Mark van Houdenhoven

Robust surgery loading

We consider the robust surgery loading problem for a hospital’s operating theatre department, which concerns assigning surgeries and sufficient planned slack to operating room days. The objective is to maximize capacity utilization and minimize the risk of overtime, and thus cancelled patients. This research was performed in collaboration with the Erasmus MC, a large academic hospital in the Netherlands, which has also provided historical data for the experiments. We propose various constructive heuristics and local search methods that use statistical information on surgery durations to exploit the portfolio effect, and thereby to minimize the required slack. We demonstrate that our approach frees a lot of operating room capacity, which may be used to perform additional surgeries. Furthermore, we show that by combining advanced optimization techniques with extensive historical statistical records on surgery durations can significantly improve the operating room department utilization.

Predicting the unpredictable: A new prediction model for operating room times using individual characteristics and the surgeon's estimate

Background:Routine predictions made by surgeons or historical mean durations have only limited capacity to predict operating room (OR) time. The authors aimed to devise a prediction model using the surgeons estimate and characteristics of the surgical team, the operation, and the patient. Methods:Seventeen thousand four hundred twelve consecutive, elective operations from the general surgical department in an academic hospital were analyzed. The outcome was OR time, and the potential predictive factors were surgeons estimate, number of planned procedures, number and experience of surgeons and anesthesiologists, patients age and sex, number of previous hospital admissions, body mass index, and eight cardiovascular risk factors. Linear mixed modeling on the logarithm of the total OR time was performed. Results:Characteristics of the operation and the team had the largest predictive performance, whereas patient characteristics had a modest but distinct effect on OR time: operations were shorter for patients older than 60 yr, and higher body mass index was associated with longer OR times. The surgeons estimate had an independent and substantial contribution to the prediction, and the final model explained 27% of the residual variation in log (OR time). Using the prediction model instead of the surgeons prediction based on historical averages would reduce shorter-than-predicted and longer-than-predicted OR time by 2.8 and 6.6 min per case (a relative reduction of 12 and 25%, respectively), assessed on independent validation data. Conclusions:Detailed information on the operative session, the team, and the patient substantially improves the prediction of OR times, but the surgeons estimate remains important. The prediction model may be used in OR scheduling.

Managing the overflow of intensive care patients

Many hospitals in the Netherlands are confronted with capacity problems at their intensive care units (ICUs) resulting in cancelling operations, overloading the staff with extra patients, or rejecting emergency patients. In practice, the last option is a common choice because for legal reasons, as well as for hospital logistics, rejecting emergency patients has minimal consequences for the hospital. As a result, emergency patients occasionally have to be transported to hospitals far away. In this work, we propose a cooperative solution for the ICU capacity problem. In our model, several hospitals in a region jointly reserve a small number of beds for regional emergency patients. We present a mathematical method for computing the number of regional beds for any given acceptance rate. The analytic approach is inspired by overflow models in telecommunication systems with multiple streams of telephone calls. Simulation studies show that our model is quite accurate. We conclude that cooperation between hospitals helps to achieve a high acceptance level with a smaller number of beds resulting in improved service for all patients.

A Framework for Healthcare Planning and Control

Rising expenditures spur healthcare organizations to organize their processes more efficiently and effectively. Unfortunately, healthcare planning and control lags behind manufacturing planning and control. We analyze existing planning and control concepts or frameworks for healthcare operations management and find that they do not address various important planning and control problems. We conclude that they only focus on hospitals and are too narrow, focusing on a single managerial area, such as resource capacity planning, or ignoring hierarchical levels. We propose a modern framework for healthcare planning and control that integrates all managerial areas in healthcare delivery operations and all hierarchical levels of control, to ensure completeness and coherence of responsibilities for every managerial area. The framework can be used to structure the various planning and control functions and their interaction. It is applicable to an individual department, an entire healthcare organization, and to a complete supply chain of cure and care providers. The framework can be used to identify and position various types of managerial problems, to demarcate the scope of organization interventions and to facilitate a dialogue between clinical staff and managers.

