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An economic lot-size model with non-linear holding cost hinging on time and quantity

Author

Listed:
  • Pando, Valentín
  • San-José, Luis A.
  • García-Laguna, Juan
  • Sicilia, Joaquín

Abstract

This paper develops an economic lot size inventory model where the demand rate depends on the stock level and the cumulative holding cost is non-linear on both the quantity and the time they are stored. More concretely, it is supposed that the demand rate is a concave potential function of the inventory level and the holding cost is potential on both time and quantity. Moreover, shortages are not allowed. A general procedure to determine the optimal lot size and the maximum inventory profit is developed. Also, some results about the profitability of the inventory system are presented. This work extends several inventory models previously considered in the literature. Finally, numerical examples, which help us to understand the theoretical results, are also given.

Suggested Citation

  • Pando, Valentín & San-José, Luis A. & García-Laguna, Juan & Sicilia, Joaquín, 2013. "An economic lot-size model with non-linear holding cost hinging on time and quantity," International Journal of Production Economics, Elsevier, vol. 145(1), pages 294-303.
    • Handle: RePEc:eee:proeco:v:145:y:2013:i:1:p:294-303
    DOI: 10.1016/j.ijpe.2013.04.050
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    References listed on IDEAS

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    1. Urban, Timothy L., 2008. "An extension of inventory models with discretely variable holding costs," International Journal of Production Economics, Elsevier, vol. 114(1), pages 399-403, July.
    2. P-S You, 2005. "Inventory policy for products with price and time-dependent demands," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(7), pages 870-873, July.
    3. Padmanabhan, G. & Vrat, Prem, 1995. "EOQ models for perishable items under stock dependent selling rate," European Journal of Operational Research, Elsevier, vol. 86(2), pages 281-292, October.
    4. Weiss, Howard J., 1982. "Economic order quantity models with nonlinear holding costs," European Journal of Operational Research, Elsevier, vol. 9(1), pages 56-60, January.
    5. Dye, Chung-Yuan & Ouyang, Liang-Yuh, 2005. "An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging," European Journal of Operational Research, Elsevier, vol. 163(3), pages 776-783, June.
    6. Goh, M., 1994. "EOQ models with general demand and holding cost functions," European Journal of Operational Research, Elsevier, vol. 73(1), pages 50-54, February.
    7. Urban, Timothy L., 2005. "Inventory models with inventory-level-dependent demand: A comprehensive review and unifying theory," European Journal of Operational Research, Elsevier, vol. 162(3), pages 792-804, May.
    8. Berman, Oded & Perry, David, 2006. "An EOQ model with state-dependent demand rate," European Journal of Operational Research, Elsevier, vol. 171(1), pages 255-272, May.
    9. Giri, B.C. & Chaudhuri, K.S., 1998. "Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost," European Journal of Operational Research, Elsevier, vol. 105(3), pages 467-474, March.
    10. Alfares, Hesham K., 2007. "Inventory model with stock-level dependent demand rate and variable holding cost," International Journal of Production Economics, Elsevier, vol. 108(1-2), pages 259-265, July.
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    Cited by:

    1. Irfan Ali & Srikant Gupta & Aquil Ahmed, 2019. "Multi-objective linear fractional inventory problem under intuitionistic fuzzy environment," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(2), pages 173-189, April.
    2. Mahmood Vahdani & Zeinab Sazvar & Kannan Govindan, 2022. "An integrated economic disposal and lot-sizing problem for perishable inventories with batch production and corrupt stock-dependent holding cost," Annals of Operations Research, Springer, vol. 315(2), pages 2135-2167, August.
    3. Valentín Pando & Luis A. San-José & Joaquín Sicilia, 2021. "An Inventory Model with Stock-Dependent Demand Rate and Maximization of the Return on Investment," Mathematics, MDPI, vol. 9(8), pages 1-18, April.
    4. Sicilia, Joaquín & González-De-la-Rosa, Manuel & Febles-Acosta, Jaime & Alcaide-López-de-Pablo, David, 2014. "Optimal policy for an inventory system with power demand, backlogged shortages and production rate proportional to demand rate," International Journal of Production Economics, Elsevier, vol. 155(C), pages 163-171.
    5. San-José, L.A. & Sicilia, J. & García-Laguna, J., 2015. "Analysis of an EOQ inventory model with partial backordering and non-linear unit holding cost," Omega, Elsevier, vol. 54(C), pages 147-157.
    6. Totan Garai & Dipankar Chakraborty & Tapan Kumar Roy, 2019. "Multi-objective Inventory Model with Both Stock-Dependent Demand Rate and Holding Cost Rate Under Fuzzy Random Environment," Annals of Data Science, Springer, vol. 6(1), pages 61-81, March.
    7. ASADABADI Mehdi Rajabi, 2016. "A Revision On Cost Elements Of The Eoq Model," Studies in Business and Economics, Lucian Blaga University of Sibiu, Faculty of Economic Sciences, vol. 11(1), pages 5-14, April.
    8. 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.
    9. Minakshi Panda & Anuradha Sahoo, 2023. "Novel Methods for Solving Multi-Objective Non-linear Inventory Model of Highly Deteriorating Items," SN Operations Research Forum, Springer, vol. 4(3), pages 1-22, September.
    10. R. Sundararajan & M. Palanivel & S. Vaithyasubramanian, 2023. "On the EOQ Models with Advertisement-Price-Dependent Demand and Quantity Discount with Expiration Date Under Shortage," SN Operations Research Forum, Springer, vol. 4(4), pages 1-31, December.
    11. Yang, Chih-Te, 2014. "An inventory model with both stock-dependent demand rate and stock-dependent holding cost rate," International Journal of Production Economics, Elsevier, vol. 155(C), pages 214-221.
    12. Ata Allah Taleizadeh & Bita Hazarkhani & Ilkyeong Moon, 2020. "Joint pricing and inventory decisions with carbon emission considerations, partial backordering and planned discounts," Annals of Operations Research, Springer, vol. 290(1), pages 95-113, July.
    13. Al-Amin Khan, Md. & Shaikh, Ali Akbar & Konstantaras, Ioannis & Bhunia, Asoke Kumar & Cárdenas-Barrón, Leopoldo Eduardo, 2020. "Inventory models for perishable items with advanced payment, linearly time-dependent holding cost and demand dependent on advertisement and selling price," International Journal of Production Economics, Elsevier, vol. 230(C).
    14. S. Dari & B. Sani, 2020. "An EPQ model for delayed deteriorating items with quadratic demand and linear holding cost," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 46-72, March.

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