Optimal trade credit and replenishment policies for non-instantaneous deteriorating items

¹ Department of Operational Research, Faculty of Mathematical Sciences, New Academic Block, University of Delhi, 110007 Delhi, India
² Department of Mathematics, Shyam Lal College, University of Delhi, 110032 Delhi, India
³ The Logistics Institute – Asia Pacific, National University of Singapore, 21 Heng Mui Keng Terrace, 119613 Singapore, Singapore
⁴ Department of Industrial & Systems Engineering, Building: Engineering II, Room 3-10, University of Pretoria, 0002 Pretoria, South Africa

^* Corresponding author: sunil.tiwari047@gmail.com

Received: 14 August 2018
Accepted: 7 November 2019

Abstract

The present study presents a fuzzy inventory model for non-instantaneous deteriorating items under conditions of permissible delay in payments. In the current paper, we incorporate the condition in which, the supplier accepts the partial payment at the end of the credit period and the reaming amount after that period under the term and condition. Here, the demand rate is a function of the selling price. Also, it is assumed that shortages are allowed and are fully backlogged. The present paper also considers that the interest earned (I_E) on the fixed deposit amount, i.e., revenue generated by fulfilling the shortage, balance amount, after settling the account is higher than that of usual interest rate (I_e). Hence, the objective of this study is to determine the retailer’s optimal policies that maximize the total profit. Also, some theoretical results are obtained, which shows that the optimal solution not only exists, it is unique also. The impact of the new proposed credit policy is investigated on the optimality of the solution for the non-instantaneous deteriorating products. The validation of the proposed model and its solution method is demonstrated through the numerical example. The results indicate that the inventory model, along with the solution method, provides a powerful tool to the retail managers under real-world situations. Results demonstrate that it is essential for the managers to consider the inclusion of new proposed credit policy significantly increases the net annual profit.