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Int. J. Services and Operations Management, Vol. 26, No. 3, 2017
Theory of constraints applied to scheduled and
unscheduled patient flows: does it improve process
Stefania Bisogno*, Armando Calabrese and
Nathan Levialdi Ghiron
Department of Enterprise Engineering ‘Mario Lucertini’,
University of Rome ‘Tor Vergata’,
via del Politecnico, 1 – 00133, Rome, Italy
Email: [email protected]
Email: [email protected]
Email: [email protected]
*Corresponding author
Alberto Pacifici
DS Tech srl,
Via Guido Reni, 33 – Rome, Italy
Email: [email protected]
Abstract: Theory of constraints (TOC) is particularly effective for improving
processes and maximising efficiency in systems that are resource-constrained.
One of the most common applications of TOC in the service sector is
healthcare, particularly patient flows which can be considered analogous to
‘production lines’. However, one of the main TOC techniques, ‘drum-bufferrope’ (DBR), is still poorly implemented in healthcare services. The study
provides a new approach where traditional DBR or ‘DBR for goods’ (DBRG) is
customised to improve admissions scheduling in a scheduled patient flow.
However, when arrivals of patients are necessarily unscheduled the DBRG is
not applicable. For these circumstances, a new procedure is also provided. This
procedure uses a variant of DBR (‘DBR for services’, DBRS) that is adapted
here for an unscheduled patient flow. The purpose of both the adapted DBRG
and DBRS is to provide rules to control the throughput of patients. As ever in
flow systems, there is a trade-off between minimising patient flow times and
maximising the patient throughput volumes. The decision on where to be on
this trade-off is the decision of service managers, perhaps subject to
service-level agreements. To demonstrate this trade-off under the TOC DBR
rules, several simulation experiments are conducted.
Keywords: process improvement; theory of constraints; TOC; simulation;
drum-buffer-rope; DBR; patient flows.
Reference to this paper should be made as follows: Bisogno, S., Calabrese, A.,
Ghiron, N.L. and Pacifici, A. (2017) ‘Theory of constraints applied
to scheduled and unscheduled patient flows: does it improve process
performance?’, Int. J. Services and Operations Management, Vol. 26, No. 3,
Copyright © 2017 Inderscience Enterprises Ltd.
S. Bisogno et al.
Biographical notes: Stefania Bisogno is a PhD candidate in Management
Engineering at the University of Rome ‘Tor Vergata’ and a Visiting Researcher
at Manchester Business School, University of Manchester. Her research interest
includes systems performance management and process improvement in
healthcare, involving process analysis, modelling and simulation.
Armando Calabrese is an Assistant Professor in Management Engineering at
the University of Rome ‘Tor Vergata’ and a Visiting Research Fellow at the
Aston Centre for Servitization Research and Practice, Aston Business School.
He received his PhD in Economic and Management Engineering from the
University of Rome ‘Tor Vergata’. His research interests are service
management and economics, corporate sustainability, health management and
public management.
Nathan Levialdi Ghiron is a Full Professor in Management Engineering and the
Head of the Department of Enterprise Engineering ‘Mario Lucertini’ at the
University of Rome ‘Tor Vergata’. He received his PhD in Economic
and Management Engineering from the University of Rome ‘Tor Vergata’.
His research involves network economics, health management, service
management and economics, corporate sustainability, and public management.
Alberto Pacifici is Project Manager and Data Analyst at DS Tech in Rome,
Italy. His experience is in health management, project management, business
planning, process optimisation and business development.
The main mission of a hospital is to meet quality-care standards within financial
restrictions (Does et al., 2014). Thus, the efficient management of patient flows (PFs)
draws considerable attention (Hyer et al., 2009; McDermott and Stock, 2011). A
patient flow is defined as “the movement of patients or equipment between healthcare
departments, staff groups or organisations as part of a patient’s treatment pathway”
(NHS, 2008). The performance of PFs can mainly be measured in terms of maximising
the number of treated patients, and at the same time minimising the times and costs of
treatment for each patient. However, in public hospital systems, the costs of treatment are
mostly exogenous, because they are mainly determined on the basis of regulated
standards. Thus, our purpose is to focus on the trade-off between minimising the time in
system per patient and maximising treated patients. The decision on where to be on this
trade-off is the decision of service managers, perhaps subject to service-level agreements.
To evaluate this trade-off, the current study applies the theory of constraints (TOC) and
in particular one of its techniques, namely ‘drum-buffer-rope’ (DBR), to different types
of PFs to improve them and streamline the healthcare ‘production lines’.
A hospital can be seen as a chain of interconnected processes where patients are
processed through the system, similar to the way materials and products are processed
through a manufacturing system (Umble and Umble, 2006; Ronen and Pass, 2010).
