Rollout algorithms for resource allocation in humanitarian logistics

Large-scale disasters and catastrophic events typically result in a significant shortage of critical resources, posing a great challenge to allocating limited resources among different affected areas to improve the quality of emergency logistics operations. This article pays attention to the performance of resource allocation, which includes three metrics: efficiency, effectiveness, and equity, respectively corresponding to economic cost, service quality, and fairness. In particular, the effectiveness metric considers human suffering by depicting it as deprivation cost, an economic valuation measurement that has been recently proposed and the equity metric concerns about the service equality at the end of planning horizon. A nonlinear integer model is first proposed and then an equivalent dynamic programming model is developed to avoid the nonlinear terms created by the introduction of the deprivation cost. The dynamic programming method can solve small-scale problems to optimality but meets difficulty when solving medium- and large-scale problems, due to the curse of dimensionality. Therefore, an approximate dynamic programming algorithm, called the rollout algorithm, is proposed to overcome this computational difficulty. The computational complexity of the proposed algorithm is theoretically analyzed. Furthermore, a modified version of the rollout algorithm is presented, with its computational complexity analyzed. Extensive numerical experiments are conducted to test the performance of the proposed algorithms, and the experimental results demonstrate that the initially proposed rollout algorithm yields optimal or near-optimal solutions within a reasonable amount of time. In addition, the impacts of some important parameters are investigated and managerial insights are drawn.