Abstract
Lot streaming involves splitting a production lot into a number of sublots, in order to allow the overlapping of successive operations, in multi-machine manufacturing systems. In no-wait flowshop scheduling, sublots are necessarily consistent, that is, they remain the same over all machines. The benefits of lot streaming include reductions in lead times and work-in-process, and increases in machine utilization rates. We study the problem of minimizing the makespan in no-wait flowshops producing multiple products with attached setup times, using lot streaming. Our study of the single product problem resolves an open question from the lot streaming literature. The intractable multiple product problem requires finding the optimal number of sublots, sublot sizes, and a product sequence for each machine. We develop a dynamic programming algorithm to generate all the nondominated schedule profiles for each product that are required to formulate the flowshop problem as a generalized traveling salesman problem. This problem is equivalent to a classical traveling salesman problem with a pseudopolynomial number of cities. We develop and computationally test an efficient heuristic for this problem. Our results indicate that solutions can quickly be found for flowshops with up to 10 machines and 50 products. Moreover, the solutions found by our heuristic provide a substantial improvement over previously published results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Abadi, I. N. K., N. G. Hall, and C. Sriskandarajah, “Minimizing cycle time in a blocking flowshop,” Oper. Res., 48, 177-180 (2000).
Baker, K. R., Introduction to Sequencing and Scheduling, Addison-Wesley, Reading, MA, 1974.
Baker, K. R., “Solution procedures for the lot-streaming problem,” Decision Sci., 21, 475-491 (1990).
Baker, K. R., “Lot streaming in the two machine flow shop with setup times,” Ann. Oper. Res., 57, 1-11 (1995).
Carpaneto, G. and P. Toth, “Some new branching and bounding criteria for the asymmetric traveling salesman problem,” Manage. Sci., 26, 736-743 (1980).
Gendreau, M., and G. Laporte, D. Simchi-Levi, “A degree relaxation algorithm for the asymmetric generalized traveling salesman problem,” Publication CRT-800, Centre for Research on Transportation, Montreal, 1991.
Gilmore, P. C. and R. E. Gomory, “Sequencing a one-state variable machine: A solvable case of the travelling salesman problem,” Oper. Res., 12, 665-679 (1964).
Glass, C. A., J. N. D. Gupta, C. N. Potts, “Lot streaming in three-stage process,” Eur. J. Oper. Res., 75, 378-394 (1994).
Glover, F. and M. Laguna, Tabu Search, Kluwer, Boston, 1997.
Gonzalez, T. and S. Sahni, “Openshop scheduling to minimize finish time,” J. Assoc. Comput. Mach., 23, 665-679 (1976).
Goyal, S. K. and C. Sriskandarajah, “No-wait shop scheduling: Computational complexity and approximate algorithms,” Opsearch, 25, 220-244 (1988).
Hall, N. G., G. Laporte, E. Selvarajah, C. Sriskandarajah, “Scheduling and lot streaming in openshops with no-wait in process,” Working Paper, Fisher College of Business, The Ohio State University, Columbus, Ohio, submitted for publication, December, 2002.
Hall, N. G. and C. Sriskandarajah, “A survey of machine scheduling problems with blocking and no-wait in process,” Oper. Res., 44, 510-525 (1996).
Hsu, E. and M. Stein, “Anodize load scheduling for diamond aluminum,” Undergraduate Thesis, Department of Industrial Engineering, University of Toronto, Canada, 1991.
Karp, R. M., “A patching algorithm for the nonsymmetric traveling-salesman problem,” SIAM J. Comput., 8, 561-573 (1979).
Kumar, S., T. P. Bagchi, C. Sriskandarajah, “Lot streaming and scheduling heuristics for m-machine no-wait flowshops,” Comput. Indust. Eng., 38, 149-172 (2000).
Lawler, E. L., J. K. Lenstra, and A. H. G. Rinnooy Kan, D. B. Shmoys, The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, Wiley, Chichester, UK, 1985.
Monma, C. L. and A. H. G. Rinnooy Kan, “A concise survey of efficiently solvable special cases of the permutation flow-shop problem,” RAIRO Recherche Opérationelle, 17, 105-119 (1983).
Noon, C. E. and J. C. Bean, “A Lagrangian based approach for the asymmetric generalized traveling salesman problem,” Oper. Res., 39, 623-632 (1991).
Noon, C. E. and J. C. Bean, “An efficient transformation of the generalized traveling salesman problem,” INFOR, 31, 39-44 (1993).
Pinedo, M., Scheduling: Theory, Algorithms, and Systems, Prentice-Hall, Englewood Cliffs, NJ, 1995.
Potts, C. N. and K. R. Baker, “Flowshop scheduling with lot streaming,” Oper. Res. Lett., 8, 297-303 (1989).
Potts, C. N. and L. N. Van Wassenhove, “Integrating scheduling with batching and lot-sizing: A review of algorithms and complexity,” J. Oper. Res. Soc., 43, 395-406 (1992).
Röck, H., “The three machine no-wait flowshop problem in NP-complete,” J. Assoc. Comput. Mach., 31, 336-345 (1984).
Sriskandarajah, C. and E. Wagneur, “Lot streaming and scheduling multiple products in two-machine no-wait flowshops,” IIE Trans., 31, 695-707 (1999).
Trietsch, D. and K. R. Baker, “Basic techniques for lot streaming,” Oper. Res., 41, 1065-1076 (1993).
Vickson, R. G., “Optimal lot streaming for multiple products in a two-machine flowshop,” Eur. J. Oper. Res., 85, 556-575 (1995).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hall, N.G., Laporte, G., Selvarajah, E. et al. Scheduling and Lot Streaming in Flowshops with No-Wait in Process. Journal of Scheduling 6, 339–354 (2003). https://doi.org/10.1023/A:1024042209719
Issue Date:
DOI: https://doi.org/10.1023/A:1024042209719