Robust Heterogeneous Vehicle Routing Optimization for Hazmat Transportation Under Time-Varying Risk

This study addresses the heterogeneous vehicle routing problem for hazardous material transportation under time-varying risk and demand uncertainty. To reflect realistic urban conditions, the road network is constructed as an incomplete graph from geographic and administrative connectivity rules. The risk assessment model captures the spatial heterogeneity and temporal variation in population density and incorporates vehicle-type-specific risk coefficients, with each trip discretized into segments to evaluate population exposure and environmental damage. A bi-objective robust optimization model minimizes total transport cost and risk, with the Bertsimas–Sim uncertainty budget controlling the trade-off between robustness and optimality under demand uncertainty. The model is solved by NSGA-II and benchmarked against NSGA-III, SPEA2, and MOEA/D at both solution and front levels. Case study results from one Beijing chlorine plant serving 30 customers show that NSGA-II achieves the best front quality and favorable cost–risk balance. Sensitivity analysis reveals the nonlinear price of robustness: a minimal budget restructures the fleet and routes, whereas further increases yield only marginal adjustments. Out-of-sample experiments confirm that the robust plan is feasible in all budget-covered realizations, delivering 36~65-percentage-point feasibility gains over the deterministic plan at a 4.71% cost premium, with the mean realized risk staying within 0.55% of the nominal value.