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We consider the problem of maximizing the number of people that a dining roomcan accommodate provided that the chairs belonging to different tables aresocially distant. We introduce an optimization model that incorporates severalcharacteristics of the problem, namely: the type and size of surface of thedining room, the shapes and sizes of the tables, the positions of the chairs,the sitting sense of the customers, and the possibility of adding spaceseparators to increase the capacity. We propose a simple, yet general,set-packing formulation for the problem. We investigate the efficiency of spaceseparators and the impact of considering the sitting sense of customers in theroom capacity. We also perform an algorithmic analysis of the model, and assessits scalability to the problem size, the presence of (or lack thereof) roomseparators, and the consideration of the sitting sense of customers. We alsopropose two constructive heuristics capable of coping with large probleminstances otherwise intractable for the optimization model.

On the optimal layout of a dining room in the era of COVID-19 using mathematical optimization