The design of an on-demand transport system with origin and destination matrices is studied. Two objectives are considered; one is to minimize the sum (over all users) of travel time per unit time and the other is to minimize the sum of the total cost of track built. Firstly, we show that even the minimum total cost problem without consideration of the travel time is not a simple minimum spanning tree problem. Then, for the bi-objective problem, we transform one objective to a constraint condition. With this transformation, we transform the bi-objective problem to a single-objective problem and give the optimal solution by the branch and bound method. Finally, we propose a fast approximate algorithm and analyze its complexity.