IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v248y2016i3p849-855.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715007067
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.07.052?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Zied Jemai & Y Bouchery & Asma Ghaffari & Yves Dallery, 2012. "Including sustainability criteria into inventory models," Post-Print hal-01672398, HAL.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Engebrethsen, Erna & Dauzère-Pérès, Stéphane, 2019. "Transportation mode selection in inventory models: A literature review," European Journal of Operational Research, Elsevier, vol. 279(1), pages 1-25.
    2. Suzanne, Elodie & Absi, Nabil & Borodin, Valeria, 2020. "Towards circular economy in production planning: Challenges and opportunities," European Journal of Operational Research, Elsevier, vol. 287(1), pages 168-190.
    3. Ma, Junhai & Hou, Yaming & Wang, Zongxian & Yang, Wenhui, 2021. "Pricing strategy and coordination of automobile manufacturers based on government intervention and carbon emission reduction," Energy Policy, Elsevier, vol. 148(PA).
    4. Coelho, Leandro Callegari & De Maio, Annarita & Laganà, Demetrio, 2020. "A variable MIP neighborhood descent for the multi-attribute inventory routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 144(C).
    5. Hong, Zhaofu & Chu, Chengbin & Zhang, Linda L. & Yu, Yugang, 2017. "Optimizing an emission trading scheme for local governments: A Stackelberg game model and hybrid algorithm," International Journal of Production Economics, Elsevier, vol. 193(C), pages 172-182.
    6. Cao, Cejun & Liu, Yang & Tang, Ou & Gao, Xuehong, 2021. "A fuzzy bi-level optimization model for multi-period post-disaster relief distribution in sustainable humanitarian supply chains," International Journal of Production Economics, Elsevier, vol. 235(C).
    7. Hong, Zhaofu & Dai, Wei & Luh, Hsing & Yang, Chenchen, 2018. "Optimal configuration of a green product supply chain with guaranteed service time and emission constraints," European Journal of Operational Research, Elsevier, vol. 266(2), pages 663-677.
    8. Svoboda, Josef & Minner, Stefan & Yao, Man, 2021. "Typology and literature review on multiple supplier inventory control models," European Journal of Operational Research, Elsevier, vol. 293(1), pages 1-23.
    9. Darvish, Maryam & Archetti, Claudia & Coelho, Leandro C., 2019. "Trade-offs between environmental and economic performance in production and inventory-routing problems," International Journal of Production Economics, Elsevier, vol. 217(C), pages 269-280.
    10. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    11. Barbosa-Póvoa, Ana Paula & da Silva, Cátia & Carvalho, Ana, 2018. "Opportunities and challenges in sustainable supply chain: An operations research perspective," European Journal of Operational Research, Elsevier, vol. 268(2), pages 399-431.
    12. Konur, Dinçer, 2017. "Non-collaborative emission targets joining and quantity flow decisions in a Stackelberg setting," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 105(C), pages 60-82.
    13. M. Turkensteen (Marcel) & van den Heuvel, W., 2019. "The trade-off between costs and carbon emissions from lot-sizing decisions," Econometric Institute Research Papers EI2019-19, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    14. Tamssaouet, Karim & Engebrethsen, Erna & Dauzère-Pérès, Stéphane, 2023. "Multi-item dynamic lot sizing with multiple transportation modes and item fragmentation," International Journal of Production Economics, Elsevier, vol. 265(C).
    15. Cejun Cao & Congdong Li & Qin Yang & Fanshun Zhang, 2017. "Multi-Objective Optimization Model of Emergency Organization Allocation for Sustainable Disaster Supply Chain," Sustainability, MDPI, vol. 9(11), pages 1-22, November.
    16. Konur, Dinçer & Campbell, James F. & Monfared, Sepideh A., 2017. "Economic and environmental considerations in a stochastic inventory control model with order splitting under different delivery schedules among suppliers," Omega, Elsevier, vol. 71(C), pages 46-65.
    17. Silbermayr, Lena & Jammernegg, Werner & Kischka, Peter, 2017. "Inventory pooling with environmental constraints using copulas," European Journal of Operational Research, Elsevier, vol. 263(2), pages 479-492.
