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A fuzzy production inventory control model using granular differentiability approach

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Abstract

In this paper, we have created a single-period fuzzy production inventory control model on the finite time horizon. A new nonlinear demand function has been introduced, which depends on the stock, selling price and product quality. The realistic reasons come from logistical function and entry into the initial demand for the product and the reliance on uncertain advertising rates, uncertain stock rates, uncertain selling prices and uncertain product quality. In order to control and test the stability, the model needs to be defuzzified. The concept of granular differentiability has been applied to defuzzification. Granular differentiability is the new definition of fuzzy derivatives based on the function of horizontal membership. For the first time in this paper, we have used the granular differentiation method in production inventory systems. We analyzed vaguely optimized controls in terms of granular differentiation analytically and numerically.

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References

  • Avagyan V, Esteban-Bravo M, Vidal-Sanz JM (2014) Licensing radical product innovations to speed up the diffusion. Eur J Oper Res 239(2):542–555

    Article  MathSciNet  Google Scholar 

  • Bede B (2013) Mathematics of fuzzy sets and fuzzy logic. In: Kacprzyk J (ed) Studies in fuzziness and soft computing. Springer. ISSN: 1434-9922

  • Chenavaz R (2012) Dynamic pricing, product and process innovation. Eur J Oper Res 222(3):553–557

    Article  MathSciNet  Google Scholar 

  • Chenavaz R et al (2011) Dynamic pricing rule and R&D. Econ Bull 31(3):2229–2236

    Google Scholar 

  • Dong NP, Long HV, Khastan A (2020) Optimal control of a fractional order model for granular SEIR epidemic with uncertainty. Commun Nonlinear Sci Numer Sim 88:105312

    Article  MathSciNet  Google Scholar 

  • Hollier R, Mak K (1983) Inventory replenishment policies for deteriorating items in a declining market. Int J Prod Res 21(6):813–836

    Article  Google Scholar 

  • Hossen MA, Hakim MA, Ahmed SS, Uddin MS (2016) An inventory model with price and time dependent demand with fuzzy valued inventory costs under inflation. Ann Pure Appl Math 11:21–32

    Google Scholar 

  • Islam ME, Ukil SI, Uddin MS (2016) A time dependent inventory model for exponential demand rate with constant production where shelf-life of the product is finite. Open J Appl Sci 6(01):38

    Article  Google Scholar 

  • Khatua D, De A, Kar S, Samanta E, Seikh A A, Guha D (2020) A fuzzy dynamic optimal model for covid-19 epidemic in india based on granular differentiability. Available at SSRN 3621640

  • Khatua D, De A, Maity K, Kar S (2019a) Use of “e” and “g” operators to a fuzzy production inventory control model for substitute items. RAIRO-Oper Res 53(2):473–486

    Article  MathSciNet  Google Scholar 

  • Khatua D, Maity K (2017) Stability of fuzzy dynamical systems based on quasi-level-wise system. J Intell Fuzzy Syst 33(6):3515–3528

    Article  Google Scholar 

  • Khatua D, Maity K, Kar S (2019b) A fuzzy optimal control inventory model of product-process innovation and fuzzy learning effect in finite time horizon. Int J Fuzzy Syst 21(5):1560–1570

    Article  MathSciNet  Google Scholar 

  • Khatua D, Samonto E, Maity K, Kar S (2019c) A single period fuzzy production inventory control model with exponential time and stock dependent fuzzy demand. In: International conference on information technology and applied mathematics, pp 403–413. Springer

  • Lambertini L, Mantovani A (2009) Process and product innovation by a multiproduct monopolist: a dynamic approach. Int J Ind Organ 27(4):508–518

    Article  Google Scholar 

  • Landowski M (2015) Differences between MOORE and RDM interval arithmetic. In: Angelov P, Atanassov KT, Doukovska L, Hadjiski M, Jotsov V, Kacprzyk J, Kasabov N, Sotirov S, Szmidt E, Zadrożny S (eds) Intelligent systems’ 2014. Springer, pp 331–340

  • Landowski M (2016) Comparison of rdm complex interval arithmetic and rectangular complex arithmetic. In: International multi-conference on advanced computer systems. Springer, pp 49–57

  • Landowski M (2017) Usage of RDM interval arithmetic for solving cubic interval equation. In: Advances in fuzzy logic and technology 2017. Springer, pp 382–391

  • Landowski M (2019) Method with horizontal fuzzy numbers for solving real fuzzy linear systems. Soft Comput 23(12):3921–3933

    Article  Google Scholar 

  • Liu B (2007) Uncertainty theory. In: Uncertainty theory. Springer, pp 205–234

  • Liu B (2008) Fuzzy process, hybrid process and uncertain process. J Uncertain Syst 2(1):3–16

    Google Scholar 

  • Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10

    Google Scholar 

  • Long HV, Son NTK, Hoa NV (2017a) Fuzzy fractional partial differential equations in partially ordered metric spaces. Iran J Fuzzy Syst 14(2):107–126

    MathSciNet  MATH  Google Scholar 

  • Long HV, Son NTK, Tam HTT (2017b) The solvability of fuzzy fractional partial differential equations under caputo gh-differentiability. Fuzzy Sets Syst 309:35–63

