SICE Transactions on Industrial Application
Vol. 8, No.7, 54/67 (2009)

Nursing Care Scheduling Problem: Analysis of Inpatient Nursing
Mingang Cheng1 Hiromi Itoh Ozaku2 Noriaki Kuwahara3 Kiyoshi Kogure4 and Jun Ota5
In most Japanese hospitals, different nurses handle the pre-assigned nursing cares in different ways, which directly affect thequality of nursing cares. Thus, it is necessary to quantitatively elucidate the nurses' action rules for nursing instruction in
high-quality care provision and evaluation of staffing levels. Keeping track of times of relative effectiveness in meeting andconnecting with another can reveal and extend one's skills of engagement in practical nursing cares. Therefore, modelling
inpatient nursing from the viewpoint of scheduling, we propose a new method to quantitatively elucidate the implicit action rulesof nurses on their provision of nursing cares engaged in practical nursing cares, according to a set of candidate existing
dispatching rules. In simulations to match the nursing care schedules planned by dispatching rules with the observed ones, weconclude that (1) nurses make schedules based on the rules similar to the dispatching rule of earliest due date (EDD), whichmeans they refer the evaluated preparation times of activities and their expected finishing times assigned in worksheets, and (2)nursing staffing level have an inverse relation (-0.68 for preparation coefficients - the ratio of preparation time evaluated to that inmanuals - to work tenures based on the linear regression analysis) with the evaluated preparation times, which should be one
issue on the possibilities that nurses provide nursing cares as scheduled in worksheets.
Keywords: Nursing modeling, nurse action rule, dispatching rule, staffing level.

1.

contribute to increasing their working hours. However, it will
result in higher rates of the risk of misses like sharp andneedle-stick injury(3). In a total view, nurses provide the cares,
which consist of a set of expected activities pre-assigned inworksheets and unexpected activities termed as interruptions,according to the technological procedures in the manuals. As
described by the abstract nursing model in Fig.1, they determine
the processing orders of the pre-assigned nursing activities in theirown ways (termed as the nurses' action rules, including referenced
information and scheduling algorithm), and quickly response to
the unexpected activities. Normally, nurses with lower nurse
staffing levels provide their nursing cares in worse processingorders, which directly lower the quality of nursing cares. Thus,
hospitals with low nursing staffing levels tends to have higher
rates of poor patient outcomes(4). Consequently, to provide ahigh-quality of nursing cares, besides the technology of nursing, it
is more important to define the processing orders of nursing cares.
As we know, scheduling is a problem to define the processingorders of a serial of jobs. In recent years, similar to the normalscheduling problems, several methods have been proposed tonursing scheduling problems(5)(6). Using the agent-basedscheduling methods, they can obtain a nursing schedule in a better
quality. However, these methods are limited on their practicalapplication by current staffing levels and realistic nursing
environments. In current hospital societies, nurses mainly acquire
their own ways to provide the nursing cares by gaining thefragmentary knowledge of the elder nurses in hospitals on theircase-by-case ways to provide nursing cares. However, in actual,no one can explain the detailed way to define the processingorders of pre-assigned activities, that is, to summary that (1) what
is based on and (2) how do they define the processing orders,
during the provision of nursing cares.

INTRODUCTION

Inpatient nursing is defined as the diagnosis and treatment ofpatient responses to actual or potential health problems. It highly
depends on the dynamic hospital environment and diverse nurse
staffing levels, which directly result in an undesirable waiting time(that is, a delay from the planned time) of patients. In addition,
Japanese hospitals have to face two serious problems in recent
years: (i) shortage of nurses: contrast to the ratio of the number ofnurses in per 1,000 population in Sweden: 10.3 population, theratio in Japan is 6.4 population only in 2004(1); (ii) complexity ofnursing due to the increasing responsibility for providing highquality nursing cares in the aging society (the rate of the elderly 65
years old and over in the population is 20.2% in 2005(2)). In thisrespect, nursing is recognized as one of the toughest job in Japan,
especially for the nurse novices. As we know, with thedevelopment of medical technology in recent years, the nurses’
responsibility for providing high quality cares with effectivenessand efficiency is pursued by the hospitals and the public.
In general, it is recognized that more nursing time per patientresults in better patient outcomes, so that a lot of practitioners
1

Department of Precision Engineering, The University of Tokyo,
7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656 Japan.
2
Information Management Office, National Institute of Information andCommunications Technology (NICT),
4-2-1 Nukui-Kitamachi,Koganei, Tokyo, 184-8795 Japan.
3
Department of Advanced Fibro-Science, Kyoto Institute of Technology,
1 Hashigami-Cho, Matsugasaki, Sakyo-Ku, Kyoto, Japan
4
College of Engineering, Kanazawa Institute of Technology,
7-1 Ohgigaoka, Nonoichi, Ishikawa 921-8501, Japan
5
Research into Artifacts, Center for Engineering (RACE), The Universityof Tokyo,
Kashiwanoha 5-1-5, Kashiwa, Chiba 277-8568, Japan(Received December 22, 2008)

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Fig.1 The abstract nursing modelFig.2 The abstract model of the analysis method

and nurse novices. As we know, almost all of these literatures
obtained their conclusions based on the nurses’ dialogues. In thisway, there may be an influence of nurses’ subjective thoughts on
the results to some extent. To our knowledge, there is not any
research on the quantitatively analysis of nursing cares to
elucidate the nurses’ implicit scheduling algorithms.
On the other hand, many researches on the modeling of action
rules have been studied based on the stochastic models(11)(12).
Considering the human action rules as a serial of stochastictransitions from one state to another state, they can recognize
human actions, and furthermore induct the human actions with theempirical support. However, these models are only of thedescriptions of human action rules to some extent. As we know, it
is impossible to explain human action rules like referenced
information in nurse action rules.
Consequently, in this paper, we will quantitatively explain theimplicit nursing action rules from the viewpoint of scheduling, by
analyzing their inpatient nursing cares. Now, in our E-Nightingale
project(13), using the ubiquitous sensor network (mainly including
the voice records and infrared passing sensors, according to which
we obtain the voice data on the execution of providing nursing
cares and location data of nurses) technology, we are developing anursing support system to measure and analyze inpatient nursing
cares(14) by furthermore segmenting it into a serial of nursing
activities (the ones pre-assigned in worksheets, and interruptions)

