Dynamic routing occurs when customers are not known in advance, e.g. for real-time routing. Two heuristics are proposed that solve the balanced dynamic multiple travelling salesmen problem (BD-mTSP). These heuristics represent operational (tactical) tools for dynamic (online, real-time) routing. Several types and scopes of dynamics are proposed. Particular attention is given to sequential dynamics. The balanced dynamic closest vehicle heuristic (BD-CVH) and the balanced dynamic assignment vehicle heuristic (BD-AVH) are applied to this type of dynamics. The algorithms are applied to a wide range of test instances. Taxi services and palette transfers in warehouses demonstrate how to use the BD-mTSP algorithms in real-world scenarios. Continuous approximation models for the BD-mTSP's are derived and serve as strategic tools for dynamic routing. The models express route lengths using vehicles, customers, and dynamic scopes without the need of running an algorithm. A machine learning approach was used to obtain regression models. The mean absolute percentage error of two of these models is below 3%.