Events

This paper examines dynamic assortment optimization in service systems where customer purchasing decisions are influenced by real-time congestion, as seen in food delivery platforms and 3D printing services. We address two key questions: (1) How should firms adjust product or service variety when customer choices depend on evolving congestion levels? and (2) How do product features, such as profit margins and service times, shape optimal assortment strategies?

We model the system as an M/D/1 queue and develop a dynamic control framework under a general discrete choice model with impatient customers, where the system state reflects congestion and the decision variable is the assortment offered. We first establish the existence of a concave solution function under a general choice model.

For the multinomial logit (MNL) choice model, we show that the optimal policy follows an adjusted-margin-ordered structure, where product adjusted margins depend on product features (margin and service time) and system congestion. The ordering between two products shifts at most once as congestion increases. We characterize conditions under which the optimal assortment follows a nested structure and highlight key differences from the revenue-ordered policies commonly found in the literature. Unlike these traditional models, we find that optimal assortments in service systems are generally non-monotonic. In a special two-product setting, we provide sufficient conditions for this non-monotonicity. Our results reveal a novel tradeoff consisting of two counteracting forces: while higher congestion may lead to smaller assortments to improve service efficiency, firms may also expand offerings to sustain demand.

Joint work with Chen-An Lin, Purdue University