Clustering clinical departments for wards to achieve a prespecified blocking probability

When the number of available beds in a hospital is limited, it can be beneficial to cluster several clinical departments such that the probability of not being able to admit a patient is acceptably small. However, not all clinical departments can be clustered for cross-infection reasons. In addition, patients from one clinical department should not be spread out over the entire hospital as this complicates the process of doing rounds and may result in alternate level of care. In this paper, we consider a situation where wards with a fixed number of beds are given. The question is how to cluster the clinical departments and to determine the assignment of these clustered departments to the available wards such that the assigned beds are sufficient to guarantee a blocking probability below a prespecified percentage. We first give an exact formulation of the problem to be able to achieve optimal solutions. However, computational experiments show that the resulting computation times for this model are too long for it to be applicable in practice. To reduce the computation time, we introduce two heuristic solution approaches. The first heuristic uses the same formulation as the exact model, however, the number of required beds is approximated by a linear function. The resulting model is again solved by an exact solver. The second heuristic uses a restricted version of the exact model within a local search approach. Hereby, the local search is used to determine the assignment of clinical departments to clusters and the exact model is used to determine the assignment of clusters to wards.

Fewer intensive care unit refusals and a higher capacity utilization by using a cyclic surgical case schedule

PURPOSE Mounting health care costs force hospital managers to maximize utilization of scarce resources and simultaneously improve access to hospital services. This article assesses the benefits of a cyclic case scheduling approach that exploits a master surgical schedule (MSS). An MSS maximizes operating room (OR) capacity and simultaneously levels the outflow of patients toward the intensive care unit (ICU) to reduce surgery cancellation. MATERIALS AND METHODS Relevant data for Erasmus MC have been electronically collected since 1994. These data are used to construct an MSS that consisted of a set of surgical case types scheduled for a period or cycle. This cycle was executed repetitively. During such a cycle, surgical cases for each surgical department were scheduled on a specific day and OR. The experiments were performed for the Erasmus University Medical Center and for a virtual hospital. RESULTS Unused OR capacity can be reduced by up to 6.3% for a cycle length of 4 weeks, with simultaneous optimal leveling of the ICU workload. CONCLUSIONS Our findings show that the proposed cyclic OR planning policy may benefit OR utilization and reduce surgical case cancellation and peak demands on the ICU.

A Simulation Model for Determining the Optimal Size of Emergency Teams on Call in the Operating Room at Night

BACKGROUND: Hospitals that perform emergency surgery during the night (e.g., from 11:00 pm to 7:30 am) face decisions on optimal operating room (OR) staffing. Emergency patients need to be operated on within a predefined safety window to decrease morbidity and improve their chances of full recovery. We developed a process to determine the optimal OR team composition during the night, such that staffing costs are minimized, while providing adequate resources to start surgery within the safety interval. METHODS: A discrete event simulation in combination with modeling of safety intervals was applied. Emergency surgery was allowed to be postponed safely. The model was tested using data from the main OR of Erasmus University Medical Center (Erasmus MC). Two outcome measures were calculated: violation of safety intervals and frequency with which OR and anesthesia nurses were called in from home. We used the following input data from Erasmus MC to estimate distributions of all relevant parameters in our model: arrival times of emergency patients, durations of surgical cases, length of stay in the postanesthesia care unit, and transportation times. In addition, surgeons and OR staff of Erasmus MC specified safety intervals. RESULTS: Reducing in-house team members from 9 to 5 increased the fraction of patients treated too late by 2.5% as compared to the baseline scenario. Substantially more OR and anesthesia nurses were called in from home when needed. CONCLUSION: The use of safety intervals benefits OR management during nights. Modeling of safety intervals substantially influences the number of emergency patients treated on time. Our case study showed that by modeling safety intervals and applying computer simulation, an OR can reduce its staff on call without jeopardizing patient safety.

