In this paper an optimization container transport system with three transport modes (road trucks, railway, airplanes) is considered. The system assumes, among others, a number of orders to be transported with limited container number, limited capacity, limited airports availability and penalty costs for late delivering of orders. The system allows for a single container to travel between a given pair of cities multiple times. The problem is formulated and solution representation based on the Giant Tour representation is proposed. Effective procedure for determining the value of the goal function and detection of infeasible solutions in linear time is presented. Two heuristic solving methods are proposed: a greedy algorithm and Tabu Search metaheuristic. A dataset of 300 problem instances is prepared based on real-life geospatial data for 30 large cities in Poland. Transport costs are approximated using real-life data where possible. Computer experiment using the prepared dataset is conducted. The results indicate high effectiveness of the greedy algorithm, despite its running time complexity of \(O(n^4)\) . Moreover, the Tabu Search metaheuristic allowed to improve the results in reasonable time.