Verification and Optimisation of an Operating Room Workflow

Proceedings of the 35th Hawaii International Conference on System Sciences - 2002

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Verification and Optimisation of an Operating Room Workflow K.Barkaoui, Ph. Dechambre, R.Hachicha Lab. CEDRIC, CNAM – Paris email : [email protected] Abstract This paper presents an outcome of a workflow research project that will allow hospital organizations to master their costs and to improve their quality of service. Indeed, to reach this objective, the hospital business processes have to be modelled. This work is illustrated here through the analysis of operating room processes modelled in terms of Petri nets. After soundness verification of the procedures underlying these business processes, we show how we can optimise the performances of a system by performing process reengineering. Due to the context, this optimisation is achieved by introducing a balance between specialization and generalization and between centralization and decentralization of resource classes (equipment and staff) while preserving the soundness property.

1. Introduction Workflow Management and Business Process Reengineering consider industrial systems composed of business processes competing for resources [5], [6]. The aim of Workflow Management Systems (WFMS for short) is to control administrative tasks in large organisations. It is possible to distinguish two different categories of workflow software, which support respectively structured and unstructured processes. Structured processes have a fixed behaviour, and they will not change during the time. Unstructured processes are, on the contrary, susceptible to be influenced by external actions. In a hospital, the staff schedule and the treatment device availability strongly depend on the arrival of patients, the knowledge or diagnosis of their disease… Numerous WFMS are nowadays available. This signifies the importance of the workflow paradigm. As enhanced recently in [5], a theoretical basis for WFMS tools is missing as well as tools for WFMS analysis [5], [6]. A first major step in order to overcome these drawbacks consists in modelling and analysing correctness of workflow procedures . Such work can be based on a Petri net approach. It maps in a clear manner a procedure into a Petri net, leading to a subclass of Petri nets, namely workflow nets [1]. The soundness of

a procedure can then be checked using polynomial-time algorithms. This work was extended in [3] by taking into account the use and sharing of multiple resources by several workflow procedures which influences the correctness of the complete system. The validation of such a system is done by introducing the notion of structural soundness, extension of the soundness property. Another major issue that we address here concerns the performance of the system and its optimisation by business process reengineering. Moreover, these operations do not invalidate the soundness property of the system, which can be proved beforehand. The paper is organised as follows: in section 2 we recall the basics properties of workflow nets (WF-net). In section 3, we present the hospital case explaining processes and we represent the business processes as a workflow. In section 4, we map this Workflow Management System into Petri net model. In section 5, we present the possibilities of performances improvement of the whole system by introducing a balance between specialisation and generalisation and between centralisation and decentralisation of resource classes (equipment and staff) while preserving the soundness. To compare our models, we based them on the two following principal elements: • The mean waiting time (for the patients), • The busy rate (of resources).

2. Basics properties of Workflow A Petri net that defines a business process is defined. Definition 2.1 : A Petri net N is a WF-net if & only if : (I) N has two special places : i and o. Place i is a source place : •i = ∅. Place o is a sink place : o• = ∅ (II) If we add a transition t* to N, connecting place o with I, i.e. •t* = {o} and t*• = {i}, the Petri net N* obtained is strongly connected. N* is called the augmented net of N. Conditions refer :

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Proceedings of the 35th Annual Hawaii International Conference on System Sciences (HICSS-35’02) 0-7695-1435-9/02 $17.00 © 2002 IEEE

