Resilience model development for multi-depot vehicle routing problems with probability constraints under disturbance conditions

The object of this study is the multi-depot vehicle routing problem (MDVRP), which seeks optimal vehicle routes from multiple depots to geographically dispersed customers. The study addresses the problem of low reliability in traditional deterministic MDVRP models that fail to perform effectively under uncertain and disruptive conditions such as traffic congestion, infrastructure failures, demand fluctuations, and natural disasters. To overcome this limitation, a resilience-based optimization model is proposed by formulating the MDVRP with probability constraints that capture the likelihood of disturbances affecting route feasibility. The model integrates stochastic components into the routing process to balance cost minimization with service reliability under uncertainty. Computational experiments on an agro-logistics case involving five depots and twenty customers demonstrated that the proposed model reduced expected transportation costs by 36.4% compared with the Genetic Algorithm approach (494 vs. 777) and maintained service continuity in 100% of feasible scenarios with a reliability threshold of α = 0.7. Moreover, approximately 25–30% of potential routes were identified as infeasible under disturbance scenarios, validating the model’s probabilistic filtering mechanism. These results confirm that incorporating chance constraints and a Tabu search heuristic enhances the adaptability and robustness of multi-depot routing systems. The developed model can be practically applied to large-scale logistics systems, humanitarian relief operations, and distribution networks operating in regions prone to demand volatility or infrastructure disruptions, providing decision-makers with a reliable tool for sustainable and resilient route planning