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Multi-item reliability dependent imperfect production inventory optimal control models with dynamic demand under uncertain resource constraint

Author

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  • J.N. Roul
  • K. Maity
  • S. Kar
  • M. Maiti

Abstract

In this paper, imperfect multi-item production inventory models are considered over a finite time horizon with known dynamic demands. The production rates are functions of time which are taken as control variables. In the production process, reliability plays an important role to improve the quality of products and to decrease the defective rate. The said defective units are partially or fully reworked. The unit production cost is a function of production rate and also dependent on raw material cost, development cost due to reliability and wear-tear cost. There is a constraint on the total production cost termed as budget constraint which is crisp/imprecise/random in nature. The objective of the present investigation is to fix the optimum reliabilities of the production system to have maximum return. Thus, the models are formulated as optimal control problems for the maximisation of profit and solved using Hamiltonian (Pontryagin’s Maximum Principle), fixed-final time and free-final state system, Kuhn–Tucker conditions and Generalised Reduced Gradient Method. Several particular cases are derived from the general model. The models are illustrated numerically and graphically and some managerial decisions are derived.

Suggested Citation

  • J.N. Roul & K. Maity & S. Kar & M. Maiti, 2015. "Multi-item reliability dependent imperfect production inventory optimal control models with dynamic demand under uncertain resource constraint," International Journal of Production Research, Taylor & Francis Journals, vol. 53(16), pages 4993-5016, August.
    • Handle: RePEc:taf:tprsxx:v:53:y:2015:i:16:p:4993-5016
    DOI: 10.1080/00207543.2015.1012601
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    Cited by:

    1. Falguni Mahato & Chandan Mahato & Gour Chandra Mahata, 2023. "Sustainable optimal production policies for an imperfect production system with trade credit under different carbon emission regulations," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 25(9), pages 10073-10099, September.
    2. Glock, Christoph H. & Grosse, Eric H., 2021. "The impact of controllable production rates on the performance of inventory systems: A systematic review of the literature," European Journal of Operational Research, Elsevier, vol. 288(3), pages 703-720.
    3. Ahmed Abdel-Aleem & Mahmoud A. El-Sharief & Mohsen A. Hassan & Mohamed G. El-Sebaie, 2017. "A surface response optimization model for EPQ system with imperfect production process under rework and shortage," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 735-751, December.
    4. Milia Habib & Farouk Yalaoui & Hicham Chehade & Iman Jarkass & Nazir Chebbo, 2017. "Multi-objective design optimisation of repairable -out-of- subsystems in series with redundant dependency," International Journal of Production Research, Taylor & Francis Journals, vol. 55(23), pages 7000-7021, December.
    5. Kuen-Suan Chen & Tsun-Hung Huang & Kuo-Ching Chiou & Wen-Yang Kao, 2024. "Fuzzy Evaluation Model for Products with Multifunctional Quality Characteristics: Case Study on Eco-Friendly Yarn," Mathematics, MDPI, vol. 12(10), pages 1-11, May.
    6. Kuen-Suan Chen & Feng-Chia Li & Kuei-Kuei Lai & Jung-Mao Lin, 2022. "Green Outsourcer Selection Model Based on Confidence Interval of PCI for SMT Process," Sustainability, MDPI, vol. 14(24), pages 1-12, December.

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