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(I) means that start and end : a case starts at the input place pi and always end in the place po. (II) means that every transition (task) t must be in a path leading from pi to po. This requirement ensures the absence of dangling task. An interesting feature of Petri net modelling is the design of WFMS is that some properties (such that boundedness, deadlock freeness, quasi-liveness, liveness, soundness) can be checked before a specification is put into execution in the workflow engine. The soundness property states that, for any case (corresponding to one token in pi) , the procedure will terminate eventually, and at the moment the procedure terminates, there is a token in place po and all other places are empty. Definition 2.2 : A WF-net (PN,M0) (n being the number of cases to process, M0 = ni) is sound if and only if : (I) ∀ M ∈ [n.i〉, n.o ∈ [M〉 ; (II) ∀ M ∈ [n.i〉 : M(o) ≥ n ⇒ M = n.o ; (III) ∀ t ∈ T, ∃ M ∈ [n.i〉 : M[t〉. A WF-net with resources is basically a WF-net plus a set of places modelling the resources. We demand the WF-net (without resource) to be sound, and the resources to be preserved by the net, i.e. a resource requested will eventually be released and a resource released has previously been requested. Several resources can be requested/released at the same time. The resource preservation can be expressed by a place invariant of the system. Definition 2.3 : A WFR-net is a tuple PNR = (M0 = ni + Σ where ki is the number of resources of type ri ∈PR ) where : (I) PN = is a sound WF-net, (II) PR ≠ ∅ and P ∩PR = ∅ (set of resources) (III) FR ⊆ (PR×T) ∪ (T×PR) (flow relation for resources) (IV) ∀u ∈ FR, WR(u) ≤ 1 (resource use) (V) ∀r ∈ PR, ∃ fr ≥ 0 : t fr.C = 0 and ║fr║∩PR = {r} (resource preservation) Then, we can compose several WFR-nets by fusion the places representing the shared resources. The obtained system is called WFRS. The WF-nets are generally circuit-free (named CFWFnets), in this case, we have the following result [3] :

Theorem 1 : Let N be a WFRS. N is sound if & only if (N*,M0) is bounded, quasi-live and satisfies the csproperty [2]. With WFRS, one can model resources of a workflow and study their characteristics (classes and status). Starting from the model, we performed simulations in order to evaluate the incidence of changing of the classes and/or the statutes of the resources on the performances, at the same time of these resources and also of the whole process. We have assisted, for a few years a turning of the public policy of health in France which aims at increasing the productivity of the establishments of care. The organization of the production of the care thus takes an increasingly significant place in research. Our goal is to show that by a better use of the resources, we can improve the productivity significantly, without increasing costs. To date, the resources are primarily allocated by the intermediary of a model statistic. This method is very effective, but allows optimization with difficulty. In a hospital, the practices of the care and, particularly the process of the execution operation cycle, are not easily flexible because of the complexity of the nature of the activities and the vital aspects which they bring into play. This is why, one can act only on the characterization and the resource allocation which are available for health care. We can only intervene on human or material resources.

3. case study : Operating room workflow This paper discusses management optimisation possibilities for an operating hospital room through the use of WFMS. This is a new approach for hospitals organizations for which management and allocation of resources (equipment and staff) policies rely more on statistical data than on results obtained through the use of computer models and systems designed to monitor performance and efficiency of management procedures. Generally speaking, human resources are used with respect to existing structural constraints (e.g. building architecture and configuration, equipment availability and location, etc.). The "waiting period" aspect is the typical example of a disrupting factor as it generates a "bottleneck" effect with a negative impact on the smooth running of hospital functions. Often the situation arises that on the one hand there are patients undergoing length waiting times before being attended to, whilst on the other hand there is staff and equipment available waiting to be used [4].

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HOSPITALISATION ENTRY

To the extent that surgery can be conceived as a production process, one can refer to production techniques and practices and the theories from which they are derived. This is a vocabulary which is new in the hospital environment, but which is of importance for professionals involved in managing flows.

Reception Room [MA] Reception activity (AA)

Transfer activity (AA)

This paper aims to show that the design of WFMS and Petri Nets models (WFRS) can constitute a valuable source to improve sharing resources and to reduce the waiting period for the patients. That makes it possible to check the load-balancing between the resources of comparable nature. The benchmark data for the case come from statistics held by the hospital.

Induction Room [MI] Induction activity (AI)

Operating Room [MO] Induction activity (AI)

Transfer activity (AO)

According to the definition of the modelling of process given by [3] we define the following elements: • •

•

• • •

the process : the execution operating cycle, The activities [stages of the process]: reception [AA], transfer [AT], induction [AI], surgical operation [AO], and awakening [AR]. Each activity is broken up into tasks [Axn] actors [having a role in the activity]: Surgeon [RCh],Anaesthetist [RA], surgeon assistant [RInt], nurse [IH], nurse anaesthetist [RIA], nurse for bandage[RIP], nurse for medical instruments [RII], nurse's aide [RAS] the route [transition between activities]: from which each transition can be crossed only after the respect of constraints, "The patient" [which forwards by activities and routes and which undergoes transformations] : the patient who undergoes a surgical operation. Resources : as humans [by occupation] and in material [a number and type of rooms]