Hospitals are resource-constrained systems in which the time in system is a crucial factor
because the resources limit the process speed. TOC helps to both identify the constraint
and reduce the time in system (Young, 2005; Sadat et al., 2013). Though this theory
naturally fits resource-constrained healthcare systems, Sadat et al. (2013) have
Theory of constraints applied to scheduled and unscheduled patient flows
highlighted that literature addressing the adaptations of TOC to publicly-funded health
systems is scarce. Moreover, several scholars (Umble and Umble, 2006; Moss, 2007;
Sadat, 2009; Groop et al., 2011; Sadat et al., 2013) have also advocated to increase
applications of DBR in services and especially in health care, where only a small number
of studies consider this technique. In particular, the use of TOC as one of the relevant
process improvement approaches is encouraged by combining it with discrete-event
simulation or system dynamics (Young, 2005; Umble and Umble, 2006). Indeed,
simulation techniques tend to be particularly useful when applied to study complex realworld systems, such as healthcare organisations, in combination with the main operations
improvement approaches, such as TOC.
To fulfil this purpose, we focus on analysing PFs and their improvement by
employing DBR both with the traditional approach (DBR for goods, DBRG) and in its
variation for services (DBR for services, DBRS). This research provides conceptual
analysis frameworks for implementing these techniques (i.e., DBRG and DBRS) in two
different hospital units (i.e., outpatient clinic and emergency department), to both
evaluate the PFs’ performance and improve the processes by maximising the treated
patients while minimising the time in system per patient.
The current work provides an application of the traditional ‘DBR for goods’ (DBRG)
approach for a scheduled patient flow (SPF) in an Italian hospital, showing how the use
of a scheduling system helps to better manage the critical resource(s). However, in the
situation of an unscheduled patient flow (UnsPF), where patient arrivals cannot be
controlled, it is impossible to apply a typical DBRG (Umble and Umble, 2006; Stratton
and Knight, 2010; Sadat et al., 2013). Thus, for an UnsPF of an emergency room (ER)
department, we provide an application of a ‘DBR for services’ (DBRS) and
accompanying capacity management policy (Ricketts, 2007). To the best of our
knowledge, there is only one study (Umble and Umble, 2006) that describes the
successful implementation of a TOC-for-services technique to the Accident and
Emergency departments of three hospitals in the UK with the aim of improving
productivity, mainly in terms of reducing waiting times.
In this paper the applicability and the feasibility of both the adapted DBRG and DBRS
approaches are tested on real clinical processes through discrete-event simulation (DES),
which considers operations as discrete sequence of events in time. DES is effective in
investigating the clinical processes and the relationships of system variables, and
evaluating the impact of potential changes (Jacobson et al., 2006; Lu et al., 2012).
Simulations obtain rapid and repeatable results and permit the evaluation of the
performance of controlled experiments in different scenarios (Young, 2005; Ricketts,
2007). Practitioners have made particularly extensive use of DES in TOC applications,
demonstrating the successful impact of TOC on the time in the system (Steele et al.,
2005; Rhee et al., 2010; Sabbadini et al., 2014). In particular, Rhee et al. (2010) have
shown that a DBR-based method accompanied by simulation analyses can successfully
support the performance improvement of business processes and their management.
The next section of the paper provides a review of the relevant literature regarding
TOC, its application in services and particularly in health care. Section 3 describes the
research method, giving detailed descriptions of the analysis steps for applying the two
proposed DBR techniques (DBRG and DBRS) to the different patient flows (SPF and
UnsPF). Section 4 presents the application of the two DBR techniques for the scheduled
pathway of an orthopaedic clinic and the unscheduled pathway of an emergency room
(both in a northern Italian hospital) and shows the results of simulation experiments.
S. Bisogno et al.
Section 5 concludes the paper, highlighting the practical implications and current
limitations of the proposed method, as well as suggesting further directions for research.
Literature review
Process improvement and continuous improvement approaches applied to the
performance of healthcare systems include total quality management (TQM), business
process reengineering (BPR), business process management (BPM), TOC and Lean Six
Sigma (George, 2003; Van Der Aalst and Van Hee, 2004; Davies et al., 2005;
Watson et al., 2007; Cox and Schleier, 2010; Ronen and Pass, 2010; Chiarini, 2013;
Pereira Librelato et al., 2014; Mashhadi et al., 2015; Bisogno et al., in press; Salam and
Khan, in press). All these approaches have common features. For example, they consider
the complexity of interactions among individual activities, identify weaknesses and
bottlenecks and suggest remedial action to enhance the efficiency and effectiveness of the
processes. In this research the main focus is on one of the most frequently adopted
theories in operations management, namely the TOC (Walker et al., 2015). The TOC
approach to continuous improvement focuses on the system constraint(s), which limits
the system’s performance (Goldratt and Cox, 1984; Şimşita et al., 2014; Walker et al.,
TOC argues that the majority of organisational problems are due to a limited number
of causes or constraints. In particular, the theory provides a set of techniques for
efficiently managing organisational constraints in order to maximise performance
(Goldratt and Cox, 1984; Goldratt, 2010). The initial diffusion of TOC was limited
because of its conflict with the dominant paradigm of cost accounting (Mabin and
Balderstone, 2003; Watson et al., 2007; Blackstone, 2010), which encourages the full
exploitation of the production capacity of all resources, including of those that are not
system constraints (Goldratt, 1990). Originally conceived for the manufacturing field, in
recent years TOC has been consolidated as a useful approach in managerial theory and
several successful applications in the service sector have appeared (Watson et al., 2007;
Rhee et al., 2010; Mateen and More, 2013). However, when shifting to services,
TOC applications encounter some difficulties (Moss, 2007; Ricketts, 2007; Ronen
and Pass, 2010; Groop et al., 2011). One of the conceptual problems is that the
production/manufacturing language used in TOC (e.g. setup, inventory, and buffer) often
does not readily translate into a service context. Moreover, there are difficulties in
defining the goals and in measuring the performance of not-for-profit organisations, a
situation that also holds for many healthcare organisations (Moss, 2007; Ricketts, 2007;
Ronen and Pass, 2010; Groop et al., 2011). In spite of these difficulties, Ronen and Pass
(2010) reported that various TOC techniques have been shown as valid for improving the
operational performance of services. The majority of these techniques are specifically
suited to the distinctive characteristics of service organisations, such as the thinking
processes (TPs) and the process of ongoing improvement (POOGI) (Coman and Ronen,
1995; Yang et al., 2002; Reid, 2007).
