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Various natural and manmade disasters during last decades have highlighted the need of further improving on governmental preparedness to emergency events, and a relief supplies distribution problem named Inventory Slack Routing Problem (ISRP) has received increasing attentions. In an ISRP, inventory slack is defined as the duration between reliefs arriving time and estimated inventory stock-out time. Hence, a larger inventory slack could grant more responsive time in facing of various factors (e.g., traffic congestion) that may lead to delivery lateness. In this study, the relief distribution problem is formulated as an optimization model that maximize the minimum slack among all dispensing sites. To efficiently solve this problem, we propose a two-stage approach to tackle the vehicle routing and relief allocation sub-problems. By analyzing the inter-relations between these two sub-problems, a new objective function considering both delivery durations and dispensing rates of demand sites is applied in the first stage to design the vehicle routes. A hierarchical routing approach and a sweep approach are also proposed in this stage. Given the vehicle routing plan, the relief allocation could be easily solved in the second stage. Numerical experiment with a comparison of multi-vehicle Traveling Salesman Problem (TSP) has demonstrated the need of ISRP and the capability of the proposed solution approaches.

Inventory slack routing application in emergency logistics and relief distributions