In a continuous manufacturing environment where production and consumption occur simultaneously, one of the biggest challenges is the efficient management of production and inventory system. In order to manage the integrated production inventory system economically it is necessary to identify the optimal production time and the optimal production reorder point that either maximize the profit or minimize the cost. In addition, during production the process has to go through some natural phenomena like random breakdown of machine, deterioration of product over time, uncertainty in repair time that eventually create the possibility of shortage. In this situation, efficient management of inventory & production is crucial. This paper addresses the situation where a perishable (deteriorated) product is manufactured and consumed simultaneously, the demand of this product is stable over the time, machine that produce the product also face random failure and the time to repair this machine is also uncertain. In order to describe this scenario more appropriately, the continuously reviewed Economic Production Quantity (EPQ) model is considered in this research work. The main goal is to identify the optimal production uptime and the production reorder point that ultimately minimize the expected value of total cost consisting of machine setup, deterioration, inventory holding, shortage and corrective maintenance cost.

This paper derives a production inventory model over infinite planning horizon with flexible but unreliable manufacturing process and the stochastic repair time. Demand is stock dependent and during the period of sale it depends on reduction on selling price. Production rate is a function of demand and reliability of the production equipment is assumed to be exponentially decreasing function of time. Repair time is estimated using uniform probability density function. The objective of the study is to determine the optimal policy for production system, which maximizes the total profit subject to some constraints under consideration. The results are discussed with a numerical example to illustrate the theory.