[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Discontinuity, Nonlinearity and Complexity
ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Valuation of Memory Effect of Fuzzy EOQ Model with Constant Demand Rate

Discontinuity, Nonlinearity, and Complexity 13(3) (2024) 437--453 | DOI:10.5890/DNC.2024.09.004

Rituparna Pakhira$^1$, Bapin Mondal$^2$, Uttam Ghosh$^2$, Vishnu Narayan Mishra$^3$

$^1$ Academy of Technology, Adisaptagram, Hooghly, West Bengal, India

$^2$ Department of Applied Mathematics, University of Calcutta, Kolkata-700009, India

$^3$ Department of Applied Mathematics Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh, India

Download Full Text PDF

 

Abstract

It is well-known to everyone that the system is very much disturbed by the past experience effect so past experiences should be incorporated into the system. For a rapidly changing market, the cost parameters of the inventory system are highly uncertain. Due to the above reasons, in this paper, we want to develop an EOQ model with a constant demand rate for non - deteriorating items where shortages are not allowed with Caputo fractional order derivative under a fuzzy environment. Here, we have used the concept ``fractional order is an index of memory''. Two types of memory indexes have been established. Memory effect has been observed by the step of long memory, short memory, and memoryless stages. The fractional order inventory model has been defuzzified using the graded mean integration method and signed distance method. Our numerical analysis clears us that profit is maximum for the presence of both memory indexes. In the long memory effect, inventory level changes roughly but this type of change happens, in reality, i.e., once increases then decrease again increases. From the graphical presentations, it can be suggested that there is a critical value of the ordering interval where long memory affected the total average cost and short memory affected total average cost becomes equal in both defuzzification techniques graded mean integration method, signed distance method.