    18. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    2. Konur, Dinçer & Campbell, James F. & Monfared, Sepideh A., 2017. "Economic and environmental considerations in a stochastic inventory control model with order splitting under different delivery schedules among suppliers," Omega, Elsevier, vol. 71(C), pages 46-65.
    3. Konur, Dinçer, 2017. "Non-collaborative emission targets joining and quantity flow decisions in a Stackelberg setting," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 105(C), pages 60-82.
    4. Schaefer, Brian & Konur, Dinçer, 2015. "Economic and environmental considerations in a continuous review inventory control system with integrated transportation decisions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 80(C), pages 142-165.
    5. Hong, Zhaofu & Chu, Chengbin & Yu, Yugang, 2016. "Dual-mode production planning for manufacturing with emission constraints," European Journal of Operational Research, Elsevier, vol. 251(1), pages 96-106.
    6. Y Bouchery & Asma Ghaffari & Zied Jemai & Jan C Fransoo, 2016. "Sustainable transportation and order quantity: insights from multiobjective optimization," Post-Print hal-01954465, HAL.
    7. Bouchery, Yann & Ghaffari, Asma & Jemai, Zied & Tan, Tarkan, 2017. "Impact of coordination on costs and carbon emissions for a two-echelon serial economic order quantity problem," European Journal of Operational Research, Elsevier, vol. 260(2), pages 520-533.
    8. Yann Bouchery & Asma Ghaffari & Zied Jemai & Jan Fransoo, 2016. "Sustainable transportation and order quantity: insights from multiobjective optimization," Flexible Services and Manufacturing Journal, Springer, vol. 28(3), pages 367-396, September.
    9. Chung-Lun Li & Qingying Li, 2016. "Polynomial-Time Solvability of Dynamic Lot Size Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-20, June.
    10. M. Turkensteen (Marcel) & van den Heuvel, W., 2019. "The trade-off between costs and carbon emissions from lot-sizing decisions," Econometric Institute Research Papers EI2019-19, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Barbosa-Póvoa, Ana Paula & da Silva, Cátia & Carvalho, Ana, 2018. "Opportunities and challenges in sustainable supply chain: An operations research perspective," European Journal of Operational Research, Elsevier, vol. 268(2), pages 399-431.
    12. 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.
    13. Hu, Qiwei & Boylan, John E. & Chen, Huijing & Labib, Ashraf, 2018. "OR in spare parts management: A review," European Journal of Operational Research, Elsevier, vol. 266(2), pages 395-414.
    14. Mallidis, Ioannis & Vlachos, Dimitrios & Iakovou, Eleftherios & Dekker, Rommert, 2014. "Design and planning for green global supply chains under periodic review replenishment policies," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 210-235.
    15. Engebrethsen, Erna & Dauzère-Pérès, Stéphane, 2019. "Transportation mode selection in inventory models: A literature review," European Journal of Operational Research, Elsevier, vol. 279(1), pages 1-25.
    16. McDonald, Conor M., 2016. "Integrating packaging and supply chain decisions: Selection of economic handling unit quantities," International Journal of Production Economics, Elsevier, vol. 180(C), pages 208-221.
    17. Battini, Daria & Glock, Christoph H. & Grosse, Eric H. & Persona, Alessandro & Sgarbossa, Fabio, 2017. "Reprint of “Ergo-lot-sizing: An approach to integrate ergonomic and economic objectives in manual materials handling”," International Journal of Production Economics, Elsevier, vol. 194(C), pages 32-42.
    18. Hong, Zhaofu & Dai, Wei & Luh, Hsing & Yang, Chenchen, 2018. "Optimal configuration of a green product supply chain with guaranteed service time and emission constraints," European Journal of Operational Research, Elsevier, vol. 266(2), pages 663-677.
    19. Esra Koca & Hande Yaman & M. Selim Aktürk, 2014. "Lot Sizing with Piecewise Concave Production Costs," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 767-779, November.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:248:y:2016:i:3:p:849-855. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.