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An O(Tˆ3) algorithm for the capacitated lot sizing problem with minimum order quantities

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  • Okhrin, Irena
  • Richter, Knut

Abstract

This paper explores a single-item capacitated lot sizing problem with minimum order quantity, which plays the role of minor set-up cost. We work out the necessary and suffcient solvability conditions and apply the general dynamic programming technique to develop an O(T³) exact algorithm that is based on the concept of minimal sub-problems. An investigation of the properties of the optimal solution structure allows us to construct explicit solutions to the obtained sub-problems and prove their optimality. In this way, we reduce the complexity of the algorithm considerably and confirm its efficiency in an extensive computational study. --

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Bibliographic Info

Paper provided by European University Viadrina Frankfurt (Oder), Department of Business Administration and Economics in its series Discussion Papers with number 284.

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Date of creation: 2010
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Handle: RePEc:zbw:euvwdp:284

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Related research

Keywords: production planning; capacitated lot sizing problem; single item; minimum order quantities; capacity constraints; dynamic programming;

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  1. Baier, Antje & Bolle, Friedel, 2005. "Cyclical price fluctuations caused by information inertia : evidence from the German call-by-call telephone market," Discussion Papers 225, European University Viadrina Frankfurt (Oder), Department of Business Administration and Economics.
  2. Bolle, Friedel & Kritikos, Alexander S., 2004. "Altruistic Behavior Under Incomplete Information," Discussion Papers 229, European University Viadrina Frankfurt (Oder), Department of Business Administration and Economics.
  3. Friedel Bolle & Alexander Kritikos, 2006. "Reciprocity, Altruism, Solidarity: A Dynamic Model," Theory and Decision, Springer, vol. 60(4), pages 371-394, 06.
  4. Kritikos, Alexander S. & Bolle, Friedel, 2006. "Utility versus Income-Based Altruism," Discussion Papers 249, European University Viadrina Frankfurt (Oder), Department of Business Administration and Economics.
  5. Jonathan Tan & Friedel Bolle, 2006. "On the Relative Strengths of Altruism and Fairness," Theory and Decision, Springer, vol. 60(1), pages 35-67, 02.
  6. Pichtchoulov, Grigori & Richter, Knut, 2005. "Economic effects of mobile technologies on operations of sales agents," Discussion Papers 226, European University Viadrina Frankfurt (Oder), Department of Business Administration and Economics.
  7. Tan, Jonathan H.W. & Zizzo, Daniel John, 2008. "Groups, cooperation and conflict in games," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 37(1), pages 1-17, February.
  8. Perugini, Marco & Tan, Jonathan H. W. & Zizzo, Daniel John, 2005. "Which is the More Predictable Gender? Public Good Contribution and Personality," Discussion Papers 236, European University Viadrina Frankfurt (Oder), Department of Business Administration and Economics.
  9. Kritikos, Alexander & Bolle, Friedel, 2001. "Distributional concerns: equity- or efficiency-oriented?," Economics Letters, Elsevier, vol. 73(3), pages 333-338, December.
  10. Tan, Jonathan H.W., 2006. "Religion and social preferences: An experimental study," Economics Letters, Elsevier, vol. 90(1), pages 60-67, January.
  11. Vogel, Claudia & Heimel, Jana & Bolle, Friedel, 2004. "Crowding out and imitation behavior in the solidarity game," Discussion Papers 223, European University Viadrina Frankfurt (Oder), Department of Business Administration and Economics.
  12. Alexander Kritikos & Frank Wiesner, 2000. "Ein zweiter Kreditmarkt für eine zweite Chance," Perspektiven der Wirtschaftspolitik, Verein für Socialpolitik, vol. 1(3), pages 357-378, 08.
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Cited by:
  1. Hellion, Bertrand & Mangione, Fabien & Penz, Bernard, 2012. "A polynomial time algorithm to solve the single-item capacitated lot sizing problem with minimum order quantities and concave costs," European Journal of Operational Research, Elsevier, vol. 222(1), pages 10-16.

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