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Journal of Environmental Accounting and Management
António Mendes Lopes (editor), Jiazhong Zhang(editor)
António Mendes Lopes (editor)

University of Porto, Portugal

Email: aml@fe.up.pt

Jiazhong Zhang (editor)

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China

Fax: +86 29 82668723 Email: jzzhang@mail.xjtu.edu.cn


Solving Nonlinear Inventory Model for Deteriorating Items using Fractional Differential Method

Journal of Environmental Accounting and Management 10(1) (2022) 31--38 | DOI:10.5890/JEAM.2022.03.004

M.V. Jeyanthi$^1$ , P.S. Sheik Uduman$^1$, Dowlath Fathima$^2$

$^1$ B.S.A. Crescent Institute of Engineering and Technology, India

$^2$ Saudi Electronic University, Saudi Arabia

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Abstract

In this paper, a nonlinear inventory model with demand as a derivative of time is developed for deteriorating items with no shortages are allowed. The model is solved initially by using Differential Transform Method (DTM) and further, the model is modified to Caputo Derivative Fractional Order (CDFO) and solved by Homotopy Perturbation Method with triangular fuzzy initial conditions. The results for both models in terms of non-linearity of DTM and HPM are analyzed and compared numerically.

References

  1. [1]  Arikoglu, A. and Ozkol, I. (2007), Solution of fractional differential equations by using differential transform method, Chaos Solitons and Fractals, 34(5), 1473-1481.
  2. [2]  Abdel-Halim Hassan, I.H.(2004), Differential transformation technique for solving higher-order initial value problems, Appl. Math.Comput., 154, 299-311.
  3. [3]  Caputo, M. (1967), Linear models of dissipation whose Q is almost frequency independent, Part II, J. Roy. Austral.Soc., 13, 529-539.
  4. [4]  Chen, C., and Monahan, G.E. (2010), Environmental safety stock: The impacts of regulatory and voluntary control policies on production planning, inventory control, and environmental performance, European Journal of Operational Research, 207(3), 1280-1292.
  5. [5] Datta, T.K., and Paul, K., (2001), An inventory system with stock-dependent, price-sensitive demand rate, Production Planning and Control, 12, 13-20.
  6. [6] Ghoreishi, M., Weber, G.W., and Mirzazadeh, A. (2015), An inventory model for non-instantaneous deteriorating items with partial backlogging, permissible delay in payments, inflation-and selling price-dependent demand and customer returns, Annals of Operations Research, 226(1), 221-238.
  7. [7] Gokdogan, A., Merdan M., and Yildirim, A. (2012), Adaptive multi-step differential transformation method for solving nonlinear equations, Mathematical and Computer Modeling, 761-769.
  8. [8]  He, J.H. (1999), Homotopy perturbation techniques, Computer Methods in Applied Mechanics and Engineering, 178, 257-262.
  9. [9] Hung, K.C. (2011), An inventory model with generalized type demand, deterioration and backorder rates, European Journal of Operational Research, 208, 239-242.
  10. [10] Khan, Y. and Wu, Q.(2011), Homotopy Perturbation Transform Method for nonlinear equations using He's Polynomials, Computers and Mathematics with Applications, 61, 1963-1967.
  11. [11] Lewis, H. and Gertsakis, J. (2001), Design environment: a global guide to designing greener goods, Greenleaf Publishing, Sheffield.
  12. [12]  Lin, W. (2007), Global existence theory and chaos control of fractional differential equations, Journal of Mathematical Analysis and Applications, 332, 709-726.
  13. [13] Mandal, B., and Pal, A.K. (1998), Order level inventory system with ramp type demand rate for deteriorating items, Journal of Interdisciplinary Mathematics, 1, 49-66.
  14. [14] MKareem, M.F., and Uduman, P.S. (2016), The Numerical Solution of Chua-Nonlinear Tumor Model by Three Different Transform Methods, International Journal of Engineering Studies, ISSN 0975-6469, 2(8), 147-158.
  15. [15] Panda, S., (2010), An EOQ model with stock dependent demand and imperfect quality items, Yugoslav Journal of Operations Research, 20(2), 237-247.
  16. [16] Roy, T. and Chaudhuri, K.S. (2012), An EPLS model for a variable production rate with stock-price sensitive demand and deterioration, Yugoslav Journal of Operations Research, 22(1), 19-30.
  17. [17] Sana, S.S., Goyal, S.K., and Chaudhuri, K.S. (2007), An imperfect production process in a volume flexible inventory model, International Journal of Production Economics, 105, 548-559.
  18. [18]  Sathaye, N., Horvath, A., and Madanat, S. (2010), Unintended impacts of increased truck loads on pavement supply-chain emissions, Transportation Research , Part A 44, 1-5.
  19. [19]  Sheik Uduman, P.S. and Divya, A. (2015), A Review of fuzzy risk analysis model and predator prey model in fuzzy, International Journal Of Applied Engineering Research, 10(42), 30969-30975.
  20. [20] Silver, E.A. and Peterson, R. (1985), Decision Systems for Inventory Management and Production Planning, 2nd Edition. Wiley: New York.
  21. [21] Tapaswini, S. and Chakraverty, S. (2013), Numerical Solution of Fuzzy Arbitrary Order Predator-Prey Equations, International Journal Of AAM, 8(2), 647-672.
  22. [22]  Wahab, M.I.M., Mamun, S.M.H., and Ongkunaruk, P. (2011), EOQ models for a coordinated two-level international supply chain considering imperfect items and environmental impact, International Journal of Production Economics, 134, 151-158.
  23. [23] Yadav, D., Singh, S.R. and Kumari, R.(2012), Inventory model of deteriorating items with two warehouse and stock dependent demand using genetic algorithm in fuzzy environment, Yugoslav Journal of Operations Research, 22(1), 51-78.
  24. [24] Yadav, D., Singh, S.R., and Kumari, R. (2016), Inventory model of deteriorating items with two warehouse and stock dependent demand using genetic algorithm in fuzzy environment, International journal of pure and applied Mathematics, 109(5), 75-83.
  25. [25] Yang, H.L., Teng, J.T. and Chern, M.S. (2010), An inventory model under inflation for deteriorating items with stock-dependent consumption rate and partial backlogging shortages, International Journal of Production Economics, 123, 8-19.
  26. [26] Zadeh, L.A. (1965), Fuzzy Sets, Information and computation, 8(3), 338-353.
  27. [27]  Zhou, J.K. (1986), Differential Transformation and Its Applications for Electrical Circuits (in Chinese), Huazhong University Press, Wuhan, China.