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An Inventory Model for Non-Instantaneously Deteriorating Items with Nonlinear Stock-Dependent Demand, Hybrid Payment Scheme and Partially Backlogged Shortages

Author

Listed:
  • Md Al-Amin Khan

    (Department of Mathematics, Jahangirnagar University, Dhaka 1342, Bangladesh)

  • Ali Akbar Shaikh

    (Department of Mathematics, The University of Burdwan, Burdwan 713104, India)

  • Leopoldo Eduardo Cárdenas-Barrón

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

  • Abu Hashan Md Mashud

    (Department of Mathematics, Hajee Mohammad Danesh Science and Technology University, Dinajpur 5200, Bangladesh)

  • Gerardo Treviño-Garza

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

  • Armando Céspedes-Mota

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

Abstract

This research work presents an inventory model that involves non-instantaneous deterioration, nonlinear stock-dependent demand, and partially backlogged shortages by considering the length of the waiting time under a hybrid prepayment and cash-on-delivery scheme. The corresponding inventory problem is formulated as a nonlinear constraint optimization problem. The theoretical results for the unique optimal solution are presented, and eight special cases are also identified. Moreover, a salient theoretical result is provided: a certain condition where the optimal inventory policy may or may not involve deterioration. Finally, two numerical examples are provided using a sensitivity analysis to show the validity range of the inventory parameters.

Suggested Citation

  • Md Al-Amin Khan & Ali Akbar Shaikh & Leopoldo Eduardo Cárdenas-Barrón & Abu Hashan Md Mashud & Gerardo Treviño-Garza & Armando Céspedes-Mota, 2022. "An Inventory Model for Non-Instantaneously Deteriorating Items with Nonlinear Stock-Dependent Demand, Hybrid Payment Scheme and Partially Backlogged Shortages," Mathematics, MDPI, vol. 10(3), pages 1-23, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:434-:d:737786
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    References listed on IDEAS

    as
    1. Ali Akbar Shaikh & Abu Hashan Md Mashud & Md. Sharif Uddin & Md. Al-Amin Khan, 2017. "Non-instantaneous deterioration inventory model with price and stock dependent demand for fully backlogged shortages under inflation," International Journal of Business Forecasting and Marketing Intelligence, Inderscience Enterprises Ltd, vol. 3(2), pages 152-164.
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    Cited by:

    1. Zsolt Tibor Kosztyán & Zoltán Kovács, 2023. "Preface to the Special Issue on “Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling”," Mathematics, MDPI, vol. 11(1), pages 1-3, January.
    2. Ajoy Hatibaruah & Sumit Saha, 2023. "An inventory model for two-parameter Weibull distributed ameliorating and deteriorating items with stock and advertisement frequency dependent demand under trade credit and preservation technology," OPSEARCH, Springer;Operational Research Society of India, vol. 60(2), pages 951-1002, June.

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