The energy consumption of the Internet has a huge impact on the world economy and it is likely to increase every year. In present backbone networks, pairs of nodes are connected by “bundles” of multiple physical cables that form one logical link and energy saving can be achieved by shutting down unused network resources. The hose model can support traffic demand variations among node pairs in different time periods because it accommodates multiple traffic matrices unlike the pipe model which supports only one traffic matrix. This paper proposes an OSPF (Open Shortest Path First) link weight optimization scheme to reduce the network resources used for the hose model considering single link failures. The proposed scheme employs a heuristic algorithm based on simulated annealing to determine a suitable set of link weights to reduce the worst-case total network resources used, and considering any single link failure preemptively. It efficiently selects the worst-case performance link-failure topology and searches for a link weight set that reduces the worst-case total network resources used. Numerical results show that the proposed scheme is more effective in the reduction of worst-case total network resources used than the conventional schemes, Start-time Optimization and minimum hop routing.