Solving a large oral examination timetabling problem using a multidimensional knapsack MILP formulation

TL;DR

This paper models a large-scale oral examination scheduling problem as a multidimensional knapsack MILP, demonstrating effective candidate assignment and scheduling within computational constraints.

Contribution

It introduces a novel MILP formulation for large-scale exam timetabling by reducing complexity through candidate-to-schedule assignment.

Findings

Successfully scheduled 7,796 candidates out of 7,804 within 20 minutes.

The MILP model effectively manages complex constraints and large problem size.

Experimental results validate the approach on real data.

Abstract

This paper addresses the Oral Examination Timetabling Problem (OETP) for France's prestigious engineering schools, an organization managed by the Service des Concours Communs Polytechniques (SCCP). The scheduling is highly complex, involving over 7,000 candidates across a four-week period while accounting for constraints such as exam overlaps, geographic origin, and visa requirements. To manage this scale, the paper shows how to model the problem as a Multidimensional Knapsack Problem (MKP) using a Mixed-Integer Linear Programming (MILP) formulation. Their strategy reduces combinatorial complexity by assigning candidates to a predetermined set of pre-validated schedules rather than individual time slots. Experimental results using the SCIP solver on a real 2025 data instance successfully accommodated 7,796 out of 7,804 candidates within a 20-minute time limit.