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An Inventory Model in a Three-Echelon Supply Chain for Growing Items with Imperfect Quality, Mortality, and Shortages under Carbon Emissions When the Demand Is Price Sensitive

Author

Listed:
  • Cynthia Griselle De-la-Cruz-Márquez

    (Tecnologico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, Monterrey 64849, NL, Mexico)

  • Leopoldo Eduardo Cárdenas-Barrón

    (Tecnologico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, Monterrey 64849, NL, Mexico)

  • Buddhadev Mandal

    (Regent Education and Research Foundation, Barrackpore, Kolkata 700121, India)

  • Neale R. Smith

    (Tecnologico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, Monterrey 64849, NL, Mexico)

  • Rafael Ernesto Bourguet-Díaz

    (Tecnologico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, Monterrey 64849, NL, Mexico)

  • Imelda de Jesús Loera-Hernández

    (Tecnologico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, Monterrey 64849, NL, Mexico)

  • Armando Céspedes-Mota

    (Tecnologico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, Monterrey 64849, NL, Mexico)

  • Gerardo Treviño-Garza

    (Tecnologico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, Monterrey 64849, NL, Mexico)

Abstract

This research develops an optimization model for growing items in a supply chain with three stages: farmer, processor, and retailer while considering imperfect quality, mortality, shortages with full backordering, and carbon emissions. In the farmer stage, during the growing period, not all articles survive until the end of the period, so a density function of the probability of survival and death of the growing articles is taken into account. Moreover, it is considered imperfect quality in the retailer’s stage because as the supply chain goes down, there exists a greater probability of product defects. Here, the end customer (consumer) can detect poor-quality aspects such as poorly cut, poorly packed, expired products, etc. An inventory model that maximizes the expected total profit is formulated for a single type of growing items with price-dependent polynomial demand. An algorithm is developed to solve the optimization problem generating the optimal solution for order quantity, backordering quantity, selling price, and the number of shipments that maximizes the expected total profit per unit of time, and a numerical example is used to describe the applicability of the proposed inventory model. Finally, a sensitivity analysis has been carried out for all the input parameters of the inventory model, where the effect of each of the parameters on the decision variables is shown to extract some management knowledge. It was found that holding costs in the three stages of the supply chain have a substantial impact on the total profit per unit of time. In addition, as the demand scale parameter increases, the company must raise the selling price, which directly impacts the expected total profit per unit of time. This inventory model has the advantage that it can be applied to any growing item, including animals or plants, so it helps the owners of farms or crops to generate the most significant possible profit with their existing resources.

Suggested Citation

  • Cynthia Griselle De-la-Cruz-Márquez & Leopoldo Eduardo Cárdenas-Barrón & Buddhadev Mandal & Neale R. Smith & Rafael Ernesto Bourguet-Díaz & Imelda de Jesús Loera-Hernández & Armando Céspedes-Mota & Ge, 2022. "An Inventory Model in a Three-Echelon Supply Chain for Growing Items with Imperfect Quality, Mortality, and Shortages under Carbon Emissions When the Demand Is Price Sensitive," Mathematics, MDPI, vol. 10(24), pages 1-41, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4684-:d:999342
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    References listed on IDEAS

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    1. Adrián Macías-López & Leopoldo Eduardo Cárdenas-Barrón & Rodrigo E. Peimbert-García & Buddhadev Mandal, 2021. "An Inventory Model for Perishable Items with Price-, Stock-, and Time-Dependent Demand Rate considering Shelf-Life and Nonlinear Holding Costs," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-36, April.
    2. Leopoldo Eduardo Cárdenas-Barrón & María José Lea Plaza-Makowsky & María Alejandra Sevilla-Roca & José María Núñez-Baumert & Buddhadev Mandal, 2021. "An Inventory Model for Imperfect Quality Products with Rework, Distinct Holding Costs, and Nonlinear Demand Dependent on Price," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
    3. Kartick Dey & Debajyoti Chatterjee & Subrata Saha & Ilkyeong Moon, 2019. "Dynamic versus static rebates: an investigation on price, displayed stock level, and rebate-induced demand using a hybrid bat algorithm," Annals of Operations Research, Springer, vol. 279(1), pages 187-219, August.
    4. Cynthia Griselle De-la-Cruz-Márquez & Leopoldo Eduardo Cárdenas-Barrón & Buddhadev Mandal, 2021. "An Inventory Model for Growing Items with Imperfect Quality When the Demand Is Price Sensitive under Carbon Emissions and Shortages," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-23, April.
    5. Pourmohammad-Zia, Nadia & Karimi, Behrooz & Rezaei, Jafar, 2021. "Food supply chain coordination for growing items: A trade-off between market coverage and cost-efficiency," International Journal of Production Economics, Elsevier, vol. 242(C).
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    9. Makoena Sebatjane & Olufemi Adetunji, 2022. "Optimal inventory replenishment and shipment policies in a three-echelon supply chain for growing items with expiration dates," OPSEARCH, Springer;Operational Research Society of India, vol. 59(3), pages 809-838, September.
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    Cited by:

    1. Amir Hossein Nobil & Erfan Nobil & Leopoldo Eduardo Cárdenas-Barrón & Dagoberto Garza-Núñez & Gerardo Treviño-Garza & Armando Céspedes-Mota & Imelda de Jesús Loera-Hernández & Neale R. Smith, 2023. "Economic Order Quantity for Growing Items with Mortality Function under Sustainable Green Breeding Policy," Mathematics, MDPI, vol. 11(4), pages 1-21, February.
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