Optimal route decision with a geometric ground-airborne hybrid model under weather uncertainty

Adverse weather is the dominant cause of delays in the National Airspace System (NAS). Since the future weather condition is only predictable with a certain degree of accuracy, managing traffic in the weather-affected airspace is a challenging task. In this paper, we propose a geometric model to generate an optimal combination of ground delay and route choice to hedge against weather risk. The geometric recourse model (GRM) is a strategic Probabilistic Air Traffic Management (PATM) model that generates optimal route choice, incorporating route hedging and en-route recourse to respond to weather change: hedged routes are routes other than the nominal or the detour one, and recourse occurs when the weather restricted airspace becomes flyable and aircraft are re-routed to fly direct to the destination. Among several variations of the GRM, we focus on the hybrid Dual Recourse Model (DRM), which allows ground delay as well as route hedging and recourses, when the weather clearance time follows a uniform distribution. The formulation of the hybrid DRM involves two decision variables – ground delay and route choice – and four parameters: storm location, storm size, maximum storm duration time, and ground-airborne cost ratio. The objective function has two components: expected total ground delay cost and expected total airborne cost. We propose a solution algorithm that guarantees to find the global optimum of the hybrid-DRM. Based on the numerical analysis, we find that ground-holding is effective only when combined with the nominal route. Otherwise, it is optimal to fly on the route determined by the DRM without ground delay. We also find the formula of the threshold ground-airborne cost ratio, which we call the Critical Cost Ratio (CCR), that determines the efficacy of ground delay: the higher the CCR, the more effective the strategies involving ground delay. We conclude that both ground delay and route hedging should be considered together to produce the best ATM decisions.