In response to customer specific service time guarantee requirements, service providers can offer differentiated services. Although response time agreements offer more flexibility, most of the theoretical models for customer differentiation are based on fill rates, due to the difficulty of calculating the response time distribution in the presence of priorities. In this paper we focus on the (S−1,S,K) model with two customer classes, in which low priority customers are served only if the inventory level is above K. For this model, we derive the exact distribution of the response time (within lead time) for the lower priority class and provide a new closed-form approximation for the fill rate for high priority customers. Via numerical experiments, we show that the fill rate approximation performs comparable to the best approximations in the literature, while its implementation requires only elementary operations.

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Keywords Inventory, Queueing, Response time, Service differentiation
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Journal European Journal of Operational Research
Gabor, A.F, van Vianen, L.A, Yang, G, & Axsäter, S. (2018). A base-stock inventory model with service differentiation and response time guarantees. European Journal of Operational Research. doi:10.1016/j.ejor.2018.02.039