Optimal Allocation of Surgery Blocks to Operating Rooms Under Uncertainty

Abstract

The allocation of surgeries to operating rooms (ORs) is a challenging combinatorial optimization problem. There is also significant uncertainty in the duration of surgical procedures, which further complicates assignment decisions. In this article, we present stochastic optimization models for the assignment of surgeries to ORs on a given day of surgery. The objective includes a fixed cost of opening ORs and a variable cost of overtime relative to a fixed length-of-day. We describe two types of models. The first is a two-stage stochastic linear program with binary decisions in the first-stage and simple recourse in the second stage. The second is its robust counter-part, in which the objective is to minimize the maximum cost associated with an uncertainty set for surgery durations. We describe the mathematical models, bounds on the optimal solution, and solution methodologies, including an easy-to-implement heuristic. Numerical experiments based on real data from a large health care provider are used to contrast the results for the two models, and illustrate the potential for impact in practice. Based on our numerical experimentation we find that a fast and easy-toimplement heuristic works fairly well on average across many instances. We also find that the robust method performs approximately as well as the heuristic, is much faster than solving than the stochastic recourse model, and has the benefit of limiting the worst-case outcome of the recourse problem.

Integrated decision making in healthcare : an operations research and management science perspective

“…The service mix stipulates which surgery types can be performed, and therefore impacts the net contribution of a facility [256]. Specific examples of services are medical devices to perform noninvasive surgeries and robotic services for assisting in specialized surgery [130]. In general, the service mix decision is not made at a surgical care service level, but at the regional or hospital level, as it integrally impacts the ambulatory, emergency, surgical and inpatient care services.…”

“…Equipment may be required to perform particular surgeries. Examples are imaging equipment [229] or robotic equipment [130]. Equipment may be transferable between rooms, which increases scheduling flexibility.…”

“…Staff in surgical care services include surgeons, anesthesiologists, surgical assistants and nurse anesthetists [5,72,130,256]. Staffing costs are a large portion of costs in surgical care services [10,130].…”

“…Staff in surgical care services include surgeons, anesthesiologists, surgical assistants and nurse anesthetists [5,72,130,256]. Staffing costs are a large portion of costs in surgical care services [10,130]. Significant cost savings can be achieved by increasing staffing flexibility [130], for example by (i) cross-training surgical assistants for multiple types of surgeries [228], (ii) augmenting nursing staff with short-term contract nurses [130], and (iii) drawing nurses from less critical parts in the hospital during demand surges [130].…”

“…Methods: computer simulation [281,300,301,302,334,432,433,490], heuristics [72,130,256], mathematical programming [23,72,130,469], queueing theory [334], literature review [282,351].…”