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POOLING HOSPITAL BEDS
SHARING CAPACITY FOR HOSPITAL EFFICIENCY
Master thesis, MSc Technology & Operations Management University of Groningen, Faculty of Economics and Business
June 21, 2013 N. Goossens student number: 1905503 e-mail: n.goossens@student.rug.nl
Supervisor / university dr. ir. D.J. van der Zee
Co-assessor / university dr. H. Balsters
Supervisor / field of study ir. A.P. Goudswaard MBA
T.J.J. Hoogstins MSc I.A. van der Weide MSc University Medical Center Groningen
Abstract
Purpose: The purpose of this research is to develop and test pooling concepts that can be used for redesigning nursing departments to increase efficiency while maintaining availability targets.
Traditionally hospitals are functionally organized: each specialty has its own nursing ward. Nursing wards have to cope with variability in demand. Pooling is a way to reduce variability by combining multiple sources of variability. As a result the number of beds may be reduced without getting problems in the availability of beds.
Method: The research focuses on the bed usage of nursing wards. Findings from literature, interviews with planners and company data are used to set up the system description, analysis and pooling designs. A simulation study was performed based on data of 13 nursing wards of the University Medical Center Groningen.
Findings: Larger (pooled) nursing wards need less spare capacity. However, full pooling all wards may not be possible due to the barriers for pooling, such as lack of formal cooperation, staff requirements, coordination issues and in-house logistics. Clustering is proposed as an alternative to pooling all wards together. Coordination and cooperation get easier when fewer wards are involved.
Limited overflow between wards is introduced to ensure that only a part of the nursing staff has to be cross-trained.
In the simulation study three alternative scenarios were tested: no pooling, pooling in clusters and pooling all wards. Within these scenarios different overflow levels were tested. Bed availability increases significantly if ward are pooled in clusters. Full pooling benefits the availability even more.
Remarkably, the availability of wards already significantly increases when a limited overflow of 10%
between wards within a cluster is allowed.
Efficiency optimization results show that the UMCG section B&C uses fewer hospital beds than expected. Guaranteeing 97.5% availability on all wards in the no pooling situation would require at least 281 beds. At the moment 250 beds are in use. This would either indicate that wards currently do not reach their availability target or that wards already use informal forms of cooperation. Pooling significantly lowers the hospital bed requirements and significantly improves the occupation rate.
Conclusion: Simulation results show that clustering can be used as an alternative to full pooling.
Limited overflow is a way to approach the balance between costs of unused capacity and pooling investments, such as the cross-training of nursing staff. The Erlang B model is a feasible alternative for determining the required number of beds, compared to time consuming and costly simulation efforts.
Recommendations: Consider pooling in clusters with limited overflow. To ensure patient safety, pooling and cross-training interventions should be formalized. For the reduction of capacity a phased approach is proposed. A cost-benefit analysis should be made to weigh the costs and benefits of both the unpooled and pooled scenarios, such as idle staff time and cross-training investments.
Value: This research evaluates intermediate forms of pooling that especially fit to the hospital context.
Preface
This Master thesis is the final project for my Master of Science in Technology and Operations Management at the University of Groningen. The goal of this thesis was to explore the potential of pooling hospital beds to improve hospital efficiency. Insights on feasible pooling configurations were obtained by doing a case based simulation study within the University Medical Center Groningen.
Performing a research based on practice has been a great and challenging experience to me. I would like to thank Mr. Goudswaard, Mr. Hoogstins and Mr. van der Weide from the UMCG for their constructive feedback and valuable insights on the complexity of hospital practice. Their advice and involvement in setting up the analysis and the development of the simulation models helped me a lot.
I would like to thank my supervisor Mr. van der Zee for sharing his experience on the process of making a clear and structured report. During the feedback meetings I received many insightful ideas and comments. His positive approach motivated me to perform as much as I was able to.
I thank my co-assessor Mr. Balsters and my fellow students of the healthcare thesis theme group for their feedback on earlier drafts of this thesis. Finally, I thank the staff of the TOM master for providing such an interesting year making it the perfect preparation for writing this thesis.
Groningen, June 2013 Nick Goossens
Table of Contents
1. Introduction ... 7
2. Research objectives and setup... 8
2.1 Background ... 8
2.2 Research objectives ... 8
2.3 Research design... 9
3. Theoretical framework ... 10
3.1 Need for hospital efficiency ... 10
3.2 Pooling hospital beds... 11
3.3 Partial pooling ... 11
3.4 Methods for performance evaluation... 12
4. System description ... 14
4.1 Process overview... 14
4.2 Patient characteristics ... 15
4.3 Staff and resources ... 15
4.4 Planning and control... 15
5. Analysis... 18
5.1 Current performance nursing wards ... 18
5.2 Opportunities for pooling ... 18
5.3 Barriers for pooling ... 19
6. Design... 20
6.1 Addressing barriers for pooling... 20
6.2 Pooling clusters ... 21
6.3 Overflow mechanisms ... 22
7. Testing... 23
7.1 Experimental design ... 23
7.2 Simulation modeling ... 23
7.3 Simulation setup ... 24
7.4 Results ... 24
8. Discussion ... 27
8.1 Comparison simulation and queuing theory... 27
9. Conclusion & suggestions for further research ... 28
9.1 Conclusion... 28
9.2 Recommendations ... 29
9.3 Limitations and suggestions for further research ... 29
References ... 31
Appendix A: Organizational chart UMCG... 33
Appendix B: Travel distances ... 34
Appendix C: Conceptual model simulation study... 35
Appendix D: Model coding... 36
Appendix E: Warm-up length, replications and run length... 37
Appendix F: Model validation ... 38
Appendix G: Simulation results ... 39
Appendix H: Input distributions simulation study ... 43
1. Introduction
Over the last decade hospitals have been increasingly busy with improving the efficiency of their operations (Vanberkel et al., 2010). This attention is due to developments in the health care sector such as increasing expenditures, an aging population, government cuts and the increased attention on managed competition (Okma et al., 2013; Vanberkel et al., 2010). Increasing efficiency is a way to lower hospital expenditures. However, hospitals have to keep up high standard for the quality of care (Joustra, Sluis, & Van Dijk, 2009; Vanberkel et al., 2010). The pooling of nursing facilities, especially staff and beds, addresses this growing emphasis on efficiency (Bruin et al., 2009; Joustra et al., 2009).
