Single machine stochastic appointment sequencing and scheduling

We develop algorithms for a single machine stochastic appointment sequencing and scheduling problem with waiting time, idle time, and overtime costs. This is a basic stochastic scheduling problem that has been studied in various forms by several previous authors. Applications for this problem cited previously include scheduling of surgeries in an operating room (Denton, 2007, Denton and Gupta,2003), scheduling of appointments in a clinic (Robinson and Chen, 2003, Vanden Bosch, 2000), (Wang, 1997) mentions the application of this problem to scheduling of ships in a port. Begen and Queyranne (2009) discuss this problem in the context of scheduling exams in an examination facility (MRI, Scans). In this paper the problem is formulated as a stochastic integer program using sample average approximation. A heuristic solution approach based on Benders' decomposition is developed and compared to exact methods and to previously proposed approaches. Extensive computational testing shows that the proposed methods produce good results compared to previous approaches. In addition we prove that the finite scenario sample average approximation problem is NP-complete.