An EPQ model with stock and selling price dependent demand and variable production rate in interval environment

Abstract

The motto of this paper is to develop a production inventory model in real life situation. In reality, demand of a certain product becomes highly effected by on-hand stock level in stores and the selling price of the product. In the proposed model, demand of the product is dependent on these two vital deceive factors. In real life production systems, always there are some defective products which requires reworking in order to make them useful. The possibility of producing some defective items in regular production process and their reworking has been taken into account in the model. In case of inventories of highly demandable products, it is observed that production rate is proportional to demand. The situation also arises in case of launching a new product or in a multi-stage production system. In this model, production rate is a variable and it varies with the demand rate. Shortages are allowed and it is backlogged fully. Based on these assumptions, several researchers worked on but they considered that the associated inventory cost parameters are fixed real numbers. However, these are not fixed in reality and may vary time to time depending upon some scenario. Main objective of the paper is to develop a production inventory model under those assumptions considering various cost parameters as interval numbers. As a result the corresponding optimization problem is also interval valued. Quantum behaved particle swarm optimization technique has been applied to find the maximum profit in a single cycle. Numerical example and sensitivity analysis are given to illustrate the proposed inventory model.