In this respect, it is practically mandatory to quantitatively
elucidate the implicit nursing scheduling algorithms of nurses byanalyzing their inpatient nursing cares. Therefore, we are possible
to (i) have a quantitative evaluation of the nursing staffing levels
other than the working tenures, and furthermore (ii) propose aneffective nursing care instruction system in actual nursing
environments based on the elucidated referenced information
during the nurses' provision of nursing cares.
In recent years, more and more researchers have emphasized
their studies on the analysis of inpatient nursing cares aiming at
extracting important points during the provision of nursing
cares(7)(8)(9)(10). From the study by Benner in 1982, a lot of
researches have been studied on the decision making models(scheduling algorithm in Fig.1) of nurses, mainly according to the
dialogues (interviews and/or questionnaires) on their provision ofnursing cares. Benner(8) did a research about the nursing staffing
levels by studying the experiential learning. It is based on the
dialogues about the therapeutic cases of nurses. In addition,
Lauri(9) emphasized the research on the identification of decision
making model. Using the structured questionnaires with 5 point
scale on 56 items, the research shows the result on the variables ofthe decision making. And furthermore, Yokouchi(10) proposed atask classification system using the ethno-methodological word
mining method. Based on the interviews with nurses on theirscheduling methods, the research shows a comparison of experts

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Fig.3 Part of a sample worksheet

according to the manuals. Contrary to the normal schedulingproblems to propose a method to generate optimal schedules, we
aim at elucidating the implicit nursing action rules according tothe obtained data (worksheets, interruptions, manual, and actual
nursing cares), as shown in Fig.2. Hypothetically modeling thenurses’ action rules as a set of candidate dispatching rules,
according to which different nursing care schedules can begenerated for actual worksheets and interruptions, wequantitatively elucidate nurses' action rules based on the mostsimilar dispatching rules, obtained by evaluating the similarities ofthe planned nursing cares with observed ones.
The remained of this paper is organized as follows. Section 2
describes the nursing care scheduling problems. Section 3
introduces several single dispatching-rule based methods. Section
4 elucidates the implicit nursing scheduling algorithms, anddiscusses the difference of staffing levels. And finally, Section 5
has a description of conclusions and future works.

Fig.4 Construction of nursing activity

Fig.5 Nursing care scheduling problem - allocation of nursing activity- Occurring time.

(3).Manual (Nursing Activity & Tasks): Documents describing thestandard methods to handle the nursing activity with the
purpose to care patients, e.g., blood pressure measure,environment maintenance. It is mainly including the following
information:- Commodities.
- Technical procedures of nursing.
- Evaluated processing time of nursing activities.
In actual, nursing is practiced in real settings with realconstraints, possibilities, and resources, and working
environments may constrain one's practice beyond his or her
ability to respond effectively. Here, to represent the constraints in
actual nursing, we model the manual in a hierarchical frame. Fig.4
shows the construction of an nursing activity. In this figure, thevertical representation shows the decomposition of nursing
activity by nursing tasks, and nursing task by nursing sub-tasks,
which is connected by the straight lines. In addition, the horizontal
arcs shows the procedure constraints among tasks. Moreover, inthe hierarchical construction of sub-tasks, the verticalrepresentation states the procedure constraints among sub-tasks,
and the horizontal representation states the partial order relationsof sub-tasks, respectively. For example, subtask111 should be

2. NURSING CARE SCHEDULING PROBLEM
In hospitals, nurses provide patients with direct or indirectly
nursing cares up to 24 hours a day, which is generally consistingof a serial of nursing activities.
2.1. Inpatient Nursing Care
Normally, nursing care, including the pre-assigned nursing
activities in worksheets and unexpected nursing activities(interruptions), is provided to corresponding patients according to
the nursing procedures in the manuals.
(1).Worksheet: A piece of paper recording a serial of nursing
activities planned or done on a therapeutic plan. As a sample
of worksheet in Fig.3 shows, the worksheet is mainly
including the following information:- Patient information (patient name and bed information).
- Nursing activities category.
- Expected execution time constraint (the constraint that thecare included in the nursing activity should be provided topatients in the expected execution time.).
For example, the nursing activities of "Blood pressure check" in
Fig.3 are desired to be provided to "Patient a" and "Patient b"
within the interval from 10:00 to 10:30.
(2).Interruption: the nursing activities, different from thosepre-assigned in the worksheet, are occurring at an unexpected
time, and should generally be handled immediately, such as
the contact among nurses/patients, and interruptions from thenurse call. The interruption is mainly including the following
information when it occurs:- Patient information (patient name and bed information).
- Nursing activities category.

performed before subtask121 and subtask131 , while subtask121
can be performed before or after subtask131 because of their
partial order relations.
Normally, each nursing activity generally consists of
preparation tasks, execution tasks, and clean-up tasks according to
the description in manuals. Moreover, each task can also be
decomposed into a set of sub-tasks according to its characteristics.
As we know, the execution of each nursing task involves atransition or movement between locations. Thus, we introduce thesub-tasks according to the transitional positions in this study. For

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Table I Dispatching Rules
Expected execution time:[TLB, TUB]*

Evaluated
processingtime**

Items

LB

LB&UB

FCFS

EDD

Execution tasks only

MPT

SLACK

Execution & Preparation tasks

extended MPT

extended SLACKNo
Yes* TLB: lower bound of expected execution time, UB: upper bound of expected execution time in the worksheet;** "No": out of consideration of evaluated processing times, "Yes": in consideration of evaluated processing times.

activity due to some reasons like the lasting characteristic ofnursing tasks. For example, the nursing task of intravenous drip
reservation should be handled after the start of the drip with an
expectable interval, during which the other tasks can be handled.
(vi) Expected execution time constraints: Some execution tasksof nursing activities should be handled during an expected
execution time interval [TLB, TUB] as planned in the worksheets.
For example, the nursing activity of food provision should be
handled during the noon time (normally from 11:00 to 13:00).
In a word, nursing care scheduling problem, formulated as the
problem to determine the processing orders of nursing tasks, is toobserve the above soft constraints when satisfying the hardconstraints. To elucidate the implicit nursing schedulingalgorithms of nurses, we should find out a scheduling algorithm
among the candidate ones, according to which we generate themost similar nursing care schedules with the actual ones, as
described in Eq.1.

