Minimizing total completion time for flowshop scheduling problem with uncertain processing times

The four-machine flowshop scheduling problem is investigated with the objective of minimizing total completion time. Job processing times are uncertain where only the lower and upper bounds are known. This problem is common in some manufacturing environments. Some mathematical (dominance) relations are established, and an algorithm (with ten scenarios) is proposed. The proposed algorithm converts the four-machine problem to a single machine problem for which an optimal solution is known for the deterministic problem. The difference among the scenarios is related to the weights assigned to the lower and upper bounds of processing times on the machines. The proposed algorithm is further improved by the established mathematical relations and are evaluated based on extensive computational experiments. The computational results indicate that three scenarios of the proposed algorithm perform much better than the others, and the errors of these three scenarios get better as the size of the problem increases. The results are statistically verified by constructing the confidence intervals.

[1]  Ali Allahverdi,et al.  A new heuristic for m-machine flowshop scheduling problem with bicriteria of makespan and maximum tardiness , 2004, Comput. Oper. Res..

[2]  Ali Allahverdi,et al.  Increasing the profitability and competitiveness in a production environment with random and bounded setup times , 2013 .

[3]  Ali Allahverdi,et al.  Production in a two-machine flowshop scheduling environment with uncertain processing and setup times to minimize makespan , 2015 .

[4]  Kai Wang,et al.  A decomposition-based approach to flexible flow shop scheduling under machine breakdown , 2012 .

[5]  Ali Allahverdi,et al.  The third comprehensive survey on scheduling problems with setup times/costs , 2015, Eur. J. Oper. Res..

[6]  Morteza Kiani,et al.  An efficient imperialist competitive algorithm for scheduling in the two-stage assembly flow shop problem , 2014 .

[7]  Ali Allahverdi,et al.  Two-machine flowshop scheduling problem with bounded processing times to minimize total completion time , 2010, Comput. Math. Appl..

[8]  Ali Allahverdi,et al.  Heuristics for the two-machine flowshop scheduling problem to minimise makespan with bounded processing times , 2010 .

[9]  Ali Allahverdi,et al.  Two-machine no-wait flowshop scheduling problem with uncertain setup times to minimize maximum lateness , 2018 .

[10]  Jose M. Framiñan,et al.  New approximate algorithms for the customer order scheduling problem with total completion time objective , 2017, Comput. Oper. Res..

[11]  Ali Allahverdi,et al.  A better dominance relation and heuristics for Two-Machine No-Wait Flowshops with Maximum Lateness Performance Measure , 2021, Journal of Industrial & Management Optimization.

[12]  T.-C. Lai,et al.  Sequencing with uncertain numerical data for makespan minimisation , 1999, J. Oper. Res. Soc..

[13]  Jose M. Framiñan,et al.  The 2-stage assembly flowshop scheduling problem with total completion time: Efficient constructive heuristic and metaheuristic , 2017, Comput. Oper. Res..

[14]  Ali Allahverdi,et al.  The Tricriteria Two-Machine Flowshop Scheduling Problem , 2001 .

[15]  Ali Allahverdi,et al.  Minimizing total completion time in a two-machine no-wait flowshop with uncertain and bounded setup times , 2020, Journal of Industrial & Management Optimization.

[16]  Ali Allahverdi,et al.  Two–machine flowshop minimum–length scheduling problem with random and bounded processing times , 2003 .

[17]  Nasser Salmasi,et al.  Makespan minimisation in flexible flowshop sequence-dependent group scheduling problem , 2013 .

[18]  Ali Allahverdi,et al.  Algorithms for four-machine flowshop scheduling problem with uncertain processing times to minimize makespan , 2020, RAIRO Oper. Res..

[19]  Frank Werner,et al.  Optimal makespan scheduling with given bounds of processing times , 1997 .

[20]  Ali Allahverdi,et al.  A survey of scheduling problems with no-wait in process , 2016, Eur. J. Oper. Res..

[21]  Jeng-Fung Chen.  Unrelated parallel-machine scheduling to minimize total weighted completion time , 2015, J. Intell. Manuf..

[22]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[23]  Socorro Rangel,et al.  A survey of case studies in production scheduling: Analysis and perspectives , 2017, J. Comput. Sci..

[24]  A Gerodimos,et al.  Robust Discrete Optimization and its Applications , 1996, J. Oper. Res. Soc..

[25]  P. Tayanithi,et al.  A knowledge-based simulation architecture to analyze interruptions in a flexible manufacturing system , 1992 .

[26]  Daniele Ferone,et al.  A biased-randomized simheuristic for the distributed assembly permutation flowshop problem with stochastic processing times , 2017, Simul. Model. Pract. Theory.

[27]  Ali Allahverdi,et al.  Algorithms for minimizing the number of tardy jobs for reducing production cost with uncertain processing times , 2017 .

[28]  Ali Allahverdi,et al.  The significance of reducing setup times/setup costs , 2008, Eur. J. Oper. Res..

[29]  Ali Allahverdi,et al.  Heuristics for the two-machine flowshop scheduling problem to minimize maximum lateness with bounded processing times , 2010, Comput. Math. Appl..

[30]  Ali Allahverdi,et al.  Flowshop scheduling problem to minimize total completion time with random and bounded processing times , 2004, J. Oper. Res. Soc..