In this paper we present a multicost algorithm for the joint time scheduling of the communication and computation resources that will be used by a task. The proposed algorithm selects the computation resource to execute the task, determines the path to route the input data, and finds the starting times for the data transmission and the task execution, performing advance reservations. We initially present an optimal scheme of non-polynomial complexity and by appropriately pruning the set of candidate paths we also give a heuristic algorithm of polynomial complexity. We evaluate the performance of our algorithm and compare it to that of algorithms that handle only the computation or communication part of the problem separately. We show that in a Grid network where the tasks are CPU- and dataintensive important performance benefits can be obtained by jointly optimizing the use of the communication and computation resources.