Assortment optimization and pricing in a queue

Abstract

The service times at the counter or kiosk of a fast-food/quick-service restaurant are dominated by the time the customers take in choosing their items. Sellers hence trade off the potentially higher per-customer revenue from offering a large number of options with the delay that this may cause to the other customers while a customer is making their choice, and the subsequent risk of losing some customers because of the long queues. In light of this, a recent practice at many quick-service restaurants is to introduce a well-designed spotlight menu (a subset of the full menu) that can both improve per-customer revenue and shorten customers' decision time. In this paper, we study the spotlight assortment optimization problem of deciding the size and composition of the spotlight menu items, which balance expected per-customer revenue and service times, to maximize the overall revenue rate. We obtain structural properties of the impact of demand arrival rate and system capacity on the optimal spotlight assortment, develop Knapsack formulation under throughput approximation, and characterize when simple assortments such as revenue-or attractiveness-ordered ones are optimal. Furthermore, we study the joint assortment and pricing problem and show that the optimal solution prescribes two common profit levels for products in and out of the spotlight menu, respectively, and spotlight and non-spotlight products have sufficiently different intrinsic values and costs. Our results provide insights into the design of spotlight assortments and prices when service rate plays a role.