Economic lot-sizing of three warehouses EOQ type model: AM-GM inequality-based optimization technique

Year 2025, Volume: 8 Issue: 1, 65 - 75, 03.07.2025

Md Sadikur Rahman

https://doi.org/10.53508/ijiam.1610875

Abstract

This paper focuses on the optimal policy of a classical three warehouses inventory problem which is
modelled under some assumptions like the Harris-Wilson model. In this model, among three
warehouses, one is own warehouse and remaining two are rented. Now, the main purpose is to minimize
the system's average cost and find out economic order quantity and cycle length using arithmetic mean-
geometric mean (AM-GM) inequality. Finally, all the findings illustrating the system's optimality
conditions are validated by numerical examples

Keywords

Three warehouse , Optimality , Arithmetic mean- Geometric mean

Ethical Statement

NA

Supporting Institution

No

References

• Asoke Kumar Bhunia and Manoranjan Maiti. A two warehouse inventory model for deteriorating items with a linear trend in demand and shortages. Journal of the Operational Research Society, 49(3):287–292, 1998.
• Yong-Wu Zhou. A multi-warehouse inventory model for items with time-varying demand and shortages. Computers & Operations Research, 30(14):2115–2134, 2003.
• Yong-Wu Zhou and Shan-Lin Yang. A two-warehouse inventory model for items with stock-level-dependent demand rate. International Journal of Production Economics, 95(2):215–228, 2005.
• Yanlai Liang and Fangming Zhou. A two-warehouse inventory model for deteriorating items under conditionally permissible delay in payment. Applied Mathematical Modelling, 35(5):2221–2231, 2011.
• Asoke Kumar Bhunia, Chandra K Jaggi, Anuj Sharma, and Ritu Sharma. A two-warehouse inventory model for deteriorating items under permissible delay in payment with partial backlogging. Applied Mathematics and Computation, 232:1125 1137, 2014.
• Seyed Ashkan Hoseini Shekarabi, Abolfazl Gharaei, and Mostafa Karimi. Modelling and optimal lot-sizing of integrated multi-level multi-wholesaler supply chains under the shortage and limited warehouse space: generalised outer approximation. International Journal of Systems Science: Operations & Logistics, 6(3):237–257, 2019.
• Robert W Grubbström and Asli Erdem. The eoq with backlogging derived without derivatives. International Journal of Production Economics, 59(1-3):529–530, 1999.
• Leopoldo Eduardo Cárdenas-Barrón. The economic production quantity (epq) with shortage derived algebraically. International Journal of Production Economics, 70(3):289–292, 2001.
• Tsu-Pang Hsieh and Chung-Yuan Dye. A note on “the epq with partial backordering and phase-dependent backordering rate”. Omega, 40(1):131–133, 2012.
• Md Sadikur Rahman and Rukhsar Khatun. 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, 23:90–99, 2023.