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Product process innovation model of fuzzy optimal control of nonlinear system with finite time horizon under granular differentiability concept

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  • S. Hati

    (Mugberia Gangadhar Mahavidyalaya)

  • K. Maity

    (Mugberia Gangadhar Mahavidyalaya)

Abstract

This article explores developed a fuzzy production inventory control model of product-process innovation effecting with learning by doing. It is also a single objective profit maximization problem with the single period finite time horizon under uncertain environment.In real world, most of the companies are going to face some uncertainty for inventory cost, prices, demand, stock, etc. To make the proposed model more realistic, we consider all variables (control variable, state variable, co-state variable) are fuzzy in nature. In fuzzy optimal control system, to convert all fuzzy variables into crisp variables, here used granular differentiability, a new concept of fuzzy dynamical system. In this study, the demand of the product depends on quality, selling price and stock. Here the stock and quality have positive effect to the demand but the selling price has negative effect to it. Moreover the quality/cost of the product is increased / deceased with increase the gathering knowledge accumulation of product and process innovation. Here selling price, production rate, instantaneous investment rate on process innovation and product innovation are control variables and quality, cost, stock, knowledge gathering on process innovation and product innovation are state variables. Finally, this optimal control problem is solved by using Pontryagin Maximum principle and for numerical result and graphical representation we use Runge–Kutta forward-backward method of fourth order in MATLAB software. Subsequently, the numerical results are presented both in tabular form and graphically.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:opsear:v:60:y:2023:i:2:d:10.1007_s12597-023-00630-7
    DOI: 10.1007/s12597-023-00630-7
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    References listed on IDEAS

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    1. Chenavaz, Régis, 2012. "Dynamic pricing, product and process innovation," European Journal of Operational Research, Elsevier, vol. 222(3), pages 553-557.
    2. Susan Athey & Armin Schmutzler, 1995. "Product and Process Flexibility in an Innovative Environment," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 557-574, Winter.
    3. Lambertini, Luca & Mantovani, Andrea, 2009. "Process and product innovation by a multiproduct monopolist: A dynamic approach," International Journal of Industrial Organization, Elsevier, vol. 27(4), pages 508-518, July.
    4. Utterback, James M & Abernathy, William J, 1975. "A dynamic model of process and product innovation," Omega, Elsevier, vol. 3(6), pages 639-656, December.
    5. Souresh Saha, 2007. "Consumer preferences and product and process R&D," RAND Journal of Economics, RAND Corporation, vol. 38(1), pages 250-268, March.
    6. 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.
    7. Pan, Xiaojun & Li, Shoude, 2016. "Dynamic optimal control of process–product innovation with learning by doing," European Journal of Operational Research, Elsevier, vol. 248(1), pages 136-145.
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