Optimizing Hospital Room Layout to Reduce the Risk of Patient Falls

Sarvenaz Chaeibakhsh

, Roya Sabbagh Novin

, Tucker Hermans

, Andrew Merryweather

and Alan Kuntz

Department of Mechanical Engineering, University of Utah, UT, U.S.A.

School of Computing, University of Utah, UT, U.S.A.

Keywords:

Hospital Layout Planning, Fall Risk, Computerized Layout Planning, Simulated Annealing.

Abstract:

Despite years of research into patient falls in hospital rooms, falls and related injuries remain a serious concern

to patient safety. In this work, we formulate a gradient-free constrained optimization problem to generate and

reconﬁgure the hospital room interior layout to minimize the risk of falls. We deﬁne a cost function built on a

hospital room fall model that takes into account the supportive or hazardous effect of the patient’s surrounding

objects, as well as simulated patient trajectories inside the room. We deﬁne a constraint set that ensures the

functionality of the generated room layouts in addition to conforming to architectural guidelines. We solve

this problem efﬁciently using a variant of simulated annealing. We present results for two real-world hospital

room types and demonstrate a signiﬁcant improvement of 18% on average in patient fall risk when compared

with a traditional hospital room layout and 41% when compared with randomly generated layouts.

1 INTRODUCTION

Patient falls in healthcare settings have a severe im-

pact on patient outcomes, resulting in increased mor-

bidity, length of stay, and reduced quality of life. Fur-

ther, unnecessary falls incur signiﬁcant ﬁnancial costs

to both patients and the healthcare system. Every year

in the US 700,000 to 1,000,000 people fall in hos-

pitals (Hughes, 2008). Studies have shown that close

to one-third of these falls are preventable (Cameron

et al., 2012).

Substantial research studying hospital falls and re-

lated fall injuries has been done, yet the range of

preventive and protective interventions is still some-

what limited. Current preventive interventions mostly

include solutions to notify staff when the patient

egresses, such as bed alarms and video monitoring,

with the intention that the staff can intervene with

the patient prior to a fall occurring (Alert, 2015; Cal-

lis, 2016). Safety measures have also been studied

to reduce injury severity when a fall occurs, such as

hip protectors and compliant ﬂooring (Willgoss et al.,

2010). Yet fall rates continue to be unacceptably high

and are even increasing (Hsiao, 2016; Alert, 2015),

representing a serious threat to patient safety.

A variety of causes contribute to patient falls.

However, environmental hazards and accidents have

been identiﬁed as the most common causes of falls

(a) Traditional layout (b) Optimized layout

for traditional layout

(d) Risk of fall heatmap

for optimized layout

Figure 1: Traditional and optimized room layout evalua-

tion with respect to fall risk. Figures (a) and (b) show the

schematic of the rooms and ﬁgures (c) and (d) show the

corresponding heat map of the risk of fall as evaluated by

the fall risk model.

Chaeibakhsh, S., Novin, R., Hermans, T., Merryweather, A. and Kuntz, A.

Optimizing Hospital Room Layout to Reduce the Risk of Patient Falls.

DOI: 10.5220/0010226300360048

In Proceedings of the 10th International Conference on Operations Research and Enterprise Systems (ICORES 2021), pages 36-48

ISBN: 978-989-758-485-5

among the elderly (Commission et al., 2015). Re-

cently, a metric of patient fall risk during unassisted

ambulation in a hospital room was proposed that con-

siders the layout of the room (Novin et al., 2020). This

method estimates the fall risk of a room by consider-

ing room design factors including lighting, ﬂooring

type, door operation (swinging or sliding), and sup-

porting objects (e.g., furniture, grab bars, bed rails,

etc) in the room.

However, the relationship between the fall risk and

the room layout as deﬁned by the metric in (Novin

et al., 2020) is complex and non-intuitive, making

manually adjusting the layout to reduce the fall risk

infeasible.