This research provides a case study analysis within the University Medical Center Groningen (UMCG). Currently, beds are mostly dedicated to a medical specialty. Hospital data shows that the utilization rates are relatively low, mainly because of the high requirements for bed availability in combination with uncertainty about patient arrival and their service needs (UMCG, 2012). The study investigates to what extent the pooling of hospital beds from different nursing wards can improve the bed usage efficiency and at the same time guarantee the bed availability.
The concept of pooling can be described as the activity of combining customer demands in order to yield operational improvements such as hospital beds (Vanberkel et al., 2010). Traditionally most hospitals are functionally organized (Bruin et al., 2009; Vanberkel et al., 2010). In this situation all specialties have their own dedicated nursing facilities (Vissers & Beech, 2005: 59). When hospital wards share their facilities they may better cope with variability of demand and as a result the total number of beds can be reduced without lowering the service level targets (Vanberkel et al., 2010).
Research on pooling within a hospital context showed that there are numerous variables that may influence the usefulness of pooling such as clinical load, ward size, appointment length variability, etc.
(Vanberkel et al., 2010).
Queuing models have been developed to determine how many beds in a nursing ward are required to meet demand within the target service level (Bruin et al., 2009; Joustra et al., 2009; Vanberkel et al., 2010). The advantage of these models is that they are straightforward and simple to use (Bruin et al., 2009). Another often used method is simulation. One of the big advantages of simulation is that can be used to accurately investigate the influence of variability, i.e. in demand patterns (Bruin et al., 2009;
Joustra et al., 2009; Vanberkel et al., 2010). However, simulation based on real data is time- consuming, complex and costly due to efforts in modeling and data collection. On the other hand, in general simulation model outputs have a higher communicative value and reach closer to reality (Robinson, 2004: 9-10). Both described methods can be used as a performance evaluation tool to investigate the trade-off between bed usage efficiency and bed availability (Bruin et al., 2009).
Due to the large number of variables that influence the effect of pooling and the complex interrelations between them it remains unsure to what extent the pooling of hospital beds should exactly be implemented in order to gain maximum benefits from it (Vanberkel et al., 2010). Therefore, this study weighs the opportunities for pooling against implementation requirements and obstacles - the barriers for pooling - and tests pooling scenarios using simulation.
2. Research objectives and setup
This chapter gives an overview of the content and scope of the research. Paragraph 2.1 describes the problem background. Paragraph 2.2 defines the research objective. Sub-questions are set up to approach the research in a structured way. Paragraph 2.3 discusses the research design.
2.1 Background
In 2010 the UMCG initiated organizational-wide action for the realization of structural cost reductions by reducing unused capacity as much as possible. Economic performance improvements may not interfere with the performance on availability. Both rational and emotional sentiments caused that decisions on capacity reduction were postponed.
In 2012 hospital sections (see appendix A) asked the UMCG logistics & innovation department to give advice about hospital bed pooling scenarios. To do so, the Erlang B model was used as a quantitative tool. Results showed that larger (pooled) nursing wards would need less spare capacity to guarantee similar availability (UMCG, 2012).
Nursing staff is not convinced that pooling will work out. At the UMCG the operational planning of nursing wards is decentralized. Each nursing ward has its own planners. In practice it sometimes happens that all beds are occupied. According the planners this shows that capacity reductions are not possible. Nursing wards are careful as capacity evaluations may show that capacity can be reduced.
The sentiment exists that such an evaluation will be done once and that the results will be permanent.
Possible solutions are only valuable if they are evaluated within a wider perspective. Therefore the analysis starts with reviewing existing theory and collecting information about the current system and working procedures. Next, the opportunities and barriers for pooling are identified and addressed resulting in configurations that fit the hospital context.
2.2 Research objectives
The main objective of this study is to develop and test pooling concepts that can be used for redesigning nursing departments to increase efficiency while maintaining availability targets.
Efficiency is defined as the percentage occupancy of hospital beds.
Availability is defined as the percentage of times a patient is directly admitted
Sub-questions of the research are formulated in accordance with the steps of the regulative cycle (van Strien, 1997). Answers to the main objective and sub-questions are evaluated in the discussion (§8).
Sub-questions:
1. System description What are the characteristics of the current system for planning hospital beds?
2. Analysis What opportunities and barriers for pooling can be identified?
3. Design How should the opportunities and barriers for pooling be addressed?
4. Testing How do pooling concepts influence hospital efficiency and bed availability?
2.3 Research design Step 1: System description
In order to investigate the effects of pooling in practice it is necessary to know more about the current system for planning hospital beds within the UMCG. Describing the characteristics of the system is important as it provides a framework and thus creates the starting point in which further research should take place. Characteristics and operational procedures of the different nursing wards were investigated by conduction interviews with operational planners of two different wards.
Step 2: Analysis
The analysis describes and discusses the current performance of the UMCG nursing wards. Queuing theory is used as a tool to estimate current availability and occupation rate. Next to that, the possible solution ‘pooling’ is reflected against the system description and literature. Both the opportunities as well as the barriers for pooling are investigated using company data, literature and findings from the interviews with operational planners.
Step 3: Design
In the design phase alternative configurations to be tested are developed. Critical success factors and design parameters are identified based on the findings of the analysis. Based on both the analysis and the literature review ward composition criteria and overflow mechanisms are defined. This results in possible pooling designs.
Step 4: Testing
In this step alternative solutions (design scenarios) are tested using simulation. Simulation is used as a method for performance evaluation as it can cope with variability, interconnectedness and complexity (Robinson, 2004:4).
According to Robinson (2004:63) it is important to start with setting up a conceptual model. Such a model shows the impact on many factors of the study like data requirements, feasibility and validity and affects the confidence that is placed in the results (Robinson 2004:63). The conceptual model is used for making decisions on what data to include in the model and what model implications should be implemented to guarantee feasibility.
The data in this research is due to the limited amount of time mainly either available or uncollectable.
Data on capacity and its usage was available via the logistic department of the UMCG. Due to the time-frame it was not possible to collect additional data on urgency levels and staff costs. When data was not obtainable it was estimated or treated as an experimental factor (Robinson, 2004:98).
The simulation study investigates the current situation and weighs it against pooling configurations identified in the design phase. To ensure the efficient use of simulation a plan was set up. This plan gives an overview of the different experiments that were performed. Sensitivity analysis is performed to identify the effect of availability targets and waiting times.
