Restaurant revenue management

We develop two classes of optimization models to maximize revenue in a restaurant (while controlling average waiting time as well as perceived fairness) that may violate the first-come-first-serve (FCFS) rule. In the first class of models, we use integer programming, stochastic programming, and approximate dynamic programming methods to decide dynamically when, if at all, to seat an incoming party during the day of operation of a restaurant that does not accept reservations. In a computational study with simulated data, we show that optimization-based methods enhance revenue relative to the industry practice of FCFS by 0.11% to 2.22% for low-load factors, by 0.16% to 2.96% for medium-load factors, and by 7.65% to 13.13% for high-load factors, without increasing, and occasionally decreasing, waiting times compared to FCFS. The second class of models addresses reservations. We propose a two-step procedure: Use a stochastic gradient algorithm to decide a priori how many reservations to accept for a future time and then use approximate dynamic programming methods to decide dynamically when, if at all, to seat an incoming party during the day of operation. In a computational study involving real data from an Atlanta restaurant, the reservation model improves revenue relative to FCFS by 3.5% for low-load factors and 7.3% for high-load factors.