Stochastic production scheduling model with generalised Pareto rate of production and Weibull decay

Abstract

This paper addresses the development and analysis of an EPQ model with random production and deterioration. Here it is assumed that the life time of the commodity is random and follows a Weibull distribution. It is also further assumed that the production process is random and the number of units produced per a unit time follows a generalised Pareto distribution. The generalised Pareto distribution is capable of including different types of production rates. Assuming that the shortages are allowed and fully backlogged, the inventory level at any time 't' is derived. With suitable cost considerations the total production cost is obtained and minimised with respect to the production uptime and downtime. Through sensitivity analysis, it is observed that the production distribution parameters and deterioration distribution parameters have significant influence on optimal production schedules and total production cost. This model is extended to the case of without shortages.