TOC has also provided a number of ‘application’ tools to improve the system, such as
DBR. In particular, DBR is a mechanism to achieve the appropriate exploitation of the
limiting constraint (the capacity-constrained resource, CCR) and to subordinate the
Theory of constraints applied to scheduled and unscheduled patient flows
process to the CCR (Ricketts, 2010; Wu et al., 2010). The principal steps of
implementing TOC are:
identifying the system constraint(s)
deciding how to exploit the constraint(s)
subordinating everything to the above decision
elevating the system constraint(s)
if, in the previous steps, a constraint has been broken, going back to the first step.
The DBR technique focuses on the implementation of the first three steps. The most
limiting resource (i.e. the constraint) is referred to as the ‘drum’, as it determines the pace
or ‘beat’ of production of the entire system. The ‘buffer’ consists of the scheduling
measures that protect the constraint from starvation due to the variability of the various
non-constrained production flows, and thus ensure the effective, continuous utilisation of
the constraint. The ‘rope’ is essentially a system that connects the constraint to all the
release points of the non-constrained resources and thus ensures they are available in a
synchronised manner to support the work of the constraint (Goldratt, 1990). Thus, the
DBR technique helps to utilise the available capacity of the constraint in the most suitable
way, especially where the resource constraints limit the system capacity (Cox and
Schleier, 2010). However, DBR is not yet widely used in service applications, despite the
positive results in manufacturing (Rhee et al., 2010); the literature records very few
applications of DBR in the service sector (Siha, 1999; Ricketts, 2010). In the healthcare
sector, the application of DBR to patient flows should permit increases in the number of
treatments provided by leveraging the constraint resource, while also improving time in
system (Goldratt, 1990; Umble and Umble, 2006). Nevertheless, to the best of our
knowledge, only a few studies (Umble and Umble, 2006; Sadat, 2009) deal with the
application of DBR in a hospital department. For example, Sadat (2009) specifically
refers to the application of DBR to a scheduled clinical process, demonstrating the
effectiveness of DBR in improving the trade-off between instances of delayed treatment
and average patient wait times. Several other studies have indicated the difficulty of
applying DBR to unscheduled clinical processes, which are an inevitable aspect of
operations in emergency rooms (ERs), even though these are among the most critical of
all departments in the hospital system (Kershaw, 2000; Umble and Umble, 2006; Sadat,
2009; Stratton and Knight, 2010; Sadat et al., 2013; Sabbadini et al., 2014). This
difficulty is due to the impossibility of controlling patient arrivals, and thus the
infeasibility of the rope component of scheduling in the system (Umble and Umble,
2006). Therefore, a modified DBR, or DBR for services (DBRS) has been introduced
(Ricketts, 2007, 2010). In DBRS, the rope is responsible for triggering the ‘capacity
management’ system. In particular, the two approaches (namely, DBRG and DBRS) are
built on similar principles, but work differently: “thus, DBRG does buffer management of
operations with fixed capacity, while DBRS does capacity management of processes with
variable capacity” (Ricketts, 2010). Indeed, DBRS controls adjustment in the capacity of
the constraint resource (either an increase or decrease) depending on the variation of the
arrival rate. The assumption underlying this application of DBR in the services sector is
that the constraints, typically human resources, are more flexible than in the
manufacturing sector. In fact, human resources can speed up more easily than industrial
machines (Ricketts, 2007).
S. Bisogno et al.
Research method
DBR is used to program the rate (drum) of the system’s production according to the
production capacity of its constraint (the capacity-constrained resource, CCR). The
technique aims to optimise the utilisation of the CCR and to prevent its inactivity through
a properly-sized buffer. It provides for the synchronisation of the non-constrained
resource activities with the constrained-resource actions, by means of an information
system (rope) (Rhee et al., 2010). In the case of healthcare services, the CCR could be
either a human resource (doctors, nurses, laboratory technicians) (Rotstein et al., 2002;
Sabbadini et al., 2014) or a physical resource (equipment, dimension of areas, patient
beds or chairs) (Kershaw, 2000; Sadat, 2009).
