Value of Simple Menus with Price and Delay Sensitive Customers

We consider a service firm that caters to price and delay sensitive customers by offering a menu of service grades. Each service grade is associated with posted price and delay. Noting that an optimal menu size could be quite large when there are many classes, we study whether the firm can offer a simplified menu with a few service grades without significant revenue loss. There is a well developed stream of work that studies optimal menu design for price and delay sensitive customers. Most results show that the number of grades equal the number of classes. However, in practice, we observe a handful number of grades. This raises the question of how much is the optimality gap when firm employs a simple menu relative to the optimal one. Our analysis utilizes a large system approximations where we assume that the firm has ample capacity to serve the entire market. We set up an optimization model and make use of Taylor series and asymptotic arguments to obtain the solution. We show that, under a simplified menu, the firm could lose a significant fraction of its revenue in the worst case scenario. This happens when there is significant heterogeneity between the customer classes. In contrast, noting that customer heterogeneity may typically be less extreme, we show that the firm can in fact provide a simplified menu while providing a guarantee on worst case revenue that can be obtained as a fraction of the optimal. We characterize the worst case optimal menu and provide asymptotic bounds to the worst case revenue loss as the number of customer types grow without bound. Characterization of the firm's worst case revenue loss in terms of a measure of heterogeneity can be used to guide decision making when offering a simplified menu of service grades