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

TL;DR

This paper develops a mathematical optimization model to maximize dining room capacity during COVID-19 by considering social distancing, table arrangements, and space separators, with heuristic solutions for large instances.

Contribution

It introduces a comprehensive set-packing optimization model for dining room layout considering multiple real-world constraints and analyzes the effectiveness of space separators and sitting orientations.

Findings

Space separators can significantly increase capacity.

Considering sitting sense affects optimal layout.

Heuristics enable solving large-scale problems efficiently.

Abstract

We consider the problem of maximizing the number of people that a dining room can accommodate provided that the chairs belonging to different tables are socially distant. We introduce an optimization model that incorporates several characteristics of the problem, namely: the type and size of surface of the dining room, the shapes and sizes of the tables, the positions of the chairs, the sitting sense of the customers, and the possibility of adding space separators to increase the capacity. We propose a simple, yet general, set-packing formulation for the problem. We investigate the efficiency of space separators and the impact of considering the sitting sense of customers in the room capacity. We also perform an algorithmic analysis of the model, and assess its scalability to the problem size, the presence of (or lack thereof) room separators, and the consideration of the sitting sense of customers. We also propose two constructive heuristics capable of coping with large problem instances otherwise intractable for the optimization model.