Algorithms for a class of single-machine weighted tardiness and earliness problems European Journal of Operational Research 52 (1991) 167–178 (original) (raw)
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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.
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.
This paper addresses Single-machine total weighted tardiness scheduling problem with dependent setup time. The problem, even in absence of setup time, is strongly NP-hard and cannot be solved using common optimization methods in reasonable time. In this paper, first a mathematical model for solving the problem is presented and then, two meta-heuristics; Genetic Algorithm (GA) and Simulated Annealing (SA), as well as a hill climbing heuristic are suggested. Each algorithm is examined individually and then two hybrid models are considered. The computational result shows that SA performs more efficient among the non-hybrid models while the hybrid of SA and Hill climbing is the best solution in general.
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.
The International Journal of Advanced Manufacturing Technology, 2007
In this paper intelligent search technique of variable structure learning automata (VSLA) has been used to solve single machine total weighted tardiness job scheduling problem. The goal is investigating reduction in delays result in late execution of the jobs after specified deadline as well as reducing the time required to find the best execution order of the jobs. For this reason, fixed structure learning automata and genetic algorithm approaches has been studied and then a new scheduling approach called VSLA-Scheduler has been proposed by employing variable structure learning automata technique. In order to identify strengths and weaknesses of the proposed method, its performance is compared with other intelligent techniques. In this regard, for performance evaluation of the proposed method and comparing it with other methods, computer simulations have been used. Finally, the results produced by the proposed and previous algorithms have been compared with the best solutions in OR library. Experimental results show that the proposed algorithm's performance (VSLA-Scheduler) is more acceptable than other methods.
Local Search Heuristics for the Single Machine Total Weighted Tardiness Scheduling Problem
INFORMS Journal on Computing, 1998
This paper presents several local search heuristics for the problem of scheduling a single machine to minimize total weighted tardiness. We introduce a new binary encoding scheme to represent solutions, together with a heuristic to decode the binary representations into actual sequences. This binary encoding scheme is compared to the usual “natural” permutation representation for descent, simulated annealing, threshold accepting, tabu search and genetic algorithms on a large set of test problems. Computational results indicate that all of the heuristics which employ our binary encoding are very robust in that they consistently produce good quality solutions, especially when multistart implementations are used instead of a single long run. The binary encoding is also used in a new genetic algorithm which performs very well and requires comparatively little computation time. A comparison of neighborhood search methods which use the permutation and binary representations shows that the...
Single-machine scheduling with sequence dependent setup to minimize total weighted squared tardiness
Iie Transactions, 1999
This paper addresses the NP-hard problem of scheduling N independent jobs on a single machine with release dates, due dates, sequence dependent setup times, and no preemption where the objective is to minimize the weighted sum of squared tardiness. A Lagrangian relaxation based approach is developed for single-machine scheduling with sequence dependent setup times that is based on a list scheduling concept in conjunction with Lagrangian relaxation. Sequence dependent setup times are formulated as capacity constraints, and then are relaxed using Lagrangian multipliers. The primal problem is decomposed into job-level subproblems which are solved optimally and an approximate dual problem is then solved using a sub-gradient technique. The result of the relaxation is a list of jobs sequenced by beginning times that is then improved via a three-way swap. Experimental results are compared with EDD (Earliest Due Date) and ATCS (Apparent Tardiness Cost with Setups) dispatching rules, a four-way swap local search, tabu search, and simulated annealing. The adopted approach results in superior solution quality with respect to EED, ATCS, four-way swap, and tabu search results. It has comparable solution quality to the simulated annealing results, but is substantially more computationally efficient. Overall, the approach is capable of dealing with realistically sized single machine scheduling problems with release dates, due dates, and sequence dependent setup times.
European Journal of Operational Research, 1996
We consider the dynamic single-machine scheduling problem where the objective is to minimize the sum of weighted earliness and weighted tardiness costs. A single pass heuristic, based on decision theory, is developed for constructing schedules. The heuristic permits schedules with idle time between jobs and behaves like a dispatching procedure. The performance of the new heuristic is examined using 116 published problems for which the optimum solution is known. Its performance is also investigated using 540 randomly generated problems covering a variety of conditions by comparing it to two well known dispatching procedures, adapted for dynamic early/tardy problems. The results indicate that the heuristic performs very well.
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...