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The single-item green lot-sizing problem with fixed carbon emissions

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  • Absi, Nabil
  • Dauzère-Pérès, Stéphane
  • Kedad-Sidhoum, Safia
  • Penz, Bernard
  • Rapine, Christophe

Abstract

We consider in this paper a single-item lot sizing problem with a periodic carbon emission constraint. In each period, the carbon emission constraint defines an upper limit on the average emission per product. Different modes are available, each one is characterized by its own cost and carbon emission parameters. The problem consists in selecting the modes used in each period such that no carbon emission constraint is violated, and the cost of satisfying all the demands on a given time horizon is minimized. This problem has been introduced in Absi et al. (2013), and has been shown polynomially solvable when only unit carbon emissions are considered. In this paper, we extend the analysis for this constraint to the realistic case of a fixed carbon emission associated with each mode, in addition to its unit carbon emission. We establish that this generalization renders the problem NP-hard. Several dominant properties are presented, and two dynamic programming algorithms are proposed. We also establish that the problem can be solved in polynomial time for a fixed number of modes when carbon emission parameters are stationary.

Suggested Citation

  • Absi, Nabil & Dauzère-Pérès, Stéphane & Kedad-Sidhoum, Safia & Penz, Bernard & Rapine, Christophe, 2016. "The single-item green lot-sizing problem with fixed carbon emissions," European Journal of Operational Research, Elsevier, vol. 248(3), pages 849-855.
  • Handle: RePEc:eee:ejores:v:248:y:2016:i:3:p:849-855
    DOI: 10.1016/j.ejor.2015.07.052
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    References listed on IDEAS

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    1. Retel Helmrich, Mathijn J. & Jans, Raf & van den Heuvel, Wilco & Wagelmans, Albert P.M., 2015. "The economic lot-sizing problem with an emission capacity constraint," European Journal of Operational Research, Elsevier, vol. 241(1), pages 50-62.
    2. Önal, Mehmet & Romeijn, H.Edwin & Sapra, Amar & van den Heuvel, Wilco, 2015. "The economic lot-sizing problem with perishable items and consumption order preference," European Journal of Operational Research, Elsevier, vol. 244(3), pages 881-891.
    3. Palak, Gökçe & Ekşioğlu, Sandra Duni & Geunes, Joseph, 2014. "Analyzing the impacts of carbon regulatory mechanisms on supplier and mode selection decisions: An application to a biofuel supply chain," International Journal of Production Economics, Elsevier, vol. 154(C), pages 198-216.
    4. Okhrin, Irena & Richter, Knut, 2011. "An O(T3) algorithm for the capacitated lot sizing problem with minimum order quantities," European Journal of Operational Research, Elsevier, vol. 211(3), pages 507-514, June.
    5. Michael Florian & Morton Klein, 1971. "Deterministic Production Planning with Concave Costs and Capacity Constraints," Management Science, INFORMS, vol. 18(1), pages 12-20, September.
    6. 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.
    7. Dobos, Imre & Gobsch, Barbara & Pakhomova, Nadezhda & Pishchulov, Grigory & Richter, Knut, 2011. "A vendor-purchaser economic lot size problem with remanufacturing and deposit," Discussion Papers 304, European University Viadrina Frankfurt (Oder), Department of Business Administration and Economics.
    8. Bouchery, Yann & Ghaffari, Asma & Jemai, Zied & Dallery, Yves, 2012. "Including sustainability criteria into inventory models," European Journal of Operational Research, Elsevier, vol. 222(2), pages 229-240.
    9. Arıkan, Emel & Jammernegg, Werner, 2014. "The single period inventory model under dual sourcing and product carbon footprint constraint," International Journal of Production Economics, Elsevier, vol. 157(C), pages 15-23.
    10. Okhrin, Irena & Richter, Knut, 2011. "The linear dynamic lot size problem with minimum order quantity," International Journal of Production Economics, Elsevier, vol. 133(2), pages 688-693, October.
    11. Konur, Dinçer, 2014. "Carbon constrained integrated inventory control and truckload transportation with heterogeneous freight trucks," International Journal of Production Economics, Elsevier, vol. 153(C), pages 268-279.
    12. Absi, Nabil & Dauzère-Pérès, Stéphane & Kedad-Sidhoum, Safia & Penz, Bernard & Rapine, Christophe, 2013. "Lot sizing with carbon emission constraints," European Journal of Operational Research, Elsevier, vol. 227(1), pages 55-61.
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    4. repec:eee:transe:v:105:y:2017:i:c:p:60-82 is not listed on IDEAS
    5. repec:gam:jsusta:v:9:y:2017:i:11:p:2103-:d:119203 is not listed on IDEAS
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    8. Wu, Xiang & (Yale) Gong, Yeming & Xu, Haoxuan & Chu, Chengbin & Zhang, Jinlong, 2017. "Dynamic lot-sizing models with pricing for new products," European Journal of Operational Research, Elsevier, vol. 260(1), pages 81-92.

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