An analytical modeling framework for determining the optimal table mix in restaurants

Abstract

We present a queuing theory based optimization model for determining the optimal table mix in a restaurant. The optimal table mix problem is formulated for an allotment policy in which the largest available group is allotted the table. A walk-in restaurant with tables of three different capacities is considered. It is interpreted as a system of interacting multi-server queues. The cost function is composed of two parts. The first part considers the cost due to waiting times. Customer batches, upon seeing a long queue, move to less busy restaurants. To account for this behaviour, the cost due to waiting times is taken as a non-linear function of queue length. The second part of the cost function incorporates the cost due to under utilization of table capacity. The motive is to choose the number of tables of each class such that the cost function is minimized. The paper concludes with results from numerical experiments to illustrate the methodology and applicability.