example, as for the preparation task of intravenous drip, we define
a set of sub-tasks: sub-task in Nurse Station (for Karte check),
sub-task in Drip Preparation Room (for the preparation of
medicine, drip tube), and sub-task in Sick Room (for theconfirmation of the patient on its in the room). Therefore, in our
E-Nightingale project (14), we can properly know the activity
information pre-assigned in the worksheet or interruptions basedon the voice data (15, 16), and the sub-task information of theactivity based on the location data during the provision of nursing
cares. In this way, we are possible to model the nursing manual
through observed inpatient nursing cares.
2.2. Nursing Care Scheduling Problem
Nursing care scheduling problem, defined as the problem todecide the processing orders to handle a set of nursing activities, isto allocate the subtasks of each activity over time while obeying
the technical procedures in manuals and time constraints inworksheets (Fig.5). This allocation must obey a set of constraints
that reflect the temporal relationships between the tasks and thecapacity limitation of the nurse. In general, there are several basic
kinds of constraints as follows:(i) Release time constraints: For any nursing activity, its any
task cannot be handled until its release time. For some reasons likethe absence of the nurses or the shortage of medicine, the nursing
activities cannot be handled. In this paper, we restrict ourselves tothe case where it is the prefered start point of the nursing activity,
which is mainly determined by its preparation time (later we willstate a detailed description).
(ii) Procedure Constraints: The processing of nursing tasks of anursing activity should observe the technical procedure in manuals,that is, a nursing task cannot be handled until the previous task ofthe same nursing activity is finished. For example, the execution
task cannot be handled before the preparation task.
(iii) Capacity Constraints: Nurses have the limited processing
capacity to handle their work. In general, they can handle only one
nursing task at a time. For example, during the provision of
intravenous drip, it is impossible to provide the toilet assistance topatients.
Besides the above three kinds of constraints (termed as hardconstraints, which a nursing care schedule should observe), thereis the other three (termed as soft constraints, which the scheduleshould satisfy as possible as it can).
(iv) Due date constraints: The last nursing tasks of a certain
nursing activity must finish before the due date of the nursing
activity. In this paper, we simply model it as the end point of the
duty time.
(v) Implicit time constraints: Some nursing tasks cannot be
handled immediately after their previous task of the same nursing

Problem:arg max Similarity Rule…………...(1)RuleSubject to:
Observe the above six kinds of constraints.
Here, SimilarityRule is the performance to evaluate the rate of thesimilar part between the actual nursing cares schedule and theplanned one, which is obtained based on the candidate schedulingalgorithm Rule.
To model and elucidate the implicit nursing action rules, wewill introduce a set of candidate scheduling algorithms to thenursing care scheduling problems in the next section, followed by
the detailed induction of the performance measure on similarity.

3. NURSING SCHEDULING METHODSAs described in the literatures of scheduling methods,
dispatching rule is a policy according to which the processingorders of a set of jobs are defined. It is recognized as theimplementation of human thoughts, and widely used in thescheduling fields. Therefore, to elucidate the implicit nursing
scheduling algorithms, we will model them as a set of candidate
dispatching rules and evaluate their similarities by comparing
planned nursing care schedules with the actual observed ones.
In general, nurses can only grasp the following information
before the provision of nursing cares: (1) expected execution time
[TLB, TUB] from the worksheet, and (2) evaluated processing timewith different slack times from their experience. Thus, wehypothesize that a nurse make schedules for assigned nursing

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SICE Transactions on Industrial Application
Vol. 8, No.7, 54/67 (2009)activities according to the above two information. By evaluating
all of possible dispatching rules considering expected execution
time and evaluated processing time, we are able to elucidate theaction rules of nurses on their provision of nursing cares. In recent
years, above 100 dispatching rules has been proposed (13), andmost of the complicated dispatching rules can be considered as anextension or combination of some single ones. As mentioned by
Panwalkar in 1977, the most prominent dispatching rules are
first-come-first-service (FCFS), shortest processing time (SPT),
most work remaining (MWKR), minimum batch size (MBS),earliest arrival time (EAT), largest processing time (LPT), shortest
setup plus processing time (SSPT), shortest remaining processing
time (SRPT), shortest slack time (SLACK), and earliest due date(EDD). As interviewed with several nurses on their action rules on
the provision nursing cares, they general handle the nursing
activities by referring the information in worksheets. In these rules,
only FCFS, SPT, EAT, LPT, SLACK, EDD can simply consider
the information in worksheets. Here, FCFS and EAT are of thesimilar functions, and SPT and LPT are of the opponent functions
during the scheduling process. As shown in some observed
nursing cares, nurses perform the activity with larger processing
time first. Consequently, we only consider 6 kinds of single
dispatching rules in this study: FCFS, EDD, MPT (maximal
processing time, also termed as LPT), extended MPT, SLACK, andextended SLACK, as shown in Table I.

Fig.6 Illustration of evaluated processing time of preparation tasks

tasks to be handled immediately after finishing the execution tasks
during the scheduling process, which is certificated by most of
nursing activities in the obtained nursing cares.
3.1.2 Release Time of Nursing Activity
In addition, as for the preparation tasks, it is unrealistic to be
dealt at any time before the handling of the execution tasks. In thispaper, we simply consider the lower bound of preparation tasks
handling bounds to be release time of the nursing activity, as
shown in Fig.6, which is decided only by the preparation
coefficient α and defined by Eq.2. On the contrary, the lower
bound of the execution task handling bounds is pre-assigned in theworksheet as described in Section 2. In this respect, we considered
the execution time coefficient β only in the process of schedulingin this paper.
As mentioned, all of the above 6 kinds of dispatching rules are
related to the preparation coefficient α; meanwhile, MPT,
extended MPT, SLACK, and extended SLACK is also related to the
execution coefficient β.

