Imed Kacem

Approach by localization and multiobjective evolutionary optimization for flexible job-shop scheduling problems

Traditionally, assignment and scheduling decisions are made separately at different levels of the production management framework. The combining of such decisions presents additional complexity and new problems. We present two new approaches to solve jointly the assignment and job-shop scheduling problems (with total or partial flexibility). The first one is the approach by localization (AL). It makes it possible to solve the problem of resource allocation and build an ideal assignment model (assignments schemata). The second one is an evolutionary approach controlled by the assignment model (generated by the first approach). In such an approach, we apply advanced genetic manipulations in order to enhance the solution quality. We also explain some of the practical and theoretical considerations in the construction of a more robust encoding that will enable us to solve the flexible job-shop problem by applying the genetic algorithms (GAs). Two examples are presented to show the efficiency of the two suggested methodologies.

Pareto-optimality approach for flexible job-shop scheduling problems: hybridization of evolutionary algorithms and fuzzy logic

Most scheduling problems are complex combinatorial problems and very difficult to solve [Manage. Sci. 35 (1989) 164; F.S. Hillier, G.J. Lieberman, Introduction to Operations Research, Holden-Day, San Francisco, CA, 1967]. That is why, lots of methods focus on the optimization according to a single criterion (makespan, workloads of machines, waiting times, etc.). The combining of several criteria induces additional complexity and new problems. In this paper, we propose a Pareto approach based on the hybridization of fuzzy logic (FL) and evolutionary algorithms (EAs) to solve the flexible job-shop scheduling problem (FJSP). This hybrid approach exploits the knowledge representation capabilities of FL [Fuzzy Sets Syst. 1 (1989)] and the adaptive capabilities of EAs. The integration of these two methodologies for the multi-objective optimization has become an increasing interest. The objective considered is to minimize the overall completion time (makespan), the total workload of machines and the workload of the most loaded machine. Many examples are presented to illustrate some theoretical considerations and to show the efficiency of the suggested methodology.

Single-machine scheduling with an availability constraint to minimize the weighted sum of the completion times

In this article, we consider a single-machine scheduling problem with one unavailability period, with the aim of minimizing the weighted sum of the completion times. We propose three exact methods for solving such a problem: a branch-and-bound method based on new properties and lower bounds, a mixed integer programming model, and a dynamic programming method. These methods were coded and tested on randomly generated instances, and their performances were analyzed. Our numerical experiments show that the branch-and-bound method and the dynamic programming method are complementary. Using these approaches, we are able to solve problems with up to 3000 jobs within a reasonable computation time.

Worst-case analysis of the WSPT and MWSPT rules for single machine scheduling with one planned setup period

In this article, we consider the single machine scheduling problem with one planned setup period, with the aim of minimizing the weighted sum of the completion times. We study the WSPT and MWSPT heuristics and we show that the worst-case performance ratio is 3 for the two heuristics in some cases and it is unbounded otherwise. We also show that these worst-case performance ratios are tight.

Approximation algorithm for the weighted flow-time minimization on a single machine with a fixed non-availability interval

In this article, we consider the non-resumable case of the single machine scheduling problem with a fixed non-availability interval. We aim to minimize the weighted sum of completion times. No polynomial 2-approximation algorithm for this problem has been previously known. We propose a 2-approximation algorithm with O(n^2) time complexity where n is the number of jobs. We show that this bound is tight. The obtained result outperforms all the previous polynomial approximation algorithms for this problem.

Approximation algorithms for the makespan minimization with positive tails on a single machine with a fixed non-availability interval

Abstract In this article, we consider the non-resumable case of the single machine scheduling problem with a fixed non-availability interval. We aim to minimize the makespan when every job has a positive tail. We propose a polynomial approximation algorithm with a worst-case performance ratio of 3/2 for this problem. We show that this bound is tight. We present a dynamic programming algorithm and we show that the problem has an FPTAS (Fully Polynomial Time Approximation Algorithm) by exploiting the well-known approach of Ibarra and Kim (J. ACM 22:463–468, 1975). Such an FPTAS is strongly polynomial. The obtained results outperform the previous polynomial approximation algorithms for this problem.

Assignment and Scheduling in Flexible Job-Shops by Hierarchical Optimization

In this paper, we propose a new hierarchical method for the flexible job-shop scheduling problem (FJSP). This approach is mainly adapted to a job-shop problem (JSP) with high flexibility and is based on the decomposition of the problem in an assignment subproblem and a sequencing subproblem. For the first subproblem, we propose two methods: the first one is based successively on a heuristic approach and a local search; the second one, however, is based on a branch-and-bound algorithm. The quality of the assignment is evaluated by a lower bound. For the second subproblem we apply a hybrid genetic algorithm to deal with the sequencing problem. Computational tests are finally presented.

Short Communication: Fully polynomial time approximation scheme for the weighted flow-time minimization on a single machine with a fixed non-availability interval

In a recent paper [Theoretical Computer Science 363, 257-265], He, Zhong and Gu considered the non-resumable case of the scheduling problem with a fixed non-availability interval under the non-resumable scenario. They proposed a polynomial time approximation scheme (PTAS) to minimize the total completion time. In this paper, we propose a fully polynomial-time approximation scheme to minimize the total weighted completion time. The FPTAS has O(n^2/@e^2) time complexity, where n is the number of jobs and @e is the required error bound. The proposed FPTAS outperforms all the previous approximation algorithms designed for this problem and its running time is strongly polynomial.

Genetic algorithm for the flexible job-shop scheduling problem

In this paper, we are interested in the multiobjective optimization of the schedule performance in the flexible job shops. The flexible job shop scheduling problem (FJSP) is known in the literature as one of the hardest combinatorial optimization problems and presents many objectives to be optimized. In this way, we aim to solve such a problem according to a set of some criteria, which characterize the feasible solutions of such a problem. The studied criteria are the following: the makespan, the workload of the critical machine, and the total workload of all the machines. Our study relates to the determination of a practical method using genetic algorithm in order to obtain the best performance of the production system. The solution performance is evaluated by comparing the values of the different values of the criteria with the corresponding lower bounds.

Earliness---tardiness minimization on a single machine to schedule preventive maintenance tasks: metaheuristic and exact methods

In this paper, we consider the problem of scheduling a set of M preventive maintenance tasks to be performed on M machines. The machines are assigned to execute production tasks. We aim to minimize the total preventive maintenance cost such that the maintenance tasks have to continuously be run during the schedule horizon. Such a constraint holds when the maintenance resources are not sufficient. We solve the problem by two exact methods and meta-heuristic algorithms. As exact procedures we used linear programming and branch and bound methods. As meta-heuristics, we propose a local search approach as well as a genetic algorithm. Computational experiments are performed on randomly generated instances to show that the proposed methods produce appropriate solutions for the problem. The computational results show that the deviation of the meta-heuristics solutions to the optimal one is very small, which confirms the effectiveness of meta-heuristics as new approaches for solving hard scheduling problems.