zbMATH — the first resource for mathematics

Uncertain flexible flow shop scheduling problem subject to breakdowns. (English) Zbl 1366.90102
Summary: Flexible flow shop scheduling problems become more complex when uncertain factors are taken into consideration. Most literature are under the assumption that machines are continuous available. But, a machine can be unavailable for many reasons, such as breakdown and planned preventive maintenance. Once a machine breaks down, then the original schedule can not be executed and we must make the corresponding adjustment according to the actual situation. This paper deals with a flexible flow shop scheduling problem with uncertain processing and repair time subject to breakdowns. Machines are non-continuously available, i.e., they break down at arbitrary time instance not knownin advance. The problem with breakdowns is modeled as a series of problems without breakdowns. To solve the problem, approaches including genetic algorithm and particle swarm optimization are used in this paper. A numerical example shows the effectiveness of the proposed approach.

90B35 Deterministic scheduling theory in operations research
PDF BibTeX Cite
Full Text: DOI
[1] Allahverdi, Two-machine ordered flowshop scheduling under breakdown, Mathematical and Computer Modelling 20 (2) pp 9– (1994) · Zbl 0810.90060
[2] Allahverdi, Two-stage production scheduling with separated setup times and stochastic breakdowns, of the Operational Research Society, The Journal of the Operational Research Society 46 (7) pp 896– (1995) · Zbl 0832.90048
[3] Allahverdi, Two-machine proportionate flowshop scheduling with breakdowns to minimize maximum lateness, Computers & Operations Research 23 (10) pp 909– (1996) · Zbl 0863.90080
[4] Allahverdi, Dual criteria scheduling on a two-machine flowshop subject to random breakdowns, International Transactions in Operational Research 5 (4) pp 317– (1998)
[5] Alcaide, An approach to solve the minimum expected makespan flowshop problem subject to breakdowns, European Journal of Operational Research 140 (2) pp 384– (2002) · Zbl 1001.90031
[6] Alcaide, A heuristic approach to minimize expected makespan in open shops subject to stochastic processing times and failures, International Journal of Flexible Manufacturing Systems 17 (3) pp 201– (2005) · Zbl 1172.90412
[7] Albers, Scheduling with unexpected machine breakdowns, Discrete Applied Mathematics 110 (2) pp 85– (2001) · Zbl 1074.90523
[8] Al-Hinai, Robust and stable flexible job shop scheduling with random machine breakdowns using a hybrid genetic algorithm, International Journal of Production Economics 132 (2) pp 279– (2011)
[9] Allaoui, Scheduling two-stage hybrid flow shop with availability constraints, Computers & Operations Research 33 (5) pp 1399– (2006) · Zbl 1126.90017
[10] Ding, Two empirical uncertain models for project scheduling problem, Journal of the Operational Research Society 66 (9) pp 1471– (2015)
[11] Gao, Continuous dependence theorems on solutions of uncertain differential equations, Applied Mathematical Modelling 38 pp 3031– (2014)
[12] Hasan, Genetic algorithm for job-shop scheduling with machine unavailability and breakdowns, International Journal of Production Research 49 (16) pp 4999– (2011)
[13] Holthaus, Scheduling in job shops with machine breakdowns: An experimental study, Computers & Industrial Engineering 36 (1) pp 137– (1999)
[14] Kasap, Minimizing makespan on a single machine subject to random breakdowns, Operations Research Letters 34 (1) pp 29– (2006) · Zbl 1080.90048
[15] Ke, Uncertain random multilevel programming with application to production control problem, Soft Computing 19 (6) pp 1739– (2015) · Zbl 1364.90236
[16] Li, Stochastic scheduling on a single machine subject to multiple breakdown according to different probabilities, Operations Research Letters 18 (2) pp 81– (1995) · Zbl 0857.90059
[17] Liu, Uncertainty Theory (2007)
[18] Liu, Theory and Practice of Uncertain Programming (2009) · Zbl 1158.90010
[19] Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty (2010)
[20] Liu, Why is there a need for uncertainty theroy?, Journal of Uncertain Systems 6 (1) pp 3– (2012)
[21] Shahul, A grasp algorithm for m-machine flowshop scheduling problem with bicriteria of makespan and maximum tardiness, International Journal of Computer Mathematics 84 (12) pp 1731– (2007) · Zbl 1134.90385
[22] Sheng, Optimistic value model of uncertain optimal control, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 21 (7) pp 75– (2013) · Zbl 1322.93064
[23] Yan, Bang-bang control model for uncertain switched systems, Applied Mathematical Modelling 39 (10-11) pp 2994– (2014)
[24] Yao, Uncertain differential equation with jumps, Soft Computing 19 (7) pp 2063– (2015) · Zbl 1361.60048
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.