A Stochastic Production Inventory Model for Deteriorating Items with Bayesian Estimation

Abstract

A stochastic inventory periodic review production system with inter demand time as exponential distribution is considered in this paper. The model is developed on the basis of constant production rate for deteriorating items. The rate of deterioration follows two parameters Weibull distribution. The shape and scale parameters of Weibull distribution are estimated through MLE. Shortages are not allowed and the unit production cost is inversely proportional to the demand rate. The model contains the exponential parameter which is unknown and is estimated through MLE and Baye’s under a squared error loss function.  The conjugate Gamma prior is used as the prior distribution of exponential distribution. Finally, a numerical MCMC simulation is used to compare the estimators obtained with Expected risk and are shown graphically. The objective of the paper is to develop an optimum policy that minimizes the total average cost by using the above estimates of the parameter. The sensitivity analysis is also carried out for the model with percentage change in the parameters.