Abstract
In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of company employees as an effective way to curb the spread, and use integer programming techniques to model it. The goal of the model is to maximize the number of direct interactions between employees who are essential for company’s work subject to the constraint that all employees should be partitioned into components of no more than a certain size implied by the regulations. Then we further develop the basic model to take into account different restrictions and provisions. We also give heuristics for solving the problem. Our computational results include sensitivity analysis on some of the models and analysis of the heuristic performance.
Highlights
Statement To fight the Covid-19 pandemic, measures restricting social gatherings were taken by many countries and states
In this paper we develop modeling techniques for a social partitioning problem
Different social interaction regulations are imposed during pandemics to prevent the spread of diseases
Summary
Background and Problem Statement To fight the Covid-19 pandemic, measures restricting social gatherings were taken by many countries and states. Many restrictions set limits on the number of people allowed in gatherings. Germany and UK at some point limited social gatherings of more than 2 people [1] while in many US states that number was 10 [2]. While that type of restrictions might help to prevent the spread of the disease they have the following shortcoming. A sick but asymptomatic person could attend several meetings of no more than 10 people (different people in each meeting). People from those meetings could get the virus and at-
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