3. Theoretical framework
This section gives an overview of literature on pooling. Section 3.1 discusses the general characteristics of a hospital when addressing the trade-off between efficiency and availability. Section 3.2 explains the concept of pooling hospital beds. Section 3.3 considers the options for partial pooling.
Section 3.4 discusses methods for performance evaluation.
3.1 Need for hospital efficiency
Hospitals are under great pressure to reduce costs while maintaining high quality standards. One way to address this is by delivering care more efficiently (Vanberkel et al., 2010). Bruin et al. (2009) acknowledge this. They state that capacity planning issues are nowadays primarily driven by financial and operational performance indicators specifically tailored to the health care sector. For example, the funding of Dutch hospitals is based on fixed reimbursements per case; the diagnosis treatment combination system (Niemeijer et al., 2012).
Traditionally, most hospitals are divided into functional departments based on medical specialty (Vanberkel et al., 2010). The division of resources among these departments is often to a great extent based on historically obtained rights rather than objectively substantiated from the field of operations management (Bruin et al., 2009). In practice, resources are often directly allocated to the different departments. This also applies to hospital beds. In general hospitals organize their available beds into units used by one or more clinical disciplines (Vanberkel et al., 2010). According to Bruin et al.
(2009) pooling departments or mixing patient flows may be a good solution to improve efficiency as fewer beds are required for reaching the same availability.
Patients can only be admitted if there is a bed available. Therefore, it can sometimes happen that admissions have to be refused due to variation in the arrival of patients. The higher the occupancy in a certain configuration the more likely it is that patients have to be refused (Bruin et al., 2009). In practice, a refused admission can result in a diversion to another hospital or to another clinical ward (Bruin et al., 2009) or it might be the case that patients have to wait longer than the target time set by the management (Joustra et al., 2009). Pooling hospital beds may be the solution in such situations as it may lead to higher occupancy with the same availability target (Vanberkel et al., 2010). However, this depends on the degree of heterogeneity (and interchangeability) of the demand (Ata & Van Mieghem, 2008; Bruin et al., 2009; Joustra et al., 2009; Vanberkel et al., 2010).
Figure 1: Pooling hospital beds - Influential factors
Figure 1 gives an overview of the research. The performance is the result of the patient inflow and the
3.2 Pooling hospital beds
Pooling can be described as the principle of combining two (or multiple) queues into a single one (Joustra et al., 2009) and is a way to reduce variability by ‘combining multiple sources of variability’
(Hopp & Spearman, 2011: 298) in order to use capacity more efficiently (Joustra et al., 2009). A combined patient stream uses the total capacity of multiple streams resulting in a higher total availability (Bruin et al., 2009; Vanberkel et al., 2010) and therefore offers the potential to increase performance without adding additional resources (Vanberkel et al., 2010).
In a pooled situation customers may achieve shorter waiting times than in an unpooled situation where facilities are dedicated to a more limited range of customer types (Vanberkel et al., 2010). Vanberkel et al. (2010) illustrate this as follows. In the unpooled situation, where all departments have their own dedicated facilities, one customer could be waiting while facilities in another department are still available. If the system had been pooled, then the customer could have been helped immediately.
Joustra et al. (2009) state that pooling from a theoretical perspective is ‘ultimate efficiency’. They describe pooling as a situation in which two separate queues and two separate servers are combined.
In this situation neither of the two severs can ever be idle while a customer is waiting.
One of the main advantages of pooling is economies of scale. Image two queuing systems, a smaller and a larger one: the larger system can reach a higher occupancy while the availability targets are the same. This effects was shown by Bruin et al. (2009) when they investigated the effect of sharing resources among nursing wards. As they state it, especially smaller units have trouble keeping a bed available for an arriving patient. According to Vanberkel et al. (2010) in general it is true that the higher occupied departments can gain more from pooling than the lower occupied ones. Furthermore, smaller patient groups experience a greater loss of economies of scale when departments are un- pooled. As they explain it is harder for the smaller than for the larger departments to proportionally divide resources.
In practice demand for care tends to be heterogeneous, which reduces the value of pooling (Ata & Van Mieghem, 2008; Vanberkel et al., 2010). Joustra et al. (2009) debate the influence of different service characteristics in pooling. They state that pooling can add variability to the system. Even when systems have a substantially larger capacity it could be advantageous to keep queues separate as pooling can significantly increase mean waiting times in the system. According to Van Dijk & Van der Sluis (2008) pooling theoretically enhances performances as capacity is used more efficiently and it is therefore often seen as the superior approach.
3.3 Partial pooling
Full pooling may not be the best solution as demand tends to be heterogeneous (Ata & Van Mieghem, 2008; Vanberkel et al., 2010). Not pooling departments also has benefits for hospital efficiency.
Because of the relative lower complexity departments can focus on doing fewer things better (Vanberkel et al., 2010) as resources remain dedicated to a specific department allowing resource specialization (Ata & Van Mieghem, 2008). Research indicates (Mueller, 2012) that there is a negative relationship between team size and individual performance due to losses in coordination, motivation and social relationships.
From an organizational point of view the benefits from pooling and from focus have to be weighted (Vanberkel et al., 2010). When departments are pooled nursing staff has to be cross-trained as they are
part of the hospital bed capacity (Bruin et al., 2009; Van Dijk & Van der Sluis, 2008) which will require a certain investment. Additional investment costs such as the adjustments of beds and buildings also have to be considered in pooling decisions. Vanberkel et al. (2010) say that the partial pooling of resources ‘may be a beneficial compromise to strict pooling’. In such a situation generic resources are shared among hospital departments whereas specialist resources remain dedicated.
Partial pooling can be implemented in different ways. In an overflow system departments remain separate. Capacity is only used in case of overflow (Van Dijk & Van der Sluis, 2009). Only a smaller part of the nursing staff has to be cross-trained. As a result investment costs are kept to a minimum.
Teams remain smaller enhancing the motivation (Mueller, 2012). The overflow from one department to another may be limited to a certain extent as it is done in inventory sharing systems (Zhao, Deshpande, & Ryan, 2005).
A threshold system is an overflow system in which a distinction is made between different types of demand, i.e. urgent and elective patients (Van Dijk & Van der Sluis, 2009). Again, departments remain separate. However, in this case capacity of the other department may only be used for patients with a high priority level. Joustra et al. (2009) performed a research on pooling in which they differentiated between regular and urgent patients. In their case the system performed better when both patient streams were un-pooled.
