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Allahverdi Ali (College of Engineering and Petroleum, Kuwait University, Kuwait)
Three-Machine Flowshop Scheduling Problem to Minimize Total Completion Time with Bounded Setup and Processing Times
Decision Making in Manufacturing and Services, 2007, vol. 1, nr 1/2, s. 5-23, tab., rys., bibliogr. 17 poz.
Słowa kluczowe
Maszyny i urządzenia, Pomiary, Obliczenia matematyczne, Eksperyment badawczy
Machinery and equipment, Measurement, Mathematic calculations, Scientific experiment
The three-machine flowshop scheduling problem to minimize total completion time is studied where setup times are treated as separate from processing times. Setup and processing times of all jobs on all machines are unknown variables before the actual occurrence of these times. The lower and upper bounds for setup and processing times of each job on each machine is the only information that is available. In such a scheduling environment, there may not exist a unique schedule that remains optimal for all possible realizations of setup and processing times. Therefore, it is desired to obtain a set of dominating schedules (which dominate all other schedules) if possible. The objective for such a scheduling environment is to reduce the size of dominating schedule set. We obtain global and local dominance relations for a three-machine flowshop scheduling problem. Furthermore, we illustrate the use of dominance relations by numerical examples and conduct computational experiments on randomly generated problems to measure the effectiveness of the developed dominance relations. The computational experiments show that the developed dominance relations are quite helpful in reducing the size of dominating schedules. (original abstract)
Pełny tekst
  1. Allahverdi, A., Two-machine flowshop scheduling problem to minimize total completion time with bounded setup and processing times, International Journal of Production Economics 103 (2006), 386-400.
  2. Allahverdi, A., Minimizing mean flowtime in a two-machine flowshop with sequence independent setup times, Computers & Operations Research 27 (2000), 111-127.
  3. Allahverdi, A., and Al-Anzi, F., A branch-and-bound algorithm for three-machine flowshop scheduling problem to minimize total completion time with separate setup times, European Journal of Operational Research 169 (2006), 767-780.
  4. Allahverdi, A., Ng, C.T., Cheng, T.C.E., and Kovalyov, M.Y., A survey of scheduling problems with setup times or costs, European Journal of Operational Research, 2007. (in press)
  5. Allahverdi, A., Aldowaisan, T., and Sotskov, Y.N., 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 39 (2003), 2475-2486.
  6. Allahverdi, A., Gupta, J.N.D, and Aldowiasan, T., A review of scheduling research involving setup considerations, OMEGA The International Journal of Management Sciences 27 (1999), 219-239.
  7. Allahverdi, A., and Sotskov, Y.N., Two-machine flowshop minimum length scheduling problem with random and bounded processing times, International Transactions in Operational Research 10 (2003), 65-76.
  8. Bagga, P.C., and Khurana, K., Two-machine flowshop with separated sequence-independent setup times: mean completion time criterion, Indian Journal of Management and Systems 2 (1986), 47-57.
  9. Chandrasekaran, C., Rajendran, C., Chetty, O.V.K., Hanumanna, D., Metaheuristics for solving economic lot scheduling problems (ELSP) using time-varying lot-sizes approach, European Journal of Industrial Engineering 1 (2007), 152-181.
  10. Johnson, S.M., Optimal two and three-stage production schedules with setup times included, Naval Research Logistics Quarterly 1 (1954), 69-81.
  11. Kim, S.C., Bobrowski, P.M., Scheduling jobs with uncertain setup times and sequence dependency, Omega, International Journal of Management Science 25 (1997), 437-447.
  12. Lai, T.C., and Sotskov, Y.N., Sequencing with uncertain numerical data for makespan minimization, Journal of the Operational Research Society 50 (1999), 230-243.
  13. Lai, T.C., Sotskov, Y.N., Sotskova, N.Y., and Werner, F., Optimal makespan scheduling with given bounds of processing times, Mathematical and Computer Modelling 26 (1997), 67-86.
  14. Li, X., Ye, N., Xu, X., Sawhey, R., Influencing factors of job waiting time variance on a single machine, European Journal of Industrial Engineering 1 (2007), 56-73.
  15. Logendran, R., Carson, S., Hanson, E., Group scheduling in flexible flow shops, International Journal of Production Economics 96 (2005), 143-155.
  16. Sotskov, Y.N., Allahverdi, A., and Lai, T.C., Flowshop scheduling problem to minimize total completion time with random and bounded processing times, Journal of Operational Research Society 55 (2004), 277-286.
  17. Tang, L., and Huang, L., Optimal and near-optimal algorithms to rolling batch scheduling for seamless steel tube production, International Journal of Production Economics, 2005, In Press.
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