    Article  MathSciNet  Google Scholar 

  • Mazandarani M, Najariyan M (2014) Differentiability of type-2 fuzzy number-valued functions. Commun Nonlinear Sci Numer Simul 19(3):710–725

    Article  MathSciNet  Google Scholar 

  • Mazandarani M, Najariyan M (2015) A note on “a class of linear differential dynamical systems with fuzzy initial condition”. Fuzzy Sets Syst 265:121–126

    Article  MathSciNet  Google Scholar 

  • Mazandarani M, Pariz N (2018) Sub-optimal control of fuzzy linear dynamical systems under granular differentiability concept. ISA Trans 76:1–17

    Article  Google Scholar 

  • Mazandarani M, Pariz N, Kamyad AV (2018) Granular differentiability of fuzzy-number-valued functions. IEEE Trans Fuzzy Syst 26(1):310–323

    Article  Google Scholar 

  • Mazandarani M, Zhao Y (2018) Fuzzy bang-bang control problem under granular differentiability. J Franklin Inst 355(12):4931–4951

    Article  MathSciNet  Google Scholar 

  • Najariyan M, Farahi MH (2013) Optimal control of fuzzy linear controlled system with fuzzy initial conditions. Iran J Fuzzy Syst 10(3):21–35

    MathSciNet  MATH  Google Scholar 

  • Najariyan M, Farahi MH (2014) A new approach for the optimal fuzzy linear time invariant controlled system with fuzzy coefficients. J Comput Appl Math 259:682–694

    Article  MathSciNet  Google Scholar 

  • Najariyan M, Farahi MH (2015) A new approach for solving a class of fuzzy optimal control systems under generalized hukuhara differentiability. J Franklin Inst 352(5):1836–1849

    Article  MathSciNet  Google Scholar 

  • Najariyan M, Farahi MH, Alavian M (2011) Optimal control of hiv infection by using fuzzy dynamical systems. J Math Comput Sci 2(4):639–649

    Article  Google Scholar 

  • Najariyan M, Zhao Y (2017) Fuzzy fractional quadratic regulator problem under granular fuzzy fractional derivatives. IEEE Trans Fuzzy Syst 26(4):2273–2288

    Article  Google Scholar 

  • Ngo VH (2015) Fuzzy fractional functional integral and differential equations. Fuzzy Sets Syst 280:58–90

    Article  MathSciNet  Google Scholar 

  • Piegat A, Landowski M (2012) Is the conventional interval-arithmetic correct? J Theor Appl Comput Sci 6(2):27–44

    Google Scholar 

  • Piegat A, Landowski M (2013) Two interpretations of multidimensional rdm interval arithmetic: Multiplication and division. Int J Fuzzy Syst 15(4):486–496

    MathSciNet  Google Scholar 

  • Piegat A, Landowski M (2015) Horizontal membership function and examples of its applications. Int J Fuzzy Syst 17(1):22–30

    Article  MathSciNet  Google Scholar 

  • Piegat A, Landowski M (2017) Is fuzzy number the right result of arithmetic operations on fuzzy numbers? In: Advances in fuzzy logic and technology. Springer, pp 181–194

  • Piegat A, Pluciński M (2015) Fuzzy number addition with the application of horizontal membership functions. Sci World J 2015:16. https://doi.org/10.1155/2015/367214

    Article  MATH  Google Scholar 

  • Saha S (2007) Consumer preferences and product and process R&D. Rand J Econ 38(1):250–268

    Article  Google Scholar 

  • Shah NH, Vaghela CR (2017) Economic order quantity for deteriorating items under inflation with time and advertisement dependent demand. Opsearch 54(1):168–180

    Article  MathSciNet  Google Scholar 

  • Son NTK, Long HV, Dong NP (2019) Fuzzy delay differential equations under granular differentiability with applications. Comput Appl Math 38(3):107

    Article  MathSciNet  Google Scholar 

  • Tomaszewska K, Piegat A (2015) Application of the horizontal membership function to the uncertain displacement calculation of a composite massless rod under a tensile load. In: Soft computing in computer and information science. Springer, pp 63–72

  • Van Hoa N (2015) Fuzzy fractional functional differential equations under Caputo gH-differentiability. Commun Nonlinear Sci Numer Simul 22(1–3):1134–1157

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Basic Science and Humanities, Global Institute of Science and Technology, Haldia, West Bengal, India

    D. Khatua

  2. Department of Mathematics, National Institute of Technology, Durgapur, West Bengal, India

    D. Khatua & S. Kar

  3. Department of Mathematics, Mugberia Gangadhar Mahavidyalaya, Bhupati Nagar, West Bengal, India

    K. Maity

Authors
  1. D. Khatua
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  2. K. Maity
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  3. S. Kar
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Correspondence to S. Kar.

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Communicated by V. Loia.

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Khatua, D., Maity, K. & Kar, S. A fuzzy production inventory control model using granular differentiability approach. Soft Comput 25, 2687–2701 (2021). https://doi.org/10.1007/s00500-020-05329-1

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