3.1. Referenced Information
3.1.1 Evaluated Processing Time
In actual dynamic nursing environments, considering thepossible occurrence of unexpected events, nurses handle their
nursing activities with slack times to ensure to provide the nursing
cares as pre-assigned in the worksheets, as described by several
nurses in our companied hospital. Normally, the slack times arerecognized as the enlarging of the processing times from theaverage values of the nursing activities. Thus, here we considered
the following two coefficients: preparation coefficient α forpreparation tasks and execution coefficient β for execution tasks,and hypothesis that the evaluated processing time has a linear
relation with average processing times of nursing tasks:PTi    pt ij ,  : preparation coefficient.

…………... (2)ETi    pt ij ,  : execution coefficient.

…………... (3)3.2. Dispatching-Rule based Methods
3.2.1 Dispatching Rule
Dispatching rule is a policy according to which the processing
priorities of nursing activities are determined. In general, thenursing activities with higher priority would be handled first. Here,we will have a detailed description of 6 kinds of dispatching rules.
a) First Come First Service (FCFS)
Step1: Define the lower bound TLB of expected execution timeas the arrival time of the nursing activity.
Step2: Decide the processing orders of nursing activities
according to the arrival time: the earlier the arrival time is, thehigher the priority of the activity is.
Step3: If there is some idle time before handling a execution
tasks with the highest priority, deal with the following acceptabletask (preparation task or execution tasks) according to its possible
start time (i.e., the lower bound of preparation/execution task
handling area), and go to Step2. Otherwise, update the current
time and deal with the execution tasks.

jJ PijJ Ei

Where, 1  i  N .
Here, N is the total number of the activities pre-assigned to anurse, JPi, JEi are the collections of the preparation subtasks andexecution subtasks of i-th activity, ptij is the average processing
time of j-th subtask, and PTi, ETi are the evaluated preparation
time and evaluated execution time of i-th activity. The larger the
preparation coefficient α is, the more the slack time that a nurse
considers for handling the preparation tasks is during thescheduling process, and the earlier the nurses will start to deal
with the preparation tasks. Similarly, the larger the execution
coefficient β is, the more the slack time is for handling theexecution tasks during the scheduling process. Besides the
preparation and execution tasks, the clean-up tasks may also affectthe nursing cares. In this paper, we will simply consider clean-upb) Earliest Due Date (EDD)
Step1: Define the upper bound TUB of expected execution timeas the expected finishing time of the nursing activity.
Step2: Decide the processing orders according to the expectedfinishing time: the earlier the expected finishing time is, the higher
the priority the nursing activity is.
Step3: If there is some idle time before handling a execution
tasks with the highest priority, deal with the following acceptabletask (preparation task or execution tasks) according to its possible
start time (i.e., the lower bound of preparation/execution task
handling area), and go to Step2. Otherwise, update the current

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Items/Nursing Activity

Table II Illustration of Dispatching Rules – Nursing Activity Information
Nursing Activity A
Nursing Activity B
Blood pressure measure
Foot bathWorksheet Information Expected execution time
Preparation sub-task
Processing
Execution sub-task
time
Clean-up sub-task
Representation[9:30, 10:00][9:30, 10:00]

10 minutes
20 minutes
10 minutes

20 minutes
15minutes
10 minutes

task (preparation task or execution tasks) according to its possible
start time (i.e., the lower bound of preparation/execution task
handling area), and go to Step2. Otherwise, update the current
time and deal with the execution tasks.

time and deal with the execution tasks.
c) Maximum Processing Time (MPT)
Step1: Decide the processing orders according to the total
processing time of the execution tasks: the larger the processing
time is, the higher the priority of the nursing activity is.
Step2: If there is some idle time before handling a execution
tasks with the highest priority, deal with the following acceptabletask (preparation task or execution tasks) according to its possible
start time (i.e., the lower bound of preparation/execution task
handling area), and go to Step1. Otherwise, update the current
time and deal with the execution tasks.

3.2.2 Illustration
To explain the detailed procedures of each dispatching rule, we
provide a simple nursing care scheduling problem including 2
nursing activities (blood pressure measure and foot bath). The
basic information in the worksheet and manual is listed in Table II.
Furthermore, we consider the preparation coefficient α to be 3.0
and execution coefficient β to be 1.0. In this way, we can obtain
the relative information referenced in the process of scheduling(Table III), according to which a series of nursing care plans canbe generated based on the above 6 dispatching rules (Fig.71):d) extended MPT
Step1: Decide the processing orders according to the total
processing time of the preparation tasks and execution tasks: thelarger the processing time is, the higher the priority of the nursing
activity is.
Step2: If there is some idle time before handling a execution
tasks with the highest priority, deal with the following acceptabletask (preparation task or execution tasks) according to its possible
start time (i.e., the lower bound of preparation/execution task
handling area), and go to Step1. Otherwise, update the current
time and deal with the execution tasks.

a)First Come First Service (FCFS): In this case, blood pressure
measure and foot bath have the same lower bound of expected
execution time (i.e., 9:30am). This means that blood pressure
measure is of the same priority with the foot bath. However, in thescheduling process, blood pressure measure is of the higher
priority, since it precedes foot bath in the input order, The
scheduling process is as follows:
Step (1): Handled the preparation sub-task of blood pressure
measure first, and update the current time CT to be 9:10am.
Step (2): Due to the current time CT 9:10am < 9:30am which is
the lower bound of the execution sub-task of blood pressure
measure, handle the next acceptable sub-task - the preparation
sub-task of foot bath, and update the current time CT to be 9:30am
Step (3) and (4): Due to 9:30am >= 9:30am, handle theexecution sub-task of blood pressure measure, and then theclean-up sub-task since it is considered to be handled immediately
after the execution sub-tasks are finished, as mentioned above.
Furthermore, update the current time CT to be 10:00am.
Step (5) and (6): Due to the current time CT 10:00am > 9:30am,
which is the lower bound of the execution sub-task of foot bath,handle the remaining sub-tasks of foot bath.

e) SLACK
Step1: Define the upper bound TUB of expected execution timeas the expected finishing time of its execution tasks.
Step2: Decide the processing orders according to the SLACK
rule based on expected finishing time: the lower the slack time(that is, the time for handling the remained nursing execution
tasks) before the expected finishing time is, the higher the priorityof the nursing activity is.
Step3: If there is some idle time before handling a execution
tasks with the highest priority, deal with the following acceptabletask (preparation task or execution tasks) according to its possible
start time (i.e., the lower bound of preparation/execution task
handling area), and go to Step2. Otherwise, update the current
time and deal with the execution tasks.