We define a point of initialisation (i) of the workflow :"entry of the patient in reception room and a point of termination (o) : "exit of the patient from the recovery room". The operating room suite is composed of four operating rooms : one for emergencies, three for other types of surgery. We will study the emergency surgery [US] compared with the other field under the name of "Hospitalised Surgery"[HS] Business Process : The execution operation cycle is given by the figure below :

Recovery Room [MR] Recovery activity (AR)

EXIT

Classes of patients: - emergencies : patients operated in emergency, they account for 20% of the entries. These patients have priority and enter directly in room of induction with a simplified procedure of reception and transfer. - hospitalized: patients for whom operation is planned, they account for 80% of the entries. Classes of resources: - Class depending on the type of actor that uses it (in our example there exists 2 types of actors: patients in hospitalisation and patients in emergency): + Generalized Resources : used by actors of the different types, + Specialized Resources : used by actors of the same type. - Class depending on the site where the resource is used (room of reception, transfer, room of induction, operating rooms, recovery room): + Centralized Resources : used in a single site, + Decentralized Resources : used in several sites. Status of a resource: - Dedicated Resources : it is a specialised and centralised resource (for example, an operating room treats only one type of patient and in one place), -

Shared Resources : it is a resource which either is generalised (for example the nurse assistant can deal with emergency patients or with hospitalised) o r decentralised (the anaesthesiologist works in the room of induction and in the operating room).

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EMERGENCY ENTRY

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-4Specification of the studied case : The quantitative parameters are taken from the statistics collected by the hospital (probabilities of occurrences of the events and the average duration of the activities). Table 1 presents these data: (when an activity is specific to a type of patients, it is distinguished between " hospitalization " and "emergency")

Resource specifications - Table 2 RESOURCES Ref.

Activity specifications – Table 1

Emergency Installation [AO1] Preparation [AO2] OPERATING [AO3] Hospitalisation Emergency TRANSFER [AO4] RECOVERY [AR] RECYCLING [AO5]

Event

Prob.

Duration

Entry Entry

0,8 0,2 1

4' 4' 2'

Short Long Short Long

0.93 0.07 0.95 0.05 1 1

10' 30' 10' 30' 4' 4'

Short Average Long Short Average Long

0.60 0.30 0.10 0.40 0.30 0.30 1 1 1

20' 43' 80' 20' 43' 80' 3' 50' 10'

MSI

The business process workflow is shown on the ANNEXE 2 – Graphic 1. It shows the advance of a patient, from reception to the exit of the recovery room.

Nurse for reception

Status

Used by activity in room

1

Generalized Centralized

Shared

Shared

Reception in reception room Induction in induction room Operation in operating room

3 of each

Specialized Centralized

Operating in Dedicated hospitalisation operating room

1 of each


Dedicated

Operating in urgency operating room

RAS

Nurse assistant

1

Generalized Decentralized

Shared

Transfer [AT] Installation [AO1] Recycling [AO5] Transfer [AO4]

MSR

Other anaesthetist Staff Doctor Anaesthetist Nurse anaesthetist recovery room Nurse's aide recovery

1 of each


Dedicated

Recovery in recovery room

MA

Reception room

Place available in induction room for emergencies Place available in MIH induction room for hospitalised Operating room AOU for emergencies Operating room AOH for hospitalisations Places available MR1 into Recovery Room MIU

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Class(es)

Anaesthesiologist staff 4 of Generalized anaesthesiologist each Decentralized Nurse anaesthetist

Medical staff for hospitalisations Surgeon – Surgeon assistant MSH – Nurse for bandage – Nurse for medical instruments Medical staff for emergencies Surgeon – Surgeon assistant MSU – Nurse for bandage – Nurse for medical instruments

Table 2 shows the characteristics of the material (rooms) and man resources. The distinction between patients in hospitalisation and patients in emergency is not made any more starting from the exit of the operating room. It is why resources MSR and MR1 have the statute of "dedicated ".

