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We address the problem of dispatching and pro-actively repositioning service resources in service networks such that fast responses to service requests are realized in a cost-efficient way. By formulating this problem as a Markov decision process, we are able to investigate the structure of the optimal policy in the application domain of service logistics. Using these insights, we then propose scalable dynamic heuristics for both the dispatching and repositioning sub-problem, based on the minimum weighted bipartite matching problem and the maximum expected covering location problem, respectively. The dynamic dispatching heuristic takes into account real-time information about both the state of equipment and the fleet of service engineers, while the dynamic repositioning heuristic maximizes the expected weighted coverage of future service requests. In a test bed with a small network, we show that our most advanced heuristic performs well with an average optimality gap of 4.3% for symmetric instances and 5.8% for asymmetric instances. To show the practical value of our proposed heuristics, extensive numerical experiments are conducted on a large test bed with service logistics networks of real-life size where significant savings of up to 56% compared to a state-of-the-art benchmark policy are attained.