Operating rooms (ORs) play a substantial role in hospital profitability, and their optimal utilization is conducive to containing the cost of surgical service delivery, shortening surgical patient wait times, and increasing patient admissions. We extend the OR planning and scheduling problem from a single independent hospital to a coalition of multiple hospitals in a strategic network, where a pool of patients, surgeons, and ORs are collaboratively planned. To solve the resulting mixed-integer dual resource constrained model, we develop a novel logic-based Benders’ decomposition approach that employs an allocation master problem, sequencing sub-problems for each hospital-day, and novel multistrategy Benders’ feasibility and optimality cuts. We investigate various patient-to-surgeon allocation flexibilities, as well as the impact of surgeon schedule tightness. Using real data obtained from the General Surgery Departments of the University Health Network (UHN) hospitals, consisting of Toronto General Hospital, Toronto Western Hospital, and Princess Margret Cancer Centre in Toronto, Ontario, Canada (who already engage in some collaborative resource sharing), we find that on average, collaborative OR scheduling with traditional patient-to-surgeon allocation flexibility results in 6% cost-savings, while flexible patient-to-surgeon allocation flexibility increases cost-savings to 40%, and surgeon schedule tightness can impact costs by 15%. The collective impact of our collaboration and patient flexibility results in between 45% and 63% savings per surgery. We also use a game theoretic approach to fairly redistribute the payoff acquired from a coalition of hospitals and to empirically show coalitional stability among hospitals. Data and the online supplement are available at https://doi.org/10.1287/ijoc.2017.0745 .

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The critical node detection problem (CNDP) aims to fragment a graph G = (V, E) by removing a set of vertices R with cardinality |R| ≤ k, such that the residual graph has minimum pairwise connectivity for user-defined value k. Existing optimization algorithms are incapable of finding a good set R in graphs with many thousands or millions of vertices due to the associated computational cost. Hence, there exists a need for a time-and space-efficient approach for evaluating the impact of removing any v ∈ V in the context of the CNDP. In this paper, we propose an algorithm based on a modified depth-first search that requires O(k(|V| + |E|)) time complexity. We employ the method within in a greedy algorithm for quickly identifying R. Our experimental results consider small-(≤ 250 nodes) and medium-sized (≤ 25, 000 nodes) networks, where it is possible to compare to known optimal solutions or results obtained by other heuristics. Additionally, we show results using six real-world networks. The proposed algorithm can be easily extended to vertex-and edge-weighted variants of the CNDP.

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Stereotactic radiosurgery (SRS) is an effective technique to treat brain metastasis for which several inverse planning methods may be appropriate. We compare three different optimization models for segment duration optimization in SRS using Leksell Gamma Knife Icon (Elekta, Stockholm, Sweden). We investigate (1) a linear programming approach, (2) a piecewise quadratic penalty approach, and (3) an unconstrained convex moment-based penalty approach. We examine the performances of these approaches using anonymized data from 14 previously treated cases. In addition, we investigate the important modeling question of selecting weights for the objective functions where we use a simulated annealing algorithm to determine these weights for each model. The inverse plans obtained via optimization models are compared against each other and against the clinical plans. The three inverse planning models can all yield optimal treatment plans in a reasonable amount of time and the treatment plans obtained by these models meet or exceed clinical guidelines while displaying high conformity.

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We study a generalized operating room planning and scheduling (GORPS) problem at the Toronto General Hospital (TGH) in Ontario, Canada. GORPS allocates elective patients and resources (i.e., operating rooms, surgeons, anesthetists) to days, assigns resources to patients, and sequences patients in each day. We consider patients’ due‐date, resource eligibility, heterogeneous performances of resources, downstream unit requirements, and lag times between resources. The goal is to create a weekly surgery schedule that minimizes fixed‐ and over‐time costs. We model GORPS using mixed‐integer and constraint programming models. To efficiently and effectively solve these models, we develop new‘ multi‐featured logic‐based Benders decomposition approaches. Using data from TGH, we demonstrate that our best algorithm solves GORPS with an average optimality gap of 2.71% which allows us to provide our practical recommendations. First, we can increase daily OR utilization to reach 80%—25% higher than the status quo in TGH. Second, we do not require to optimize for the daily selection of anesthetists—this finding allows for the development of effective dominance rules that significantly mitigate intractability. Third, solving GORPS without downstream capacities (like many papers in literature) makes GORPS easier to solve, but such OR schedules are only feasible in 24% of instances. Finally, with existing ORs’ safety capacities, TGH can manage 40% increase in its surgical volumes. We provide recommendations on how TGH must adjust its downstream capacities for varying levels of surgical volume increases (e.g., current urgent need for more capacity due to the current Covid‐19 pandemic).