<p style='text-indent:20px;'>This paper studies single vehicle scheduling problems with two agents on a line-shaped network. Each of two agents has some customers that are situated at some vertices on the network. A vehicle has to start from <inline-formula><tex-math id="M1">\begin{document}$ v_{0} $\end{document}</tex-math></inline-formula> to serve all customers. The objective is to schedule the customers to minimize <inline-formula><tex-math id="M2">\begin{document}$ C_{max}^A+\theta C_{max}^B $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M3">\begin{document}$ C_{max}^X $\end{document}</tex-math></inline-formula> is the latest completion time of the customers for agent <inline-formula><tex-math id="M4">\begin{document}$ X $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ X\in \{A,B\} $\end{document}</tex-math></inline-formula>. We first propose a polynomial time algorithm for the problem without release time. Next, the problem with release time is proved to be NP-hard despite of a network with only two vertices. Then, we present a <inline-formula><tex-math id="M6">\begin{document}$ \frac{3+\sqrt{5}}{2} $\end{document}</tex-math></inline-formula>-approximation algorithm. Finally, numerical experiments are carried out to verify the approximation algorithm is effective.</p>