Skip to main content

Capacitated Lot Sizing Problem with Production Carryover and Setup Crossover Across Periods (CLSP:PCSC): Mathematical Model 1 (MM1) and a Heuristic for Process Industries

  • Chapter
  • First Online:
  • 451 Accesses

Abstract

The capacitated lot sizing problem (CLSP) is a lot sizing model in which the production of multiple products is allowed within a time period on a single machine, with a condition that the entire demand for a product within that period should be met from the production in that period and/or the inventory carried from the previous periods, without any backorders or lost sales. Finding a minimum cost production plan that satisfies all the demand requirements without exceeding the capacity limits of a period is the main objective of the CLSP.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Akartunalı, K., and A. J. Miller. 2009. A heuristic approach for big bucket multi-level production planning problems. European Journal of Operational Research 193(2): 396–411.

    Article  Google Scholar 

  • Belo-Filho, M. A., F. M. Toledo, and B. Almada-Lobo. 2013. Models for capacitated lot-sizing problem with backlogging, setup carryover and crossover. Journal of the Operational Research Society 65(11): 1735–1747.

    Article  Google Scholar 

  • Belvaux, G. and L. A. Wolsey. 2000. Bc—prod: a specialized branch-and-cut system for lot-sizing problems. Management Science 46(5): 724–738.

    Article  Google Scholar 

  • Bitran, G. R. and H. H. Yanasse. 1982. Computational complexity of the capacitated lot size problem. Management Science 28(10): 1174–1186.

    Article  Google Scholar 

  • Caserta, M., A. Ramirez, and S. Voß. 2010. A math-heuristic for the multi-level capacitated lot sizing problem with carryover. Applications of evolutionary computation, 462–471. Springer.

    Google Scholar 

  • Caserta, M., A. Ramirez, S. Voß, and R. Moreno. 2009. A hybrid algorithm for the multi level capacitated lot sizing problem with setup carry-over. Logistik management, 123–138. Springer.

    Google Scholar 

  • Caserta, M. and S. Voß. 2013. A mip-based framework and its application on a lot sizing problem with setup carryover. Journal of Heuristics 19(2): 295–316.

    Article  Google Scholar 

  • Gopalakrishnan, M. 2000. A modified framework for modelling set-up carryover in the capacitated lotsizing problem. International Journal of Production Research 38(14): 3421–3424.

    Article  Google Scholar 

  • Gopalakrishnan, M., K. Ding, J.-M. Bourjolly, and S. Mohan. 2001. A tabu-search heuristic for the capacitated lot-sizing problem with set-up carryover. Management Science 47(6): 851–863.

    Article  Google Scholar 

  • Gopalakrishnan, M., D. Miller, and C. Schmidt. 1995. A framework for modelling setup carryover in the capacitated lot sizing problem. International Journal of Production Research 33(7): 1973–1988.

    Article  Google Scholar 

  • Goren, H. G., S. Tunali, and R. Jans. 2012. A hybrid approach for the capacitated lot sizing problem with setup carryover. International Journal of Production Research 50(6): 1582–1597.

    Article  Google Scholar 

  • Haase, K. and A. Drexl. 1994. Capacitated lot-sizing with linked production quantities of adjacent periods. Operations Research’93, 212–215. Springer.

    Google Scholar 

  • Karimi, B., S. Ghomi, and J. Wilson. 2006. A tabu search heuristic for solving the clsp with backlogging and set-up carry-over. Journal of the Operational Research Society 57(2): 140–147.

    Article  Google Scholar 

  • Mohan, S., M. Gopalakrishnan, R. Marathe, and A. Rajan. 2012. A note on modelling the capacitated lot-sizing problem with set-up carryover and set-up splitting. International Journal of Production Research 50(19): 5538–5543.

    Article  Google Scholar 

  • Nascimento, M. C. and F. Toledo. 2008. A hybrid heuristic for the multi-plant capacitated lot sizing problem with setup carry-over. Journal of the Brazilian Computer Society 14(4): 7–15.

    Article  Google Scholar 

  • Ramya, R., C. Rajendran, and H. Ziegler. 2016. Capacitated lot-sizing problem with production carry-over and set-up splitting: mathematical models. International Journal of Production Research 54(8): 2332–2344.

    Article  Google Scholar 

  • Sahling, F., L. Buschkühl, H. Tempelmeier, and S. Helber. 2009. Solving a multi-level capacitated lot sizing problem with multi-period setup carry-over via a fix-and-optimize heuristic. Computers & Operations Research 36(9): 2546–2553.

    Article  Google Scholar 

  • Sox, C. R. and Y. Gao 1999. The capacitated lot sizing problem with setup carry-over. IIE Transactions 31(2): 173–181.

    Google Scholar 

  • Stadtler, H. 2003. Multilevel lot sizing with setup times and multiple constrained resources: Internally rolling schedules with lot-sizing windows. Operations Research 51(3): 487–502.

    Article  Google Scholar 

  • Suerie, C. and H. Stadtler. 2003. The capacitated lot-sizing problem with linked lot sizes. Management Science 49(8): 1039–1054.

    Article  Google Scholar 

  • Sung, C. and C. T. Maravelias. 2008. A mixed-integer programming formulation for the general capacitated lot-sizing problem. Computers & Chemical Engineering 32(1): 244–259.

    Article  Google Scholar 

  • Toledo, C. F. M., M. da Silva Arantes, M. Y. B. Hossomi, P. M. França, and K. Akartunalı. 2015. A relax-and-fix with fix-and-optimize heuristic applied to multi-level lot-sizing problems. Journal of Heuristics 21(5): 687–717.

    Article  Google Scholar 

  • Ventura, J. A., D. Kim, and F. Garriga. 2002. Single machine earliness–tardiness scheduling with resource-dependent release dates. European Journal of Operational Research 142(1): 52–69.

    Article  Google Scholar 

  • Wagner, H. M. and T. M. Whitin. 1958. Dynamic version of the economic lot size model. Management Science 5(1): 89–96.

    Article  Google Scholar 

  • Wu, T., K. Akartunalı, J. Song, and L. Shi. 2013. Mixed integer programming in production planning with backlogging and setup carryover: modeling and algorithms. Discrete Event Dynamic Systems 23(2): 211–239.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ramya, R., Rajendran, C., Ziegler, H., Mohapatra, S., Ganesh, K. (2019). Capacitated Lot Sizing Problem with Production Carryover and Setup Crossover Across Periods (CLSP:PCSC): Mathematical Model 1 (MM1) and a Heuristic for Process Industries. In: Capacitated Lot Sizing Problems in Process Industries. Springer, Cham. https://doi.org/10.1007/978-3-030-01222-9_3

Download citation

Publish with us

Policies and ethics