Joustra et al. (2009) propose a system in which reserved capacity for an urgent patient can be used by a regular patient. When the reserved capacity is not used, then the bed becomes available for a regular patient. The aim of such a system is handling the idle capacity (Van Dijk & Van der Sluis, 2009). The approach implies that a regular patient can be scheduled i.e. one day before admission. In practice this may not always be possible. However, with a success rate of 50% it shows that the necessary spare capacity drops over 30% (Joustra et al., 2009).
3.4 Methods for performance evaluation
Both queuing theory and simulation can be used to investigate the effect of pooling. Queuing models use long time averages whereas a simulation model can handle data of individual patients (Robinson, 2004:9).
3.4.1 Simulation
One of the big advantages of simulation is that can be used to accurately investigate the influence of variation, i.e. in demand patterns (Bruin et al., 2009; Joustra et al., 2009; Vanberkel et al., 2010). In general simulation does not require many assumptions. However, Assumptions have to be made to simplify the model and deal with shortage of data. (Robinson, 2004: 9). Setting up a simulation study based on real data is more time-consuming, complex and costly than using a generalized mathematical model that uses long-time averages as an input. On the other hand the communicative value of a simulation model may be way higher (Robinson, 2004: 9-10).
3.4.2 Queuing theory
Joustra et al. (2009) reported queuing theory as an insightful method useful for quickly analyzing different scenarios. It gives insights in relationships between variables and helps with defining parameters and setting up more advanced methods like simulation (Gautam, 2012:8).
According to (Bruin et al., 2009) patient inflow can be described by a standard queuing model, the Erlang loss model / Erlang B model. In the model no customer can ever wait for service. If there is a server available a customer enters the system, otherwise service is rejected (Gautam, 2012: 60). In other words, a patient that needs to be treated in a hospital bed cannot be treated without that bed, so if there is no bed available the patient has to be sent home or elsewhere. The Erlang loss model can be used to determine the required number of operational beds (Bruin et al., 2009).
The Erlang loss model (i) assumes patient arrival according to a Poisson distribution. It takes the average number of scheduled arrivals as an input variable. Such measurements are relatively easy to obtain and process (Bruin et al., 2009). However, queuing theory assumes homogenous demand: in practice demand is often heterogeneous (Vanberkel et al., 2010). In their research Bruin et al. (2009) did not distinguish between specific arrival patterns like, day, week or weekend patterns as they wanted to develop a generalizable tool. Also, the formula (i) is insensitive for the length of stay meaning that length of stay distributions are not taken into account.
= / !
∑ / !
(i)
P = fraction patients blocked λ = patient arrival
μ = service rate s = nr of beds
4. System description
This chapter describes the primary process of the UMCG nursing wards. Paragraph 4.1 gives an overview of the process of a nursing ward. Paragraph 4.2 and 4.3 describe the influence of patient characteristics and staff/resources, respectively. Paragraph 4.4 addresses planning and control of nursing wards.
(1) ‘What are the characteristics of the current system for planning hospital beds?’
4.1 Process overview
Figure 2 gives an overview of the key elements of a nursing ward. The process starts with the arrival of a patient. An arriving patient has a certain urgency level and needs a specific treatment. Based on the availability of beds in combination with the urgency level of the patient a patient is admitted, has to wait or is refused. A refused patient may be send to another nursing ward or hospital. A not urgent refused patient can also be asked to come back to the hospital on another moment.
Figure 2: System description UMCG nursing ward
When a patient is admitted it will undergo treatment. From a system point of view this means that the patient is using capacity of the nursing ward for a certain amount of time. Capacity can be subdivided in staff and resources (see §4.3). The time a patient spends on the ward is called the length of stay (LOS). After the treatment is completed the patient leaves the nursing ward.
A patient that leaves the ward for a short amount of time, for example for an examination or operation, is not a discharge. In other words, only when the whole treatment program on the nursing ward is finished the patient is registered as discharged in the hospital information system.
4.2 Patient characteristics
The UMCG uses a triage system to categorize their patients. The urgency level of an incoming patient is determined before the patient enters the nursing ward (see figure 2). The urgency level is known by the planners and used to determine if there is a bed available. Urgent patients get priority over less urgent patients.
Next to that, patients differ in the type of treatment they need. The allocation of staff and resources is tailored to the specific treatment requirements (see figure 2). For example, severe patients get a private room and more staff allocated.
4.3 Staff and resources
Staff: Each nursing ward has a fixed team of staff members. A team consists of medical specialists, doctors in training, nurse practitioners, nurses, nutrition assistants and department assistants. Staff members are educated and trained according to the specialty of their nursing ward. This is especially true for specialists and nurses. Still every member of the nursing staff has a mandatory general knowledge about the treatment of patients.
In addition to the fixed staff patients sometimes get treatments from several other disciplines such as psychotherapy, dietetics and from specialists from other medical specialties. The daily management of a ward is coordinated by the head nurse. The head nurse is supported by a control nurse. The control nurse verifies if the daily care provided by the ward is according to standards.
Equipment and Beds: Nursing wards mostly use standardized beds. Most hospital beds and additional pieces of equipment are moveable and can be used on all wards.
Rooms: Nursing departments have rooms for 1, 2 and 4 patients. When a patient has to be treated in quarantine and all 1 patient rooms are full, than a patient may be allocated to a 2 patient room. This causes that the capacity for one patient cannot be used.
Building: The wards of the UMCG are divided over 4 floors. The hospital is approximately 175 meters wide and 300 meters long. Travel distance approximations between wards of the section B&C can be found in appendix B, as well as the number of admissions per ward.
4.4 Planning and control
Hans, Van Houdenhoven, & Hulshof (2011) developed a framework for health care planning and control. One of the managerial domains they address is ‘resource capacity planning’. Within this domain four hierarchical levels are distinguished: strategic, tactical, operational offline and operational online. The current planning policies of the UMCG nursing wards are described below according to this subdivision.
4.4.1 Strategic planning
According to Hans et al. (2011) ‘strategic planning addresses structural decision making’. Strategic planning has a long planning horizon based on forecasts and highly aggregated data.