b)Earliest Due Date (EDD): In this case, blood pressure
measure and foot bath have the same upper bound of expected
execution time (i.e., 10:00am). This means that blood pressure
measure is of the same priority with the foot bath. Similar to thedescriptions in the illustration of the rule of FCFS, blood pressure
measure is of the higher priority. The scheduling process (Step (1)to Step (6)) is similar to that based on the rule of FCFS.

f) extended SLACK
Step1: Define the preparation tasks and execution tasks of anursing activity separately. Furthermore, consider the lower bound
TLB of expected execution time as the expected finishing time of
preparation tasks, and the upper bound TUB as the expectedfinishing time of execution tasks.
Step2: Decide the processing orders of the nursing activities
according to the slack time for parathion tasks and the slack timefor execution tasks. The lower the slack time for handling theremained tasks, the higher the priority of the nursing activity is.
Step3: If there is some idle time before handling a execution
tasks with the highest priority, deal with the following acceptablec)Maximum Processing Time (MPT): In this case, the priority isdetermined by the execution sub-tasks' processing time of blood1
In this figure, emphasizing the difference on the processing orders
determined by the dispatching rules, we exclude the parts representing the
movement between two sub-tasks.

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Table III Referenced information
Items

Notation

Definition

Value

Current time before scheduling

CT

9:00

Preparation coefficientα

3.0

Execution coefficientβ1.0

Nursing activity A
Expected execution time
Lower bound

LBA

9:30

Upper bound

UBA

10:00

Evaluated processing time
Preparation sub-tasks

PTPA

α * 10 min.

30 min.

Execution sub-tasks

PTEA

β * 20 min.

20 min.

STA

LBA - PTPA

9:00

Possible start time of
preparation task

Nursing activity B
Expected execution time
Lower bound

LBB

9:30

Upper bound

UBB

10:00

Evaluated processing time
Preparation sub-tasks

PTPB

α * 20 min.

60 min.

Execution sub-tasks

PTEB

β * 15 min.

15 min.

STB

LBB - PTPB

8:30

Possible start time of
preparation task

20 minutes: 0 + 20 minutes) is smaller than that of foot bath (i.e.,
15 minutes: 0 + 15 minutes). In addition, the current time CT
9:30am >= 9:30am, which is the lower bound of the execution
sub-task of blood pressure measure. Therefore, handle theexecution sub-task, and then clean-up sub-task of blood pressure
measure. Moreover, update the current time CT to be 10:00am.
Step (5) and (6): Due to the current time CT 10:00am >=9:30am, which is the lower bound of the execution sub-task offoot bath, handle the remaining sub-tasks of foot bath.

pressure measure and foot bath. The processing time of theexecution sub-task of blood pressure measure (i.e., 20 minutes) islarger than that of foot bath (i.e., 15 minutes). This means thatblood pressure measure is of the higher priority than the foot bath.
The scheduling process (Step (1) to Step (6)) is similar to thatbased on the rule of FCFSd)extended MPT: In this case, the priority is determined by theprocessing times of preparation sub-tasks and execution sub-tasksof blood pressure measure and foot bath. The scheduling process
is as follows:
Step (1): The processing time of the preparation sub-task andexecution sub-task of blood pressure measure (i.e., 50 minutes: 30+ 20 minutes) is smaller than that of foot bath (i.e., 75 minutes: 60+ 15 minutes). This means that foot bath is of the higher priority
than blood pressure measure. Therefore, handle the preparation
sub-task of foot bath first, and update the current time CT to be
9:20am.
Step (2): The processing time of the preparation sub-task andexecution sub-task of blood pressure measure (i.e., 50 minutes: 30+ 20 minutes) is smaller than that of foot bath (i.e., 15 minutes: 0+ 15 minutes). This means that blood pressure measure is of thehigher priority than foot bath. Therefore, handle the preparation
sub-task of blood pressure measure, and update the current time
CT to be 9:30am.
Step (3) and (4): The processing time of the preparation
sub-task and execution sub-task of blood pressure measure (i.e.,e)SLACK: In this case, the slack time of the execution sub-taskof the blood pressure measure (i.e., 9:40 - CT minutes: 10:00am 20 minutes - CT) is smaller than that of foot bath (i.e., 9:50 - CT
minutes: 10:00am - 10 minutes - CT) in the whole schedulingprocess. This means that the blood pressure measure is of thehigher priority than foot bath. The scheduling process (Step (1) to
Step (6)) is similar to that based on the rule of FCFS.
f)extended SLACK: In this case, the priority of an nursing
activity is determined by the slack time for its preparation
sub-tasks and that for its execution sub-tasks. The schedulingprocess is as follows:
Step (1): The slack times of the preparation sub-task of bloodpressure measure (i.e., 0 minutes: 9:30am - 30 minutes - 9:00am)
is larger than that of foot bath (i.e., -30 minutes(9:30am - 60
minutes - 9:00am). This means that foot bath is of the higher
priority than blood pressure measure. Therefore, handle the60

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Fig.7 Illustration of dispatching rules - planned nursing cares

the sake of convenience, the interruptions are assumed to be thenursing activities that should be started by corresponding attendantnurses without any delay from their starting time in the observed
nursing cares. Once an interruption occurs during the execution ofnursing cares, they will be assigned the highest priorities to behandled immediately. On the other hand, there should be someplural activities (the nursing activities that are done by two or
more nurses), which are generally pre-assigned in the worksheetof one nurse. Therefore, we simply consider the activity as theunexpected events for the other companied nurses in this paper.
Based on the above candidate dispatching-rule based methods,
we can obtain different nursing care schedules with different
processing orders for the nursing activities in the actual nursing
cares. Comparing the planned schedules with the actual ones, we
can elucidate the implicit nursing scheduling algorithms in Fig.2.
Moreover, according to the different slack times included in theprocessing times (that is, different value of preparation coefficient
α and execution coefficient β) during the process of scheduling,
we can analyze the inpatient nursing cares in a quantitative way.

