A Set of Algorithms for Solving the Generalized Tardiness Flowshop Problems (original) (raw)
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Computational results for the flowshop tardiness problem
Computers & Industrial Engineering, 2013
This paper reports on computational experiments involving optimal solutions to the flowshop tardiness problem. Of primary interest was a generic approach: solutions were obtained using a spreadsheet-based, mixed-integer programming code. However, the results compare favorably with those from a specially-tailored branch and bound algorithm. The main implication is that hardware and software have developed to the point that generic tools may offer the best way to solve combinatorial problems in scheduling.
Heuristic rules for tardiness problem in flow shop with intermediate due dates
The International Journal of Advanced Manufacturing Technology, 2014
In this paper, the tardiness flow shop models with intermediate due date were considered. The flow shop models consist of a set of jobs each having a number of operations, while each operation is performed in a single machine. All the jobs are considered having the same unidirectional precedence order. In the tardiness flow shop models with intermediate due date, which we call the generalized tardiness flow shop models, there exist a due date associated with the completion of each operation, and we want to find a schedule which minimizes the total tardiness of the jobs. This is a more general version of tardiness flow shop in the sense that, by assigning a large value to each of the intermediate due dates, we can obtain the traditional flow shop models. Considering the generalized tardiness flow shop models as the NP-hard problems, a set heuristic sequencing rules for finding the best permutation schedule for such problems is proposed. We conducted an extensive computational experiment using randomly generated test problems for evaluating the efficiency of the proposed rules in obtaining a near-optimal solution. The efficiency of the rules was evaluated, and those rules with better solutions were designated and reported.
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This note considers the problem of sequencing jobs to minimize total tardiness in a two-machine flowshop. The note shows how three dominance conditions and a lower bound previously developed for this problem can be improved. The note also proposes a new dominance condition. A branch-and-bound algorithm is developed that uses the improvements and new dominance condition. The algorithm is tested on randomly generated problems and the results of the test show that the improvements and new dominance condition improves the branch-and-bound algorithm's efficiency.
International Journal of Industrial Engineering Computations, 2022
We consider a no-wait m-machine flowshop scheduling problem which is common in different manufacturing industries such as steel, pharmaceutical, and chemical. The objective is to minimize total tardiness since it minimizes penalty costs and loss of customer goodwill. We also consider the performance measure of total completion time which is significant in environments where reducing holding cost is important. We consider both performance measures with the objective of minimizing total tardiness subject to the constraint that total completion time is bounded. Given that the problem is NP-hard, we propose an algorithm. We conduct extensive computational experiments to compare the performance of the proposed algorithm with those of three well performing benchmark algorithms in the literature. Computational results indicate that the proposed algorithm reduces the error of the best existing benchmark algorithm by 88% under the same CPU times. The results are confirmed by extensive statis...
Permutation flow shop scheduling with earliness and tardiness penalties
International Journal of Production Research, 2009
We address the permutation flowshop scheduling problem with earliness and tardiness penalties (E/T) and common due date of jobs. Large number of process and discrete parts industries follow flowshop type of production process. There are very few results reported for multi-machine E/T scheduling problems. We show that the problem can be sub-divided into three groups-one, where the due date is such that all jobs are necessarily tardy; the second, where the due date is such that it is not tight enough to act as a constraint on scheduling decision; and the third is a group of problems where the due date is in between the above two. We develop analytical results and heuristics for problems arising in each of these three classes. Computational results of the heuristics are reported. Most of the problems in this research are addressed for the first time in the literature. For problems with existing heuristics, the heuristic solution is found to perform better than the existing results.
Efficient procedures for the weighted squared tardiness permutation flowshop scheduling problem
Flexible Services and Manufacturing Journal, 2019
This paper addresses a permutation flowshop scheduling problem, with the objective of minimizing total weighted squared tardiness. The focus is on providing efficient procedures that can quickly solve medium or even large instances. Within this context, we first present multiple dispatching heuristics. These include general rules suited to various due date-related environments, heuristics developed for the problem with a linear objective function, and procedures that are suitably adapted to take the squared objective into account. Then, we describe several improvement procedures, which use one or more of three techniques. These procedures are used to improve the solution obtained by the best dispatching rule. Computational results show that the quadratic rules greatly outperform the linear counterparts, and that one of the quadratic rules is the overall best performing dispatching heuristic. The computational tests also show that all procedures significantly improve upon the initial solution. The non-dominated procedures, when considering both solution quality and runtime, are identified. The best dispatching rule, and two of the non-dominated improvement procedures, are quite efficient, and can be applied to even very largesized problems. The remaining non-dominated improvement method can provide somewhat higher quality solutions, but it may need excessive time for extremely large instances.
The m-machine, n-job, permutation flowshop problem with the total tardiness objective is a common scheduling problem, known to be NP-hard. Branch and bound, the usual approach to finding an optimal solution, experiences difficulty when n exceeds 20. Here, we develop a genetic algorithm, GA, which can handle problems with larger n. We also undertake a numerical study comparing GA with an optimal branch and bound algorithm, and various heuristic algorithms including the well known NEH algorithm and a local search heuristic LH. Extensive computational experiments indicate that LH is an effective heuristic and GA can produce noticeable improvements over LH.
International Journal of Operational Research, 2017
In this paper, we investigate the problem of n-jobs scheduling in an m-machine permutation flowshop with exact time lags between consecutive operations of each job. The exact time lag is defined as the time elapsed between every couple of successive operations of the same job which is equal to a prescribed value. The aim is to find a feasible schedule that minimises the total tardiness and earliness. We propose three mathematical formulations, which are then solved by running the commercial software CPLEX to provide an optimal solution for small size problems. As the problem is shown to be strongly NP-hard, we propose new improved upper and lower bounds useful for large size problems. We then evaluate their effectiveness through an extensive computational experiment.