We propose an algorithm to compute the optimum departure time and path for a commuter in a congested network. Constant costs for use of arc, cost functions of travel time depending on exogenous congestion and schedule delay are taken into account. The best path for a given departure time is computed with a previous algorithm for the generalized shortest path problem. The globally optimal departure time and the optimal path are determined by adapting Piyavskii's algorithm to the case of one-sided Lipschitz functions.