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The Uncapacitatied Dynamic Single-Level Lot-Sizing Problem under a Time-Varying Environment and an Exact Solution Approach

Author

Listed:
  • Yiyong Xiao

    (School of Reliability and System Engineering, Beihang University, Beijing 100191, China)

  • Meng You

    (School of Reliability and System Engineering, Beihang University, Beijing 100191, China)

  • Xiaorong Zuo

    (School of Reliability and System Engineering, Beihang University, Beijing 100191, China)

  • Shenghan Zhou

    (School of Reliability and System Engineering, Beihang University, Beijing 100191, China)

  • Xing Pan

    (School of Reliability and System Engineering, Beihang University, Beijing 100191, China)

Abstract

The dynamic lot-sizing problem under a time-varying environment considers new features of the production system where factors such as production setup cost, unit inventory-holding cost, and unit price of manufacturing resources may vary in different periods over the whole planning horizon. Traditional lot-sizing theorems and algorithms are no longer fit for these situations as they had assumed constant environments. In our study, we investigated the dynamic lot-sizing problem with deteriorating production setup cost, a typical time-varying environment where the production setup is assumed to consume more preparing time and manufacturing resources as the production interval lasts longer. We proposed new lot-sizing models based on the traditional lot-sizing model considering the changing setup cost as a new constraint, called uncapacitatied dynamic single-level lot-sizing under a time-varying environment (UDSLLS-TVE for short). The UDSLLS-TVE problem has a more realistic significance and higher research value as it is closer to reality and has higher computational complexity as well. We proposed two mathematical programming models to describe UDSLLS_TVE with or without nonlinear components, respectively. Properties of the UDSLLS-TVE models were extensively analyzed and an exact algorithm based on forward dynamic programming (FDP) was proposed to solve this problem with a complexity of O ( n 2 ). Comparative experiments with the commercial MIP solver CPLEX on synthesized problem instances showed that the FDP algorithm is a global optimization algorithm and has a high computational efficiency.

Suggested Citation

  • Yiyong Xiao & Meng You & Xiaorong Zuo & Shenghan Zhou & Xing Pan, 2018. "The Uncapacitatied Dynamic Single-Level Lot-Sizing Problem under a Time-Varying Environment and an Exact Solution Approach," Sustainability, MDPI, vol. 10(11), pages 1-14, October.
    • Handle: RePEc:gam:jsusta:v:10:y:2018:i:11:p:3867-:d:178012
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    References listed on IDEAS

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    1. Uladzimir Rubasheuski & Johan Oppen & David L. Woodruff, 2018. "A stochastic programming approach to solve a coordinated capacitated stochastic dynamic demand lot-sizing problem with emergency supplies," International Journal of Logistics Systems and Management, Inderscience Enterprises Ltd, vol. 29(2), pages 173-189.
    2. Alan S. Manne, 1958. "Programming of Economic Lot Sizes," Management Science, INFORMS, vol. 4(2), pages 115-135, January.
    3. Michalis Nikiforos, 2013. "The (Normal) Rate of Capacity Utilization at the Firm Level," Metroeconomica, Wiley Blackwell, vol. 64(3), pages 513-538, July.
    4. Xiao, Yiyong & Zhang, Renqian & Zhao, Qiuhong & Kaku, Ikou & Xu, Yuchun, 2014. "A variable neighborhood search with an effective local search for uncapacitated multilevel lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 235(1), pages 102-114.
    5. Almeder, Christian & Klabjan, Diego & Traxler, Renate & Almada-Lobo, Bernardo, 2015. "Lead time considerations for the multi-level capacitated lot-sizing problem," European Journal of Operational Research, Elsevier, vol. 241(3), pages 727-738.
    6. 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.
    7. Marcos Mansano Furlan & Maristela Oliveira Santos, 2017. "BFO: a hybrid bees algorithm for the multi-level capacitated lot-sizing problem," Journal of Intelligent Manufacturing, Springer, vol. 28(4), pages 929-944, April.
    8. Haase, Knut & Kimms, Alf, 2000. "Lot sizing and scheduling with sequence-dependent setup costs and times and efficient rescheduling opportunities," International Journal of Production Economics, Elsevier, vol. 66(2), pages 159-169, June.
    9. Dye, Chung-Yuan & Hsieh, Tsu-Pang & Ouyang, Liang-Yuh, 2007. "Determining optimal selling price and lot size with a varying rate of deterioration and exponential partial backlogging," European Journal of Operational Research, Elsevier, vol. 181(2), pages 668-678, September.
    10. Hui-Ling Yang, 2011. "A partial backlogging production-inventory lot-size model for deteriorating items with time-varying production and demand rate over a finite time horizon," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(8), pages 1397-1407.
    11. Karimi, B. & Fatemi Ghomi, S. M. T. & Wilson, J. M., 2003. "The capacitated lot sizing problem: a review of models and algorithms," Omega, Elsevier, vol. 31(5), pages 365-378, October.
    12. Chung-Yee Lee & Sila Çetinkaya & Albert P. M. Wagelmans, 2001. "A Dynamic Lot-Sizing Model with Demand Time Windows," Management Science, INFORMS, vol. 47(10), pages 1384-1395, October.
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