The organization of the UMCG consists of six sections each responsible for their own results. Each section supervises a number of nursing wards (see appendix A). Annually, the Board makes agreements with the sections about objectives and resources (budget). The strategic capacity allocation
focuses on how many treatments each specialty in a section will perform in a year. Historical data and forecasts of possible growth or decline are used to approximate production volumes per specialty.
However, the number of beds on a nursing ward is not evaluated on a structural (yearly) basis. The division of hospital beds is historically grown. Until 1997 each specialty had its own clinic in separate buildings. These clinics had obtained their bed capacity throughout the years. Shortages in hospital beds observed in practice caused that clinics increased the number of beds. In 1997, when the clinics moved together into the current building the division of bed capacity remained as it was before.
In conclusion, financial planning is used to allocate production volumes to specialties. On the strategic level sections focus at their production targets. However, the usage of hospital beds by nursing wards is not reflected on a strategic level.
4.4.2 Tactical planning
The tactical planning addresses the execution of the health care delivery process (Hans et al., 2001).
Currently, the UMCG has no tactical planning to determine how many hospital beds each nursing ward needs. Demand forecasts are not made. Information on seasonal changes, waiting lists or the number of patients that are currently treated on the ward is not used.
4.4.3 Operational offline planning
The operational planning of nursing wards in the UMCG is decentralized, meaning that each ward has its own planners. These planners are responsible for allocating the capacity in terms of beds, rooms and staff to the different patients. According to Hans et al. (2001) the offline planning is the detailed planning of operations in advance, such as appointment scheduling and nurse rostering.
The available timeslots in the operating theatre (OT) serve as an input for the ward planning. Wards fill these timeslots with appointments for elective patients and keep some spare capacity for urgent cases. For this a planning horizon of one week is used. The planning of the operating theatre gives a good indication of how many patients there will be arriving in the following week. For the planning of the nursing staff both the OT planning and the current occupation of the ward are used.
Most wards do not check the availability of beds in advance. Predictions about discharge dates of patients on the ward are also not used. Some wards reserve beds based on their weekly planning, others don’t.
4.4.4 Operational online planning
Online planning involves the controlling and monitoring of the process, ‘reacting to unforeseen or unanticipated events’ (Hans et al., 2001) and involves the planning on a daily basis.
The planners from a nursing ward start their day with a meeting. Planners and medical staff discuss the arriving patients, planning of the staff and occupation of the ward. The rest of the day the planners are mainly busy with making appointments for the following week and controlling the flow of the patients through the ward.
On a daily basis urgent patients are the main concern. Due to the unpredictability of urgent demand the
planners make a distinction between urgent and ‘really urgent’ patients. Based on this comparison a patient will be admitted, has to wait or is refused.
Some wards keep a few beds reserved for urgent patients, while others don’t. When there is no bed available for an urgent patient, then the planners have to look for other ways to serve the patient. In practice, when a ward is fully occupied informal channels are used to see if there is a bed available on another ward. For example, wards with adjacent fields of knowledge call each other to see if they have spare capacity.
If a ward is fully occupied patients sometimes get referred to another ward. In most cases the patient will be send back as soon as there is a bed available on the preferred ward. There are some exceptions.
For example, a patient that leaves the hospital within one day will not be transferred anymore. Also, if a patient unexpectedly needs an operation capacity will be created by reserving a bed or switching with a patient that is staying on the preferred ward.
When comparing the operational planning methods of different nursing wards it can be noticed that there are many rules and working policies which differ per ward and even per planner. There are no formal rules for planning hospital beds. Most planning of beds is done on the operational online level and can for the larger part be characterized as ad hoc.
5. Analysis
This chapter reflects on the current system for hospital bed planning. Paragraph 5.1 discusses the current performance of hospital wards on bed usage. Paragraph 5.2 investigates pooling as a potential performance enhancing solution. Paragraph 5.3 investigates the barriers for pooling.
(2) ‘What opportunities and barriers for pooling can be identified?’
5.1 Current performance nursing wards
Data of department B&C over the year 2012 is used to evaluate the current performance, see table 1.
As described in the literature review the Erlang B queuing theory may be used as a tool to evaluate the performance on bed usage, see chapter 3.4.2. To do so, first the number of admissions and the average length of stay per nursing ward were determined. The number of hospital beds available on each ward is also available. With this input the Erlang B queuing model was used to calculate the availability rate (long run fraction of patients directly admitted) and the occupation rate (the fraction of time a bed is occupied by a patient).
Specialty Specialty # admissions # Average
Length of Stay
# Beds in use
Availability rate
Occupation rate
CAB CTX
Abdominal surgery
Transplantation surgery 1485 7.61 25 73.6% 91.2%
CHP CLT
Hepatobiliary surgery
Liver transplantation surgery 426 9.54 15 93.8% 69.6%
CON Oncology 729 4.90 20 99.8% 48.9%
MOA Oral surgery 526 3.03 12 99.9% 36.3%
KNO Otorhinolaryngology 1584 3.53 32 100% 47.9%
MDL Gastroenterology + Hematology 1200 8.61 27 83.6% 87.6%
O&G Obstetrics and Gynecology 922 3.47 14 97.6% 60.8%
OHA Ophthalmology 303 1.22 32 100% 3.1%
ORA Orthopedics 1118 6.90 31 99% 67.5%
CPL Plastic surgery 652 2.39 9 98.2% 46.6%
CTR Traumatology 1198 6.76 30 97.8% 72.3%
CUR Urology 1340 3.22 20 99.1% 58.6%
CVA Vascular surgery 851 5.37 15 89.9% 75.0%
Data: admissions section B&C 2012
Table 1: Bed usage per nursing ward section B&C
5.2 Opportunities for pooling
Results show that the capacity is not optimally divided. There are large differences between nursing wards on availability and occupation rate. In literature an availability target of 95% is common to use (Bruin et al., 2009). The UMCG uses an availability target of 97.5% for each ward. The hospital wants to achieve structural cost reductions by reducing unused spare capacity. The availability rate estimates indicate that wards might have too much spare capacity.
In the literature review pooling is described as the way to reduce variability by combining multiple sources of variability (see §3.2). Cooperation on bed usage between nursing wards would cause that the highly occupied wards can use capacity of the less occupied ones. Next to that, larger nursing wards (by pooling) need less spare capacity to absorb the variation in demand. Pooling would therefore result in higher efficiency improvements compared to just downsizing current nursing wards.