preparation sub-task of foot bath first, and update the current time
CT to be 9:20am.
Step (2): The slack times of the preparation sub-task of bloodpressure measure (i.e., -20 minutes: 9:30am - 30 minutes 9:20am) is smaller than that of the execution sub-task of foot bath(i.e., 25 minutes(10:00am - 15 minutes - 9:20am). This means thatblood pressure measure is of the higher priority than bloodpressure measure. Therefore, handle the preparation sub-task ofblood pressure measure, and update the current time CT to be
9:30am.
Step (3) and (4): The slack time of the execution sub-task ofblood pressure measure (i.e., 10 minutes: 10:00am - 20 minutes 9:30am) is smaller than that of foot bath (i.e., 15 minutes:
10:00am - 15 minutes - 9:30am). In addition, the current time CT
9:30am >= 9:30am, which is the lower bound of the execution
sub-task of blood pressure measure. Therefore, handle theexecution sub-task, and then clean-up sub-task of blood pressure
measure. Moreover, update the current time CT to be 10:00am.
Step (5) and (6): Due to the current time CT 10:00am >=9:30am, which is the lower bound of the execution sub-task offoot bath, handle the remaining sub-tasks of foot bath.

4. SIMULATION AND RESULTS

3.3. Interruption Accommodation

4.1. Performance Measures

In general, nursing is a high statistic work with a high occurring
frequency of disturbances (about 8.4 operational failures/8-hour
shift(16)), which are recognized to be one of the most important
items affecting the execution of nursing cares. In this paper, forTo evaluate how well a nursing algorithm schedule's result fits
the actual schedule, we adopt a measure of similarity in time STimeas the performance measure. It is defined as a measure considering
the ratio of the difference of each nursing subtask on its execution

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Fig.8 Nursing ward - Layout- Ophthalmologic and otolaryngology department.
- 11 sickrooms: 4 of them are single rooms, 6 of them are
six-patient rooms, and the other 1 are 3-patient rooms.
Figure 8 shows the detailed layout of the nursing ward in a
hospital. As shown in this figure, the sickrooms are separated into
two parts and laid on both sides of the nurse station. In addition,
the whole size of the nursing ward is about 1000 m2 (25 meters ×
40 meters). The ellipses represents the passing sensors in
E-nightingale project (14), each of which consists of a couple ofsensor. As described by the Ohmura, each couple of sensors arelocated on both sides of the entrance of each room and accepting
the signals individually from the sender located in the nurses'
heads (17). Once a nurse passes the entrance of a room, the coupleof sensors will accept the signals from the nurse one by one, andon this basis we can conclude that the nurse enter into or go out of
the room. In this way, we can accurately know the changing
position of nurses in the time axis (with a synchronization error of
71ms/day). In addition, only the sensors marked by the ellipses
with digital IDs in the figure are in action.

times (starting time and ending time) to the makespan (defined as
the total working time from the start to the end of the inpatient
nursing care) between the planned schedule and the observed one:

S Time  1 

DMiddle 100%.
makespan * N Task…………... (4)Where, DMiddle   d ij   ( st ij  st ij 0  et ij  et ij 0 ) / 2 ,
i

j

i

j

et ij  st ij  pt ij .
Here, stij, etij, stij0, and etij0 are the starting time and the endingtime of the j-th nursing subtask of the i-th nursing activity in theplanned schedule and that in the observed one, respectively; ptij is
the real processing time of the j-th nursing subtask of the i-th
nursing activity; DMiddle is the difference on the time (starting timeand ending time) between the subtasks in the planned scheduleand that in the actual one; and NTask is the total number of thesubtasks.
Next, we will evaluate the similarity of the described 6
dispatching rules through a set of actual nursing cares.

Actual observed nursing cares:- 6 nurses2: Ns.a, Ns.b: experts with 5-year experience; Ns.c:
proficient with 4 years experience; Ns.d, Ns.e: advanced
beginners with 2-year experience; and Ns.f: novice with
1-year experience.
- Each nurse covers 5 ~ 7 patients' nursing cares, which is
decided by the nurse leader according to the quantity ofnursing cares and the danger level of patients.
- Totally 9 observed nursing cares3 (day shift from 8:00 am to

4.2. Experiments and Results
By evaluating the similarity on the execution time between theplanned nursing schedules and the actual observed ones, we canfind out the most similar rules to elucidate the implicit nursing
scheduling algorithms, and furthermore, to discuss the nursing
staffing levels in a quantitative way.
4.2.1 Simulation Set-up
To investigate the difference of ways of nurses to provide
nursing cares to patients and their staffing levels, we implement
the above dispatching-rule based methods on several observed
nursing care scheduling problems, and evaluate the similarities ofthe planned nursing schedules with the observed ones. The basic
information of the nursing ward and the nursing cares issummarized as follows:
Nursing ward:2

As mentioned by Benner, nurses can be classified in accordance with
their experience into five stages that are called novice, advanced beginner,competent, proficient, and expert (8). In this study, we simply classify
expert and proficient into the expert nurses, advanced beginner and novice
into the novice nurses, as described by most nurses in the hospitals inJapan.
3
Here, 3 of the 9 observed nursing cares were performed by Ns.c, and2 were performed by Ns.f, and the others were performed by other nurses
one by one.

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Table IV the Data from the Sensor Network - an example (15)

Table V Classification in Job Categories - an example (16)Table VI Classification of Nursing Activities and Sub-tasks - an example