The healthcare sector is characterised by two types of processes: the SPF, which is
typical of hospital outpatient services, and the unUnsPF, typical of an emergency room.
Since an SPF is similar to a manufacturing process, it is well suited to an adapted
application of the traditional DBR (DBRG). The first subsection below provides an
adaptation of the DBRG for a scheduled clinical context. But since DBRG is not
applicable to systems without control over the patient arrivals (Umble and Umble, 2006;
Sadat, 2009; Stratton and Knight, 2010), as in emergency departments, for these UnsPFs
we also propose an application of DBRS (Ricketts, 2007), seen in the second subsection
3.1 Design of a DBRG application for a SPF
Figure 1 illustrates the analysis framework to show how to apply a scheduling system,
such as DBRG, to an SPF. In particular, DBRG here is adapted for the healthcare
environment from a typical manufacturing setting and it is valid only for incoming
patient flows that can be controlled, that is, where it is possible to control the rate at
which patients arrive.
Figure 1
DBRG analysis framework for SPFs
Theory of constraints applied to scheduled and unscheduled patient flows
The DBRG prescribes a constant drum, which sets the pace of ‘production’ of the entire
process, and a buffer in terms of patients. In order to ensure that the other non-constraint
resources support the work ‘pace’ of the constraint without increasing the time in system,
the rope may activate the ‘buffer management’ system (Umble and Umble, 2006;
Blackstone, 2010).
For an SPF, the first step in the DBR procedure (Figure 1) is the identification of the
utilisation rate of resources involved in the process in order to identify the resource
constraint, CCR (i.e., second step in Figure 1). In the particular case of a healthcare
process, the utilisation rate of ith resource (URi) can be formulated by adapting the
relationship of Ha et al. (2006), as follows:
URi =
λt ⋅ pt , r
μt , r
ft ⋅ pt , r
μt , r
∀t ∈ T
is the set of tasks in the process, e.g. T = {tk | k = 1,…,K}
is a single task
is the arrival rate of tth task
pt,r is the task assignment probability of a task t to a resource r
μt,r is the average service rate of a resource r to a task t
is the set of arrival rates of patients
is the expected execution frequency of the tth task.
Once URi is defined for each resource in the SPF, then the CCR (the resource with the
highest utilisation rate, i.e. URCCR = URmax = max[URi]) can be identified (i.e., second
step in Figure 1). This is the particular resource that limits the system in the achievement
of its objective (Wei et al., 2002; Rhee et al., 2010).
The third step in Figure 1 is the calculation of some performance measures, such as
throughput (Th) and lead time (LT). In particular, Th is the number of patients that can be
processed in a given time and LT is the time in system per patient. As ever in flow
systems, there is a trade-off between maximising the patient throughput (Thmax) and
minimising patient lead times (LTmin). To support management decision making on where
to be on this trade-off, several simulation experiments are conducted. Upon the
identification of Thmax, the maximum speed of task processing is determined with
reference to the CCR (drum). This allows for the minimisation of the lead time (LT), that
is, drummax = max[1 / LT].
In keeping with the literature, in order to improve the utilisation of the CCR, the
buffer size (BS) (in terms of patients) is calculated heuristically through numerical
simulations (Radovilsky, 1998; Louw and Page, 2004; Sadat, 2009; Rhee et al., 2010).
The last step in Figure 1 is the identification of the rope, which is the system for
scheduling arrivals into the system in order to best conform to the pace of the CCR.
S. Bisogno et al.
3.2 Design of a DBRS application for an UnsPF
The analysis framework in Figure 2 describes the main steps for applying DBRS to an
UnsPF. The procedure is applicable only to the ‘unscheduled’ type of patient flows where
it is not possible to control the rate of incoming patients.
Figure 2
DBRS framework for UnsPFs
Because of the uncontrolled nature of arrivals, the application of the DBRS requires a
variable drum. We adopted a ‘time buffer’ that is related to the constraint production
capacity and sets the time interval by which the patient should be processed; it protects
the both system from potentially reduced throughput (caused by starvation of the CCR),
and the patients from potentially increased lead time (caused by excessive demand on the
CCR) (Goldratt, 1990; Umble and Umble, 2006; Ricketts, 2010). It is typically
recommended that the time buffer should be divided into three zones of equal length
(d/3): lower red, green, and upper red zones (Figure 3). The green zone is the ‘safety’
zone, corresponding to the time interval by which the patient can be processed without
impacting on the constraint production capacity (Umble and Umble, 2006; Stratton and
Knight, 2010).
Theory of constraints applied to scheduled and unscheduled patient flows
Figure 3
Buffer zones and sizes for UnsPF [based on Umble and Umble (2006), Ricketts (2007)
and Stratton and Knight (2010)]
The buffer time is ‘bidirectional’ in triggering ‘capacity management’, ‘pulling the rope’
when the buffer state moves out of the green zone (Ricketts, 2007). That is, if the rate at
which patients arrive decreases then utilisation of the constraint decreases, and if this is
sufficient to shift from the green zone to the lower red zone this would suggest triggering
reduction in the constraint production capacity. If the arrival rate increases sufficiently to
shift utilisation from the green zone to the upper to red zone, then this would signal a
need to increase the constraint production capacity.
