This research introduces a new application of mathematical modelling for designing cellular manufacturing systems integrated with group scheduling aspects under uncertain conditions. The mixed 0–1 quadratic model is able to optimize group scheduling decisions under lower satisfaction of cell formation decisions. In this way, the required processing time of parts on machines is assumed to be uncertain and also is explained by a discrete set of scenarios. This model tries to optimize the expected scheduling cost in cells plus the subcontracting cost for exceptional operations. In addition, the objectives associated with the cell formation decisions are regarded as constraints by considering the bounded objective technique, one of the multi-objective decision-making techniques. The scheduling problem in a cellular manufacturing framework is treated as group scheduling problem, which assumes that all parts in a part family are processed in the same cell and no intercellular transfer is needed. An efficient modified simulated annealing technique is proposed to solve this complex problem under an optimization rule as a subordinate section. This integrative combination algorithm is compared with global solutions and a heuristic algorithm introduced in the literature. Finally, the performance of the algorithm is verified through some test problems.
WuXChuC.-HWangYYueD. Genetic algorithms for integrating cell formation with machine layout and scheduling. Comput. Ind. Engng, 2007, 53. 277–289.
3.
JeonGLeepH. R. Forming part families by using genetic algorithm and designing machine cells under demand changes. Comput. Oper. Res., 2006, 33. 263–283.
4.
SolimanpurMVratPShankarR. A heuristic to optimize makespan of cell scheduling problem. Int. J. Prod. Econ., 2004, 88. 231–241.
5.
SaadS. M. The reconfiguration issues in manufacturing systems. J. Mater. Process. Technol., 2003, 138. 277–283.
6.
AnejaY. PKamounH. Scheduling of parts and robot activities in a two machine robotic cell. Comput. Oper. Res., 1999, 26. 297–312.
7.
ParthasarathySRajendranC. Scheduling to optimize mean tardiness and weighted mean tardiness in flowshop and flowline-based manufacturing cells. Comput. Ind. Engng, 1998, 34((2)), 531–546.
8.
WuXChuC.-HWangYYanW. A genetic algorithm for cellular manufacturing design and layout. Eur. J. Oper. Res., 2007, 181. 156–167.
9.
InderfurthKJaniakAKovalyovM. YWernerF. Batching work and rework processes with limited deterioration of reworkables. Comput. Oper. Res., 2006, 33. 1595–1605.
10.
ChengT. C. EJaniakAKovalyovM. Y. Single machine batch scheduling with resource dependent set-up and processing times. Eur. J. Oper. Res., 2001, 135. 177–183.
11.
WuC.-CLeeW.-C. Single-machine group-scheduling problems with deteriorating setup times and job-processing times. Int. J. Prod. Econ., 2008, 115. 128–133.
12.
LockwoodW. TMahmoodiFRubenR. AMosierC. T. Scheduling unbalanced cellular manufacturing systems with lot splitting. Int. J. Prod. Res., 2000, 38((4)), 951–965.
13.
TsaiC. CChuC. HBartaT. Analysis and modeling of a manufacturing cell formation problem with 17 fuzzy integer programming. IIE Trans., 1997, 29((7)), 533–547.
14.
MahdaviIJavadiBFallah-AlipourKSlompJ. Designing a new mathematical model for cellular manufacturing system based on cell utilization. Appl. Math. Comput., 2007, 190. 662–670.
15.
WuX. DChuC. HWangY. FYanW. L. Concurrent design of cellular manufacturing systems: a genetic algorithm approach. Int. J. Prod. Res., 2006, 44((6)), 1217–1241.
16.
VenkataramanaiahS. Scheduling in cellular manufacturing systems: an heuristic approach. Int. J. Prod. Res., 2007, 45((1)), 1–21.
17.
PapaioannouGWilsonJ. M. Fuzzy extensions to integer programming of cell formation problem in machine scheduling. Ann. Oper. Res., 2008, 1–19.
18.
RavichandranK. SChandra Sekhara RaoK. A new approach to fuzzy part family formation in CMS. Int. J. Adv. Mfg Technol., 2001, 18((8)), 591–597.