References

  1. [1]  Zadeh, L.A. (1965), Fuzzy sets, Information and Control, 8(3), 338-353.
  2. [2]  Saeedian, M., Khalighi, M., Azimi-Tafreshi, N., Jafari, G.R., and Ausloos, M. (2017), Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model, Physical Review E, 95(2), 022409.
  3. [3]  Du, M., Wang, Z., and Hu, H. (2013), Measuring memory with the order of fractional derivative, Scientific Reports, 3(1), 1-3.
  4. [4]  Tarasova, V.V. and Tarasov, V.E. (2016), Memory effects in hereditary Keynesian model, Problems of Modern Science and Education, 80, 55-60.
  5. [5]  Tarasova, V.V. and Tarasov, V.E. (2016), A generalization of the concepts of the accelerator and multiplier to take into account of memory effects in macroeconomics, Journal of Economics Education and Entrepreneurship, 10, 1121-1129.
  6. [6]  Tarasova, V.V. and Tarasov, V.E. (2016), Marginal utility for economic processes with memory, Almanac of Modern Science and Education, 7(109), 108-113.
  7. [7]  Tarasova, V.V. and Tarasov, V.E. (2016), Fractional dynamics of natural growth and memory effect in economics, European Research, 12(23), 30-37.
  8. [8]  Tarasov, V.E. and Tarasova, V.V. (2016), Long and short memory in economics: fractional-order difference and differentiation, International Journal of Management and Social Sciences, 5(2), 327-334.
  9. [9]  Tarasova, V.V. and Tarasov, V.E. (2017), Economic interpretation of fractional derivatives, Progress in Fractional Differential and Applications, 3(1), 1-6.
  10. [10]  Das, A.K. and Roy, T.K. (2017), Fractional order generalized EPQ model, International Journal of Applied and Computational Mathematics, 12(2), 525-536.
  11. [11]  Das, A.K. and Roy, T.K. (2015), Fractional order EOQ model with linear trend of time-dependent demand, International Journal of Intelligent Systems and Applications, 7(3), 44-53.
  12. [12]  Pakhira, R., Sarkar, S., and Ghosh, U. (2020), Study of memory effect in an inventory model for deteriorating items with partial backlogging, Computers $\&$ Industrial Engineering, 148, 106705.
  13. [13]  Pakhira, R., Ghosh, U., Sarkar, S., and Mishra, V.N. (2019), Study of memory effect in an Economic Order Quantity model for completely backlogged demand during shortage, Progress in Fractional Differentiation and Applications, 7, 1-14.
  14. [14]  Pakhira, R., Ghosh, U., and Sarkar, S. (2019), Study of memory effect in a fuzzy EOQ model with no shortage, International Journal of Intelligent Systems and Applications, 10(11), 58.
  15. [15]  Pakhira, R., Ghosh, U. and Sarkar, S. (2019), Study of memory effect in an inventory model with price dependent demand, Journal of Applied Economic Sciences, 14(2), 64.
  16. [16]  Rahaman, M., Mondal, S.P., Shaikh, A.A., Pramanik, P., Roy, S., Maiti, M.K., Mondal, R., and De, D. (2020), Artificial bee colony optimization-inspired synergetic study of fractional-order economic production quantity model, Soft Computing, 24(20), 15341-15359.
  17. [17]  Rahaman, M., Mondal, S.P., Shaikh, A.A., Ahmadian, A., Senu, N., and Salahshour, S. (2020), Arbitrary-order economic production quantity model with and without deterioration: generalized point of view, Advances in Difference Equations, 2020(1), 1-30.
  18. [18]  Mishra, L.N. and Sen, M. (2016), On the concept of existence and local attractivity of solutions for some quadratic Volterra integral equation of fractional order, Applied Mathematics and Computation, 285, 174-183.
  19. [19]  Sharma, M.K, Dhiman, N., Mishra, V.N., Mishra, L.N., Dhaka, A., and Koundal, D. (2022), Post-symptomatic detection of COVID-2019 grade based mediative fuzzy projection, Computers and Electrical Engineering, 101, 108028.
  20. [20]  Pathak, V.K. and Mishra, L.N. (2022), Application of fixed point theorem to solvability for non-linear fractional hadamard functional integral equations, Mathematics, Mathematics, 10(14), 2400.
  21. [21]  Mishra, L.N., Pathak, V.K., and Baleanu, D. (2022), Approximation of solutions for nonlinear functional integral equations, AIMS Mathematics, 7(9), 17486–17506.
  22. [22]  Mishra, L.N. (2017), On Existence and Behavior of Solutions to some Nonlinear integral equations with Applications, Ph.D. Thesis, National Institute of Technology, Silchar 788 010, India.
  23. [23]  De, P.K. and Rawat, A. (2011), A fuzzy inventory model without shortages using triangular fuzzy number, Fuzzy information and Engineering, 3(1), 59-68.
  24. [24]  Jaggi, C.K., Pareek, S., Sharma, A., and Nidhi, A. (2012), Fuzzy inventory model for deteriorating items with time-varying demand and shortages, American Journal of Operational Research, 2(6), 81-92.
  25. [25]  Saha, S. and Chakrabarti, T. (2017), A Fuzzy inventory model for deteriorating items with linear price dependent demand in a supply chain, International Journal of Fuzzy Mathematical Archive, 13(1), 59-67.
  26. [26]  Vijai Stanly, S. and Uthayakumar, R. (2015), Inventory model for deteriorating items involving fuzzy with shortages and exponential demand, International Journal of Supply and Operations Management, 2(3), 888-904.
  27. [27]  Harris, F.W. (1915), Operations and cost, A. W. Shaw Company, Chicago, 48-54,
  28. [28]  WilsonR, H. (1934), A Scientific Routine for Stock Control, Harvard Business Review, 13(1), 116-128.
  29. [29]  Miller, K.S. and Ross, B. (1993), An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley.
  30. [30]  Podlubny, I. (1999), Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 198.
  31. [31]  Caputo, M. (1967), Linear models of dissipation whose Q is almost frequency independent—II. Geophysical Journal International, 13(5), 529-539.
  32. [32]  Singh, A., Shukla, A., Vijayakumar, V., and Udhayakumar, R. (2021), Asymptotic stability of fractional order $(1, 2]$ stochastic delay differential equations in Banach spaces, Chaos, Solitons $\&$ Fractals, 150, 111095.
  33. [33]  Dineshkumar, C., Sooppy Nisar, K., Udhayakumar, R., and Vijayakumar, V. (2022), A discussion on approximate controllability of Sobolev‐type Hilfer neutral fractional stochastic differential inclusions, Asian Journal of Control, 24(5), 2378-2394.
  34. [34]  Mohan Raja, M. and Vijayakumar, V. (2022), New results concerning to approximate controllability of fractional integro‐differential evolution equations of order $1< r< 2$, Numerical Methods for Partial Differential Equations, 38(3), 509-524.
  35. [35]  Mohan Raja, M., Vijayakumar, V., Udhayakumar, R., and Nisar, K.S. (2020), Results on existence and controllability results for fractional evolution inclusions of order $1< r< 2$ with Clarke's subdifferential type, Numerical Methods for Partial Differential Equations, 40(1), e22691.
  36. [36]  Dineshkumar, C., Udhayakumar, R., Vijayakumar, V., Shukla, A. and Nisar, K.S. (2021), A note on approximate controllability for nonlocal fractional evolution stochastic integrodifferential inclusions of order $r\in(1, 2)$ with delay, Chaos, Solitons $\&$ Fractals, 153, 111565.

Copyright © 2011-2024 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates