Fair and profitable even when serving different customer classes: How pricing and lead-time quotation can help

In this paper, we model a production/inventory system serving two classes of customers with a single type of product. Demand from each class depends on the price and the lead-time quoted. One class comprises customers sensitive to delays who are willing to pay higher prices for shorter lead times. Customers of the other class are price sensitive who can tolerate waiting longer for product delivery if they are charged lower prices. By modeling the system as an Mn/M/1 type make-to-stock queue, we propose four fair policies. These fair policies assure that customers are charged lower prices when they are quoted longer lead times and a high proportion of the deliveries is made during the quoted lead times. Two FCFS (first-come, first-served) policies ignore class differences. Two multilevel rationing (MR) policies prioritize the delay-sensitive class over the other. While determining the price and the lead-time, the refined FCFS and MR policies additionally consider the order in which a customer enters the queue. With a numerical study, we explore when the MR policies taking customer differences into consideration are more profitable than the FCFS policies.