Single machine and flowshop scheduling problems with sum-of-processing time based learning phenomenon

The scheduling of the single machine is of major importance in applications. The focus of this work is to analyze the scheduling problems in single-machine scheduling in the presence of uncertain parameters. By assuming that the processing time is represented by the nominal value plus a perturbation, we propose a robust model base on event point, and we obtain the feasible job sequence with some probability confidence level.

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SINGLE MACHINE SCHEDULING WITH A LEARNING EFFECT AND A RATE-MODIFYING ACTIVITY

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595911003211 ◽

2011 ◽

Vol 28 (04) ◽

pp. 511-521 ◽

Cited By ~ 5

Author(s):

CHUANLI ZHAO ◽

HENGYONG TANG

Keyword(s):

Single Machine ◽

Processing Time ◽

Learning Effect ◽

Window Size ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Scheduling Problems ◽

Polynomial Time Algorithms ◽

Due Window ◽

Machine Scheduling Problems

In the paper, single machine scheduling problems with a learning effect and a rate-modifying activity are considered. Under the learning effect, the processing time of a job is a decreasing function of its position in the sequence. The rate-modifying activity is an event that can change the speed of the machine, and hence the processing time of jobs after the activity. The following objective functions are considered: the makespan, the total earliness, tardiness and completion time penalty, and the total earliness, tardiness, due-window starting time and due-window size penalty. Polynomial time algorithms are proposed to optimally solve the problems.

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Formulation of fuzzy flowshop scheduling problems with fuzzy processing time

Proceedings of IEEE 5th International Fuzzy Systems ◽

10.1109/fuzzy.1996.551742 ◽

2002 ◽

Cited By ~ 22

Author(s):

H. Ishibuchi ◽

T. Murata ◽

Kyu Hung Lee

Keyword(s):

Processing Time ◽

Scheduling Problems ◽

Flowshop Scheduling ◽

Fuzzy Processing Time

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Refined conditions for V-shaped optimal sequencing on a single machine to minimize total completion time under combined effects

Journal of Scheduling ◽

10.1007/s10951-019-00628-4 ◽

2019 ◽

Vol 23 (6) ◽

pp. 665-680

Author(s):

Alan J. Soper ◽

Vitaly A. Strusevich

Keyword(s):

Single Machine ◽

Processing Time ◽

Cumulative Effect ◽

Single Machine Scheduling ◽

Scheduling Problems ◽

Priority Rules ◽

Optimal Sequence ◽

Positional Effect ◽

Wide Range ◽

Completion Times

AbstractWe address single-machine scheduling problems for which the actual processing times of jobs are subject to various effects, including a positional effect, a cumulative effect and their combination. We review the known results on the problems to minimize the makespan, the sum of the completion times and their combinations and identify the problems for which an optimal sequence cannot be found by simple priority rules such as Shortest Processing Time (SPT) and/or Longest Processing Time (LPT). Typically, these are problems to minimize the sum of the completion times under a deterioration effect, and we verify under which conditions for these problems an optimal permutation is V-shaped (an LPT subsequence followed by an SPT subsequence). We demonstrate that previously used techniques for proving that an optimal sequence is V-shaped are not properly justified. We use the corrected method to describe a wide range of problems with a pure positional effect and a combination of a cumulative effect with a positional effect for which an optimal sequence is V-shaped. On the other hand, we show that even the refined approach has its limitations.

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