Placing Coffee Machines Such That Everyone Is Covered

Published April 5, 2026

Background

You own an office and care for your employees. One way in which you care for them is providing coffee access.

You would like the walk to the machine to be at most two minutes. This motivates a coverage model where every employee should be close enough to at least one coffee machine.

Data

This section describes the demand points, candidate machine locations, and coverage radius.

Each candidate location represents a possible place to install a coffee machine. Each demand point represents an employee area that needs to be covered.

Mathematical Model

Let \(x_j\) be 1 if a coffee machine is placed at location \(j\), and 0 otherwise.

Let \(a_{ij}\) be 1 if demand point \(i\) is covered by a coffee machine at location \(j\), and 0 otherwise.

The goal is to choose coffee machine locations so that every demand point is covered while using as few machines as possible.

Results

Add your selected coffee machine locations and coverage results here.

You can also report the number of machines used and which demand points are covered by each selected location.

Discussion

This section can explain why the selected locations cover the office efficiently.

You can also discuss limitations, such as assuming walking distance is circular or ignoring walls, doors, elevators, and office layout constraints.