Qty

Human resources RI

Activities & Ref. RECEPTION [AA] Hospitalisation Emergencies TRANSFER [AT] INDUCTION [AI] Hospitalisation

Description

Equipment resources Generalized Shared 1 Centralized

Reception

1


Dedicated

Induction for emergencies

3


Dedicated

Induction for hospitalisations

1


Dedicated

Operating for emergencies

3


Dedicated

Operating for hospitalisations

6

Generalized Centralized

Dedicated

Recovery

4


-54. Modelling Operating theatre block workflow into WFRS-net. Analysis and simulation From the modelling of the workflow (ANNEXE 2 Graphic 1), one can construct easily the associated WFRS-net (ANNEXE 3 - Graphic 2). Analysis and simulation of WFRS-net are done by using Danamics [7]. The passage of the abstract diagram of the workflow (ANNEXE 2 - graphic 1) to a formal graphic notation under (WFRS) is carried out by translating the states by places and the changes of state by transition. For example : State AOU5 (recycling block activity) of Graphic 1 is represented by the place P11. The change of state (i.e. block recycled) is represented by the crossing of the transition T17. The place P12 models resource AOU (emergencies operating room) and contains 1 token when it becomes available for a new operation. It can contain one token because there is only one resource of this type. Once built, this formal model makes it possible to check the properties of coherence and to evaluate the performances of the workflow considered. Using Danamics tool, we first checked the soundness property of our model and secondly, we evaluate performance of the process under the condition that the system reach saturation as soon as the mean waiting time exceeds 45 minutes before Induction activity for an emergency. 1. Process duration • Mean duration for the first part of emergencies and hospitalization ; • Mean duration for the second part of emergencies and hospitalised ; • Mean total duration for an emergency and a hospitalization. 2. Seek thresholds • Number of maximum patients that can be treated until saturation of the system. We have tested for 1.2.3.4.5 initial tokens (patients). We can see that from 5 the threshold of the constraints for mean waiting time is reached. • Detection of bottlenecks 3. Mean waiting time (MWT) at strategic points: (in minutes) • MWT before induction for emergencies ; • MWT before induction for hospitalization.

• • • •

BR for MSI (anaesthesiologist staff) ; BR for MR1 (recovery room) ; BR for AOU (operating bloc for emergencies) ; BR for AOH (operating bloc for hospitalization) ;

The results are given in Table 3. They were obtained on the basis of one million of iterations in each case. Table of results - Table 3 Parameters / Qty 4 5 1 2 3 of patients Process duration (in minutes) First part – 62 89 105.8 122.6 136.2 Emergency First part – Hosp. 61 69 78.7 89.5 106.7 Second part – 52.6 53.9 Emergency and 49.5 52.1 52.8 Hosp. Total Emergency 111.5 141.1 158.6 175.2 190.1 Total Hosp. 110.5 121.1 131.5 142.1 160.6 Total 125 125 136.4 148.2 166.7 Mean Waiting Time before induction (in minutes) - Initial constraint For emergencies. 0 8.7 19.8 47.3 33.2 For hospitalised 0.6 1.7 3 16.3 7.3 Busy Rates (in %) RI – 1 res. 3 6.3 8.8 10.8 12.2 RAS – 1 res. 15.6 21.3 40.8 50.2 56.6 MSI – 4 res. 11.5 23.2 35.2 46.3 55.5 MR1 – 6 res. 7 13.8 19.6 23.5 26.8 MOU – 1 res. 12.8 24.8 35.3 45.7 54.3 MOH – 3 res. 14.7 30.1 46.4 61.3 73.4

These results show that the process "operating theatre suite", respects the constraints of waiting before induction and can manage up to 4 patients simultaneously, with an average time of stay in the execution operation cycle of 175 ' for the patients in emergencies and of 142 ' for the hospitalizations. That means, according to the statistical distribution of the patients (80% hospitalized and 20% in emergency), those 3 patients in hospitalization can be treated per cycle. This information can make it possible to optimize the management of the operations program. 5. Business processes reengineering approach to improve performances From these simulation results it seems that theatreoperating room is well tailored (three blocks for hospitalisation, one for emergency), four patients can be treated simultaneously. Now, the question is: how we can improve by business process reengineering the number of cases which can be treated simultaneously in the whole system respecting the initial constraints.

