Dynamic Off-Premise Pricing for Capacity-Constrained Dine-In Services

This paper studies dynamic off-premise pricing for a capacity-constrained dine-in service system. We consider a food retailer with limited seating capacity, stochastic customer arrivals, and random dine-in service durations. Customers choose among dine-in consumption, off-premise ordering, and no purchase. The dine-in price is fixed, while the store dynamically controls the off-premise price. Unlike classical queue-pricing models, in which price regulates congestion by discouraging customers from entering the system, our model uses off-premise pricing to redirect customers from a capacity-consuming channel to a capacity-free channel. We develop a continuous-time Markov decision process in which the state is the number of occupied seats. The model captures the tradeoff between reducing off-premise margins and relieving future seat congestion. Numerical analysis compares optimal state-dependent pricing with the best constant-price policy and identifies the conditions under which dynamic diversion pricing improves long-run profit. The results provide managerial insights into when off-premise discounts can be used not merely as demand stimulation tools, but as congestion-management instruments in dine-in service operations.