An integrated optimization approach to cross-domain scheduling and routing

Optimization problems in multi-domain education present complex challenges with multiple objectives and constraints. This paper integrates two cross-domain problems: the University Course Timetabling Problem (UCTP) and the Capacitated Vehicle Routing Problem (CVRP). This integration is motivated by a case study at an Islamic boarding school-based university in Indonesia, where male and female campuses are located in different cities. The primary challenges include minimizing timetabling conflicts while ensuring efficient transportation for lecturers between campuses. Manual and sequential optimization of integrated problems often lead to conflicts, errors, and high costs in obtaining feasible solutions. The problem is defined as a partial integration of UCTP and CVRP with simultaneous objective functions and constraints. This study proposes a novel multi-objective model that integrates cross-domain scheduling and routing problems using Pure Integer Linear Programming (PILP) and Mixed-Integer Linear Programming (MILP) formulations. Preliminary results for the integrated optimization are also presented. To achieve this, we utilize a matheuristic approach, an established hybrid technique that combines the strengths of mathematical programming and heuristic algorithms. Specifically, this approach combines Branch-and-Bound (B&B) and the Lecturer Capacitated Vehicle (LCV) heuristic algorithm. This research aims to address lecturer and student preferences in UCTP while minimizing transportation costs in CVRP through shortest-route allocation. The model has been tested with two real-world datasets. Experimental results indicate that the proposed model meets lecturer and student preferences while simultaneously reducing transportation costs by 25% compared to the sequential manual method. This study provides valuable insights for other educational institutions facing similar logistical and timetabling challenges. • Propose an integrated approach to educational timetabling and vehicle routing with optimization. • Achieve 25% lower transportation costs through partial integration and algorithmic design. • Apply integer programming and heuristics to solve scheduling and routing jointly. • Cut manual errors and delays with automated, data-driven scheduling. • Validate with institutional data, delivering conflict-free schedules and cost savings.