The professional driver training timetabling problem: MILP formulations and efficient heuristic

According to the Moroccan Road Code 52.05, drivers involved in the transport of goods and passengers must obtain a professional card, which is issued only after completing training at accredited centers. Motivated by the challenges faced by these centers, this study, the first of its kind, focuses on modeling and solving the professional driver training timetabling problem. Its main challenge is ensuring that each group adheres to the theoretical course duration. When a group is in practice, it misses some theoretical sessions. As a result, the decision-maker must ensure that groups assigned to the same room during a given period receive an equal duration of training to prevent overlap. Mixed integer linear programming (MILP) models are proposed to optimize the use of limited resources, such as trainers, rooms, and vehicles, while complying with all constraints specified in the decree governing professional driver training. A simulation is conducted with a variable number of training groups to identify the optimal allocation of resources. The proposed MILP models meet the current needs of these centers but fail to generate feasible schedules within a reasonable time as demand and resources increase. To overcome the scalability issue, a simulated annealing (SA)-based heuristic is proposed, which uses Shift and Swap moves to explore the search space. Constraints and resource allocation are managed by a dedicated algorithm. Computational results show that the number of vehicles and rooms is proportional to that of groups, though the ratio varies by training type. Consequently, decision-makers should identify demand for each training type, allocate resources accordingly, and maximize the number of groups to be trained with available resources.