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Quantum Annealing for Staff Scheduling in Educational Environments

Alessia Ciacco, Francesca Guerriero, Eneko Osaba

TL;DR

This paper tackles a complex staff scheduling problem for school collaborators across multiple campuses and educational levels in Italy, incorporating availability, skills, gender requirements, and continuity constraints. It develops a mixed-integer optimization model with a multi-criteria objective and a domain restriction strategy, and evaluates a quantum annealing approach using D-Wave's LeapCQMHybrid to obtain high-quality, balanced schedules. Case-study results on real data from Cerisano show the quantum-hybrid solver delivering solutions that match the classical optimum with consistent runtimes, while large synthetic instances reveal scalability limits and the value of hybrid methods for near-optimal planning. Overall, the work demonstrates the practical viability of quantum optimization in educational scheduling and outlines directions for handling dynamic constraints and leveraging advanced quantum architectures in larger-scale deployments.

Abstract

We address a novel staff allocation problem that arises in the organization of collaborators among multiple school sites and educational levels. The problem emerges from a real case study in a public school in Calabria, Italy, where staff members must be distributed across kindergartens, primary, and secondary schools under constraints of availability, competencies, and fairness. To tackle this problem, we develop an optimization model and investigate a solution approach based on quantum annealing. Our computational experiments on real-world data show that quantum annealing is capable of producing balanced assignments in short runtimes. These results provide evidence of the practical applicability of quantum optimization methods in educational scheduling and, more broadly, in complex resource allocation tasks.

Quantum Annealing for Staff Scheduling in Educational Environments

TL;DR

This paper tackles a complex staff scheduling problem for school collaborators across multiple campuses and educational levels in Italy, incorporating availability, skills, gender requirements, and continuity constraints. It develops a mixed-integer optimization model with a multi-criteria objective and a domain restriction strategy, and evaluates a quantum annealing approach using D-Wave's LeapCQMHybrid to obtain high-quality, balanced schedules. Case-study results on real data from Cerisano show the quantum-hybrid solver delivering solutions that match the classical optimum with consistent runtimes, while large synthetic instances reveal scalability limits and the value of hybrid methods for near-optimal planning. Overall, the work demonstrates the practical viability of quantum optimization in educational scheduling and outlines directions for handling dynamic constraints and leveraging advanced quantum architectures in larger-scale deployments.

Abstract

We address a novel staff allocation problem that arises in the organization of collaborators among multiple school sites and educational levels. The problem emerges from a real case study in a public school in Calabria, Italy, where staff members must be distributed across kindergartens, primary, and secondary schools under constraints of availability, competencies, and fairness. To tackle this problem, we develop an optimization model and investigate a solution approach based on quantum annealing. Our computational experiments on real-world data show that quantum annealing is capable of producing balanced assignments in short runtimes. These results provide evidence of the practical applicability of quantum optimization methods in educational scheduling and, more broadly, in complex resource allocation tasks.
Paper Structure (19 sections, 8 equations, 1 figure, 3 tables)

This paper contains 19 sections, 8 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Problem definition
  3. Mathematical Formulation
  4. Decision Variables
  5. Objective function
  6. Constraints
  7. Computational study
  8. Case Study: real-world scheduling
  9. Sites and levels
  10. Collaborators
  11. Days and shifts
  12. Shift durations
  13. Continuity and preferences
  14. Realistic Large-Scale Scenarios
  15. Collaborators
  16. ...and 4 more sections

Figures (1)

  • Figure 1: Distribution of students and classes across the three campuses of the Istituto Comprensivo di Cerisano (Cerisano, Marano Marchesato, and Marano Principato), broken down by school level: kindergarten, primary school, and lower secondary school, with the corresponding number of students and classes.