Scheduling Hybrid Flowshop with Parallel Batching Machines and Task Compatibilities

C'est un résumé qui a été présenté à la conférence MAPSP07, en une partie nommé IntroductionInternational audienceWe consider a two-stage hybrid flowshop scheduling problem where each of n tasks is to be processed first at stage 1 and then at stage 2. The first stage contains m_1 identical parallel discrete machines and the second stage contains m_2 identical parallel batching machines. Each discrete machine can process no more than one task at time and each batching machine can process up to k tasks simultaneously in batch. The processing time of task j on any machine of stage one requires p_j time units and on any machine of stage two requiers q_j time units, which is given by the interval [a_j,b_j]. On the second stage the tasks are processed in batch and all tasks of the same batch start and finish together with the additional constraint that the tasks of the same batch have to be compatible. A compatibility is a symmetric binary relation in which a pair (i,j) of tasks is compatible if they share a similar processing time on the second machine (i.e, $[a_i, b_i] \cap [a_j, b_j] \neq \emptyset$). The batch processing time on the batching machine is determined as the maximum initial value a_j of compatible tasks. The objective is to find a schedule such that the completion time of the latest batch is minimized

Scheduling hybrid flowshop with parallel batching machines and compatibilities.

International audienceThis paper considers a two-stage hybrid flowshop problem in which the first stage contains several identical discrete machines, and the second stage contains several identical batching machines. Each discrete machine can process no more than one task at time, and each batching machine can process several tasks simultaneously in a batch with the additional feature that the tasks of the same batch have to be compatible. A compatibility relation is defined between each pair of tasks, so that an undirected compatibility graph is obtained which turns out to be an interval graph. The batch processing time is equal to the maximal processing time of the tasks in this batch, and all tasks of the same batch start and finish together. The goal is to make batching and sequencing decisions in order to minimize the makespan. Since the problem is NP-hard, we develop several heuristics along with their worst cases analysis. We also consider the case in which tasks have the same processing time on the first stage, for which a polynomial time approximation scheme (PTAS) algorithm is presented

Compatibility graphs in scheduling on batch processing machines

We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are modeled by an undirected graph $G$, in which compatible jobs are represented by adjacent vertices. We show that several subproblems are polynomial. We propose some exact polynomial algorithms to solve these subproblems. To solve the general case, we propose a mixed-integer linear programming (MILP) formulation alongside with heuristic approaches. Furthermore, computational experiments are carried out to measure the performance of the proposed methods.Comment: 25 pages, 11 figure

Heuristics for scheduling a two-stage hybrid flow shop with parallel batching machines: application at a hospital sterilisation plant

The model of a two-stage hybrid (or flexible) flow shop, with sequence-independent uniform setup times, parallel batching machines and parallel batches has been analysed with the purpose of reducing the number of tardy jobs and the makespan in a sterilisation plant. Jobs are processed in parallel batches by multiple identical parallel machines. Manual operations preceding each of the two stages have been dealt with as machine setup with standardised times and are sequence-independent. A mixed-integer model is proposed. Two heuristics have been tested on real benchmark data from an existing sterilisation plant: constrained size of parallel batches and fixed time slots. Computation experiments performed on combinations of machines and operator numbers suggest balancing the two stages by assigning operators proportionally to the setup time requirements

Serial-batch scheduling – the special case of laser-cutting machines

The dissertation deals with a problem in the field of short-term production planning, namely the scheduling of laser-cutting machines. The object of decision is the grouping of production orders (batching) and the sequencing of these order groups on one or more machines (scheduling). This problem is also known in the literature as "batch scheduling problem" and belongs to the class of combinatorial optimization problems due to the interdependencies between the batching and the scheduling decisions. The concepts and methods used are mainly from production planning, operations research and machine learning

Production Scheduling

Generally speaking, scheduling is the procedure of mapping a set of tasks or jobs (studied objects) to a set of target resources efficiently. More specifically, as a part of a larger planning and scheduling process, production scheduling is essential for the proper functioning of a manufacturing enterprise. This book presents ten chapters divided into five sections. Section 1 discusses rescheduling strategies, policies, and methods for production scheduling. Section 2 presents two chapters about flow shop scheduling. Section 3 describes heuristic and metaheuristic methods for treating the scheduling problem in an efficient manner. In addition, two test cases are presented in Section 4. The first uses simulation, while the second shows a real implementation of a production scheduling system. Finally, Section 5 presents some modeling strategies for building production scheduling systems. This book will be of interest to those working in the decision-making branches of production, in various operational research areas, as well as computational methods design. People from a diverse background ranging from academia and research to those working in industry, can take advantage of this volume

Scheduling Hybrid Flow Lines of Aerospace Composite Manufacturing Systems

Composite manufacturing is a vital part of aerospace manufacturing systems. Applying effective scheduling within these systems can cut the costs in aerospace companies significantly. These systems can be characterized as two-stage Hybrid Flow Shops (HFS) with identical, non-identical and unrelated parallel discrete-processing machines in the first stage and non-identical parallel batch-processing machines in the second stage. The first stage is normally the lay-up process in which the carbon fiber sheets are stacked on the molds (tools). Then, the parts are batched based on the compatibility of their cure recipe before going to the second stage into the autoclave for curing. Autoclaves require enormous capital investment and maximizing their utilization is of utmost importance. In this thesis, a Mixed Integer Linear Programming (MILP) model is developed to maximize the utilization of the resources in the second stage of this HFS. CPLEX, with an underlying branch and bound algorithm, is used to solve the model. The results show the high level of flexibility and computational efficiency of the proposed model when applied to small and medium-size problems. However, due to the NP-hardness of the problem, the MILP model fails to solve large problems (i.e. problems with more than 120 jobs as input) in reasonable CPU times. To solve the larger instances of the problem, a novel heuristic method along with a Genetic Algorithm (GA) are developed. The heuristic algorithm is designed based on a careful observation of the behavior of the MILP model for different problem sets. Moreover, it is enhanced by adding a number of proper dispatching rules. As its output, this heuristic algorithm generates eight initial feasible solutions which are then used as the initial population of the proposed GA. The GA improves the initial solutions obtained from the aforementioned heuristic through its stochastic iterations until it reaches the satisfactory near-optimal solutions. A novel crossover operator is introduced in this GA which is unique to the HFS of aerospace composite manufacturing systems. The proposed GA is proven to be very efficient when applied to large-size problems with up to 300 jobs. The results show the high quality of the solutions achieved by the GA when compared to the optimal solutions which are obtained from the MILP model. A real case study undertaken at one of the leading companies in the Canadian aerospace industry is used for the purpose of data experiments and analysis

Planning and Scheduling Optimization

Although planning and scheduling optimization have been explored in the literature for many years now, it still remains a hot topic in the current scientific research. The changing market trends, globalization, technical and technological progress, and sustainability considerations make it necessary to deal with new optimization challenges in modern manufacturing, engineering, and healthcare systems. This book provides an overview of the recent advances in different areas connected with operations research models and other applications of intelligent computing techniques used for planning and scheduling optimization. The wide range of theoretical and practical research findings reported in this book confirms that the planning and scheduling problem is a complex issue that is present in different industrial sectors and organizations and opens promising and dynamic perspectives of research and development