Effect of price-sensitive demand and default risk on optimal credit period and cycle time for a deteriorating inventory model

¹ Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University, Midnapore 721102, West Bengal, India
² Department of Mathematics and Statistics, Kingston School of Management and Science Barasat, Kolkata 700126, West Bengal, India
³ Faculty of Engineering Management Poznan University of Technology, ul. Jacka Rychlewskiego 2, 60-965 Poznan, Poland
⁴ Institute of Applied Mathematics, Middle East Technical University, 06800 Ankara, Turkey
⁵ Department of Industrial Engineering, Kharazmi University, Tehran, Iran

^* Corresponding author: sankroy2006@gmail.com

Received: 31 July 2020
Accepted: 23 September 2020

Abstract

In this paper, we formulate and solve an economic order quantity model with default risk. Our main purpose is to investigate retailer’s optimal replenishment time and credit period for deteriorating items under selling price-dependent demand while maximizing profit per unit time. Here, shortages are allowed and items are partially backlogged for interested customers. We show that optimal replenishment time and credit period not only exist but they are also unique. We solve the proposed problem analytically. An algorithm is presented to derive the optimal solution of the model. The mathematical model is evaluated by numerical examples. We use Mathematica to obtain a global maximum solution to the optimal cycle time and the optimal credit period for the proposed model. A sensitivity analysis with respect to major parameters is performed in order to examine the stability of our model. At the end of the paper, conclusions are drawn and an outlook of possible future directions is depicted.