As in the procedure for an SPF, the first step of the analysis framework for an UnsPF
is also the identification of the utilisation rates of the resources involved in the process, in
order to identify the resource that has the maximum utilisation rate (i.e. the CCR). The
objective is to determine the trade-off between maximising throughput (Thmax) and
minimising lead times (LTmin) of the UnsPF. To do this several simulation experiments
are conducted.
Once this trade-off has have been identified, the next step is to determine the upper
buffer threshold (BSU) and the lower buffer threshold (BSL), which can be considered as
the time interval within the green zone (as shown in Figure 2). These thresholds are
determined according to specific ‘service level agreements’ (SLAs), which the patient
pathway must satisfy (Umble and Umble, 2006; Ricketts, 2007; Stratton and Knight,
2010). For a specific SLA, given the dependence between URCCR and LT (expressed by
the generic function URCCR[LT]), it is possible to define the two buffer thresholds (BSL
and BSU), as two specific values of URCCR:
UR CCR = URCCR| LT =1/3d = BS L
j CCR = URCCR| LT = 2/3d = BSU
In the case utilisation dropping below the BSL, the rope triggers the decrease of CCR
production capacity. In contrast, in the case of exceeding the BSU, the rope triggers an
increase in the service speed of the CCR (speeding up the existing constraint resource) or
in the productive capacity of the CCR (adding a resource). In particular, healthcare
providers can often reemploy one extra human resource in order to improve the number
of processed instances, with such extra resources only necessary for a short period of
S. Bisogno et al.
Simulations experiments
This section presents the application of the two methods for the analysis of the different
clinical process types. The different processes are, respectively, a scheduled pathway in
an orthopaedic outpatient clinic (OC) and an unscheduled pathway of an emergency room
that involves an orthopaedic emergency room (ER). The first is the clinical pathway for a
total hip replacement procedure, and the second is for the treatment of a proximal femoral
fracture. The pathways chosen identify two typical orthopaedic process protocols with
standard data input (resources, times, etc.). In particular, both simulation experiments are
built on data and the information collected in February 2014 and provided by a small
public hospital (approximately 150 beds) located in northern Italy. The first step was to
build the conceptual model of the clinical pathways, namely the description of the model
that is to be developed (Robinson, 2014; Bisogno et al., in press). The conceptual models
(see Figure 4 and Figure 5) were built after meeting doctors and nursing staff, consulting
the clinical guidelines adopted by the hospital, and walking through the pathways on the
ground. Second, the data was gathered by querying the IT database and interviewing the
staff to overcome the lack of data availability. In particular, the lack of available data
concerned the SPF more than the UnsPF.
In an orthopaedic unit, the journeys along clinical pathways can be affected by the
diversity of patients’ age, which tends to be higher than in other hospital units (Dixon
et al., 2010). Indeed, the age of a patient can influence the duration of their treatments.
On the other hand, the duration can also be influenced by some operational causes, such
as the utilisation rates of both human and technical resources. Therefore, we used
historical data to compare the key measures of the duration times inside the clinical
process with patient age with using Spearman rank correlation. The SPF, total hip
replacement procedures, is composed of four main time-stages, namely booking, preadmission, surgical operation and then discharge. The UnsPF, the treatment of a proximal
femoral fracture is composed of a patient admission through the ER and, if the fracture is
confirmed, is surgical operation. The results of the statistical analysis of the data provided
by the hospital show that for this specific SPF age is not correlated with the time elapsed
between patients’ booking and pre-admission (Spearman’s rho = –0.1403, p-value =
0.2116), and similarly for the UnsPF age is not correlated with the time elapsed between
admission to ER and the decision to surgically operate on the patient (Spearman’s rho =
0.1275, p-value = 0.1483). As a consequence, the focus of the analyses is mainly on the
efficiency of these (sub-) pathways whose activities are not significantly influenced by
patient age, in order to exclude the influence of such an effect and concentrate on the
improvement of performance in the chosen PFs. For the SPF (Figure 4), all the activities
of the pre-admission phase are considered; for the UnsPF (Figure 5) all the activities
between admission to the ER and the decision to carry out the surgical operation are
analysed, including the transfer from the ER to the orthopaedic ward.
The conceptual model for each PF is built using well-known standard notation,
namely BPMN 2.0 using the Bizagi software package (see Figure 4 and Figure 5). Once
modelled, the PFs are simulated through discrete-event simulations (DES), using Arena
14.5 software. Features in Arena 14.5 (i.e., animation and verification) help to check the
accuracy of simulation assumptions and input data. Both process modelling and
simulation support the analysis of managerial improvements in terms of throughput and
Theory of constraints applied to scheduled and unscheduled patient flows
lead times. In particular, the input data used for running the simulation analyses are the
patient inter-arrival times, which are described as having an exponential distribution, and
the service times for each activity, which are also described as having exponential
distributions. Finally, the representativeness of the results are tested by running each
simulation many times (here 100 times for each set of simulations).
