Data-Driven Set Covering Problem Solver

Mathematical Formulation

Minimize $\sum_{i \in I} c_i \cdot x_i$

Subject to $\sum_{i \in I} a_{ij} \cdot x_i \geq 1$ for all $j \in J$

$x_i \in \{0,1\}$ for all $i \in I$

Where:

• $I$ is the set of all potential facility locations (sets)
• $J$ is the set of all demand points (elements)
• $c_i$ is the cost of opening a facility at location $i$
• $a_{ij}$ is 1 if demand point $j$ can be covered by a facility at location $i$, 0 otherwise
• $x_i$ is the decision variable: 1 if a facility is opened at location $i$ , 0 otherwise

Instructions

Upload an Excel file with the following sheets (see example file):

• 'coverage' sheet: A binary matrix where rows are sets and columns are elements
• 'sources' sheet: Contains the costs and coordinates (x, y) of each set W (with Set IDs as index)
• 'dests' sheet: Contains coordinates for elements E with columns: name, x, and y
• 'params' sheet: Contains parameters like 'budget' (optional)