19.
BalakrishnanJChengC. H. Multi-period planning and uncertainty issues in CM: a review and future directions. Eur. J. Oper. Res., 2007, 177((1)), 281–309.
20.
KurodaMTomitaT. Robust design of a cellular-line production system with unreliable facilities. Comput. Ind. Engng, 2005, 48((3)), 537–551.
21.
Simeu-AbaziZSassineC. Maintenance integration in manufacturing systems using stochastic Petri nets. Int. J. Prod. Res., 1999, 37((17)), 3927–3940.
22.
AsgharpourM. JJavadianN. Solving a stochastic cellular manufacturing model using genetic algorithm. Int. J. Engng Trans. A Basics, 2004, 17((2)), 145–156.
23.
GhezavatiV. RSaidi-MehrabadM. Designing integrated cellular manufacturing systems with scheduling considering stochastic processing time. Int. J. Adv. Mfg Technol., 2010, 48((5–8)), 701–717.
24.
HentschelCSeligerGZussmanE. Grouping of used products for cellular recycling systems. CIRP Ann. Mfg Technol., 1995, 44((1)), 11–14.
25.
ShankerRVratP. Post design modeling for CMS with cost uncertainty. Int. J. Prod. Econ., 1998, 55((1)), 97–109.
26.
ShankerRVratP. Some design issues in CM using the fuzzy programming approach. Int. J. Prod. Res., 1999, 37((11)), 2545–2563.
27.
SongSHitomiK. Determining the planning horizon and group part family for flexible cellular manufacturing. Nippon Kikai Gakkai Ronbunshu, C Hen/Trans. Jpn Soc. Mech. Engrs Part C, 1991, 57((542)), 3364–3371.
28.
Tavakkoli-MoghaddamRJavadianNJavadiBSafaeiN. Design of a facility layout problem in CMS with stochastic demand. Appl. Math. Comput., 2007, 184((2)), 721–728.
29.
BalakrishnanJChengC. H. Dynamic CM under multi-period planning horizon. J. Mfg Technol. Mgmt, 2005, 16((5)), 516–530.
30.
SongS.-JHitomiK. Integrating the production planning and cellular layout for flexible cellular manufacturing. Prod. Plann. Contr., 1996, 7((6)), 585–593.
31.
SunY.-LYihY. An intelligent controller for manufacturing cell. Int. J. Prod. Res., 1996, 34((8)), 2353–2373.
32.
AndresCLozanoSAdenso-DiazB. Disassembly sequence planning in a disassembly cell. Robot. Comput. Integrated Mfg, 2007, 23((6)), 690–695.
33.
SnyderL. V. Facility location under uncertainty: a review. IIE Trans., 2006, 38. 537–554.
34.
GhezavatiV. RJabal-AmeliM. SMakuiA. A new heuristic method for distribution networks considering service level constraint and coverage radius. Expert Syst. Applic. Part 1, 2009, 36((3)), 5620–5629.
35.
MobasheriFOrrenL. HSioshansiF. P. Scenario planning at southern California Edison. Interfaces, 1989, 19((5)), 31–44.
36.
MulveyJ. M. Generating scenarios for the Towers Perrin investment system. Interfaces, 1996, 26((2)), 1–15.
37.
HosseiniM. M. An inspection model with minimal and major maintenance for a system with deterioration and Poisson failures. IEEE Trans. Reliab., 2000, 49((1)), 88–98.
38.
GloverFWoolseyL. Converting the 0–1 polynomial programming problem to a 0–1 linear program. Oper. Res., 1974, 22. 180–182.
39.
ChangC.-TChangC.-C. A linearization method for mixed 0–1 polynomial programs. Comput. Oper. Res., 2000, 27. 1005–1016.
40.
KirkpatrickSGelattC. DVecchiM. P. Optimization by simulated annealing. Science, 1983, 220((4598)).
41.
SafaeiNSaidi-MehrabadMJabal-AmeliM. S. A hybrid simulated annealing for solving an extended model of dynamic cellular manufacturing system. Eur. J. Oper. Res., 2008, 185. 563–592.
