The transport routes of chartered container ships or tows in inland waterway transport are investigated in this paper. The optimal values of parameters that influence the efficient utilization of these ships or tows or business success of a container shipping company with available container ships of this kind in its fleet are also determined. These parameters include size of container ship on a certain route, number of containers loaded or unloaded at each port on a route, ship speed, realized revenues, costs and profit, and others. The proposed model helps in evaluating whether an inland waterway container ship or tow should be chartered or not. The optimal values of all parameters, based on the developed mixed-integer linear programming model, are determined by using LINGO, specialized software for mathematical programming.