Riad Aggoune

Minimizing the makespan for the flow shop scheduling problem with availability constraints

This paper deals with the scheduling of a flow shop with availability constraints (FSPAC). In such a problem, machines are not continuously available for processing jobs due to a preventive maintenance activity. A small number of solution methods exists in the literature for solving problems with at most two machines and to the authors knowledge only a few of them make use of the non-preemptive constraint. In this paper, two variants of the non-preemptive FSPAC with an arbitrary number of machines and an arbitrary number of unavailability periods on each of them are considered. In the first variant, starting times of maintenance tasks are fixed while in the second one the maintenance tasks must be performed on given time windows. Since the FSPAC is NP-hard in the strong sense, a heuristic approach based on a genetic algorithm and a tabu search is proposed to approximately solve the makespan minimization problem. Computational experiments are performed on randomly generated instances to show the efficiency of the proposed approaches.

A Lagrangian heuristic for an integrated lot-sizing and fixed scheduling problem

This paper presents a novel approach for solving an integrated production planning and scheduling problem. In theory as well as in practice, because of their complexity, these two decision levels are most of the time treated sequentially. Scheduling largely depends on the production quantities (lot sizes) computed at the production planning level and ignoring scheduling constraints in planning leads to inconsistent decisions. Integrating production planning and scheduling is therefore important for efficiently managing operations. An integrated model and an iterative solution procedure were proposed in earlier research papers: The approach has limitations, in particular when solving the planning problem. In this paper, a new formulation is proposed to determine a feasible optimal production plan, i.e. lot sizes, for a fixed sequence of operations on the machines when setup costs and times are taken into account. Capacity constraints correspond to paths of the conjunctive graph associated to the sequence. An original Lagrangian relaxation approach is proposed to solve this NP-hard problem. A lower bound is derived and an upper bound is calculated using a novel constructive heuristic. The quality of the approach is tested on numerous problem instances.

Solving the integrated lot-sizing and job-shop scheduling problem

Production planning and scheduling are usually performed in a sequential manner, thus generating unfeasibility conflicts. Moreover, solving these problems in complex manufacturing systems (with several products sharing different resources) is very challenging in production management. This paper addresses the solution of multi-item multi-period multi-resource single-level lot-sizing and scheduling problems in general manufacturing systems with job-shop configurations. The mathematical formulation is a generalisation of the one used for the Capacitated Lot-Sizing Problem, including detailed capacity constraints for a fixed sequence of operations. The solution method combines a Lagrangian heuristic, determining a feasible production plan for a fixed sequence of operations, with a sequence improvement method which iteratively feeds the heuristic. Numerical results demonstrate that this approach is efficient and more appropriate than a standard solver for solving complex problems, regarding solution quality and computational requirements.

Genetic algorithms for the flow shop scheduling problem with availability constraints

Most of the papers on scheduling take the common assumption that the machines are always available. We consider a flow shop problem with availability constraints (FSPAC), in which unavailability times of the machines are known in advance as a preventive maintenance activity. Contrary to the majority of previous works, preemption of tasks is not allowed. Two approaches are considered to deal with the maintenance activity: either the maintenance tasks are totally fixed or the location of some of them is optimized. As the problem is NP-hard, a genetic algorithm approach is proposed to solve the makespan and the total weighted tardiness minimization problems. Numerical experiments are presented to test the efficiency of the approach.

Disjunctive and time-indexed formulations for non-preemptive job shop scheduling with resource availability constraints

In many real industrial situations machines may be non-available for processing jobs for instance when a machine breaks down or when a preventive maintenance activity is scheduled. This paper deals with the job shop scheduling problem when machines are not continuously available and this for better modeling of the industry reality. We assume that no preemption is allowed and we introduce flexibility on machine unavailability periods by assuming that these latter are planned in time windows. This flexibility is relevant when scheduling preventive machine maintenance. Two mathematical models are presented and compared. The first one is based on the disjunctive graph and the second one is time-indexed. Numerical experiments on generated benchmarks were performed with ILOG CPLEX 10.

A NEW APPROACH FOR SOLVING INTEGRATED PLANNING AND SCHEDULING PROBLEM

Abstract This paper studies an integrated model for scheduling and planning in supply chains which allows determining a realistic production plan for a given sequence of jobs on each machine. Our model takes into account detailed capacity constraints and several characteristics; namely lead time, setup time and cost. A Lagrangian relaxation approach is used to obtain a lower bound and a simulated annealing is proposed to improve the sequencing of operations.

Heuristics for Job Shop Scheduling With Limited Machine Availability

Abstract In most of machine scheduling literature, resources are assumed to be continuously available which is not always true in practice. We deal with the context of unavailability periods known a priori; we are particularly interested in job shop problem where the job operations can be interrupted by resource unavailability periods that may be moved in time windows. Integrating these constraints increases the complexity of the scheduling problems. In this paper, we propose approximation methods that are construction heuristics that quickly determine a schedule based on decision strategies. Various experiments have been performed to validate the proposed methods.

A Reduced-Complexity Algorithm for Two-Job Shop Scheduling Problems with Availability Constraints

This paper addresses the complexity of scheduling problems considering two jobs to schedule and availability constraints imposed on the machines. A polynomial algorithm called temporized geometric approach is first proposed for the minimization of the makespan, under the non-preemption constraint. Then, a generalization to the preemptive case is developed. These algorithms are extensions of the geometric approach, which allows solving the classical two-job scheduling problem.