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A Dynamic Programming Approach to a Lot Size Scheduling Problem

Author

Listed:
  • Earl E. Bomberger

    (The Budd Company, Philadelphia)

Abstract

The problem considered is that of scheduling the production of several different items over the same facility on a repetitive basis. The facility is such that only one item can be produced at a time; there is a setup cost and a setup time associated with producing each item; the demand rate for each item is known and constant over an infinite planning horizon, and all demand must be met. A dynamic programming solution is developed. This solution is applied to a sample problem, and the results are compared with pertinent bounds.

Suggested Citation

  • Earl E. Bomberger, 1966. "A Dynamic Programming Approach to a Lot Size Scheduling Problem," Management Science, INFORMS, vol. 12(11), pages 778-784, July.
  • Handle: RePEc:inm:ormnsc:v:12:y:1966:i:11:p:778-784
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    File URL: http://dx.doi.org/10.1287/mnsc.12.11.778
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    References listed on IDEAS

    as
    1. M. E. Salveson, 1956. "A Problem in Optimal Machine Loading," Management Science, INFORMS, vol. 2(3), pages 232-260, April.
    2. M. Beckman & R. Muth, 1956. "An Inventory Policy for a Case of Lagged Delivery," Management Science, INFORMS, vol. 2(2), pages 145-155, January.
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    Cited by:

    1. Wagner, Michael & Smits, Sanne R., 2004. "A local search algorithm for the optimization of the stochastic economic lot scheduling problem," International Journal of Production Economics, Elsevier, vol. 90(3), pages 391-402, August.
    2. repec:eee:apmaco:v:251:y:2015:i:c:p:404-422 is not listed on IDEAS
    3. repec:eee:jomega:v:74:y:2018:i:c:p:70-81 is not listed on IDEAS
    4. Leven, Erik & Segerstedt, Anders, 2007. "A scheduling policy for adjusting economic lot quantities to a feasible solution," European Journal of Operational Research, Elsevier, vol. 179(2), pages 414-423, June.
    5. Fransoo, Jan C. & Sridharan, V. & Bertrand, J.Will M., 1995. "A hierarchical approach for capacity coordination in multiple products single-machine production systems with stationary stochastic demands," European Journal of Operational Research, Elsevier, vol. 86(1), pages 57-72, October.
    6. Salvietti, Luciano & Smith, Neale R., 2008. "A profit-maximizing economic lot scheduling problem with price optimization," European Journal of Operational Research, Elsevier, vol. 184(3), pages 900-914, February.
    7. Khouja, Moutaz, 1997. "The scheduling of economic lot sizes on volume flexible production systems," International Journal of Production Economics, Elsevier, vol. 48(1), pages 73-86, January.
    8. Oner, Selma & Bilgic, Taner, 2008. "Economic lot scheduling with uncontrolled co-production," European Journal of Operational Research, Elsevier, vol. 188(3), pages 793-810, August.
    9. Wagner, Bret J. & Davis, Darwin J., 2002. "A search heuristic for the sequence-dependent economic lot scheduling problem," European Journal of Operational Research, Elsevier, vol. 141(1), pages 133-146, August.
    10. Kim, Taebok & Hong, Yushin & Chang, Soo Young, 2006. "Joint economic procurement--production-delivery policy for multiple items in a single-manufacturer, multiple-retailer system," International Journal of Production Economics, Elsevier, vol. 103(1), pages 199-208, September.
    11. Brander, Par & Forsberg, Rolf, 2006. "Determination of safety stocks for cyclic schedules with stochastic demands," International Journal of Production Economics, Elsevier, vol. 104(2), pages 271-295, December.
    12. repec:eee:ejores:v:264:y:2018:i:1:p:327-339 is not listed on IDEAS
    13. Banerjee, Avijit & Pyreddy, Vijay R. & Kim, Seung Lae, 1996. "Investment policy for multiple product setup reduction under budgetary and capacity constraints," International Journal of Production Economics, Elsevier, vol. 45(1-3), pages 321-327, August.
    14. Grznar, J. & Riggle, C., 1997. "An optimal algorithm for the basic period approach to the economic lot scheduling problem," Omega, Elsevier, vol. 25(3), pages 355-364, June.
    15. Banerjee, Avijit, 2009. "Simultaneous determination of multiproduct batch and full truckload shipment schedules," International Journal of Production Economics, Elsevier, vol. 118(1), pages 111-117, March.
    16. Chang, Ping-Teng & Yao, Ming-Jong & Huang, Shih-Fen & Chen, Chia-Tsung, 2006. "A genetic algorithm for solving a fuzzy economic lot-size scheduling problem," International Journal of Production Economics, Elsevier, vol. 102(2), pages 265-288, August.
    17. Khouja, Moutaz & Michalewicz, Zgibniew & Wilmot, Michael, 1998. "The use of genetic algorithms to solve the economic lot size scheduling problem," European Journal of Operational Research, Elsevier, vol. 110(3), pages 509-524, November.
    18. Taleizadeh, Ata Allah & Cárdenas-Barrón, Leopoldo Eduardo & Mohammadi, Babak, 2014. "A deterministic multi product single machine EPQ model with backordering, scraped products, rework and interruption in manufacturing process," International Journal of Production Economics, Elsevier, vol. 150(C), pages 9-27.
    19. Holmbom, Martin & Segerstedt, Anders, 2014. "Economic Order Quantities in production: From Harris to Economic Lot Scheduling Problems," International Journal of Production Economics, Elsevier, vol. 155(C), pages 82-90.
    20. Brander, Par & Leven, Erik & Segerstedt, Anders, 2005. "Lot sizes in a capacity constrained facility--a simulation study of stationary stochastic demand," International Journal of Production Economics, Elsevier, vol. 93(1), pages 375-386, January.
    21. Khoury, B. N. & Abboud, N. E. & Tannous, M. M., 2001. "The common cycle approach to the ELSP problem with insufficient capacity," International Journal of Production Economics, Elsevier, vol. 73(2), pages 189-199, September.
    22. Teunter, Ruud & Tang, Ou & Kaparis, Konstantinos, 2009. "Heuristics for the economic lot scheduling problem with returns," International Journal of Production Economics, Elsevier, vol. 118(1), pages 323-330, March.
    23. Vidal-Carreras, Pilar I. & Garcia-Sabater, Jose P. & Coronado-Hernandez, Jairo R., 2012. "Economic lot scheduling with deliberated and controlled coproduction," European Journal of Operational Research, Elsevier, vol. 219(2), pages 396-404.

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