5.3 Barriers for pooling
Cooperation: Currently, there is no formal cooperation between wards in the sharing of hospital beds.
Wards mainly focus on the functioning of their own operations. The decentralized way of planning may have caused that planners only experience what happens on their own nursing ward. As a result wards have to perform ad hoc action in case of emergency. The situation on the other ward is seen as important but it has no priority to the planners.
Nursing wards are not eager to cooperate with structural capacity evaluations. Most planning efforts with regard to the allocation of beds to patients are performed on the operational online level. Nursing wards are afraid that if they reduce in capacity it will be impossible to react to urgent patients arriving at the ward. However, it seems unfair that some wards have major difficulty in finding an empty bed while other wards have beds available.
Staff requirements: Nursing staff is trained to treat patients based on the specialty of their ward. When a patient uses a bed of another ward it might be the case that the staff hasn’t got the right knowledge to treat the patient. Therefore, nurses that work for a pooled ward might have to be cross-trained to know more about the treatments of other specialties. Wards might not want to invest in this training when the available beds are nearly always used by other wards.
Coordination: Coordinating the pooling of beds between 13 specialties is more complex than coordinating 1 specialty. It would be more difficult to keep overview of bed sharing policies, availability of beds and keeping track of the patients in the hospital. As a result there would be high demands on the planners keeping in contact with all nursing wards in the section. Next to that patients would be divided over all kinds of knowledge fields within the hospital.
In-house logistics: In a pooled situation arriving patients are divided over different nursing wards if their own ward is fully occupied. As a result travel times between wards i.e. for medical specialists increase. This causes a decrease in hospital efficiency as staff can treat fewer patients during their shift.
6. Design
In this chapter alternative configurations to be tested are proposed. Paragraph 6.1 addresses the barriers for pooling. Paragraph 6.2 describes the clustering of nursing wards. Paragraph 6.3 introduces different overflow mechanisms.
(3) ‘How should the opportunities and barriers for pooling be addressed?’
6.1 Addressing barriers for pooling
Both formal cooperation and meeting staff requirements are critical success factors for pooling.
Without meeting these requirements pooling is not possible. Coordination and in-house logistics further direct the design. These are design parameters.
Critical Success factors:
Cooperation: The analysis showed a lack of cooperation between nursing wards resulting in an inefficient use of hospital beds. Planners should be made aware that their ward is part of a larger system. The formal sharing of hospital beds through pooling can help in raising this awareness. Urgent patients still can be admitted in a pooled situation after downsizing as pooling creates shared spare capacity.
Staff requirements: Nursing staff has to be cross-trained to be able to treat patients from other wards.
However, the complexity of treatments differs per patient. All nursing staff has a mandatory basic knowledge (not specialty specific) about patient treatment. So, when sharing bed capacity the less complex cases should be outsourced to other wards. Also, sharing capacity between nursing wards with overlapping fields of knowledge ensures that the nursing staff has the best possible relevant knowledge to treat the patient. This would also require the least cross-training efforts. Sections (see appendix A) have to make agreements with wards about sharing the costs and benefits of pooling in a fair way.
Design parameters:
Coordination: One option would be to share hospital beds between all nursing wards a section. Larger departments need significantly less spare capacity. However, the coordination of such a large system would become very complex. Next to that, the Erlang B model shows that the law of diminishing returns applies to pooling. The model indicates that after 50-60 beds the beneficial effects of pooling decrease. In other words, clusters optimally would be as large as 50-60 beds to gain maximum pooling benefits without getting coordination issues.
In-house logistics: From a logistic point of view clustering can also help in limiting the travel times between wards as patients are divided over fewer wards. Clusters should optimally consist of wards that are geographically close to each other.
6.2 Pooling clusters
The concept of pooling is practically tested by investigating alternative designs for the UMCG section B&C nursing wards. Currently, wards do not formally cooperate. Instead, the section consists of 13 separately operating wards. The ultimate form of cooperation is the pooling of all wards. However, due to coordination issues this may not be the optimal configuration. As an alternative the pooling in clusters is proposed. A cluster is defined as a group of wards which share their hospital beds with each other. The composition of clusters can be based on different criteria, described in table 2.
Composition criterion Description
Cooperation on other fields The degree to which wards cooperate in other ways than in the sharing of their bed capacity may be used as a composition criterion.
Staff requirements Staff requirements are a key success factor. The least cross-training efforts are required when wards are combined with the highest degree of knowledge fit.
Cluster size (coordination) Cluster size (total number of hospital beds in a cluster) may be limited due to coordination issues.
In-house logistics Staff time is used efficiently when travel times between wards are minimized.
Average length of stay To minimize delays wards with an equal average length of stay should be combined. The delay for the ward with the shorter length of stay will increase. This can be prevented by prioritizing own ward patients.
Table 2: Cluster composition criteria
Due to the barriers for pooling (§6.1) the logistics and innovation department of the UMCG proposed to use a clustered configuration, described in table 3. Staff requirements and current cooperation in patient treatment were dominant in the composition of clusters that due to the Erlang B estimates should consist of 50 to 60 beds after pooling. In-house logistics was taken into account to a lesser extent (see Appendix B). Patient delay due to variation in length of stay is prevented by prioritizing own ward patients above patients arriving from other wards in the cluster.
Cluster Ward Specialty
1 CAB
CON CTX CPL
Abdominal surgery Oncology
Transplantation surgery Plastic surgery
2 CHP
MDL CVA CLT
Hepatobiliary surgery
Gastroenterology / Hematology Vascular surgery
Liver transplantation surgery
3 MOA
KNO O&G OHA CUR
Oral surgery
Otorhinolaryngology Obstetrics and Gynecology Ophthalmology
Urology
4 ORA
CTR
Orthopedics Traumatology Table 3: Cluster sector B&C
As shown in table 3, for the section B&C having 4 clusters seems to be the optimal design solution.
An alternative to pooling all wards would be to also share capacity between clusters when a cluster is fully occupied.
6.3 Overflow mechanisms
As discussed in §3.3 there are different degrees of pooling, described in table 4. Limited overflow may be used as an efficient alternative to full overflow. In this case only a part of the nursing staff has to be cross-trained.
Degree of overflow Description
No overflow Wards can only use their own capacity.
