Fairness in hazmat routing-scheduling: A bi-objective Stackelberg game

We investigate a hazmat routing-scheduling problem. To minimize the overall expected risk, various vehicles may take different routes/schedules to avoid multiple accidents on the same link. Therefore, the company envisages two issues: (1) unfairly, a vehicle departing earlier from its origin may arrive earlier at its destination than the others leaving later; (2) focusing only on the minimization of risk may increase travel time/cost incurred by the company. We suggest a biobjective game-theoretic formulation and solve it by a modified Adaptive Large Neighborhood Search and Simulated Annealing. We test the solution on a real-life case and extract practical insights.