Fuzzy Random Periodic Review Mixture Inventory Model With Shortage Dependent Backorder Rate

1. Introduction

It is intuitively known that any business should be reviewed periodically for the purpose of monitoring and controlling it so that suitable measures can be taken in a timely manner for its smooth and efficient running. In this context periodic review inventory system is a suitable mathematical model. In this review system, the inventory level is examined periodically at equal intervals of time and then an order is placed so that it brings the inventory up to a target level (Hadley, 1963). Now, in an inventory system, when an item is out of stock then shortages occur. In real life situation, in case of shortage, some customers may wait for their orders (backorder) and some may refuse their orders (lost sales). Therefore in reality, shortage leads to a mixture of backorders and lost sales. In this regard, Montgomery et al. (1973) introduced inventory model with mixture of backorders and lost sales. Further it is observed that, an increase in shortage results in a decrease in backorder rate incurred (Ouyang and Chuang, 2001). This makes intuitive since increase in shortage may lead to more customers being unwilling to wait for their orders to arrive and may orders elsewhere. Also as observed in Ouyang and Chuang (2001) and Lee (2005), as shortage occur, the length of the lead-time increases, thereby incurring more shortages and eventually leading to a smaller backorder rate.