Figure 4
The conceptual model of the SPF (BPMN 2.0 modelling standard) (see online version
for colours)
Figure 5
The conceptual model of the UnsPF (BPMN 2.0 modelling standard) (see online
version for colours)
S. Bisogno et al.
4.1 DBRG-based approach to a SPF
A number of simulation experiments have been conducted to test our DBRG approach on
the scheduled pathway in an orthopaedic outpatient clinic. The duration of each simulated
pathway scenario was 8 hours, corresponding to a normal workday shift of the
orthopaedic outpatient clinic. Because the outpatient clinic starts and ends empty every
day, no warm-up period is necessary. The resources available considered in the
simulation of the SPF are: a physician, two nurses, a radiologist, an anaesthesiologist,
two radiographers, and three laboratory staff. The physician and nurses are dedicated to
this pathway; the others are shared among different patient flows in different wards.
Applying the method using the real input data (resources available, service times,
shift duration, etc.), the critical resource (CCR) may be identified. In particular, the
bottlenecks are not always obviously and directly visible in healthcare pathways, in
contrast to the common case in manufacturing processes; thus, simulation experiments
can contribute successfully to both detect bottlenecks and integrate the information that
derives from the observation of real-world processes (Young, 2005). Indeed, the
simulation results (Figure 6) show a greater degree of utilisation of the clinical nursing
staff (URCCR) compared to the other resources under various patient inter-arrival times.
Thus, when the arrivals are more frequent (i.e. lower mean arrival rate), the process has a
bottleneck in the first stages, which are carried out by the nurses. In practice the nurses
are involved in more activities that indicated in their own swimlane and priorities can
result in the CCR being called to attend to a patient earlier in the process resulting in a
patient later in the process waiting. This logic is incorporated into the DES models.
The simulation experiments conducted also identify the trade-off between
maximising throughput (Thmax) (i.e. 8 patients per day) and minimising the lead time
(LTmin = 158 minutes). The maximum speed of processing is equal to 1 patient processed
in 158 minutes (i.e., drummax) with an inter-arrival times mean of 37.5 minutes (Figure 6).
In this case, the recommended rope is a scheduling system under which patient
appointments can never be made with an intervening time that is less than the average
rate of arrival (37.5 minutes), even if the productive capacity of the other non-CCR
resources permitted more frequent appointments.
Resource utilisation rates; throughput (Th) and lead time (LT) (SPF) (see online version
for colours)
An. Ut
Phy OC
20 22.5 25 27.5 30 32.5
Inter-arrival times mean [mins]
Lead Times
Nurse OC
10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35 37.5 40
Inter-arrival times mean [mins]
Theroughput [patients]
Lead times [mins]
Utilization rate of resources
Figure 6
Theory of constraints applied to scheduled and unscheduled patient flows
This DBRG-based approach also allows identifying how throughput and lead time may be
improved while varying the size of the buffer. Figure 7 shows the impact of the buffer
size variation on both throughput and lead time. It shows that increasing the buffer size
beyond 1 does not improve either performance measure (i.e., throughput or lead time).
Figure 7
Buffer size variation (SPF) (see online version for colours)
Lead times [mins]
Throughput [patients]
Lead times
Buffer size [patients]
Most of the input data for the SPF was obtained by interviewing the hospital staff and
observing the process on the ground. This situation is not unusual in health care
(Santibáñez et al., 2009). Then, to validate the simulation experiments we proceeded only
with a ‘face validation’, where the visual interactive nature of the model enabled patient
pathways, waiting times, and the utilisation of the correct resources to be confirmed as
accurate by clinic staff. In particular, the clinical staff declared that the average time
spent by a patient to complete the SPF in the hospital under consideration is around three
hours (i.e., 180 mins), that is higher than the simulation output (LTmin = 158 mins). Thus,
as results show, the implementation of the DBRG, that follows the approach described in
the research method (Section 3.1), tends to reduce the current lead time and may be
considered a successful process improvement idea.
4.2 DBRS-based approach to an UnsPF
An adaptation of DBRS has been applied to the unscheduled pathway, i.e. the medical
treatment of proximal femoral fracture. As in the previous subsection, some simulation
experiments are conducted to test the practicality of the proposed approach (Figure 2).
Although emergency treatment is available over 24 hours, the dedicated pathway
modelled only operates for 12 hours a day, 5 days a week, and has its own resources, so
starts operations in an ‘empty’ state. Therefore no warm-up period is necessary in the
modelling. In this case, the resources available that we consider in the simulations of the
UnsPF are: an ER physician, four ER nurses, three orthopaedic-department physicians, a
radiologist, an anaesthesiologist, three orthopaedic-department nurses, two radiographers
and three laboratory staff.
S. Bisogno et al.
Simulating the process with real input data (available staff resources, service times,
shift duration, etc.), the CCR may be detected. In this case, the CCR is the ER physician,
who has a higher utilisation rate (URCCR) than the other resources under different average
arrival times (Figure 8). As for SPF, the CCR (i.e., ER physician in this case) can be
pulled to attend to a patient earlier in the process to deal with an early stage patient,
resulting in a patient later in the process waiting to progress further.