Limited overflow Wards use joint overflow. Patients arrive at their preferred ward. If the ward is fully occupied the patient goes to another ward. Patients can only use a limited part of the capacity of another ward. For example each ward shares maximum 10% of its beds.
Full overflow Nursing wards share all bed capacity. Again patients only go to another ward if the preferred ward is fully occupied. Full overflow means that wards will not limit the inflow of patients form other cooperating wards.
Table 4: Degree of overflow
7. Testing
A simulation study was performed to investigate the effects of different pooling configurations on hospital efficiency and bed availability. Paragraph 7.1 shows the experimental design. Paragraph 7.2 and 7.3 discuss the simulation modeling and setup, respectively. Paragraph 7.4 provides an overview of the results.
(4) How do pooling concepts influence hospital efficiency and bed availability?
7.1 Experimental design
Table 5 shows the model summary. Additional information about the scope of the model, the assumptions and simplifications can be found in the conceptual model in appendix C.
Fixed factors
Inter-arrival time distribution Empirical distribution per ward
Length of stay Empirical distribution per ward
Experimental factors
Pooling scenario 1. No pooling
2. Cluster pooling (10%; 20%; 30%; 100% (default)) 3. Pooling all wards (10%;20%;30%;100% (default))
Maximum waiting time 0 hour (default); 2 hours
Number of beds Current situation UMCG section B&C (see table 7) Outputs
Occupation rate
Availability Target: 95%; 97.5% (default); 99%
Table 5: Model summary
Fixed factors: Due to the weekly and daily pattern of arrivals the inter-arrival time was modeled using an empirical distribution: for each day of the week and each hour of the day the chance that a patient arrives is determined. The probability distributions for the length of stay were fitted using ExpertFit.
No fit was found. Therefore, the length of stay was modeled as an empirical distribution using histogram intervals.
Experimental factors: Three pooling scenarios are tested. Sensitivity analysis is performed on the maximum waiting time and the arrival volume. The range for the number of beds depends on the pooling scenario, see §7.3 for more detail.
Outputs: The hospital efficiency is evaluated by looking at the occupation rate. The UMCG uses an availability target of 97.5%. To see the influence of a target choice sensitivity analysis is performed by also including a 95% and 99% availability target.
7.2 Simulation modeling
FlexSim Healthcare 3.14 was used to carry out the simulation experiments. Model coding is described in appendix D. The length of the warm-up period – 40 weeks - was determined by using the Welch method. According to literature the run length was set at 10x the warm-up period, 400 weeks.
(Robinson, 2004: 146-152). The confidence interval method showed that 5 runs were sufficient to ensure 95% accuracy. (Robinson, 2004: 154-156), see also appendix E. Model validation can be found in Appendix F.
7.3 Simulation setup
The different pooling scenarios investigated are described in table 6. The overflow column describes the degree of overflow between wards in the cluster. The benchmark is the current situation, with 13 unpooled clusters. The potential scenario is the maximum degree of pooling. The barriers for pooling (§6.1) and the consideration between full and partial pooling (§3.3) resulted in the clustered configuration, scenario 2. To minimize possible cross-training efforts limited overflow between 13 and 4 clusters is investigated in scenario 1 and 2, respectively.
Table 6: Pooling scenarios
7.4 Results
The simulation study can be subdivided in two phases. In phase 1 the effects of different scenarios on bed availability are investigated. In Phase 2 hospital efficiency is addressed by finding the minimum number of beds necessary for each scenario.
7.4.1 Phase 1: Bed availability current situation
Nursing ward Scenario 1
(Benchmark)
Scenario 2 (Clustering)
Scenario 3 (Potential)
# Beds Availability # Beds Availability # Beds Availability
CAB / CTX 25 49.4%
54
250
CON 20 99.6%
CPL 9 96.2% 93.0%
CHP / CLT 15 94.0%
57
MDL 27 81.7%
CVA 15 86.0% 97.5%
MOA 12 99.5%
78
KNO 16 77.5%
OG 14 95.5%
OHA 16 100.0%
CUR 20 98.3% 96.4%
ORA 31 97.8%
61
CTR 30 97.7% 98.8% 100.0%
Weighted Average 86.6% 96.3% 100.0%
Table 7: percentage of patients directly admitted
To see if the results significantly differ from each other a paired t-test was performed on the weighted average availability. The availability significantly improves when wards are pooled in clusters and when all wards are pooled together (p=0.000).The availability target of 97.5% used by the UMCG is only reached in the potential scenario.
Allowing a maximum waiting time of 2 hours slightly improves the weighted average availability, mainly because the CAB / CTX ward has a bed shortage in case of no pooling (see also Appendix G).
Clusters Overflow(within cluster)
Scenario 1 Benchmark 13 0% (default) ; 10%; 20%; 30%
2 Clustering 4 100% (default) ; 10%; 20%; 30%
3 Potential 1 100%
Nursing ward Scenario 2 [10%] Scenario 2 [20%] Scenario 2 [30%] Scenario 2 [100%]
Cluster 1 89.4% 91.4% 91.9% 93.0%
Cluster 2 96.0% 97.2% 97.4% 97.5%
Cluster 3 93.7% 95.9% 96.2% 96.4%
Cluster 4 98.1% 98.8% 98.8% 98.8%
Weighted Average 94.0% 95.7% 95.8% 96.3%
Table 8: Availability clustering wards
Table 8 shows that 10% overflow between wards in a cluster already ensures a weighted average availability of 94%. The availability increases when higher degrees of overflow are allowed, differences larger than 0.7% are significant(p=0.015).
In scenario 3 (potential) limited overflow of 30% is not sufficient to ensure an availability of 97.5%
(see appendix G, table 19).
7.4.2 Phase 2: Hospital efficiency
For each pooling scenario the availability targets (95%, 97.5% and 99%) have to be covered by the simulation results. To do so, the Erlang B model was used to estimate the lower and upper limit for the number of beds needed for reaching the availability targets, see table 9.
Table 9: Simulation setup / Erlang B estimates
Verification with simulation showed that the Erlang B estimates are overly optimistic. The simulation range is therefore determined by increasing the number of beds in steps of 10 until all availability targets are measured. Table 10 shows the simulation range.
Within this range for each number of beds the availability rate and bed occupation are determined. The goal is to find the occupation and the required minimum number of beds for each pooling scenario.
