Emergency Management has received more and more attention in the recent years. Most research in this eld focused on evacuation of victims from dangerous places to safe places, but little on allocation of medical resources to safe places and/or transportation tools to the dangerous places. This thesis studies the problem of delivering medical resources from medical centers to the temporary aid site in a disaster-a ected area to help the wounded victims. In particular, this thesis describes a new algorithm for solving this problem. As requirements of medical resources for a disaster a ected area are not known in advance, the problem is in the so-called on-line environment. The algorithm for such a problem is also called on-line algorithm. The evaluation criterion for such an on-line algorithm is the so-called competitive ratio. This thesis considers four cases of such a problem: (1) the capacity of vehicles for transporting medical resources and the number of vehicles are both in nite, (2) the capacity of vehicles is in nite but the number of vehicles is one, (3) the capacity of vehicles is nite and the number of vehicles is in nite, (4) the capacity of vehicles is nite and the number of vehicles is one. Algorithms for the four cases are called H1, H2, H3, and H4, ii respectively. For all these cases, this thesis presents properties, appropriate on-line algorithms and theoretical analysis of these algorithms. The result of the analysis shows that H1 and H3 are optimal based on the competitive ratio criterion while the other two have a very small gap in terms of the optimum criterion. The thesis also presents a case study for having a sense of the performance of H2 and demonstrating practicality of the developed algorithms. The result of this thesis has contributions to the eld of resource planning and scheduling and has application in not only emergency management but also supply chain management in manufacturing and construction.