Static and dynamic resource allocation models for single-leg transportation markets with service disruptions

This work considers the stochastic resource allocation problem for single-leg transportation markets with service disruptions. The single-period version of the problem is formulated as a stochastic model with arbitrarily distributed resource capacity. We then completely characterize the optimal solution to the stochastic model. The multi-period version of the problem is formulated as a dynamic programming model. We characterize the monotone structure of the optimal solution for the dynamic model under uniform resource consumption rates. For the case with general resource consumption rates, a counterexample is provided to show that there exist cases where the optimal solution is not monotone.