Modeling a humanitarian-aid covering tour problem with location selection and vehicle assignment decisions

Abstract

In post-disaster situations, time-critical decision-making is essential. Due to high demand and limited resources, visiting all affected locations is often infeasible. This study presents a novel variant of the covering tour problem that addresses these constraints by integrating location selection and vehicle assignment decisions. In the proposed problem, vehicles depart from selected relief centers, visit a subset of victim locations, and are allowed to complete their tours at any center. The demands of unvisited locations are satisfied through demand transfers from nearby visited nodes, with associated transfer times included in the total operation time. A mixed integer linear programming (MILP) model is formulated to minimize total operation time, incorporating both travel and demand transfer times. Scenario-based analyses are performed to evaluate the model's performance under various operational conditions, including transfer time sensitivity, route flexibility, demand coverage constraints, time-based covering radius, and partial fulfillment policies. To address scalability, a two-stage clustering-based heuristic is developed, offering a practical and computationally efficient solution method. From a humanitarian logistics perspective, the findings emphasize the importance of flexible routing, strategic placement of relief centers, and careful management of coverage thresholds. Additionally, the simplicity and adaptability of the proposed heuristic make it well suited for real-time decision-making in post-disaster response operations.