Optimal profit in two-level trade credit EOQ model with default risk and reminder cost under finite time horizon having time-dependent demand and deterioration

¹ Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, West Bengal, India
² Department of Mathematics, National Institute of Technology, Durgapur 713209, India
³ Department of Applied Mathematics, Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, West Bengal, India

^* Corresponding author: gtkr1998@gmail.com

Received: 9 August 2023
Accepted: 23 June 2024

Abstract

Trade credit is a type of promotional activity that generally increases demand and revenue but also invites default risk due to dishonest customers. Due to default risk, revenue is lost, and to overcome this, an arrangement is made to remind the defaulters. A retailer dealing with a perishable item wants to exhaust the stock quickly after a certain deterioration level. Demand and deterioration of the products are normally dynamic. The business period of seasonal products is uncertain. Considering these facts, we formulate and analyze a two-level trade credit inventory model, where the wholesaler and retailer give credit periods to their corresponding downstream customers. After a certain level of deterioration, the retailer increases the credit period for the customers for early stock exhaustion, and to reduce default risk, a reminder cost is introduced. These activities increase the profit. The mathematical models under different circumstances are formulated for different time horizons. Some existing results are deduced. The models are numerically solved using a parametric study and the Generalised Reduced Gradient method through LINGO 19.0 software. Some lemmas and theorems are deduced to establish the analytical outcomes. Trade-offs between the number of the business cycle, trade credit, and reminder cost against optimum profit are separately demonstrated. The results with and without reminder cost are compared, and it is shown that the model with reminder cost fetches more profit. Profit under different uncertain environments are evaluated, and they differ marginally. Some beneficial impacts are discussed.