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Optimal Price and Lot Size for an EOQ Model with Full Backordering under Power Price and Time Dependent Demand

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  • Luis A. San-José

    (IMUVA-Mathematics Research Institute, University of Valladolid, 47011 Valladolid, Spain
    Department of Applied Mathematics, University of Valladolid, 47011 Valladolid, Spain)

  • Joaquín Sicilia

    (Department of Mathematics, Statistics and Operational Research, University of La Laguna, 38200 San Cristóbal de La Laguna, Spain)

  • Manuel González-de-la-Rosa

    (Department of Business Administration and Economic History, University of La Laguna, 38200 San Cristóbal de La Laguna, Spain)

  • Jaime Febles-Acosta

    (Department of Business Administration and Economic History, University of La Laguna, 38200 San Cristóbal de La Laguna, Spain)

Abstract

In this paper, we address an inventory system where the demand rate multiplicatively combines the effects of time and selling price. It is assumed that the demand rate is the product of two power functions, one depending on the selling price and the other on the time elapsed since the last inventory replenishment. Shortages are allowed and fully backlogged. The aim is to obtain the lot sizing, the inventory cycle and the unit selling price that maximize the profit per unit time. To achieve this, two efficient algorithms are proposed to obtain the optimal solution to the inventory problem for all possible parameter values of the system. We solve several numerical examples to illustrate the theoretical results and the solution methodology. We also develop a numerical sensitivity analysis of the optimal inventory policy and the maximum profit with respect to the parameters of the demand function.

Suggested Citation

  • Luis A. San-José & Joaquín Sicilia & Manuel González-de-la-Rosa & Jaime Febles-Acosta, 2021. "Optimal Price and Lot Size for an EOQ Model with Full Backordering under Power Price and Time Dependent Demand," Mathematics, MDPI, vol. 9(16), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1848-:d:608776
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    References listed on IDEAS

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    1. Joaquín Sicilia & Jaime Febles-Acosta & Manuel González-De La Rosa, 2012. "Deterministic Inventory Systems With Power Demand Pattern," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-28.
    2. Wu, Jiang & Skouri, Konstantina & Teng, Jinn-Tsair & Ouyang, Liang-Yuh, 2014. "A note on “optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment”," International Journal of Production Economics, Elsevier, vol. 155(C), pages 324-329.
    3. Alireza Kabirian, 2012. "The economic production and pricing model with lot-size-dependent production cost," Journal of Global Optimization, Springer, vol. 54(1), pages 1-15, September.
    4. Luis A. San-José & Joaquín Sicilia & Manuel González-De-la-Rosa & Jaime Febles-Acosta, 2020. "Best pricing and optimal policy for an inventory system under time-and-price-dependent demand and backordering," Annals of Operations Research, Springer, vol. 286(1), pages 351-369, March.
    5. Avinadav, Tal & Herbon, Avi & Spiegel, Uriel, 2014. "Optimal ordering and pricing policy for demand functions that are separable into price and inventory age," International Journal of Production Economics, Elsevier, vol. 155(C), pages 406-417.
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    9. Lin, Feng & Jia, Tao & Wu, Feng & Yang, Zhen, 2019. "Impacts of two-stage deterioration on an integrated inventory model under trade credit and variable capacity utilization," European Journal of Operational Research, Elsevier, vol. 272(1), pages 219-234.
    10. Soni, Hardik N, 2013. "Optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment," International Journal of Production Economics, Elsevier, vol. 146(1), pages 259-268.
    11. Joaquín Sicilia & Jaime Febles-Acosta & Manuel González-De la Rosa, 2013. "Economic order quantity for a power demand pattern system with deteriorating items," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 7(5), pages 577-593.
    12. Vandana, & Sharma, B.K., 2016. "An EOQ model for retailers partial permissible delay in payment linked to order quantity with shortages," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 125(C), pages 99-112.
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