Overflow (within cluster)
Erlang B estimates (number of beds)
Clusters 95% 97.5% 99%
Scenario 1 Benchmark 13 0% 252 268 294
2 Clustering 4 100% 184 193 202
3 Potential 1 100% 205 214 235
Configuration Simulation range
(beds)
Scenario 1 Benchmark 250 - 310
2 Potential 200 - 230
3 Clustering 220 - 260
Table 10: Simulation setup / Simulation estimates
Figure 3 shows the results for the required minimum number of beds per availability target. In the potential scenario 63 beds fewer are required to guarantee an availability of 97.5% for each ward. The choice for an availability target has a significant influence on the required number of beds.
Figure 3: required number of hospital beds section B&C
Wards in the clustering and potential scenario both have a significantly higher weighted average occupation compared to the benchmark scenario. This is true for all availability targets (p=0,004), see figure 4.
Figure 4: Weighted average occupancy wards
Detailed simulation results can be found in appendix G.
260
221
208 281
235
218 303
251
228
150 170 190 210 230 250 270 290 310 330 350
Benchmark [scenario 1]
Clustering [scenario 2]
Potential [scenario 3]
Number of beds
Required minimum number of beds
95% availability 97.5% availability 99% availability
66%
79%
88%
63%
76%
86%
59%
72%
83%
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
Benchmark [scenario 1]
Clustering [scenario 2]
Potential [scenario 3]
Percentage occupation
Weighted average occupation wards
90% Availability 97.5% Availability 99% Availability
8. Discussion
The main objective of this study is to develop and test pooling concepts that can be used for redesigning nursing departments to increase efficiency while maintaining availability targets.
Simulation results show an improvement in performance on availability and occupation when wards are pooled. When all wards are full pooled the increase in performance is larger than when wards are clustered, compared to the no pooling situation. Sensitivity analysis on availability target shows that the choice for a certain level of availability has a significant influence on the required number of beds.
The minimum required number of beds - with an availability target of 97.5% for each ward - is 281.
Currently, the UMCG section B&C has 250 beds in use. This is either explained by informal forms of cooperation or by the not reaching of the availability targets.
Cost-wise the hospital should consider if the efficiency gains of pooling outweigh the investments necessary to cross-train nursing staff.
8.1 Comparison simulation and queuing theory
Table 11 compares the outcomes of the Erlang B model (§3.4.2) with the simulation results for the total minimum number of hospital beds required in each scenario. In the determination of the bed range for simulation §7.3 it already came apparent that the Erlang B model was overly optimistic.
Table 11 shows that the difference between the Erlang B and simulation outputs gets larger when wards are pooled. In other words, the simulation study shows that the benefits from pooling are smaller than the estimates of the Erlang B model.
Ward composition Erlang B Simulation Underestimation
Erlang B 95% Availability
No pooling 252 260 3%
Cluster full pooling 205 221 8%
All wards full pooling 184 208 13%
97.5% Availability
No pooling 268 281 5%
Cluster full pooling 214 235 10%
All wards full pooling 193 218 13%
99% Availability
No pooling 294 303 3%
Cluster full pooling 235 251 7%
All wards full pooling 202 228 13%
Table 11: Comparison Erlang B and Simulation
The Erlang B model assumes a Poisson distribution of patient arrivals: Bruin et al. (2009) ignored the difference in arrival pattern during the week and weekend on purpose, making the model an accessible managerial decision tool. Fit on UMCG data improves if distributions are split (see appendix H, figure 7 & 8). The fit decreases if wards are pooled (see app. H, figure 9). This may explain the increasing difference in Erlang B estimates and simulation outcomes. Next to that, the busiest time of the day is in general on all wards at the same time. These daily fluctuations are not taken into account by the Erlang B model, causing that more patients get refused than estimated. The variation in the length of stay seems to be of limited impact (see app. H, table 24). In conclusion, the beneficial effects of overflow rules are less than expected due to the patient arrival distributions.
9. Conclusion & suggestions for further research
Paragraph 9.1 reflects on the main objective and research questions. Paragraph 9.2 contains the recommendations. Paragraph 9.3 discusses the limitations and gives suggestions for further research.
9.1 Conclusion
The main objective of this study was to develop and test pooling concepts that can be used for redesigning nursing departments to increase efficiency while maintaining availability targets.
What are the characteristics of the current system for planning hospital beds?
The number of hospital beds per ward is historically grown and not evaluated on a strategic or tactical level. As a result hospital beds are not always optimally divided. The operational planning of nursing wards is decentralized resulting in many rules and working procedures that differ per ward and even per planner. There are no formal rules for the planning or sharing of hospital beds. Most planning of hospital beds can be characterized as ad hoc.
What opportunities and barriers for pooling can be identified?
Hospital efficiency can be improved by pooling nursing wards. Pooling deals with variability in demand. As a result pooled nursing wards need less spare capacity to reach their bed availability target. However, there are also barriers for pooling. Currently, wards focus mainly on their own operations. Cooperation has a low priority to the ward planners. Staff may need to be cross-trained to ensure sufficient knowledge and skills about treating patients from other wards. When wards are pooled patients get dispersed through the hospital causing coordination issues and wasteful travel time between wards.
How should the opportunities and barriers for pooling be addressed?
Due to coordination issues pooling all wards may not be the optimal configuration. As an alternative the pooling in clusters is proposed. The composition of clusters can be based on different criteria. For the UMCG staff-requirements and current cooperation in patient treatment were dominant criteria. The outcomes of the Erlang B model weighted against the coordination issues resulted in a configuration with 4 clusters, see table 3. Pooling in clusters with limited overflow should be considered as an alternative to full pooling all wards due to the costs involved with cross-training.
How do pooling concepts influence hospital efficiency and bed availability?
For the availability the percentage of patients directly admitted was measured. Bed availability increases significantly if ward are pooled in clusters. Full pooling benefits the availability even more.
Availability shows little increase when patients are still admitted 2 hours after arrival. Remarkably, the availability of wards already significantly increases if a limited overflow of 10% is allowed for wards within a cluster.
Efficiency optimization results show that the UMCG section B&C uses fewer hospital beds than expected. Guaranteeing 97.5% availability on all wards in the no pooling situation would require at least 281 beds. Currently 250 beds are in use. This would either indicate that wards currently do not reach their availability targets or that wards already use informal forms of cooperation. Pooling significantly lowers the hospital bed requirements and significantly improves the occupation rate.
