Title: An EOQ model for seasonal product with ramp-type time and stock dependent demand, shortage and partial backorder

Authors: Prokash Mondal; Pritha Das; Sudhansu Khanra

Addresses: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India ' Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India ' Department of Mathematics, Tamralipta Mahavidyalaya, Purba Medinipur, West Bengal, India

Abstract: This study analyses an EOQ model for a seasonal product with ramp-type time and stock dependent demand function under permissible shortages. In the model, deterioration of seasonal products is considered with partial backlog, variable backlog rate, and backlog rate as a function of time until the next replenishment partial backlogging and the backlogging rate is variable and is dependent on waiting time for the next replenishment. Using the optimal control approach, we analytically derive the optimal total average cost and inventory strategy for the retailer over a finite time horizon. We analytically determine the best total average cost and inventory strategy for the merchant over a limited time horizon using the optimal control approach. A numerical application and sensitivity analysis demonstrate practical applicability.

Keywords: inventory; time-stock dependent demand; backlogging; deterioration.

DOI: 10.1504/IJMOR.2024.138057

International Journal of Mathematics in Operational Research, 2024 Vol.27 No.3, pp.393 - 413

Received: 20 Jan 2023
Accepted: 28 Jan 2023
Published online: 18 Apr 2024 *

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