Minimization of the total completion time for a single scheduling with learning effect and setup times consideration

Since scheduling literature has a wide range of uncertainties, it is crucial to take these into account when solving performance measure problems. Otherwise, the performance may severely be affected in a negative way. In this paper, an algorithm is proposed to minimize the total completion time (TCT) of a two-machine no-wait flowshop with uncertain setup times within lower and upper bounds. The results are compared to the best existing algorithm in scheduling literature: the programming language Python is used to generate random samples with respect to various distributions, and the TCT of the proposed algorithm is compared to that of the best existing one. Results reveal that the proposed one significantly outperforms the best one given in literature for all considered distributions. Specifically, the average percentage improvement of the proposed algorithm over the best existing one is over 90%. A test of hypothesis is conducted to further confirm the results.

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A BATCHING PROBLEM WITH LEARNING EFFECT CONSIDERATIONS

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595909002213 ◽

2009 ◽

Vol 26 (02) ◽

pp. 307-317 ◽

Cited By ~ 2

Author(s):

WEN-HUA YANG

Keyword(s):

Dynamic Programming ◽

Completion Time ◽

Processing Time ◽

Learning Effect ◽

Polynomial Function ◽

Optimal Number ◽

Total Completion Time ◽

Batch Sizing ◽

Forward Dynamic Programming ◽

Unit Processing

Consider a batch-sizing problem, where all jobs are identical or similar, and a unit processing time (p = 1) is specified for each job. To minimize the total completion time of jobs, partitioning jobs into batches may be necessary. Learning effect from setup repetition makes small-sized batches; on the contrary, job's learning effect results in large-sized batches. With their collaborative influence, we develop a forward dynamic programming (DP) algorithm to determine the optimal number of batches and their optimal integer sizes. The computation effort required by this DP algorithm is a polynomial function of job size.

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Two-machine flowshop scheduling problem to minimize makespan or total completion time with random and bounded setup times

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s016117120321019x ◽

2003 ◽

Vol 2003 (39) ◽

pp. 2475-2486 ◽

Cited By ~ 20

Author(s):

Ali Allahverdi ◽

Tariq Aldowaisan ◽

Yuri N. Sotskov

Keyword(s):

Completion Time ◽

Setup Times ◽

Total Completion Time ◽

Scheduling Problem ◽

Flowshop Scheduling ◽

Lower And Upper Bounds ◽

Dominance Relations ◽

Flowshop Scheduling Problem ◽

Global And Local ◽

Local Dominance

This paper addresses the two-machine flowshop scheduling problem with separate setup times to minimize makespan or total completion time (TCT). Setup times are relaxed to be random variables rather than deterministic as commonly used in the OR literature. Moreover, distribution-free setup times are used where only the lower and upper bounds are given. Global and local dominance relations are developed for the considered flowshops and an illustrative numerical example is given.

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