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Production inventory control model for deteriorating complementary and substitute items with shortage

Author

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  • S. Hati

    (National Institute of Technology Durgapur)

  • K. Maity

    (Mugberia Gangadhar Mahavidyalaya)

Abstract

A combination of complementary and substitute products are very significant for any business industry to make all-round profit from various prospect. How deterioration affects complementary products or substitute products is discussed in this study. A deterministic production inventory control model for complementary and/or substitute items with a constant deterioration rate is studied. Here a shortage is also allowed. During shortage period, the demand of available item increases due to the shortage of substitute items. Similarly, the demand of available item decreases due to the shortage of complementary items during the said period. The demand is both price and stock dependent and the deteriorated items are salvaged. Here the total profit function consist of sales of product, inventory holding cost, green technology cost, carbon tax, production cost and salvage value. Numerical examples illustrate the theoretical results. The Pontryagin Maximum principle is used to solve the said optimal control inventory model. To justify the effectiveness of our model we check the sensitivity analysis. The results of this model are also graphically presented with the help of MATLAB software.

Suggested Citation

  • S. Hati & K. Maity, 2024. "Production inventory control model for deteriorating complementary and substitute items with shortage," OPSEARCH, Springer;Operational Research Society of India, vol. 61(4), pages 2023-2054, December.
    • Handle: RePEc:spr:opsear:v:61:y:2024:i:4:d:10.1007_s12597-024-00770-4
    DOI: 10.1007/s12597-024-00770-4
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    References listed on IDEAS

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    1. Mokhtari, Hadi, 2018. "Economic order quantity for joint complementary and substitutable items," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 154(C), pages 34-47.
    2. Bartosz Sawik, 2023. "Space Mission Risk, Sustainability and Supply Chain: Review, Multi-Objective Optimization Model and Practical Approach," Sustainability, MDPI, vol. 15(14), pages 1-25, July.
    3. S. Hati & K. Maity, 2022. "Reliability Dependent Imperfect Production Inventory Optimal Control Fractional Order Model for Uncertain Environment Under Granular Differentiability," Fuzzy Information and Engineering, Taylor & Francis Journals, vol. 14(4), pages 379-406, October.
    4. S. Hati & K. Maity, 2023. "Product process innovation model of fuzzy optimal control of nonlinear system with finite time horizon under granular differentiability concept," OPSEARCH, Springer;Operational Research Society of India, vol. 60(2), pages 753-775, June.
    5. Sawik, Tadeusz, 2023. "Reshore or not Reshore: A Stochastic Programming Approach to Supply Chain Optimization," Omega, Elsevier, vol. 118(C).
    Full references (including those not matched with items on IDEAS)

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