Multicriteria hybrid flow shop scheduling problem: literature review, analysis, and future research

This research focuses on the Hybrid Flow Shop production scheduling problem, which is one of the most difficult problems to solve. The literature points to several studies that focus the Hybrid Flow Shop scheduling problem with monocriteria functions. Despite of the fact that, many real world problems involve several objective functions, they can often compete and conflict, leading researchers to concentrate direct their efforts on the development of methods that take consider this variant into consideration. The goal of the study is to review and analyze the methods in order to solve the Hybrid Flow Shop production scheduling problem with multicriteria functions in the literature. The analyses were performed using several papers that have been published over the years, also the parallel machines types, the approach used to develop solution methods, the type of method develop, the objective function, the performance criterion adopted, and the additional constraints considered. The results of the reviewing and analysis of 46 papers showed opportunities for future researchon this topic, including the following: (i) use uniform and dedicated parallel machines, (ii) use exact and metaheuristics approaches, (iv) develop lower and uppers bounds, relations of dominance and different search strategiesto improve the computational time of the exact methods,  (v) develop  other types of metaheuristic, (vi) work with anticipatory setups, and (vii) add constraints faced by the production systems itself

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Flow shop scheduling with earliness, tardiness and intermediate inventory holding costs

We consider the problem of scheduling customer orders in a flow shop with the objective of minimizing the sum of tardiness, earliness (finished goods inventory holding) and intermediate (work-in-process) inventory holding costs. We formulate this problem as an integer program, and based on approximate solutions to two di erent, but closely related, Dantzig-Wolfe reformulations, we develop heuristics to minimize the total cost. We exploit the duality between Dantzig-Wolfe reformulation and Lagrangian relaxation to enhance our heuristics. This combined approach enables us to develop two di erent lower bounds on the optimal integer solution, together with intuitive approaches for obtaining near-optimal feasible integer solutions. To the best of our knowledge, this is the first paper that applies column generation to a scheduling problem with di erent types of strongly NP-hard pricing problems which are solved heuristically. The computational study demonstrates that our algorithms have a significant speed advantage over alternate methods, yield good lower bounds, and generate near-optimal feasible integer solutions for problem instances with many machines and a realistically large number of jobs

On the exact solution of the no-wait flow shop problem with due date constraints

Peer ReviewedThis paper deals with the no-wait flow shop scheduling problem with due date constraints. In the no-wait flow shop problem, waiting time is not allowed between successive operations of jobs. Moreover, the jobs should be completed before their respective due dates; due date constraints are dealt with as hard constraints. The considered performance criterion is makespan. The problem is strongly NP-hard. This paper develops a number of distinct mathematical models for the problem based on different decision variables. Namely, a mixed integer programming model, two quadratic mixed integer programming models, and two constraint programming models are developed. Moreover, a novel graph representation is developed for the problem. This new modeling technique facilitates the investigation of some of the important characteristics of the problem; this results in a number of propositions to rule out a large number of infeasible solutions from the set of all possible permutations. Afterward, the new graph representation and the resulting propositions are incorporated into a new exact algorithm to solve the problem to optimality. To investigate the performance of the mathematical models and to compare them with the developed exact algorithm, a number of test problems are solved and the results are reported. Computational results demonstrate that the developed algorithm is significantly faster than the mathematical models

Production Scheduling in Integrated Steel Manufacturing

Steel manufacturing is both energy and capital intensive, and it includes multiple production stages, such as iron-making, steelmaking, and rolling. This dissertation investigates the order schedule coordination problem in a multi-stage manufacturing context. A mixed-integer linear programming model is proposed to generate operational (up to the minute) schedules for the steelmaking and rolling stages simultaneously. The proposed multi-stage scheduling model in integrated steel manufacturing can provide a broader view of the cost impact on the individual stages. It also extends the current order scheduling literature in steel manufacturing from a single-stage focus to the coordinated multi-stage focus. Experiments are introduced to study the impact of problem size (number of order batches), order due time and demand pattern on solution performance. Preliminary results from small data instances are reported. A novel heuristic algorithm, Wind Driven Algorithm (WDO), is explained in detail, and numerical parameter study is presented. Another well-known and effective heuristic approach based on Particle Swarm Optimization (PSO) is used as a benchmark for performance comparison. Both algorithms are implemented to solve the scheduling model. Results show that WDO outperforms PSO for the proposed model on solving large sample data instances. Novel contributions and future research areas are highlighted in the conclusion

Lagrangian approach to minimize makespan of non-identical parallel batch processing machines

Advisors: Purushothaman Damodaran.Committee members: Omar Ghrayeb; Murali Krishnamurthi; Christine Nguyen.Batch Processing Machines (BPMs) are commonly used in electronics manufacturing, semi-conductor manufacturing, and metal-working - to name a few. Scheduling these machines are not an easy task; practical considerations and the exponential number of decision variables involved impede schedulers (or decision makers) from making good decisions. This research focuses on minimizing the makespan of a set of non-identical parallel batch processing machines. In order to schedule jobs on these machines, two decisions are to be made. The first decision is to group jobs to form batches such that the machine capacity is not exceeded. The second decision is to sequence the batches formed on the machines such that the makespan is minimized. Both the decisions are intertwined as the processing time of the batch is determined by the composition of the jobs in the batch. The problem under study is shown to be NP-hard. A mathematical model from the literature is adopted to develop a solution approach which would help the decision maker to make meaningful decisions.Lagrangian Relaxation approach has been shown to be very effective in solving scheduling problems. Using this decomposition approach, the mathematical model is decomposed and a sub-gradient approach was used to update the multipliers. Two sets of constraints were relaxed to consider two Lagrangian Relaxation models. Experiments were conducted with data sets from the literature. The solution quality of the proposed approach was compared with meta-heuristics (i.e. Particle Swarm Optimization (PSO) and Random Key Genetic Algorithm (RKGA)) published in the literature and a commercial solver (i.e. IBM ILOG CPLEX). On smaller instances (i.e. 10 and 20 jobs), the proposed approach outperformed PSO and RKGA. However, the proposed approach and CPLEX report the same results. On larger instances (i.e. 50, 100 and 200 job instances) with two and four-machines, the proposed approach was better than PSO whenever the variability in the processing times were smaller. The proposed approach generally outperformed RKGA and CPLEX on larger problem instances. Out of 200 experiments conducted, the proposed approach helped to find new improved solution on 34 instances and comparable on 105 instances when compared to PSO. The PSO approach was much faster than all other approaches on larger problem instances. The experimental study clearly identifies the problem instances on which the proposed approach can find a better solution. The proposed Lagrangian Relaxation solution approach helps the schedulers to make more informed decisions. Minor modifications can be made to use the proposed solution approach for other practical considerations (e.g. job ready times, tardiness objective, etc.) The main contribution of this research is the proposed solution approach which is effective in solving a class of non-identical batch processing machine problems with better solution quality when compared to existing meta-heuristics.M.S. (Master of Science