A Norm Utilisation for Scarce Hospital Resources: Evidence from Operating Rooms in a Dutch University Hospital

BackgroundUtilisation of operating rooms is high on the agenda of hospital managers and researchers. Many efforts in the area of maximising the utilisation have been focussed on finding the holy grail of 100% utilisation. The utilisation that can be realised, however, depends on the patient mix and the willingness to accept the risk of working in overtime.Materials and methodsThis is a mathematical modelling study that investigates the association between the utilisation and the patient mix that is served and the risk of working in overtime. Prospectively, consecutively, and routinely collected data of an operating room department in a Dutch university hospital are used. Basic statistical principles are used to establish the relation between realistic utilisation rates, patient mixes, and accepted risk of overtime.ResultsAccepting a low risk of overtime combined with a complex patient mix results a low utilisation rate. If the accepted risk of overtime is higher and the patient mix is less complex, the utilisation rate that can be reached is closer to 100%.ConclusionBecause of the inherent variability of health-care processes, the holy grail of 100% utilisation is unlikely to be found. The method proposed in this paper calculates a realistic benchmark utilisation that incorporates the patient mix characteristics and the willingness to accept risk of overtime.

Optimizing intensive care capacity using individual length-of-stay prediction models.

IntroductionEffective planning of elective surgical procedures requiring postoperative intensive care is important in preventing cancellations and empty intensive care unit (ICU) beds. To improve planning, we constructed, validated and tested three models designed to predict length of stay (LOS) in the ICU in individual patients.MethodsRetrospective data were collected from 518 consecutive patients who underwent oesophagectomy with reconstruction for carcinoma between January 1997 and April 2005. Three multivariable linear regression models for LOS, namely preoperative, postoperative and intra-ICU, were constructed using these data. Internal validation was assessed using bootstrap sampling in order to obtain validated estimates of the explained variance (r2). To determine the potential gain of the best performing model in day-to-day clinical practice, prospective data from a second cohort of 65 consecutive patients undergoing oesophagectomy between May 2005 and April 2006 were used in the model, and the predictive performance of the model was compared with prediction based on mean LOS.ResultsThe intra-ICU model had an r2 of 45% after internal validation. Important prognostic variables for LOS included greater patient age, comorbidity, type of surgical approach, intraoperative respiratory minute volume and complications occurring within 72 hours in the ICU. The potential gain of the best model in day-to-day clinical practice was determined relative to mean LOS. Use of the model reduced the deficit number (underestimation) of ICU days by 65 and increased the excess number (overestimation) of ICU days by 23 for the cohort of 65 patients. A conservative analysis conducted in the second, prospective cohort of patients revealed that 7% more oesophagectomies could have been accommodated, and 15% of cancelled procedures could have been prevented.ConclusionPatient characteristics can be used to create models that will help in predicting LOS in the ICU. This will result in more efficient use of ICU beds and fewer cancellations.

Analytical models to determine room requirements in outpatient clinics

Outpatient clinics traditionally organize processes such that the doctor remains in a consultation room while patients visit for consultation, we call this the Patient-to-Doctor policy (PtD-policy). A different approach is the Doctor-to-Patient policy (DtP-policy), whereby the doctor travels between multiple consultation rooms, in which patients prepare for their consultation. In the latter approach, the doctor saves time by consulting fully prepared patients. We use a queueing theoretic and a discrete-event simulation approach to provide generic models that enable performance evaluations of the two policies for different parameter settings. These models can be used by managers of outpatient clinics to compare the two policies and choose a particular policy when redesigning the patient process. We use the models to analytically show that the DtP-policy is superior to the PtD-policy under the condition that the doctor’s travel time between rooms is lower than the patient’s preparation time. In addition, to calculate the required number of consultation rooms in the DtP-policy, we provide an expression for the fraction of consultations that are in immediate succession; or, in other words, the fraction of time the next patient is prepared and ready, immediately after a doctor finishes a consultation. We apply our methods for a range of distributions and parameters and to a case study in a medium-sized general hospital that inspired this research.