4. Busy rates (BR) of resources: (in %) • BR for RI (reception nurse) ; • BR for RAS (nurse aide) ;

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-6In the context of a hospital, the BPR can relate only to the management of the resources because it is not possible, within this framework, to re-examine the protocol of care for the patient. Hence, one can play only on: - the degree of specialisation/generalisation or centralisation/decentralisation of these resources, - change of class (from generalized resources to a specialized resources and conversely or to pass from centralized resources to decentralized resources or conversely), - change of the status : conversely.

of dedicated to shared or

This can be achieved by reconsidering the resources status: specialization, generalization, centralization, and decentralization. In this second model (see ANNEX 4 - Graphic 3) , we have: After several scenerios, we show that the following decisions or modifications can lead to better performances of the whole system. The results are given in the Table 4. They were obtained on the basis of million iterations in each case. •

Specialised the MSI resource : 1 for emergencies and 3 for hospitalised,

•

Extended the generalisation of the RI resource who comes in supports RAS for the transfer tasks (AT1+AT2)

•

Restricted the generalisation of RAS (we have taken out the transfer task [AT])

The new associated WFRS-net and the Petri-net result is given on the ANNEX 4 - Graphic 3 The obtaines results (see Table 4) show that the process "operating theatre suite", could be improved while changing the number of patients managed simultaneously from 4 to 5. The average duration of an execution operation cycle for an emergency changes from 175 ' to 179 ' and for an execution operation cycle of a hospitalisation, of 142 ' to 145 ' That is to say a profit of 25% for the number of patients operated simultaneously, whereas the average duration of an execution operation cycle increases by less than 3%. One gains thus very appreciably in performance while limiting the lengthening of the execution operation cycles.

Table of results after a first optimisation - Table 4 Parameters / 5 6 Qty of 1 2 3 4 patients Process duration (in minutes) First part – 55.5 79.8 101 112.8 125.6 133.7 Emergency First part – 55.9 62.9 69.9 79.5 91.5 85.2 Hosp. Second part – Emergency 49.7 52.4 53.5 54 53.4 52.7 and Hosp. Total 179 186.4 105.2 132.2 154.5 166.8 Emergency Total Hosp. 105.6 115.3 123.4 133.5 144.9 137.9 Total 113 111 124 134.8 146.8 161 Mean Waiting Time before induction (in minutes) – Initial constraint For 0 0,2 0.9 21.8 33.6 49.3 emergencies. For 0 0 0.1 0.3 3.8 11.6 hospitalised Busy Rates (in %) RI – 1 res. 4.7 8.9 12.4 15.4 17.4 18.7 RAS – 1 res. 14.4 27 37.6 46.5 52.9 57.3 MSI Emergency – 10.7 20.6 30.5 38.3 44.9 49.4 1 res. MSI Hosp. – 11.8 24.6 37.6 50.2 60.6 68.2 3 res. MR1 – 6 res. 7.5 13.9 19.2 24 27.8 29.5 MOU – 1 res. 12.6 24.4 36.4 46 54.2 60 MOH – 3 res. 14.9 30.8 46.9 62.4 75.1 84.4

It is significant to stress that the resources are better exploited. Indeed, their busy-rates improve in the following way: - RI - Nurse for reception : + 60% - MSI for hospitalisations : + 30,9% - RAS - Nurse assistant : + 14,5% - MR1 – Recovery room : +18,3% - AOU – Operating room for urgency : +18,6% - AOH – Operating room for hospitalisations : +22,5% Only the busy-rate of resource MSI for emergency decreases slightly by 3%. That is due to the fact that there is one operating theatre suite for the emergencies. It appears with the insight of these results that a simple revision of the assignment of some resources without increasing there number [thus the cost] one can very appreciably improve the total performances of the process. It is possible to improve the performance of this operation cycle execution.

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-76. Conclusion

7. References

The main aim of this paper is to show through a study case that Workflow nets with shared resources (WFRS) [3] can be easily used to analyze operating room processes and to support efficiently their reengineering. Due to hospital context, this business process reengineering involve only the management of the resources. In particular, we show how the process "operating theatre suite" can be optimized by reconsidering the resources status : specialization, generalization, centralization, and decentralization.

