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A stochastic aggregate production planning model in a green supply chain : Considering flexible lead times, nonlinear purchase and shortage cost functions

Author

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  • Seyed Mohammad Javad Mirzapour Al-E-Hashem

    (EM - EMLyon Business School)

  • Armand Baboli
  • Z. Sazvar

Abstract

In this paper we develop a stochastic programming approach to solve a multi-period multi-product multi-site aggregate production planning problem in a green supply chain for a medium-term planning horizon under the assumption of demand uncertainty. The proposed model has the following features: (i) the majority of supply chain cost parameters are considered; (ii) quantity discounts to encourage the producer to order more from the suppliers in one period, instead of splitting the order into periodical small quantities, are considered; (iii) the interrelationship between lead time and transportation cost is considered, as well as that between lead time and greenhouse gas emission level; (iv) demand uncertainty is assumed to follow a pre-specified distribution function; (v) shortages are penalized by a general multiple breakpoint function, to persuade producers to reduce backorders as much as possible; (vi) some indicators of a green supply chain, such as greenhouse gas emissions and waste management are also incorporated into the model. The proposed model is first a nonlinear mixed integer programming which is converted into a linear one by applying some theoretical and numerical techniques. Due to the convexity of the model, the local solution obtained from linear programming solvers is also the global solution. Finally, a numerical example is presented to demonstrate the validity of the proposed model.

Suggested Citation

  • Seyed Mohammad Javad Mirzapour Al-E-Hashem & Armand Baboli & Z. Sazvar, 2013. "A stochastic aggregate production planning model in a green supply chain : Considering flexible lead times, nonlinear purchase and shortage cost functions," Post-Print hal-02313031, HAL.
    • Handle: RePEc:hal:journl:hal-02313031
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    Cited by:

    1. Ghanbarzadeh-Shams, M. & Ghasemy Yaghin, R. & Sadeghi, A.H., 2022. "A hybrid fuzzy multi-objective model for carpet production planning with reverse logistics under uncertainty," Socio-Economic Planning Sciences, Elsevier, vol. 83(C).
    2. Mirzapour Al-e-hashem, Seyed M.J. & Rekik, Yacine & Mohammadi Hoseinhajlou, Ebrahim, 2019. "A hybrid L-shaped method to solve a bi-objective stochastic transshipment-enabled inventory routing problem," International Journal of Production Economics, Elsevier, vol. 209(C), pages 381-398.
    3. Sobhani, A. & Wahab, M.I.M. & Neumann, W.P., 2015. "Investigating work-related ill health effects in optimizing the performance of manufacturing systems," European Journal of Operational Research, Elsevier, vol. 241(3), pages 708-718.
    4. Jabbarzadeh, Armin & Haughton, Michael & Pourmehdi, Fahime, 2019. "A robust optimization model for efficient and green supply chain planning with postponement strategy," International Journal of Production Economics, Elsevier, vol. 214(C), pages 266-283.
    5. Ameknassi, Lhoussaine & Aït-Kadi, Daoud & Rezg, Nidhal, 2016. "Integration of logistics outsourcing decisions in a green supply chain design: A stochastic multi-objective multi-period multi-product programming model," International Journal of Production Economics, Elsevier, vol. 182(C), pages 165-184.
    6. Zahiri, Behzad & Zhuang, Jun & Mohammadi, Mehrdad, 2017. "Toward an integrated sustainable-resilient supply chain: A pharmaceutical case study," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 109-142.
    7. Kuo-Ping Lin & Kuo-Chen Hung & Yu-Ting Lin & Yao-Hung Hsieh, 2017. "Green Suppliers Performance Evaluation in Belt and Road Using Fuzzy Weighted Average with Social Media Information," Sustainability, MDPI, vol. 10(1), pages 1-11, December.
    8. Waltho, Cynthia & Elhedhli, Samir & Gzara, Fatma, 2019. "Green supply chain network design: A review focused on policy adoption and emission quantification," International Journal of Production Economics, Elsevier, vol. 208(C), pages 305-318.
    9. Eduardo Gutiérrez González & Olga Vladimirovna Panteleeva, 2020. "A model for planning and optimizing an engineering company production," OPSEARCH, Springer;Operational Research Society of India, vol. 57(3), pages 669-699, September.
    10. Bairamzadeh, Samira & Saidi-Mehrabad, Mohammad & Pishvaee, Mir Saman, 2018. "Modelling different types of uncertainty in biofuel supply network design and planning: A robust optimization approach," Renewable Energy, Elsevier, vol. 116(PA), pages 500-517.
    11. Babazadeh, Reza & Razmi, Jafar & Pishvaee, Mir Saman & Rabbani, Masoud, 2017. "A sustainable second-generation biodiesel supply chain network design problem under risk," Omega, Elsevier, vol. 66(PB), pages 258-277.
    12. M. Boronoos & M. Mousazadeh & S. Ali Torabi, 2021. "A robust mixed flexible-possibilistic programming approach for multi-objective closed-loop green supply chain network design," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(3), pages 3368-3395, March.
    13. Schulte Beerbühl, S. & Fröhling, M. & Schultmann, F., 2015. "Combined scheduling and capacity planning of electricity-based ammonia production to integrate renewable energies," European Journal of Operational Research, Elsevier, vol. 241(3), pages 851-862.
    14. Mohammad Asghari & Seyed Mohammad Javad Mirzapour Al-E-Hashem & Yacine Rekik, 2022. "Environmental and social implications of incorporating carpooling service on a customized bus system," Post-Print hal-03598768, HAL.
    15. Mirzapour Al-e-hashem, S.M.J. & Rekik, Yacine, 2014. "Multi-product multi-period Inventory Routing Problem with a transshipment option: A green approach," International Journal of Production Economics, Elsevier, vol. 157(C), pages 80-88.
    16. Donya Rahmani & Arash Zandi & Sara Behdad & Arezou Entezaminia, 2021. "A light robust model for aggregate production planning with consideration of environmental impacts of machines," Operational Research, Springer, vol. 21(1), pages 273-297, March.
    17. Asghari, Mohammad & Mirzapour Al-e-hashem, S. Mohammad J., 2020. "A green delivery-pickup problem for home hemodialysis machines; sharing economy in distributing scarce resources," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 134(C).
    18. Sazvar, Z. & Mirzapour Al-e-hashem, S.M.J. & Baboli, A. & Akbari Jokar, M.R., 2014. "A bi-objective stochastic programming model for a centralized green supply chain with deteriorating products," International Journal of Production Economics, Elsevier, vol. 150(C), pages 140-154.
    19. Farnaz Barzinpour & Peyman Taki, 2018. "A dual-channel network design model in a green supply chain considering pricing and transportation mode choice," Journal of Intelligent Manufacturing, Springer, vol. 29(7), pages 1465-1483, October.
    20. Marjia Haque & Sanjoy Kumar Paul & Ruhul Sarker & Daryl Essam, 2022. "A combined approach for modeling multi-echelon multi-period decentralized supply chain," Annals of Operations Research, Springer, vol. 315(2), pages 1665-1702, August.

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