The paper presents a bi-objective integer programming model for routing and scheduling in a time-dependent directed network‎, ‎where edge weights vary with time‎. ‎It can be considered as an extension of the network flow model for the time-dependent travelling salesman problem‎. ‎The objective is to find an algorithmic solution for the optimal sequence of location/time points which gives the shortest travel distance‎, ‎with maximum number of visits‎. ‎A local search heuristic is proposed based on bi-objective integer programming model‎, ‎for time splitting and search scope‎. ‎The performance of the algorithm on real large scale sets are evaluated‎. ‎The results of this research can be used in various logistic applications specifically maritime service managements‎.