This paper formulates the pickup and delivery problem, also known as the dial-a-ride problem, as an integer program. Its polyhedral structure is explored and four classes of valid inequalities developed. The results of a branch-and-cut algorithm based on these constraints are presented.
Ruland, K. S., & Rodin, E. Y. (1997). The pickup and delivery problem: Faces and branch-and-cut algorithm. Computers and Mathematics with Applications, 33(12), 1–13. https://doi.org/10.1016/S0898-1221(97)00090-4