribution.We study the relevant properties of these processes, and we develop aquadratically convergent algorithm for finding optimal (s,S) policies. Wedevelop a simpler heuristic policy and derive a bound on its relative cost. For the gamma-distributed Levy process this bound is 7.9% ifbackordering unfilled demand is at least twice as expensive as holdinginventory.Most easily-computed (s,S) inventory policies assume theinventory position to be uniform and assume that there is no overshoot. Ourtests indicate that these assumptions are dangerous when the coefficient ofvariation 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 orspiky demand. As long as the coefficient of variation of the demand thatoccurs in one reorder interval is at least one, and the service level isreasonably high, all of the polices we tested work very well. However evenin this region it is often the case that the standard Hadley–Whitin costfunction fails to have a local minimum.

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.