Waiting for surgery caused by an ineffective schedule may lead to the loss of opportunity for care, which results in higher costs due to additional treatment and lower quality of life, and/or productivity loss. In addition, the operating room is one of the most important areas of hospital operations because of its high potentials for cost savings and its impacts on downstream resources by generating admissions to a hospital. However, randomness associated with surgery operations has been considered as a major obstacle in the development of an effective schedule. This study mainly focuses on developing stochastic models for scheduling elective surgery patients and efficient numerical algorithms.

We first consider an operating room allocation problem in which a set of patients waiting for surgery is assigned to operating rooms with aims to minimize overtime cost and patient waiting times. Particularly, this research investigates how the shortage of downstream resource (e.g. Surgical Intensive Care Unit beds) impacts the surgery schedule. This problem is formulated as stochastic mixed integer program with two-stage recourse to address randomness in surgery operations, and sample average approximate (SAA) is employed as a solution procedure. A simulation study concludes that the stochastic model outperforms a deterministic model based on expected value.

An infinite horizon Markov Decision Process (MDP) model is developed to aid the decision on building an elective schedule, which is defined in terms of the number of scheduled patients. The optimal schedule minimizes the total cost that captures overtime costs and costs associated with patient waiting. We show that an optimal surgery schedule does not only rely on the overall demand volume but also on other elements such as patient urgency level, the probability of becoming an emergency patient, time-dependent cost for surgery postponement, etc. In addition, the effects of random surgery duration and demand arrivals are investigated.

This research exploits structural properties of the MDP model to discover conditions that define an optimal action space so as to eliminate efforts to search non-optimal action space and other properties that allow the reduction of computational efforts. By employing the theoretical results, this study proposed two solution procedures: (i) modified value iteration method with bounding action space, and (ii) sampling-based finite horizon approximation. Computational experiments indicated that the proposed algorithms significantly improve computational efficiency.