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.

This paper deals with the problem of scheduling n tasks on m identical processors in the presence of communication delays. A new approach of modelisation by a decision graph and a resolution by a tabu search method is proposed. Initial solutions are constructed by list algorithms, and then improved by a tabu algorithm operating in two phases. The experiments carried on arbitrary graphs show the efficiency of our method and that it outperformed the principle existent heuristics.

In this work we propose a ranking procedure. This procedure uses an ordinal information about the criterion weights and a non-cardinal or mixed information for the potential actions evaluation. The advantage of this procedure is that it uses the linear programming software packages to compute the intervals of relative proximities from where the rankings are obtained.

We consider the simulation of transient performance measures of high reliable fault-tolerant computer systems. The most widely used mathematical tools to model the behavior of these systems are Markov processes. Here, we deal basically with the simulation of the mean time to failure (MTTF) and the reliability, R(t), of the system at time t. Some variance reduction techniques are used to reduce the simulation time. We will combine two of these techniques: Importance Sampling and Conditioning Technique. The resulting hybrid algorithm performs significant reduction of simulation time and gives stables estimations.

A second order optimality condition for multiobjective optimization with a set constraint is developed; this condition is expressed as the impossibility of nonhomogeneous linear systems. When the constraint is given in terms of inequalities and equalities, it can be turned into a John type multipliers rule, using a nonhomogeneous Motzkin Theorem of the Alternative. Adding weak second order regularity assumptions, Karush, Kuhn-Tucker type conditions are therefore deduced.

We study networks with positive and negative customers (or Generalized networks of queues and signals) in a random environment. This environment may change the arrival rates, the routing probabilities, the service rates and also the effect of signals. We prove that the steady-state distribution has a product form. This property is obtained as a corollary of a much more general result on multidimensional Markov chains.

Comparing q-ary relations on a set $\cal O$ of elementary objects is one of the most fundamental problems ofclassification and combinatorial data analysis. In this paper the specific comparison task that involves classificationtree structures (binary or not) is considered in this context. Two mathematical representations are proposed. One isdefined in terms of a weighted binary relation; the second uses a 4-ary relation. The most classical approaches totree comparison are discussed in the context of a set theoretic representation of these relations. Formal andcombinatorial computing aspects of a construction method for a very general family of association coeficients betweenrelations are presented. The main purpose of this article is to specify the components of this construction, based on apermutational procedure, when the structures to be compared are classification trees.

In this paper we study the well definedness of the central path associated to agiven nonlinear (convex) semidefinite programming problem. Under standard assumptions,we establish that the existence of the central path is equivalent to the nonemptiness andboundedness of the optimal set. Other equivalent conditions are given, such as the existenceof a strictly dual feasible point or the existence of a single central point.The monotonicbehavior of the logarithmic barrier and the objective function along the trajectory is alsodiscussed. Finally, the existence and optimality of cluster points are established.

Sequential scoring rules are multi-stage social choice tules that work as follows: at each stage of the process, a scoreis computed for each alternative by taking into account its position in the individual preference rankings, and thealternative with the lowest score is eliminated. The current paper studies the ability of these rules for choosing theCondorcet winner (or the strong Condorcet winner) when individual preferences are single-peaked.

In this paper we study bi-directional nearness in a network based on AHP (Analytic Hierarchy Process) and ANP(Analytic Network Process). Usually we use forward (one-dimensional) direction nearness based on Euclidean distance.Even if the nearest point to i is point j, the nearest point to j is not necessarily point i. Sowe propose theconcept of bi-directional nearness defined by AHP'ssynthesizing of weights “for” direction and “from” direction.This concept of distance is a relative distance based on the configuration ofthe set of points located on a plane ornetwork. In order to confirm the usefulness of our study we apply the proposed nearness to solving methods of TSP(Traveling Salesman Problem), where to find an approximate solution of TSP we improved Nearest-Neighbor Method.Some numerical experiments of TSP were carried out. To decide a nearest point we used two kind of nearness, forwarddirection nearness and bi-directional nearness. As a result, by using bi-directional nearness,we obtained goodapproximate solution of TSP. Moreover, the relation between AHP and ANP, through an example, is considered.

We show in this paper that timed Petri nets, with one resource shared by all the transitions, are directly connected tothe modelling of integer linear programs (ILP). To an ILP can be automatically associated an equivalent Petri net. Theoptimal reachability delay is an optimal solution of the ILP. We show next that a net can model any ILP. I order to dothis, we give a new sufficient reachability condition for the marking equation, which also holds for general Petri netswithout timed transitions.

A cooperative game is defined as a set of players and a cost function. The distribution of the whole cost between theplayers can be done using the core concept, that is the set of all undominated cost allocations which prevent playersfrom grouping. In this paper we study a game whose cost function comes from the optimal solution of a linear integercovering problem. We give necessary and sufficient conditions for the core to be nonempty and characterize itsallocations using linear programming duality. We also discuss a special allocation, called the nucleolus. Wecharacterize that allocation and show that it can be computed in polynomial time using a column generation method.