Inventory Control by Multiple Service Levels under Unreliable Supplying Condition

We consider an inventory system where there is random demand from customers as well as unreliable supplying capacity from supplier. In many real-world cases, supplier might fail to satisfy the amount of order from retailers or producers so that only partial proportion of order is satisfied or even fail to deliver all of the order. Moreover, recently a concern regarding unreliable supplying capacity has been increasing since the globalization makes the retailer or producer face the extended supply network with complicated and risky supplying capacity. Also, we consider two classified customers, of which one is willing to pay extra charge for expedited delivery service but the other is not reluctant to delay the delivery without any extra charge. We show that there exists an optimal threshold for inventory and price for each service level in the following sense: if the inventory level is less than the predetermined threshold, then the retailer or producer needs to order up to the threshold level and offer threshold price corresponding to service level. Otherwise, the retailer does not need to order. The risk of stockout due to unreliable supplying capacity can be mitigated by the dynamic pricing and inventory control with multiple service levels.