Authors:
Rukhsar Khatun,Goutam Chakraborty,Md Sadikur Rahman,DOI NO:
https://doi.org/10.26782/jmcms.2023.12.00002Keywords:
Interval order relation,Generalised AM-GM inequality,c-L minimizer,Interval EPQ,c-L optimal policy,Abstract
The objective of this work is to study the optimal policy of the classical economic production quantity (EPQ) model under interval uncertainty using interval inequality. To serve this purpose existing arithmetic mean-geometric mean (AM-GM) inequality is extended for interval numbers using c-L interval order relation. Then, using the said AM-GM interval inequality, the optimal policy of the classical EPQ model in the interval environment is developed. Thereafter, the optimality policy of the classical EPQ model in a crisp environment is obtained as a special case of that of the interval environment. Finally, all the optimality results are illustrated with the help of some numerical examples.Refference:
I. Bhunia, A. K., & Samanta, S. S., : ‘A study of interval metric and its application in multi-objective optimization with interval objectives.’ Computers & Industrial Engineering, 74, (2014), 169-178. 10.1016/j.cie.2014.05.014
II. Cardenas-Barron L. E., : ‘The economic production quantity (EPQ) with shortages derived algebraically.’ International Journal of Production Economics, 70, (2001), 289-292. 10.1016/S0925-5273(00)00068-2
III. Das, S., Rahman, M. S., Shaikh, A. A., Bhunia, A. K., & Ahmadian, A., : ‘Theoretical developments and application of variational principle in a production inventory problem with interval uncertainty.’ International Journal of Systems Science: Operations & Logistics, (2022), 1-20. 10.1080/23302674.2022.2052377
IV. Gani, A. N., Kumar, C. A., & Rafi, U. M., : ‘The Arithmetic Geometric Mean (AGM) inequality approach to compute EOQ/EPQ under Fuzzy Environment.’ International Journal of Pure and Applied Mathematics, 118(6), (2018), 361-370.
V. Grubbstrom. R. W., : ‘Material requirements planning and manufacturing resource planning.’ in: Warner. M (Ed.) International Encyclopaedia of Business and Management, Vol.4 Routledge, London, (1996), 3400-3420.
VI. Grubbstrom. R. W. & Erdem. A., : ‘The EOQ with back logging derived without derivatives.’ International Journal of Production Economics, 59, (1999), 529-530. 10.1016/S0925-5273(98)00015-2
VII. Manna, A. K., Rahman, M. S., Shaikh, A. A., Bhunia, A. K., & Konstantaras, I., : ‘Modeling of a carbon emitted production inventory system with interval uncertainty via meta-heuristic algorithms.’ Applied Mathematical Modelling, 106, (2022), 343-368. 10.1016/j.apm.2022.02.003
VIII. Moore, R. E., Kearfott, R. B., & Cloud, M. J., : ‘Introduction to interval analysis.’ Society for Industrial and Applied Mathematics.
IX. Rahman, M. S., Shaikh, A. A. & Bhunia, A. K., : ‘On the space of Type-2 interval with limit, continuity and differentiability of Type-2 interval-valued functions.’ (2019), arXiv preprint arXiv:1907.00644.
X. Rahman, M. S., Duary, A., Shaikh, A. A., & Bhunia, A. K., : ‘An application of parametric approach for interval differential equation in inventory model for deteriorating items with selling-price-dependent demand.’ Neural Computing and Applications, 32, (2020), 14069-14085.
XI. Rahman, M. S., Shaikh, A. A., & Bhunia, A. K., : ‘On Type-2 interval with interval mathematics and order relations: its applications in inventory control.’ International Journal of Systems Science: Operations & Logistics, 8(3), (2021), 283-295. 10.1080/23302674.2020.1754499
XII. Rahman, M. S., & Khatun, R., : ‘Generalised Arithmetic Mean-Geometric Mean Inequality And Its Application To Find The Optimal Policy Of The Classical EOQ Model Under Interval Uncertainty.’ Applied Mathematics E-Notes, 23, (2023), 90-99.
XIII. Stefanini, L., & Bede, B., : ‘Generalized Hukuhara differentiability of interval-valued functions and interval differential equations.’ Nonlinear Analysis: Theory, Methods & Applications, 71(3-4), (2009), 1311-1328. 10.1016/j.na.2008.12.005