In this work, we build upon this fall model and

employ gradient-free optimization to automatically

generate hospital room layouts that reduce the risk of

patient falls (see Fig. 1). Speciﬁcally, we adapt simu-

lated annealing to optimize features of multiple real-

world hospital rooms including the placement of ob-

jects such as the patient bed, sofa, patient chair, IV

pole, toilet and sink; the placement of lighting; and

the locations of the main door and bathroom door.

We employ real-world architectural design guide-

lines as constraints, such as speciﬁc minimum clear-

ance between sets of objects, which are representa-

tive of residential construction requirements to en-

sure room functionality (Ramsey, 2007; Neufert and

Neufert, 2012). Using these guidelines as constraints

enables the method to take steps toward designing

feasible rooms that reduce the risk of patient falls.

This paper represents the ﬁrst work that optimizes

hospital room layouts to reduce the risk of patient

falls.

2 RELATED WORK

With patient falls being a serious issue in health care

settings, many solutions have been proposed in the

literature to reduce falls and post-fall injuries(Callis,

2016; Clarke et al., 2012; Mayo et al., 1994). Our

method is conceptually similar to computerized lay-

out planning. The focus of our method is on lever-

aging optimization to reduce the risk of fall in hos-

pital rooms by changing the layout of the furniture

and medical devices to create safer surroundings and

pathways for the patient. In this section, we discuss

the history of patient falls and fall prevention meth-

ods and discuss existing applications of computerized

layout planning in general and in health care.

2.1 Hospital Fall Prevention Strategies

Despite extensive efforts to prevent patient falls, falls

in acute care hospital rooms remain a serious is-

sue(Hsiao, 2016). Around one-third of hospital falls

result in injuries to the patient and over 84% of ad-

verse incidents in hospitals that lead to co-morbidity

and mortality are associated with falls(Choi et al.,

2011; Aranda-Gallardo et al., 2013). Most previous

research on hospital falls has focused on the effect of

intrinsic factors including medications, and less atten-

tion has been paid to extrinsic factors relating to the

hospital room itself and the patient’s physical envi-

ronment (Callis, 2016). Different preventive strategies

such as patient education (Clarke et al., 2012), phys-

ical restraints, alarms (Mayo et al., 1994; Tideiksaar

et al., 1993) and ﬂooring (Donald et al., 2000) have

tried to address this serious issue. Still, hospital falls

continue to be the leading cause of injuries to the se-

nior population in health care facilities (Commission

et al., 2015).

The layout of furniture and medical equipment in

hospital rooms has been shown to have a signiﬁcant

impact on the safety of patients (Hignett and Ma-

sud, 2006). Studies such as (Commission et al., 2015)

and (Hignett and Masud, 2006) highlight the sig-

niﬁcance of patients’ physical surroundings in their

safety and suggest several environmental strategies,

such as ensuring adequate lighting and appropriate

ﬂooring types, to reduce the risk of fall. In this work,

we build on this concept; the physical layout includ-

ing furniture and equipment in a hospital room can be

optimized to improve patient safety and decrease the

risk of falls. We accomplish this using an optimization

method in a manner conceptually similar to comput-

erized layout planning.

2.2 Computerized Layout Planning

Computerized layout planning refers to leveraging

computers in allocating space while a set of criteria

and constraints are met and/or some objectives are

optimized. The demand for computerized layout plan-

ning has been growing since the 1960’s when the ﬁrst

ideas for rule-based computerized layout planning be-

gan to take shape (Liggett, 1985). Since then, much

work has been done on computerized layout plan-

ning, including a few commercialized products. Many

of the commercialized computerized layout planning

tools, such as Spacemaker (SpacemakerAI, 2016) and

Planner 5D (Planner5D, 2011), focus on automati-

cally planning the layout and space allocation for

the placement of buildings rather than interior lay-

out. These software packages use techniques in math-

Optimizing Hospital Room Layout to Reduce the Risk of Patient Falls

ematical modeling, artiﬁcial intelligence, and archi-

tectural urban development to assist architects in de-

signing multi-building residential sites and high level

planning. Some of these methods generate different

facility layouts based on predeﬁned rules (Araghi

and Stouffs, 2015) while others use machine learning

methods to design general building layouts (Merrell

et al., 2011). However, so far the application of ma-

chine learning methods have been limited in efﬁcacy

for large scale or detailed problems (Wu et al., 2018;

Jamali et al., 2020).

