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A partial backlogging inventory model for deteriorating items with time-varying demand and holding cost

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  • Debashis Dutta
  • Pavan Kumar

Abstract

In this paper, we propose a partial backlogging inventory model for deteriorating items with time-varying demand and holding cost. Deterioration rate is assumed to be constant. The demand rate varies with time until the shortage occurs; during shortages, demand rate becomes constant. Shortages are allowed and assumed to be partially backlogged. The backlogging rate is variable and is inversely proportional to the length of the waiting time for next replenishment. Taylor series is used for exponential terms approximating up to second degree terms. We solve the proposed model to obtain the optimal value of order quantity and total cost. The purpose of this paper is to minimise the total cost of inventory with optimal order quantity. The convexity of the cost function is shown graphically. Two numerical examples are given in order to show the applicability of the proposed model. Sensitivity analysis is also carried out to identify the most sensitive parameters in the system.

Suggested Citation

  • Debashis Dutta & Pavan Kumar, 2015. "A partial backlogging inventory model for deteriorating items with time-varying demand and holding cost," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 7(3), pages 281-296.
    • Handle: RePEc:ids:ijmore:v:7:y:2015:i:3:p:281-296
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    Citations

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    Cited by:

    1. Janssen, Larissa & Claus, Thorsten & Sauer, Jürgen, 2016. "Literature review of deteriorating inventory models by key topics from 2012 to 2015," International Journal of Production Economics, Elsevier, vol. 182(C), pages 86-112.
    2. Chan, Chi Kin & Wong, Wai Him & Langevin, A. & Lee, Y.C.E., 2017. "An integrated production-inventory model for deteriorating items with consideration of optimal production rate and deterioration during delivery," International Journal of Production Economics, Elsevier, vol. 189(C), pages 1-13.
    3. Md Sadikur Rahman & Subhajit Das & Amalesh Kumar Manna & Ali Akbar Shaikh & Asoke Kumar Bhunia & Leopoldo Eduardo Cárdenas-Barrón & Gerardo Treviño-Garza & Armando Céspedes-Mota, 2021. "A Mathematical Model of the Production Inventory Problem for Mixing Liquid Considering Preservation Facility," Mathematics, MDPI, vol. 9(24), pages 1-19, December.
    4. Md. Abdul Hakim & Ibrahim M. Hezam & Adel Fahad Alrasheedi & Jeonghwan Gwak, 2022. "Pricing Policy in an Inventory Model with Green Level Dependent Demand for a Deteriorating Item," Sustainability, MDPI, vol. 14(8), pages 1-16, April.
    5. Neeraj Kumar & Sanjey Kumar, 2017. "An inventory model for deteriorating items with partial backlogging using linear demand in fuzzy environment," Cogent Business & Management, Taylor & Francis Journals, vol. 4(1), pages 1307687-130, January.
    6. Aijun Liu & Yaxuan Xiao & Xiaohui Ji & Kai Wang & Sang-Bing Tsai & Hui Lu & Jinshi Cheng & Xinjun Lai & Jiangtao Wang, 2018. "A Novel Two-Stage Integrated Model for Supplier Selection of Green Fresh Product," Sustainability, MDPI, vol. 10(7), pages 1-23, July.

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