In this paper, we consider a job-shop scheduling problem. The criterion to be minimized is the makespan. To reach this goal, we propose a heuristic algorithm which gradually improves a given schedule by reversing the order in which some tasks are performed on machines. The job-shop scheduling problem being modelled as a disjunctive graph, reversing the order of two consecutive tasks which are performed on a given machine is equivalent to reversing the direction of a critical disjunctive are. The important fact is that, due to the results proposed in this paper, we are able to choose the critical disjunctive are to be reversed such that the makespan decreases at each iteration if the critical path is unique; otherwise, at least as many iterations as the number of critical paths are needed. This approach is simple and easy to implement.

This paper is concerned with inventory control in assembly systems for minimizing production costs. The system manufactures multiple products assembled from various components, and it operates according to a cyclic schedule. At the start of each cycle time, two decisions are made: the product volumes to be assembled during the current cycle, and the component-stock levels to be ordered. For a given decision, there is an associated cost incurred by backlogging of the finished products on one hand, and the component inventory holding cost, on the other hand. The objective here is to balance the two costs so as to minimize their sum. One complicating factor stems from uncertainties in both product demand levels and components yield times. These uncertainties can be modelled by probabilistic means, and hence the cost minimization problem becomes a stochastic problem. This problem can be quite difficult due to the nonlinearity of the equations involved, the mix of integer and continuous parameters, and their large number in moderate-size problems. Our approach in this paper is to first define certain control parameters and thus reduce the number of the variables involved in the optimization problem, and then solve the latter problem by using sophisticated optimization techniques in conjunction with heuristic modelling. We will demonstrate, by numerical means, the resolution of fairly difficult problems and thus establish the viability of the proposed numerical techniques.

The paper presents the major features of the ESPRIT Basic Research HIMAC, proposed to the EC after a thorough investigation of the state of the art of manufacturing systems control. HIMAC has followed a new approach, by developing a specific mathematIcs, the Manufactunng Algebra (MA), for modelling and controlling the production processes of discrete manufacturing systems. As a key feature, the MA models can be bottom-up aggregated starting from the very detailed levels used in simulation, thus making poSSIble a coherent model hierarchy at the base of the design and realization of Hierarchical control strategies and architectures. The formulation of the original mathematical approach and its validation criteria are outlined in the paper. For a deeper understanding, the mterested reader can take advantage of the list of references given at the end.

We consider a single machine scheduling problem which we studied to improve the efficiency of an automated medical laboratory. In this problem, there are not only chain structured precedence constraints, but also minimal and maximal times separating successive jobs in the same chain (separation time windows). The criterion to be minimized is the makespan. Potential applications are not restricted to medical analysis. This problem often arises in systems where chemical processes are involved. Therefore the problem studied in this paper is important in practice. We prove that the problem is nonpolynomial (NP)-complete. As a consequence, we propose three heuristics for large size problems and a branch and bound based algorithm for small size problems. Computational results are reported.

The problem of scheduling n jobs on a single machine in order to minimize the weighted sum of earliness and tardiness is NP-complete when jobs have different due dates. In most of the papers dedicated to this problem, authors assume that there is no idle time between two consecutive jobs. However, as indicated by several authors, this assumption is not consistent with the earliness-tardiness criterion. It is the reason why we do not make this assumption in this paper. To reach an optimal solution, we propose a branch-and-bound approach which takes advantage of some dominance properties and lower bounding procedures. Numerical experiments show that the algorithm can solve this problem with up to twenty jobs in a reasonable amount of time.

In this paper we propose a scheduling algorithm based on splitting up the problem into separate yet linked subproblems. We develop a heuristic algorithm to manage the remaining links between the scheduling subproblems obtained as a result of the splitting process. The complexity of the computation and the performance of the algorithms are examined and numerical examples are given to illustrate these algorithms.