Performance improvement of a service system via stocking perishable preliminary services

The typical fast food service system can be conceptualized as a queueing system of customers combined with an inventory of perishable products. A potentially effective means of improving the efficiency of such systems is to simultaneously apply time management policies and inventory management techniques. We propose such an approach, based on a combined queueing and inventory model, in which each customer's service consists of two independent stages. The first stage is generic and can be performed even in the absence of customers, whereas the second requires the customer to be present. When the system is empty of customers, the server produces an inventory of first-stage services (‘preliminary services’; PSs) and subsequently uses it to reduce future customers' overall service and sojourn times. Inventoried PSs deteriorate while in storage, creating spoilage costs. We formulate and analyze this queueing-inventory system and derive its steady-state probabilities using matrix geometric methods. We show that the system's stability is unaffected by the production rate of PSs. We subsequently carry out an economic analysis to determine the optimal PS capacity and optimal level of investment in preservation technologies.