Optimizing Multi-Actor Relief Delivery via Truck–Drone Networks: A Game-Theory Approach Incorporating Human Deprivation

In contemporary disaster-response systems, the rapid deployment of relief goods is critical, and technologies such as drones are increasingly transformative in reaching vulnerable populations. As disaster settings require coordinated action among governments, donors, and multiple non-governmental organizations (NGOs), this study investigates the strategic decision-making that governs their cooperation. A game-theory framework is constructed to capture these interactions: donors allocate funds to NGOs based on altruistic motivations and each NGO’s effectiveness in reducing deprivation cost (i.e., the social cost arising from the time individuals remain without essential supplies); NGOs compete—following a Bertrand-type competitive structure—to secure governmental financial support. Meanwhile, the government operates as a Stackelberg leader, influencing NGO strategies through its funding decisions to minimize total deprivation costs across affected regions. Operationally, each NGO manages a hybrid fleet of trucks and drones and aims to minimize both deprivation and logistics costs by solving a truck–drone routing optimization problem. Due to the non-linear and mixed-integer nature of integrating financial allocation and routing decisions, the overall model is solved using state-of-the-art mathematical optimization solvers, and a backward-induction procedure is employed to sequentially derive optimal decisions at each level, yielding the equilibrium strategies for donors, NGOs, and the government. Numerical analysis shows that incorporating deprivation-cost considerations leads to faster and more equitable distribution of relief supplies. Moreover, the competitive dynamics among NGOs ultimately enhance network-wide performance. The proposed framework offers actionable insights for policymakers, highlighting how social-impact metrics, such as deprivation cost, can guide funding rules and improve alignment among humanitarian stakeholders.

Keywords:

Deprivation Cost , Game-theory Approach , Humanitarian Logistics , Truck-Drone Routing problem