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Efficient approximation algorithms for the economic lot-sizing in continuous time

Author

Listed:
  • TELHA, Claudio

    (Université catholique de Louvain, CORE, Belgium)

  • VAN VYVE, Matthieu

    (Université catholique de Louvain, CORE, Belgium)

Abstract

We consider a continuous-time variant of the classical Economic Lot-Sizing (ELS) problem. In this model, the setup cost is a continuous function with lower bound $K_min > 0$, the demand and holding costs are integrable functions of time and the replenishment decisions are not restricted to be multiples of a base period. Starting from the assumption that certain operations involving the setup and holding cost functions can be carried out efficiently, we argue that this variant admits a simple approximation scheme based on dynamic programming: if the optimal cost of an instance is OPT, we can find a solution with cost at most $(1 + ε)OPT$ using no more than $O ({1\over ε^2} {OPT \over K_min} log {OPT \over K_min}$ of these operations. We argue, however, that this algorithm could be improved on instances where the setup costs are “generally” very large compared with $K_min$. This leads us to introduce a notion of input-size σ that is significantly smaller than $OPT/K_min$ on instances of this type, and then to define an approximation scheme that executes $O({1\over ε^2}σ^2 ({OPT \over K_min}))$ operations. Besides dynamic programming, this second approximation scheme builds on a novel algorithmic approach for Economic Lot Sizing problems.

Suggested Citation

  • TELHA, Claudio & VAN VYVE, Matthieu, 2014. "Efficient approximation algorithms for the economic lot-sizing in continuous time," LIDAM Discussion Papers CORE 2014016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2014016
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    References listed on IDEAS

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    1. Ford W. Harris, 1990. "How Many Parts to Make at Once," Operations Research, INFORMS, vol. 38(6), pages 947-950, December.
    2. Hindriks, Jean & Myles, Gareth D., 2013. "Intermediate Public Economics," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262018691, April.
    3. Albert Wagelmans & Stan van Hoesel & Antoon Kolen, 1992. "Economic Lot Sizing: An O(n log n) Algorithm That Runs in Linear Time in the Wagner-Whitin Case," Operations Research, INFORMS, vol. 40(1-supplem), pages 145-156, February.
    4. Fujita,Masahisa & Thisse,Jacques-François, 2013. "Economics of Agglomeration," Cambridge Books, Cambridge University Press, number 9780521171960, September.
    5. Nigar Hashimzade & Jean Hindriks & Gareth D. Myles, 2006. "Solutions Manual to Accompany Intermediate Public Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582694, April.
    6. MADANI, Mehdi & VAN VYVE, Mathieu, 2013. "A new formulation of the European day-ahead electricity market problem and its algorithmic consequences," LIDAM Discussion Papers CORE 2013074, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. MAULEON, Ana & ROEHL, Nils & VANNETELBOSCH, Vincent, 2014. "Constitutions and social networks," LIDAM Discussion Papers CORE 2014003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. VARDAR, N. Baris, 2013. "Imperfect resource substitution and optimal transition to clean technologies," LIDAM Discussion Papers CORE 2013072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Erik Schokkaert & Tom Truyts, 2017. "Preferences for redistribution and social structure," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(3), pages 545-576, December.
    10. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    11. VAN DIJCK, Maarten & TRUYTS, Tom, 2014. "The agricultural invasion and the political economy of agricultural trade policy in Belgium, 1875-1900," LIDAM Discussion Papers CORE 2014002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Awi Federgruen & Michal Tzur, 1991. "A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time," Management Science, INFORMS, vol. 37(8), pages 909-925, August.
    13. PAPAVASILIOU, Anthony & HE, Yi & SVOBODA, Alva, 2013. "Self-commitment of combined cycle units under electricity price uncertainty," LIDAM Discussion Papers CORE 2013051, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. LAMAS, ALEJANDRO & CHEVALIER, Philippe, 2013. "Jumping the hurdles for collaboration: fairness in operations pooling in the absence of transfer payments," LIDAM Discussion Papers CORE 2013073, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    More about this item

    Keywords

    game theory; equilibrium refinements; strategic stability; stochastic games;
    All these keywords.

    JEL classification:

    • A23 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - Graduate
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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