Improving efficiency in service systems by performing and storing “preliminary services”

We propose a novel approach to improve efficiency in service systems. The idea is to utilize the server's idle time to perform and store “preliminary services” for customers who will arrive in the future. Such a model is relevant to settings in which service consists of multiple consecutive tasks, some of which are generic and needed by all customers (and thus can be performed even in their absence), while other require the customer's presence. To show the model's benefits, we formulate a two-dimensional single-server queueing-inventory system for which we derive closed-form expressions for the system's steady-state probabilities, as well as for its performance measures. Assuming linear costs for customers waiting in line and for stored preliminary services, a cost analysis determines the optimal maximal number of stored preliminary services in the system. Numerical examples illustrated with graphs demonstrate the advantages of our approach, in terms of cost savings, as compared with the classical M/M/1 model.