5:00 pm) provided by the above 6 nurses are applied in thispaper.
The data including the actual times, positions, and utterance
related to nursing cares are collected by a sensor network with aset of voice records and passing sensors. Table IV shows anexample of the data from the sensor network. In this figure,"Elapsed Time" is the actual time recording by the passing sensors
generated by their system clock; "Time" is the time of current
utterance in all recording utterance, according to which we
synchronizes the place and utterance; "Place" is current location ofa nurse; and "Utterance" is the dialogues of the nurse related tonursing cares, respectively. According to the relation of theutterance with the job category, each nursing care is classified as aseries of job categories (which is directly related to the nursing
activities assigned in the worksheets) by several experienced
nurses according to the dialogue recorded. Table V shows anexample of classification of utterance into job categories. On thesebasis, we manually classified the nursing cares as a collection of
the nursing activities in worksheets and interruptions(unpredictable nursing activities occurring at unexpected times),
according to the information in the worksheets. Furthermore, weclassified each nursing activity as a collection of sub-tasks
including the preparation sub-tasks, execution sub-tasks, and theclean-up sub-tasks, with the changing of positions. Table VI
shows an example on the classification of nursing activities andsub-tasks. Therefore, the final data can solved as a nursing careschedule, which mainly including the information of nursing
activities, nursing sub-tasks, and their start time & end time.
In general, nursing is more complicated in the break-after partafter a rest time due to some reasons like transferring of nursing
to/from other parts such as the addition/decrease of the nurses, andadmission/discharge of patients. Therefore, it will make it difficult
to elucidate implicit nurses’ action rules to some extent. Moreover,nurses generally dispose the pre-assigned cares in the break-before
part and take rounds to collect patients' status for the handing overto the following attendants. By doing so, it tends to increase therates of idle time in the break-after part, in which nurses mainly
spend time on the handling of patients' records. Consequently, weonly considered the former part of day shift before the rest time toelucidate nurses' way in defining the processing orders of
pre-assigned nursing activities.
On the other hand, since the processing time of each sub-task
varies statistically, this study simply treats it as the average
processing time. Furthermore, to quantitatively analyze the actual
nursing cares, we consider the different slack time by setting the
preparation coefficient and execution coefficient with increment of
0.5 from 0 to 8 separately (i.e.,   [ 0 ,8 ] ,   [ 0 ,8 ] ) for eachdispatching rule in the scheduling process. Therefore, we modeled
the implicit nursing action rules as 1734 different candidate
dispatching rules (6 single dispatching rules × 17 test values for
preparation coefficient × 17 test values for execution coefficient).
4.2.2 Results and Discussions
By employing various dispatching-rule based methods, we canobtain different nursing care schedules for an actual observedschedule. Evaluating the similarity on the execution time between
the planned nursing schedules and the actual observed ones, we
can find out the most similar rules to elucidate the implicit nursing
scheduling algorithms, and furthermore, to discuss the nursing
staffing levels in a quantitative way.
Figure 9 shows the result about the comparison of the 6described kinds of single dispatching rules on their maximal
similarities to implicit nursing scheduling algorithm with theresults on standard deviations. Here, the maximal similarities are
selected from the 1734 average similarities, each of which is
obtained by taking an average of the similarities obtained whenmatching the above 9 observed nursing cares according to the rulewith the same function, i.e., the same preparation coefficient α andexecution coefficient β. The horizontal axis shows the dispatching

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Fig.9 Similarity in time (*: p<0.05)(Note: SD is standard deviation, and p is significant level.)
Table VII Preparation and Execution Coefficient with
Maximal Similarities in Each Rule
Dispatching
rule

Preparation
coefficient α
Ecutioncoefficient β

FCFS

EDD

MPT

extended
MPT

SLACK

extended
SLACK

4.5

3.0

3.5

0.5

5.5

0.0

-

-

0.0

0.0

0.5

0.0

Fig.10 Discussion on staffing levels (p<0.05)(Note: p is significant level.)point of preparation tasks usually leads to the variation in theprocessing orders. In this respect, the value of the preparation
coefficient has more impact on implicit scheduling algorithms.
In hospitals, it is general to describe the nursing staffing levelsof nurses using work tenures. Here, to quantitatively evaluate thestaffing levels, we investigate the relation of the preparation
coefficients applied in EDD and the work tenures. Figure 10
shows the results on the relation of the above 6 nurses' work
tenures and their preparation coefficients in EDD. The figure also
includes the results of scatter plot with fit according to the linear
regression analysis on the relation of work tenure and preparation
coefficient.
From the above results, we can conclude that the preparation
coefficient has an inverse relation to the work tenure; that is, thepreparation coefficients considered during the provision of nursing
cares approximately decrease with the increase of the work
tenures of nurses. Consequently, we conclude that the expert
nurses start the handling of the nursing activities with less slack
times than the novices; that is, the nurse with a higher staffing
level generally considers less evaluated processing times for the
preparation tasks, which somewhat results in the strong possibilityof providing nursing cares as scheduled.
Based on the results in this figure, the correlation coefficient of
the work tenure with the preparation coefficient is -0.68, which issignificant by applying the significant level 5%. Since nursing is ahigh dynamic work with a lot of interruptions, especially for
novice nurses, we believe that novice nurses generally start tohandle the nursing activities in an earlier time. In actual, it
generally results in an increase of nursing activities fordetermining their processing orders. Therefore, it confuses novice
nurses with the performing of the accurate nursing activity forhigh-quality care provision, and thus it should be one issue on
impossibilities that novice nurses provide nursing cares asscheduled in worksheets.

rules, and the vertical axis represents the similarity in time (start
time & end time), respectively. Moreover, the figure includes theresults of t test on the comparison of average performances, which
is obtained by the statistic analysis tool of Excel 2007. In addition,
Table VII shows the values of preparation and execution
coefficients in each rules with the maximal similarities between
the planned nursing care schedules and the actual ones. They
represent the estimation of the processing times for preparation
tasks and execution tasks, respectively. Moreover, the value '-' in
the table represents the case for all test values, that is,   [ 0 ,8 ] .
As shown in Fig.9 and Table VII, EDD in (3.0, -), SLACK in(5.5, 0.5), and extended SLACK in (0.0, 0.0) obtain the mostsimilarities. Note that, α is the coefficient of processing time forthe preparation tasks, and β is the coefficient of processing time
for the execution tasks. Moreover, EDD has a significant
difference with FCFS, MPT, and extended MPT, SLACK has asignificant difference with FCFS, and extended SLACK has asignificant difference with FCFS and MPT by applying thesignificant level 5%. Here, considering the value of execution
coefficient β to be approximately 0, extended SLACK and SLACK
are of similar function during the scheduling process, that is, only
referring the processing time of preparation tasks and upper boundof expected execution time. Moreover, among the rule of EDD,SLACK, extended SLACK, EDD obtains the most similarities. In
this respect, we conclude that nurses, either experts or novices,might define the processing orders of nursing activities similar to
EDD, which means they refer the information of the evaluatedprocessing time of preparation tasks and upper bound of expected
execution times of the nursing activities in worksheets.
As mentioned in Section 2, the part directly related to patients(i.e., the execution tasks in the nursing activity) is desired to behandled within an expected time interval. Therefore, the value ofthe execution coefficient has less impact on implicit schedulingalgorithms of nurses. On the contrary, the variation of the start

