An economic production quantity model for three levels of production with Weibull distribution deterioration and shortage

Abstract

An EPQ model plays an important role in production and manufacturing units. In this paper, we introduce three levels of economic production inventory model for deterioration items in which three different levels of production are considered and the rate of deterioration follows two parameter Weibull distributions. The total cost of production is dependent on production rate, demand rate, and rate of deteriorative items, and it is possible to switch over the production started at one rate to another rate after certain time, such a situation is desirable in the sense that by starting at a low rate of production, a large quantum of stock of manufacturing items at the initial stage is avoided, leading to reduction in the holding cost. The variation in production level provides a way of attaining consumer satisfaction and earning potential profit. The objective of the paper is to find the optimal solution of production time so that total cost of the whole cycle will be minimized. Finally numerical example and sensitivity analysis on parameters are made to validate the results of the proposed inventory system. Keywords: EPQ, Weibull distribution deterioration, Cycle time, Three levels of production