Chams Lahlou

A general approach for optimizing regular criteria in the job-shop scheduling problem

Even though a very large number of solution methods has been developed for the job-shop scheduling problem, a majority has been designed for the makespan criterion. In this paper, we propose a general approach for optimizing any regular criterion in the job-shop scheduling problem. The approach is a local search method that uses a disjunctive graph model and neighborhoods generated by swapping critical arcs. The connectivity property of the neighborhood structure is proved and a novel efficient method for evaluating moves is presented. Besides its generality, another prominent advantage of the proposed approach is its simple implementation that only requires to tune the range of one parameter. Extensive computational experiments carried out on various criteria (makespan, total weighted flow time, total weighted tardiness, weighted sum of tardy jobs, maximum tardiness) show the efficiency of the proposed approach. Best results were obtained for some problem instances taken from the literature.

Modelling and solving a practical flexible job-shop scheduling problem with blocking constraints

This paper presents a study of a practical job-shop scheduling problem modelled and solved when helping a company to design a new production workshop. The main characteristics of the problem are that some resources are flexible, and blocking constraints have to be taken into account. The problem and the motivation for solving it are detailed. The modelling of the problem and the proposed resolution approach, a genetic algorithm, are described. Numerical experiments using real data are presented and analysed. We also show how these results were used to support choices in the design of the workshop.

New complexity results for parallel identical machine scheduling problems with preemption, release dates and regular criteria

In this paper, we are interested in parallel identical machine scheduling problems with preemption and release dates in case of a regular criterion to be minimized. We show that solutions having a permutation flow shop structure are dominant if there exists an optimal solution with completion times scheduled in the same order as the release dates, or if there is no release date. We also prove that, for a subclass of these problems, the completion times of all jobs can be ordered in an optimal solution. Using these two results, we provide new results on polynomially solvable problems and hence refine the boundary between P and NP for these problems.

Single-machine scheduling with time window-dependent processing times

In the one-machine scheduling problems analysed in this paper, the processing time of a job depends on the time at which the job is started. More precisely, the horizon is divided into time windows and with each one a coefficient is associated that is used to determine the actual processing time of a job starting in it. Two models are introduced, and one of them has direct connections with models considered in previous papers on scheduling problems with time-dependent processing times. Various computational complexity results are presented for the makespan criterion, which show that the problem is NP-hard, even with two time windows. Solving procedures are also proposed for some special cases.

A note on the paper Minimizing total tardiness on parallel machines with preemptions by Kravchenko and Werner (2012)

In this note, we point out two major errors in the paper “Minimizing total tardiness on parallel machines with preemptions” by Kravchenko and Werner (2012). More precisely, they claimed to have proved that both problems P|pmtn|∑Tj and P|rj,pj=p,pmtn|∑Tj are

Idempotent version of the Fréchet contingency array problem

\mathcal{NP}

Service Level in Scheduling

-Hard. We give a counter-example to their proofs, letting the complexity of these two problems open.

Self-organization and the Maximum Empower Principle in the Framework of max-plus Algebra.

In this paper we study the idempotent version of the so-called Frechet correlation array problem. The problem is studied using an algebraic approach. The major result is that there exists a unique upper bound and several lower bounds. The formula for the upper bound is given. An algorithm is proposed to compute one lower bound. Another algorithm is provided to compute all lower bounds, but the number of lower bounds may be a very large number. Note that all these results are only based on the distributive lattice property of the idempotent algebraic structure.