[1] W.M.P. Van der Aalst , "Verification of workflow nets", LNCS n°1248, 1997. [2] K. Barkaoui and J-F. Pradat-Peyre, "On liveness and controlled siphons in Petri nets", LNCS n°1091, 1996. [3] K.Barkaoui and L.Petrucci: "Structural analysis of workflow nets with shared resources", Proc. of First International Workshop on Workflow and Petri nets, 1998. [4] P. Carvalho de Oliveira , "Modélisation par réseaux de files d'attente de l'architecture du bloc opératoire" Mémoire d'Ingénieur CNAM, 1998. [5] R.Levan : "Le projet workflow", Editions Eyrolles, 1999. [6] P. Lawrence, "Workflow Handbook", Workflow Management Coalition, John Willey and sons Editor, 1997 [7] B. Changuion, I. Davies, M. Nelte, "DaNAMiCS - a Petri Net Editor " Computer Science Department University of Cape Town.

WFMS Notation Symbols AA1+AA2

Signification

T

Tasks numbers and total duration.

4'

Routing condition with their probability of event.

Hospitalized P (A A 1) = 0.8

R eceiv e R esso u rces

Resources : equipment and staff Their quantity and status. See Table 3 for details.

H um an R I x 1 : SH AR ED

[i]

Entry of the workflow [i] – Exit [o]

[o] OR

OR

AND

(1)

(1) Or/And split : splits a route between n routes (2) Or/And join: joins n routes in one route.

AND

(2)

ANNEXE 1

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Graphic 1 : Modeling Operating-Block Workflow - Resume Tasks, Resources and Constraints - [Probability of event P] - [WfMC extended notation]

i

Receive Ressources Material 1 room MA Human RI x 1 : SHARED

OR

Receive Hosp.

Hospitalized P(AA1) = 0.8

AA

Transfert Ressources

Transfert T

AT

4'

T

Human

2'

RAS x 1 SHARED

Emergency P(AI1) = 0.2

AND Recycling Block

And

AA

T

Receive Emergency

4'

AOH5

Operating room FREE

AOU5

T

T

10'

10'

Recycling Block

Emergencies Short Induction

OR

Short P = 0.95

AI

Materiel Emergencies : MIU x 1 Hospitalized : MIH x 3 Human : Emergencies : MSI x1 Hospitalized : MSI x3

Long P = 0.05

AI

T

T

T

Installation

4' AOU2

T

Preparation

AI

OR

Long P = 0.07

T

AI

T

10'

30'

Hospitalized Operating Blocks AOH1

Installation

T 4'

T Preparation

AOH2

Operating Blocks Shared Ressources

4'

Hospitalized Long Induction

Short P = 0.93

Materiel Emergencies : MOU1 x 1 Hospitalized : MOH1 x 3 Human Emergencies : MSU x1 Hospitalized : MSH x3 [For tasks 1-2-3]

Emergencies Operating Block AOU1

Hospitalized Short Induction

Operating Blocks Ressources

30'

10'

OR

Induction Ressources

Emergencies Long Induction

Transfer room and operating room FREE

4' OR

Human : RAS x 1

Emergencies P(USC) = 0.40

AOU3

T

Emergencies P(USM) = 0.30

AOU3

20'

T

Emergencies P(USL) = 0.30

AOU3

43'

FOR TASKS : AOU1 - AOH1 AOU4 - AOH4 AOU5 - AOH5

To Recycling task

AOH3

T Operation 80'

T

AOH3

Recovery

Transfer

Hospitalized P(HSL) = 0.10

AOH3

T 43'

AO

3'

80'

T Transfer 3'

AR1

Supervision

T Operation

OR

OR

T

Hospitalized P(HSM) = 0.30

20'

OR

AO

Hospitalized P(HSC) = 0.60

T 50'

o

To Recycling task

Recovery Ressources Materiel : MR1 x 6 Human : MSR x1

ANNEXE 2

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ANNEXE 3

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ANNEXE 4

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Verification and Optimisation of an Operating Room Workflow

Verification and Optimisation of an Operating Room Workflow

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