Beyond space allocation and layout planning,

where the concern is about the physical arrangement

of objects and resources that consume space, comput-

erized layout planning has also been applied to object

placement in interior design. In (Merrell et al., 2011),

an interactive layout planner is proposed which takes

an initial furniture arrangement and constraints and

suggests new furniture conﬁgurations to the user. Gal

et al. use a rule-based method to develop a frame-

work to generate object layouts by solving a con-

straint satisfaction problem (Gal et al., 2014). With

advances in AI, virtual reality, and augmented real-

ity, AI-based interior design tools are emerging. The

IKEA PLACE platform, developed by IKEA, virtu-

ally places the company’s products in an area scanned

via a cellphone camera (IKEA, 2019). Leaperr AI

software (Leaperr, 2018) combines deep learning and

image processing to suggest a design for the interior

of a room based on a preference questionnaire ﬁlled

out by the user. Planner 5D is another AI-powered app

that turns 2D blueprints into 3D and helps users visu-

alize their desired furniture layout (Planner5D, 2011).

The established AI-powered methods in general are

designed to help a user design and visualize a space,

but generally do so without any knowledge of design

rules, layout constraints, or optimization techniques.

Hospital department layout planning is one of the

more focused research areas in computerized layout

planning for health care facilities (Zuo et al., 2019;

Rismanchian and Lee, 2017; Lin et al., 2015). In hos-

pital department layout planning the location of hos-

pital departments are rearranged to improve metrics

such as patient travel time and relocation cost (Jamali

et al., 2020). However, a method to inform the furni-

ture layout in health care facilities to improve patient

safety has yet to be studied.

In this paper, we address the placement of furni-

ture, lighting, and doorways inside a hospital room

to reduce patient falls. The concept of satisfying con-

straints and optimizing the placement of objects ex-

ists in other application domains. Next we discuss two

categories of existing methods that have been used to

accomplish similar tasks in these domains: construc-

tive (rule based) methods and iterative improvement

(optimization-based) methods.

2.2.1 Constructive/Rule based Methods

Constructive or rule-based methods build a

constraint-satisfying solution by placing objects

one-by-one in an iterative decision process. Each

object that is placed in the room has its own features

that should be compatible with the previously placed

items and the features of the speciﬁc environment,

described as constraints. For example, a bed and a

sofa cannot be stacked, but a ceiling light ﬁxture

can be located above a bed. Frequently, these re-

search questions are framed as constraint satisfaction

problems (Gh

edira, 2013), and employ backtracking

methods (Karumanchi, 2018) to solve problems with

many complex constraints.

In (Tutenel et al., 2009), the authors use a rule-

based method to automatically create scenes for sand-

box style video games. In (Merrell et al., 2011), an

interactive layout planner is proposed which takes

in an initial furniture arrangement and set of con-

straints, and suggests a new furniture conﬁguration to

the user. These proposed layouts are based on archi-

tectural guidelines to ensure functionality as well as

aesthetic appeal. In (Gal et al., 2014) Gal uses a rule-

based method to develop a framework to generate ob-

ject layouts by solving a constraint satisfaction prob-

lem in placing objects in augmented reality. However,

these constructive models generally only produce a

feasible solution that satisﬁes a set of constraints, but

do not consider producing an optimal solution under

some cost function. In this paper, we adapt the con-

cept of a constraint satisfaction problem to generate

constraint-satisfying, feasible hospital rooms during

our optimization process.

