On Solving the Assignment Problem with Conflicts

TL;DR

This paper addresses a conflict-aware assignment problem, proposing a simple MILP approach solved with CP-SAT that achieves competitive results and faster heuristics compared to existing methods.

Contribution

It introduces a straightforward MILP formulation for conflict-laden assignment problems and demonstrates its effectiveness using open-source solvers and benchmarks.

Findings

Achieves results comparable to state-of-the-art solvers.

Provides faster, better heuristic solutions.

Demonstrates simplicity and effectiveness of the MILP approach.

Abstract

A variant of the well-known Assignment Problem is studied in this paper, where pairs of assignments are conflicting, and cannot be selected at the same time. This configures a set of hard constraints. The problem, which models real applications, looks for a complete assignment that minimizes the total cost, while no conflict is violated. In this paper, we consider a previously known mixed integer linear program representing the problem and we solve it with the open-source solver CP-SAT, part of the Google OR-Tools computational suite. An experimental campaign on the instances available from the literature, indicates that the approach we propose achieves results comparable with, those of state-of-the-art solvers, notwithstanding its intrinsic conceptual and implementation simplicity. The solver adopted is also able to provide heuristic solutions quicker and better than the heuristic methods previously discussed in the literature.