We develop algorithms for a stochastic sequencing two-machine one-server problem with waiting time, and overtime costs. Scheduling surgeries for a single surgeon in two parallel operating rooms motivates the work. The problem is formulated as an integer stochastic program using sample average approximation. A decomposition method is proposed to solve
the problem. Extensive computational testing based on real data shows that the proposed methods produce acceptable processing time for practical purposes, and provides insight as to when parallel operating rooms is cost effective.