Resource utilisation rates; throughput (Th) and lead time (LT) (UnsPF) (see online
version for colours)
Lead Times [mins]
Utilization rate of resources
Throughput [patients]
Figure 8
Lead Times
Inter-arrival times mean [mins]
Nurse OW
Phy ER
Nurse ER
Phy OW
Inter-arrival times mean [mins]
Our DBRS-based approach also allows the identification of Thmax (or maximum
throughput) considering the distribution of an average inter-arrival time of 35 minutes.
Under these conditions, 13 patients (Thmax) with a ‘suspected’ proximal femoral fracture
are treated in the orthopaedic ER per work day and each treatment takes about
215 minutes to be completed (LTmin) (Figure 8). This is the trade-off between maximising
patient throughput and patient lead time for the specific UnsPF.
To validate the simulation experiments, the simulated output is compared with the
historical data. In particular, the available actual data for the UnsPF are related to the
time in system per patient (LT). Thus, we build the 95% confidential intervals (CIs) to
evaluate the interval estimation of the actual data regarding the average LT. The
processing lead time that comes from our simulations (LTmin = 215 mins) falls within the
95% CI of the actual data as shown in Table 1.
Table 1
Actual LT
Validation of the UnsPF (95% CIs for actual LTs)
Std. err.
[95% CI]
After identifying the CCR, the appropriate buffer thresholds to improve the utilisation of
the resources can be determined. The lower and upper thresholds of the buffer size
(respectively, BSL and BSU) define the time interval by which the patient can be processed
without impacting on the constraint production capacity (i.e., the green zone) (Ricketts,
2007). Capacity management is triggered when the CCR utilisation rate either drops
below BSL or exceeds BSU, causing a shift into one of the red zones. Following the DBRS
approach shown in Figure 2, the sizes of buffer thresholds are calculated as defined by
the SLAs. In this case, the SLA adopted is a 4 hours lead time, meaning that patients have
Theory of constraints applied to scheduled and unscheduled patient flows
to be processed within 4 hours from the admission to ER. Thus, given the maximum time
in system for each patient (LT) is 4 hours (d = LT = 4 h = 240 mins), each buffer zone
should have a width of 80 minutes (i.e., d/3 = 80 mins) (Umble and Umble, 2006;
Stratton and Knight, 2010).
However, in the UnsPF the ER physician is the CCR and he/she is the only available
ER physician over the shift considered, thus it is not possible to consider any decrement
of the CCR, because an ER physician has always to be present. These circumstances
bring to light a different framework compared to that suggested by Ricketts (2007),
which was illustrated in Figure 3. Instead, the framework appropriate for our case
(Figure 9) considers that the green buffer zone incorporates the lower red zone and its
duration becomes 160 minutes (80 + 80 minutes), while the upper red zone remains at
80 minutes. The next step is to determine the value of BSU, bearing in mind that URCCR ≥
BSU activates capacity management (either speeding up or numeric increment in CCR, as
in Figure 2). Returning to the formula for identification of BSU as presented in the DBRS
method, when the lead time is equal to 160 min (LT = 2/3 d), the simulations show that
the utilisation rate for the CCR is equal to 30%:
j CCRI = URCCR| LT = 2/3d = 0.30 = BSU
According to the literature (Umble and Umble, 2006; Ricketts, 2007; Stratton and
Knight, 2010), in this case capacity management should be engaged as soon as the
utilisation rate enters the red zone, meaning that URCCR reaches the value of 0.30
j CCRI ).
( BSU I = UR
To test whether further benefits could be achieved in terms of the trade-off between
maximising Th and minimising LT, we consider shifting the buffer threshold BSU I to a
point midway through the upper zone ( BSU II ), meaning LT = 5/6 d = 200 min (Figure 9).
j CCRII is equal to 75%:
Applying the function URCCR(LT), UR
j CCRII = URCCR| LT =5/6 d = 0.75 = BSU
Figure 9
Buffer sizes and different BSU (UnsPF)
S. Bisogno et al.
To test whether shifting the upper buffer threshold from BSU I to BSU II gives any
advantage in terms of Th or LT, three different scenarios are compared. In particular, we
test how capacity management potentially works under these different scenarios, where
each of them is engaged under the two proposed definitions of the buffer thresholds (both
BSU I and BSU II ).
Scenario 1 is a ‘speed-up’ in which we simulate a decrease in the average service
time for the constraint activity. Ricketts (2007) interpreted speed-up as the capacity for
human resources to increase their speed of service. However, in the contemporary
healthcare sector, a realistic interpretation would be to interpret speed-up as the
computerisation of some activities of the CCR ER physician, for example the
administrative activities. Before running the simulation, we assume that such a speed-up
would lead to a 20% reduction in the average value of CCR service times.
The other two scenarios simulate an increase in CCR capacity. In Scenario 2 one of
the other existing resources (an orthopaedic-department physician) is shifted to add to the
resource of the ER physician in the CCR activities. In Scenario 3, the addition of an ER
physician is proposed.
