A scenario-based robust optimisation approach for social cost vehicle routing problem in disaster response

Efficient, effective, and equitable disaster response is critical yet challenging due to uncertainties, particularly those in vehicle travel times caused by infrastructure damage. To address this, current study proposes a scenario-based robust optimisation social cost vehicle routing problem (SRO-SCVRP) that minimises three objectives: (1) social cost, balancing logistics and deprivation costs, with the latter quantifying survivors’ suffering from delayed access to critical supplies; (2) the variation in expected deprivation cost across travel time scenarios, reflecting solution robustness; and (3) penalties for exceeding service coverage windows (SCW), which are thresholds set by decision-makers to ensure timely deliveries, thereby enhancing model robustness. Logistics and deprivation costs operationalise efficiency and effectiveness, respectively, while the second and third objectives promote equity by reducing disparities in access and ensuring the timely fulfilment of demand. Numerical results from the SRO-SCVRP highlight a trade-off wherein gains in robustness and equity are achieved with only a modest impact on logistics cost. To assess robustness and equity, a Time and Inventory Service-Level Metric (TISM) is developed and applied to alternative water distribution strategies. Among them, the hybrid strategy yields the highest overall TISM, making it the most robust and equitable option across varied SCW thresholds and resource availability.