Designing Efficient Omni-Channel Services

Motivated by the popularity of mobile-order-and-pay applications that are especially prevalent in coffee shops, we explore how to design efficient omni-channel service systems — where customers have the option to employ mobile applications for self-ordering — with respect to sojourn times, throughput, and/or social welfare. Our models are two-stage queues with two customer classes: walk-ins require service at both stages, while mobile customers skip the first stage by self-ordering. We identify Pareto efficient prioritization policies, highlighting trade-offs between each class's mean sojourn times. We allow for customers to make strategic joining decisions based on their anticipated delays under an information structure where walk-ins observe the queue length of the first stage, and are left to infer that of the second. Our performance evaluations draw from a wide array of techniques, including steady-state, transient, busy period, and hitting-time analyses, together with matrix analytic methods. We showcase the significance of the choice of prioritization policy on the system throughput and social welfare, and we demonstrate the existence of settings where the (typically beneficial) transformation of a traditional service system to an omni-channel one can reduce throughput.