5. Conclusion
In this paper, by implementing several candidate dispatchingrules on a set of nursing activities in the observed nursing cares,

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Fig.11 Comparison of an actual nursing care schedule with the planned one on their Gantt chart.

we proposed an effective method to elucidate the implicit nursing
scheduling algorithm of nurses, and discuss the difference ofstaffing levels between novices and experts on their ways tohandle the nursing activities. Our simulation results show that (1)nurses might handle the pre-assigned activities similar to EDD,
that is, they refer the evaluated processing time of preparation
tasks and their expected execution time; (2) there is an inverse
relation of work tenures with preparation coefficients , which isrecognized as one of the key points for expert nurses to provide
high-quality nursing cares in this paper. Consequently, we believethat considering adequate slack times for preparation tasks should
result in the provision of high-quality cares.
As a future work, we should do more experiments to certificate
our standpoint. Morover, based on the obtained results, to propose
and actualize an effective instruction system for high quality
nursing cares is practically more mandatory for current hospitals.

In this figure, the vertical axis represents the nursing activities,
and the horizontal axis represents the time axis from 7:40am to
1:00pm, respectively. Moreover, the red rectangles represents thenursing tasks in the observed nursing care, and the blue rectangles
shows the nursing tasks in the planned nursing care scheduleobtained by a candidate dispatching rule. The parameters and theresult is outlined as follows:
Setups of parameters:
Dispatching rule: EDD
Preparation coefficient: 0.5
Execution coefficient: Result:
Similarity in time: 93.48%
 Similarity
As shown in this figure, the blue rectangles cannot entirely
match the red rectangles. In this study, we just test the similarity ofthe single dispatching rule with the action rules of nurses.
Although the dispatching rule is described as the implementationof some human thoughts, the action rules of nurses are generally
more complex than the single dispatching rules described above.
However, we get about the 93% similar nursing care schedule withthe actual one in this case, and thus we know that 93% of theaction rule has the same function with EDD.

ACKNOWLEDGEMENT
This research was conducted in ATR Knowledge Science
Laboratories and supported by the Natural Institute of Information
and Communications Technology.

APPENDIX

 Unsimilarity
Moreover, as shown in the figure, we can find that the error on
the matching of the planned nursing care with the observed one ismainly resulted from the nursing activity of temperaturing andgauze change, as marked by the ellipse in red dot lines. As weknow, these activities are belonging to those that are modeled as

A. Similarity in Time: Representation on the Gantt chart
Figure 11 shows an example of the comparison an observed
nursing care schedule (red rectangles) handled by Ns.c with theplanned one (blue rectangles) based on EDD on their Gantt charts,
where the similarity in time is 93.4%.

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the nursing activity with the weak expected execution time
constraints, that is, the nursing activity that can be handled in the
break-before part of the assigned shift. As we know, EDD is a ruleto decide the processing orders of nursing activities according totheir upper bound of the expected execution time. Therefore, these
two nursing activities will be normally handled in the latter part
unless there exists the idle time in the former part. As a result,
there might be some other rules to define the processing orders ofthese activities. However, as interviewed nurses explained on thisphenomenon, it is not strange for these activities to be handled
before or after, that is, there are not any specific rule or policy todefine these activities and the definition of the processing ordersof them is random during their provision of nursing cares. In
addition, the performing of them before or after seldom impacts
on the quality of nursing cares on providing the nursing cares asscheduled in case that other nursing activities are handled asscheduled. As a result, in our own opinion, to improve the EDD tomatch the error parts mentioned above for higher similarities
becomes not so necessary.

(12)

(13)
(14)

(15)

(16)

(17)

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Biographies
Mingang CHENG
Mingang Cheng was born in China in 1979. Hereceived his B.S. degree in Optical & Electronic
Information Engineering College in 2002 fromthe University of Shanghai for Science andTechnology, M.E. and Ph.D degrees from theFaculty of Engineering in 2006 and 2009 from the
University of Tokyo. His research interests
include mobile robotics and scheduling.

Hiromi Itoh OZAKUHiromi itoh Ozaku is a senior researcher at
National
InstituteofInformation
andCommunications Technology (NICT). She
received Ph.D. degree from Graduate School ofInformation Science, Nara Institute of Science andTechnology in 2004. She is a member of theInformation Processing Society of Japan (IPS), theAssociation for Natural Language Processing(NLP), the Japanese Society for Artificial Intelligence (JSAI), and theInstitute of Electronics, Information and Communication Engineers(IEICE).
Noriaki KUWAHARA
Noriaki Kuwahara Joined Sumitomo ElectricIndustry, Ltd. in 1987, and Joined ATR
Communication System Labs in 1993. In 1997, hereceived Dr.Eng from the University of Tokyo.
From 2007, he became Associated Professor of
Graduate School of Science and Technology,
Kyoto Institute of Technology. He is a member of
Human Interface Society of Japan, Information Processing Society ofJapan, The Institute of Image Information and Television Engineers, andIEEE Computer Society.

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Kiyoshi KOGURE
Kiyoshi Kogure is a professor in the College ofEngineering at the Kanazawa Institute ofTechnology. He received his Ph.D. in engineeringfrom Keio University. He is a member of theInstitute of Electronics, Information andCommunication Engineers, the Acoustical Societyof Japan, the Information Processing Society ofJapan, the Japanese Cognitive Science Society, theJapanese Society for Artificial Intelligence, and
the Association for Natural Language Processing.
Jun OTAJun Ota received B.E., M.E. and Ph.D degrees
from the Faculty of Engineering, the University ofTokyo in 1987, 1989 and 1994 respectively. From1989 to 1991, he joined Nippon Steel Cooperation.
In 1991, he was a Research Associate of the
University of Tokyo. In 1996, he became an
Associate Professor. In 2009, he became a
Professor at at Research into Artifacts, Center forEngineering (RACE), the University of Tokyo.
From 1996 to 1997, he was a visiting scholar at Stanford University. His
research interests are multiple mobile robot system and mobiligence,design for large-scale production/material handling systems, analysis on
human behavior.

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