Dynamic Control of a Multiclass Omnichannel Production System with Applications to the Restaurant Industry

Part of the Lubar Research Seminar Series

Speaker: Amir Alwan, Lubar College of Business

The growing adoption of omnichannel operational strategies has transformed production systems across various sectors, including the restaurant industry, bringing complex challenges to demand and operations management. Concurrently, it has spurred innovative solutions, notably the application of dynamic pricing within restaurants that offer omnichannel ordering. Motivated by these developments, we construct a stochastic processing network model for an omnichannel production system that caters to a market of price and delay-sensitive customers. The firm offers a variety of make-to-order (MTO) and make-to-stock (MTS) products, accessible through both walk-in and online channels at predetermined quote times. The objective is to maximize long-run average profit through dynamic pricing, production scheduling, and admission control decisions. MTO orders are subject to both earliness and tardiness costs, whereas MTS orders only face tardiness costs, alongside holding costs for the stored MTS goods. Walk-in customers have finite patience and may abandon the system if wait times are excessive, incurring abandonment costs. Given the analytical intractability of this problem, we examine an approximating Brownian control problem in the heavy-traffic regime. We establish that the optimal policy is a two-sided barrier policy with a state-dependent drift rate, which we derive in closed form, guiding a joint dynamic pricing, scheduling, and rejection policy for the original production system.