The three scenarios are now compared to the original analysis, in which capacity
management is not implemented (Scenario 0). The comparison is in terms of both
throughput (Th) and lead times (LT). In particular, we distinguish two possible situations
in which capacity management is initiated, that is, when the utilisation rate of the CCR is
equal to 0.30 ( BSU I = 0.30), which is indicated in literature, and to 0.75 ( BSU II = 0.75)
as identified above.
As seen in Figure 10, the scenarios that provide for a resource increment through the
transfer of an orthopaedic-department physician or the addition of an ER physician
(respectively scenarios 2 and 3) provide the maximum values of throughput and
minimum values of lead times, under both CCR capacity utilisation rates ( BSU I = 0.30
and BSU II = 0.75). In choosing from potential capacity management measures, both the
‘resource increment’ scenarios (that is Scenario 2 and 3) succeed best in utilising the
productive capacity of the overall resources available, and so ensure the best
performances. Following these, Scenario 1 (speed-up) provides the next-best
performance, superior to the case in which no capacity management is implemented
(Scenario 0).
Comparing the two considered values of the CCR capacity utilisation rate (i.e., BSU I
and BSU II ), we suggest engaging capacity management at the moment of exceeding the
threshold of 0.75 ( BSU I = 0.75). This result does not correspond to what has been
reported in the literature (Umble and Umble, 2006; Ricketts, 2007, 2010; Stratton and
Knight, 2010). In particular, if the buffer threshold is BSU I = 0.30, the capacity
management system will be activated when the utilisation of the CCR is equal to 30%.
This might be considered too low a threshold to activate a capacity management system
in this context. Testing several buffer thresholds by using simulation may be very useful
in order to understand how capacity system can correctly be activated to better perform
the system.
Theory of constraints applied to scheduled and unscheduled patient flows
Figure 10 Throughput (Th) and lead time (LT) under four scenarios with two different BSU
(UnsPF) (see online version for colours)
Lead Times [mins]
Throughput [patients]
Scenario 0
Scenario 1
Scenario 0
Scenario 1
Scenario 2
Scenario 3
Scenario 2
Scenario 3
Inter-arrival times mean [mins]
Inter-arrival times mean [mins]
Lead Times [mins]
Throughput [patients]
Scenario 0
Scenario 1
Scenario 0
Scenario 1
Scenario 2
Scenario 3
Scenario 2
Scenario 3
Inter-arrival times mean [mins]
Inter-arrival times mean [mins]
TOC-based approaches have been applied in some healthcare studies (Wright et al., 2006;
Schaefers et al., 2007; Boaden et al., 2008), but the number of relevant publications is
still limited (Moss, 2007; Groop et al., 2011). Several scholars have advocated for the
improvement and increase of application of DBR (a TOC efficiency technique) in
services, especially in the healthcare sector (Umble and Umble, 2006; Moss, 2007; Sadat,
2009; Groop et al., 2011; Sadat et al., 2013). To this end, the current study applies DBR
to both SPF and UnsPF. In particular, the study has demonstrated the potential to provide
a systemic process-based approach that shows how to apply the DBRG (i.e., the
traditional approach of the DBR technique) to a SPF. This approach permits the use of a
scheduling system to better manage the critical resource(s). For situations where it is
impossible to schedule patient arrivals (UnsPF), a further decision-making procedure is
illustrated. It is an application of DBRS (Ricketts, 2007) that provides a capacity
management system for the utilisation of the constraint resource. In particular, we
provide some suggestions on how the buffer thresholds can be designed in order to
improve system performance.
S. Bisogno et al.
The study provides a contribution to the TOC literature by showing how to apply the
DBR techniques to the healthcare environment to improve patient flows. Improving
patient pathways by reducing delays and length of stay may have significant beneficial
effects on the quality of care that patients receive and reduce the overall cost of care. The
research has also confirmed the potential practicality of these techniques in health care in
order to efficiently manage critical resources and improve clinical pathways, similar to
efforts in other sectors such as in banking services (Rhee et al., 2010). In particular, we
investigate the decisions on where to be on the trade-off between the maximisation of
patients treated (throughput, Th) and the minimisation of time in system per patient (lead
times, LT) in both SPF and UnsPF. From a practical point of view, both the systemic
DBR process-based approaches can be considered as a roadmap for carrying out
improvement practices in health care by using proper manufacturing techniques, such as
There are some limitations in this research. The data is based on a single clinical
pathway per application; therefore, additional pathways should be added for further,
more-complex analyses. Indeed, future studies could consider the replication of the
research approaches in different parts of the hospital or different hospitals. With the
necessary modifications, the two proposed DBR-based approaches could be applied to
other processes that are similar to those analysed in the study by following the
frameworks proposed in this paper. A suitable topic for further research would be to
compare the proposed DBRG and DBRS analytical procedures to those of other
performance measurement methods, to provide stronger contributions to performance
analysis in PF systems.
The authors thank the anonymous hospital in Emilia-Romagna (Italy) and its staff for
providing the useful information and data to conduct the analyses in this paper and
discussing the results. The authors would like to thank the anonymous reviewers for their
constructive comments and are also thankful to Dr. Nathan Proudlove for his valuable
comments and feedback on this paper.
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