Abstract
We consider n-job, m-machine lot streaming problem in a flow shop with equal size sub lots where the objective is to minimize the makespan and total flow time. Lot streaming (Lot sizing) is a technique that splits a production lot consisting of identical items into sub lots to improve the performance of a multi stage production system by over lapping the sub lots on successive machines. There is a scope for efficient algorithms for scheduling problems in m-machine flow shop with lot streaming. In recent years, much attention is given to heuristics and search techniques. To solve this problem, we propose a Differential Evolution Algorithm (DEA) and Particle Swarm Optimization (PSO) to evolve best sequence for makespan/total flow time criterion for m-machine flow shop involved with lot streaming and set up time. In this research, we propose the DEA and PSO algorithms for discrete lot streaming with equal sub lots. The proposed methods are tested and the performances were evaluated. The computational results show that the proposed algorithms are very competitive for the lot streaming flow shop scheduling problem.
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Abbreviations
- PSO:
-
Particle swarm optimization
- DEA:
-
Differential evolution algorithm
- S:
-
Initial sequence
- S’:
-
Generated sequence
- Cmax(s) :
-
Makespan time for the sequence s
- Cmax(s') :
-
Makespan time for the sequence s’
- i:
-
Machine
- j:
-
Job
- m:
-
Number of machines
- n:
-
Number of jobs
- Pij :
-
Processing time for job j on machine i
- Sij :
-
Setup time for job j on machine i
- F1 :
-
Completion time for first job
- F2 :
-
Completion time for second job
- MP:
-
Makespan
- N:
-
Last (final) job to be processed
- M:
-
Last (final) machine number
- Cmax :
-
Makespan for generated sequence
- Tmax :
-
Total flow time for generated sequence
- A:
-
Arrival time
- S:
-
Setup time
- P:
-
Processing time
- Vi,G :
-
Velocity for the generation
- Xi,G :
-
Position for the generation
- K:
-
Combination factor
- r1, r2, r3 :
-
Random population
- F:
-
Scaling factor
- CR:
-
Crossover Ratio
- D:
-
Dimensions
- rni :
-
Randomly chosen population index
- uji, G + 1 :
-
Trial vector generation
- Vji, G + 1 :
-
Mutant vector
- qji, G :
-
Target vector
- ranj :
-
Random variable
- Xr1 :
-
Randomly chosen first population
- Xr2 :
-
Randomly chosen second population
- rand1, rand2 :
-
Random number between 0 and 1
- C1 :
-
Cognitive parameter
- C2 :
-
Social parameter
- \({{\rm V}_{\rm ij}^{\rm t}}\) :
-
Current velocity of agent i at iteration t
- \({{\rm V}_{\rm ij}^{{\rm t}+1}}\) :
-
Modified velocity of agent i
- W:
-
Weight inertia for velocity of agent i
- Pbesti :
-
Particle best of agent i
- gbesti :
-
Global best of the group
- \({{\rm x}_{\rm i}^{\rm t}}\) :
-
Current position of agent i at iteration t
- \({{\rm x}_{\rm i}^{{\rm t}+1}}\) :
-
Modified position of agent i
- ss :
-
Swarm size
- Wi :
-
Initial weight
- Wf :
-
Final weight
- C:
-
Constriction function
- Anm :
-
arrival time of the nth job on mth machine
- Snm :
-
setup time of the nth job on mth machine
- Pnm :
-
processing time of the nth job on mth machine
- ANM :
-
arrival time of the Nth job on Mth machine
- SNM :
-
setup time of the Nth job on Mth machine
- PNM :
-
processing time of the Nth job on Mth machine
References
Baker K. R., Jia D. (1993) A Comparative study of lot streaming procedure. OMEGA 21: 561–566
Baker K. R., Pyke D. F. (1990) Solution procedures for the lot-streaming problem. Decision Ssciences 21: 475–491
Chan F. T. S., Wong T. C., Chan L. Y. (2008) Lot streaming for product assembly in job shop environment. Robotics and Computer Integrated Manufacturing 24(3): 321–331
Chan F. T. S., Wong T. C., Chan L. Y. (2009a) The application of genetic algorithms to lot streaming in job-shop scheduling problem. International Journal of Production Research 47(12): 3387–3412
Chan F. T. S., Wong T. C., Chan L. Y. (2009b) An evolutionary algorithm for assembly job shop with part sharing. Computers and Industrial Engineering 57(3): 641–651
Chang J. H., Chiu H. N. (2005) A comprehensive review of lot streaming. International Journal of Production Research 43: 1515–1536
