A block approach to earliness-tardiness scheduling problems

Wodecki, Mieczysław

doi:10.1007/s00170-008-1395-7

Cited by 27 publications

(18 citation statements)

References 22 publications

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“…Much more efficient moves and neighbourhoods used in single machine algorithms are described in the works [3] and [30]. The neighborhood of the π is a set of permutations …”

Section: Computational Complexity Of Executing I-move Is O(n) and O(mentioning

confidence: 99%

“…Much more efficient moves and neighbourhoods used in single machine algorithms are described in the works [3] and [30] Much more efficient moves and neighbourhoods used in single machine algorithms are described in [3,30]. (1,2,3,4,5,6,7,8,9,10) With respect to T-blocks π T in π, it should be noticed that by condition a' from Section 3.1, for any permutation of jobs within π W. Bożejko, P. Rajba, and M. Wodecki…”

Section: Computational Complexity Of Executing I-move Is O(n) and O(mentioning

confidence: 99%

“…The first two integrals are calculated using the equality (30) and (31). Then, after simple transformations, we obtain the assertion (34).…”

Section: Of Task I 2 J Ismentioning

confidence: 99%

“…In carrying out the substitution, as in the proof of Theorem 4 and using Lemma 6 (equality (30) and (31) …”

Section: E(t Imentioning

confidence: 99%

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Stable scheduling of single machine with probabilistic parameters

Bożejko

Rajba

Wodecki

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. We consider a stochastic variant of the single machine total weighted tardiness problem jobs parameters are independent random variables with normal or Erlang distributions. Since even deterministic problem is NP-hard, it is difficult to find global optimum for large instances in the reasonable run time. Therefore, we propose tabu search metaheuristics in this work. Computational experiments show that solutions obtained by the stochastic version of metaheuristics are more stable (i.e. resistant to data disturbance) than solutions generated by classic, deterministic version of the algorithm.Key words: scheduling, uncertain parameters, tabu search, stability. J = f1, 2, …, ng have to be processed without interruption on a single machine that can handle only one job at a time. All jobs become available for processing at the beginning (time zero). Each job i has an integer processing time p i , a due date d i and a positive weight w i . For a given sequence of jobs (earliest) due date C i , the tardiness T i = maxf0, C i ¡ d i g and the cost w i ¢T i of job i 2 J. The objective is to find a job sequence which minimizes the sum of the costs ∑ n i=1 w i ¢T i . This is a classical problem of scheduling theory. Literature reviewThe total weighted tardiness problem is NP-hard [15]. Enumerative algorithms (which use dynamic programming and branch and bound approaches) for the problem are described in [22,29]. The algorithms are a significant improvement over exhaustive search but they remain laborious and are applicable only to relatively small problems, with the number of jobs not exceeding 50 (80 in a multi-processor computer [29]). The enumerative algorithms mentioned above may require considerable computer resources both in terms of computation times and core storage. Therefore, many algorithms have been proposed to find near optimal schedules in reasonable time.Local search methods start from an initial solution and if repeatedly try to improve the current solution by local changes. The interchanges are continued until a solution that cannot be improved is obtained, which is a local minimum. To increase the performance of local search algorithms, metaheuristics like tabu search are used [2,7], simulated annealing [23], path relinking [4], genetic algorithms [7], ant colony optimization [9]. A very effective iterated local-search method has been proposed by Kirlik and Oguz [13]. The key aspect of the method is its ability to explore an exponential-size neighborhood in polynomial time by a dynamic programming technique.

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“…Much more efficient moves and neighbourhoods used in single machine algorithms are described in the works [3] and [30]. The neighborhood of the π is a set of permutations …”

Section: Computational Complexity Of Executing I-move Is O(n) and O(mentioning

confidence: 99%

Section: Computational Complexity Of Executing I-move Is O(n) and O(mentioning

confidence: 99%

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Stable scheduling of single machine with probabilistic parameters

Bożejko

Rajba

Wodecki

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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“…Scheduling problems with due windows have been introduced by Anger, Lee and Martin-Vega [8]. The recent list of publications concerning scheduling problems with fixed or assignable due windows includes the papers of the following authors: Cheng [9], Lee [10], Kramer and Lee [11], Weng and Ventura [12][13][14], Liman and Ramaswamy [15], Mosheiov and Lann [16,17], Koulamas [18], Azizoglu and Webster [19], Wu and Wang [20], Linn, Yen and Zhang [21], Yeung, Oguz and Cheng [22], Yoo and Martin-Vega [23], Chen and Lee [24], Biskup and Feldmann [25], and Wodecki [26]. The due window assignment in scheduling problems with a general sum-type criterion (the most interesting for us) have been considered in the following papers by: Janiak and Marek [27,28], Kramer and Lee [29], and Liman, Panwalker and Thongmee [30,31].…”

Section: Introductionmentioning

confidence: 99%

Single processor scheduling problems with various models of a due window assignment

Janiak¹,

Janiak²,

Marek³

2009

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. In the paper we investigate four single processor scheduling problems, which deal with the process of the negotiation between a producer and a customer about delivery time of final products. This process is modeled by a due window, which is a generalization of well known classical due date and describes a time interval, in which a job should be finished. Due window assignment is a new approach, which has been investigated in the scientific literature for a few years. In this paper we consider various models of due window assignment. To solve the formulated problems we have to find such a schedule of jobs and such an assignment of due windows to each job, which minimizes a given criterion dependent on the maximum or total earliness and tardiness of jobs and due window parameters. One of the main results is the mirror image of the solutions of the considered problems and other problems presented in the scientific literature. The wide survey of the literature is also given.

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