Optimal replenishment and credit policy in an inventory model for deteriorating items under two-levels of trade credit policy when demand depends on both time and credit period involving default risk

Department of Mathematics (UG & PG), Dum Dum Motijheel College, 1, Motijheel Avenue, Kolkata 700074, West Bengal, India

^* Corresponding author: gourmahata@yahoo.co.in; gcmahata@yahoo.in

Received: 17 July 2017
Accepted: 29 April 2018

Abstract

In this paper, we examine an optimal dynamic decision-making problem for a retailer’s inventory system of deteriorating items under two-level trade credit financing where the supplier, as well as the retailer, offers trade credit to the subsequent downstream member, the demand rate of which varies simultaneously with time and the length of credit period that is offered to the customers. The deterioration rate is non-decreasing over time. In addition, the risk of default increases with the credit period length. A generalized model is presented to determine the optimal trade credit and replenishment strategies that maximize the retailer’s annual total profit. We then demonstrate that the retailer’s optimal credit period and replenishment cycle time not only exist but also are unique. Thus, the search of the global optimal solution reduces to finding a local solution. Finally, we run several numerical examples to illustrate the problem and gain managerial insights.