Two phases inventory model with variable cycle length under discount policy

¹ Department of Mathematics, The University of Burdwan, 713104 Burdwan, India
² Department of Mathematics, Jalpaiguri Government Engineering College, 735102 Jalpaiguri, India

^* Corresponding author: brojo_math@yahoo.co.in

Received: 16 September 2017
Accepted: 27 September 2018

Abstract

This study deals with single stage inventory model where two phases are involved in an inventory cycle. In the first phase of the cycle, demand depends on both of inventory level and selling price while in the second, the demand depends on price only. Discount policy in selling price is offered in the second phase and inventory level at the end of the cycle is taken to be zero. Two models have been constructed on infinite time horizon. In the first model the demand rate is taken as the sum of two linear functions of inventory level and selling price and, in the second model, it is taken as a product of two power functions of inventory level and selling price. Our objective is to maximize average profit by considering ordering lot size and selling price as decision variables. Numerical examples of each model have been provided. The optimality criteria for the solutions are also checked by both graphically and numerically. Sensitivity analysis for different parameters in both models has been discussed in details to check the feasibility of the models.