A note on minimizing the weighted sum of tardy and early completion penalties in a single machine: A case of small common due date

Alidaee, Bahram; Dragan, Irinel

doi:10.1016/s0377-2217(95)00363-0

Cited by 24 publications

(16 citation statements)

References 13 publications

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“…Let us consider the 10 jobs' instance that is specid in Table 1. Let π = (1,2,3,4,5,6,7,8,9,10). Permutation π has three blocks: T 1 = (1, 2, 3, 4), T 2 = (7), T 3 = (8) and two Dcks: D 1 = (5, 6), D 2 = (9, 10).…”

Section: Ck Of Tardy Jobsmentioning

confidence: 99%

“…(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%

“…If the execution times p i or the expected jobs' due dates d˜i(i 2 J) are random variables, then tardiness T π(i) (equivalent 2) and the objective function (equivalent to 1) To prevent from arising cycle too quickly (returning to the same permutation after some small number of iterations of the algorithm), some attributes of each move are saved on so-called tabu list (list of the forbidden moves).…”

Section: Randomizationmentioning

confidence: 99%

“…• expected total weighted number of early and tardy jobs [26], • expected weighted sum of earliness and tardiness [1,18].…”

Section: Introductionmentioning

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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Section: Ck Of Tardy Jobsmentioning

confidence: 99%

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

confidence: 99%

Section: Randomizationmentioning

confidence: 99%

“…• expected total weighted number of early and tardy jobs [26], • expected weighted sum of earliness and tardiness [1,18].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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show abstract

“…Azizoglu and Webster [1997] introduced a branch-and-bound algorithm to solve the problem with setup times. Other researchers who worked on the same problems with a restricted (small) due date, included Bagchi et al [1986], Szwarc [1989Szwarc [ , 1996, , Alidee and Dragan [1997] and Mondal and Sen [2001].None of the previous papers consider sequence-dependent setup times. The majority of the literature on earliness and tardiness scheduling deals with problems that consider single machine only.…”

Section: Parallel Machines With Earliness/tardiness Problemmentioning

confidence: 99%