A decision theory based scheduling procedure for single-machine weighted earliness and tardiness problems (original) (raw)
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Hybrid heuristic algorithms for single machine total weighted tardiness scheduling problems
International Journal of Intelligent Systems Technologies and Applications, 2008
This paper addresses on solving a well known Non Polynomial (NP) hard type problem, namely the single machine total weighted-tardiness problem. The performances of three hybrid heuristic algorithms to solve the single machine scheduling problems with the objective of minimising the total weighted tardiness are presented and compared. In the first hybrid algorithm, a dynamic dispatching rule, namely Modified Due Date (MDD), is hybridised with local search mechanism. In the second hybrid algorithm, a greedy heuristic, namely backward phase, is proposed and hybridised with local search mechanisms. The third hybrid algorithm hybridises the backward phase heuristics with an iterated local search (ILS) having an evolutionary perturbation tool. The algorithms are tested by solving all the 125 benchmark problem instances available in the OR-Library for different sizes and compared with the best known values. It is observed that the hybrid algorithm with evolutionary perturbation tool is performing better than the others.
Applied Computer Systems
A problem of minimizing the total weighted tardiness in the preemptive single machine scheduling for discrete manufacturing is considered. A hyper-heuristic is presented, which is composed of 24 various heuristics, to find an approximately optimal schedule whenever finding the exact solution is practically intractable. The three heuristics are based on the well-known rules, whereas the 21 heuristics are introduced first. Therefore, the hyper-heuristic selects the best heuristic schedule among 24 schedule versions, whose total weighted tardiness is minimal. Each of the 24 heuristics can solely produce a schedule which is the best one for a given scheduling problem. Despite the percentage of zero gap instances decreases as the greater number of jobs is scheduled, the average and maximal gaps decrease as well. In particular, the percentage is not less than 80 % when up to 10 jobs are scheduled. The average gap calculated over nonzero gaps does not exceed 4 % in the case of scheduling 7...
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In this paper we consider the single machine earliness/tardiness scheduling problem with no idle time. We present two new heuristics, a dispatch rule and a greedy procedure, and also consider the best of the existing dispatch rules. Both dispatch rules use a lookahead parameter that had previously been set at a fixed value. We develop functions that map some instance statistics into appropriate values for that parameter. We also consider the use of dominance rules to improve the solutions obtained by the heuristics. The computational results show that the function-based versions of the heuristics outperform their fixed value counterparts and that the use of the dominance rules can indeed improve solution quality with little additional computational effort.
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A simple, fast, and effective heuristic for the single-machine total weighted tardiness problem
2010
We consider the single-machine total weighted tardiness problem (TWT) where a set of n jobs with general weights w_1,…, w_n, integer processing times p_1,…, p_n, and integer due dates d_1,…, d_n has to be scheduled non-preemptively. If C_j is the completion time of job j then T_j = max(0, C_j - d_j) denotes the tardiness of this job. The objective is to find a schedule S^{*}_{WT} that minimizes the weighted sum of the tardiness costs of all jobs computed as \sum_{j=1}^{n} w_j T_j. This problem is known to be unary NP-hard. Our goal is to design a constructive heuristic for this problem that yields excellent feasible solutions in short computational times by exploiting the structural properties of a preemptive relaxation.
European Journal of Operational Research, 1995
We address the problem of determining schedules for static, single-machine scheduling problems where the objective is to minimize the sum of weighted tardiness and weighted earliness. We develop optimal and heuristic procedures for the special case of weights that are proportional to the processing times of the respective jobs. The optimal procedure uses dominance properties to reduce the number of sequences that must be considered, and some of the heuristics use these properties as a basis for constructing good initial sequences. A pairwise interchange procedure is used to improve the heuristic solutions. An experimental study shows that the heuristic procedures perform very well.
Solutions to the dynamic average tardiness problem in single machine environments
2003
In dynamic scheduling arrival times as well, as some or all job attributes are unknown in advance. Dynamism can be classified as partial or total. In simplest partially dynamic problems the only unknown attribute of a job is its arrival time r j. A job arrival can be given at any instant in the time interval between zero and a limit established by its processing time, in order to ensure finishing it before the due date deadline. In the cases where the arrivals are near to zero the problem becomes closer to the static problem, otherwise the problem becomes more restrictive. In totally dynamics problems, other job attributes such as processing time p j , due date d j , and tardiness penalty w j , are also unknown. This paper proposes different approaches for resolution of (partial and total) Dynamic Average Tardiness problems in a single machine environment. The first approach uses, as a list of dispatching priorities a final (total) schedule, found as the best by another method for a similar static problem: same job features, processing time, and due dates. The second approach uses as a dispatching priority the order imposed by a partial schedule created by another heuristic, at each decision point. The details of implementation of the proposed algorithms and results for a group of selected instances are discussed in this work.
Algorithms for a class of single-machine weighted tardiness and earliness problems
European Journal of Operational Research, 1991
We address the problem of determining schedules for static, single-machine scheduling problems where the objective is to minimize the sum of weighted tardiness and weighted earliness. We develop optimal and heuristic procedures for the special case of weights that are proportional to the processing times of the respective jobs. The optimal procedure uses dominance properties to reduce the number of sequences that must be considered, and some of the heuristics use these properties as a basis for constructing good initial sequences. A pairwise interchange procedure is used to improve the heuristic solutions. An experimental study shows that the heuristic procedures perform very well.