Chiu H. N. (2004) Lot streaming models with a limited number of capacitated transporters in multistage batch production systems. Computers & Operations Research 31: 2003–2020
Dhingra A., Chandna P. (2010) A bi-criteria M-machine SDST flow shop scheduling using modified heuristic genetic algorithm. International Journal of Engineering, Science and Technology 2(5): 216–225
Hoque M. A., Goyal S. K. (2005) On lot streaming in multistage production systems. International Journal Production Economics 95: 195–202
Kalir A. A., Sarin S. C. (2001) Optimal solutions for the single batch, flow shop, lot-streaming problem with equal sublots. Decision Sciences 32: 387–397
Karimi H., Rezaeinia A. (2011) Adjusted permutation method for multiple attribute decision making with meta-heuristic solution approaches. International Journal of Industrial Engineering Computations 2: 369–384
Kim K., Jeong I. -J. (2009) Flow shop scheduling with no-wait flexible lot streaming using an adaptive genetic algorithm. International Journal of Advanced Manuacturing Technology 44: 1181–1190
Liu Su (2003) A heuristic method for discrete lot streaming with variable sub lots in a flow shop. International Journal of Advanced Manufacturing Technology 22: 662–668
Marimuthu, S., Ponnambalam, S. G., & Jawahar, N. (2005). Tabu search and simulated annealing algorithms for scheduling in flow shops with lot streaming. Proceedings of IMechE Vol. 221 Part B: J. Engineering Manufacture (pp. 334–340).
Marimuthu S., Ponnambalam S. G., Jawahar N. (2008) Evolutionary algorithms for scheduling m-machine flow shop with lot streaming. Robot Computer Integrated Manufacturing 24: 125–139
Marimuthu S., Ponnambalam S. G., Jawahar N. (2009) Threshold accepting and ant-colony optimization algorithm for scheduling m-machine flow shop with lot streaming. Journal of Material Process Technology 209: 1026–1041
Pan Q.-K., Wang L., Gao L., Li J. (2011) An effective shuffled frog-leaping algorithm for lot-streaming flow shop scheduling problem. International Journal of Advanced Manufacturing Technology 52(5–8): 699–713
Qian B., Wang L, Hu R., Huang D. X., Wang X. (2009) A DE-based approach to no-wait flow-shop scheduling. Computers & Industrial Engineering 57: 787–805
Ramasesh R. V., Fu H., Fong D. K. H., Hayy J. C. (2000) Lot streaming in multistage production systems. International Journal Production Economics 66: 199–211
Reiter S. (1966) A system for managing job shop production. The Journal of Business 34: 371–393
Sayadi M. K., Ramezanian R., Ghaffari-Nasab N. (2010) A discrete firefly meta-heuristic with local search for makespan minimization in permutation flow shop scheduling problems. International Journal of Industrial Engineering Computations 1: 1–10
Sriskandarajah C., Wagneur E. (1999) Lot streaming and scheduling products in two- machine no-wait flow shops. IIE Tranactions 31: 695–707
Steiner G., Truscott W. G. (1993) Batch scheduling to minimize cycle time, flow time and processing cost. IIE Transactions 25(5): 90–97
Szendrovits A. Z. (1975) Manufacturing cycle time determination for a multi- stage economic production quantity model. Management Science 22: 298–308
Vickson R. G., Alfredsson B. E. (1992) Two- and three- machine flow shop scheduling problem with equal sized transfer batches. International Journal of Production Research 30: 1551–1574
Wong T. C., Chan F. T. S., Chan L. Y. (2009) A resource-constrained assembly job shop scheduling problem with lot streaming technique. Computers and Industrial Engineering 57(3): 983–995
Zhang w., Yin C., Liu J., Linn R. J. (2005) Multi-job lot streaming to minimize the mean completion time in m-1 hybrid flow shops. International Journal of Production Economics 96: 189–200
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Vijay chakaravarthy, G., Marimuthu, S. & Naveen Sait, A. Performance evaluation of proposed Differential Evolution and Particle Swarm Optimization algorithms for scheduling m-machine flow shops with lot streaming. J Intell Manuf 24, 175–191 (2013). https://doi.org/10.1007/s10845-011-0552-2
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DOI: https://doi.org/10.1007/s10845-011-0552-2