2.2.2 Iterative Improvement Methods

Iterative improvement, or optimization-based meth-

ods start with an initial solution and improve upon

it over multiple iterations. The initial solution is ei-

ther generated randomly or can be introduced to

the system by the user. There are many types of

iterative improvement optimization methods (Yang,

2014). Many iterative methods do not necessarily

need gradient/derivative information, enabling them

to solve a larger class of complex and discontinuous

problems for which such gradient information may

not be available. Some iterative methods are inspired

by natural processes, such as simulated annealing and

genetic algorithms, and attempt to balance exploring

unknown regions of a parameter space and exploiting

ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems

existing knowledge in ﬁnding near-optimal solutions

(Yang, 2014).

Simulated annealing is a canonical probabilistic it-

erative improvement method that was ﬁrst proposed

by Kirkpatrick, Gelett, and Vecchi in 1983 (Kirk-

patrick et al., 1983), further improved by

Cern

y in

1985 (

Cern

y, 1985), and has been the focus of much

study since (Bertsimas et al., 1993; Dowsland and

Thompson, 2012; Nikolaev and Jacobson, 2010). This

method, as indicated by the name, is conceptually

based on the natural process of solids cooling down.

When a solid cools, it reaches an equilibrium at each

temperature. Simulated annealing takes advantage of

this natural procedure to ﬁnd the global optimum

of a cost function that has many local optima, and

does not depend on the quality of the initial solu-

tion (Van Laarhoven and Aarts, 1987; Szu and Hart-

ley, 1987; Aarts and Korst, 1988; Romeijn and Smith,

1994). In this method, the algorithm generates can-

didate solutions that are nearby the current solution.

The method accepts the candidate solution if it is bet-

ter than the current solution. If the candidate solu-

tion is worse, however, the algorithm may still accept

the candidate solution with some probability. This en-

ables the algorithm to explore sub-optimal regions of

the parameter space, helping the algorithm to escape

local optimums (Romeijn and Smith, 1994). This pro-

cess is repeated while time allows or until conver-

gence, producing near-optimal solutions (Aarts and

Korst, 1988; Romeijn and Smith, 1994).

Simulated annealing has been used for a vari-

ety of different layout planning problems (Seraﬁni,

1994; McKendall Jr et al., 2006; S¸ahin, 2011; Aho-

nen et al., 2014; Palubeckis, 2015). In 2001, Bayka-

soglu et al. (Baykaso

glu and Gindy, 2001) demon-

strated the applicability of simulated annealing in dy-

namic manufacturing facility layout planning. The al-

gorithm was further developed and used in more com-

plex static and dynamic layout planning problems

with multiple objective functions such as corridor al-

location(Ahonen et al., 2014), arranging manufactur-

ing facilities(McKendall Jr et al., 2006), and single-

row equidistant facility layout problems (Palubeckis,

2015).

Despite much research in automatic industrial and

commercial layout planning, optimizing the layout

of the interior of hospital rooms considering patient

safety has not yet been studied and is the subject of

this work.

3 METHOD

Our method optimizes the interior layout of a hospital

room to create a safer environment for the patient with

respect to risk of fall. To do so, we deﬁne a cost func-

tion built around the fall risk assessment model devel-

oped in (Novin et al., 2020). We minimize this cost

function using simulated annealing and leverage real-

world architectural design guidelines (Ramsey, 2007;

Neufert and Neufert, 2012) as constraints to ensure

room functionality.

3.1 Hospital Room Layout

A typical single-bed hospital room consists of two

sub-rooms, a main room, where the patient, visitor

and clinical zones are located, and a bathroom where

the toilet, shower and sink are located. The geometry

of the room boundaries are determined via architec-

tural considerations and are inputs to our method (See

Fig. 1 for the room geometry used in this paper).

For each of these sub-rooms, speciﬁc furniture

items must be placed, light sources included to il-

luminate the room, and doorways must connect the

bathroom to the main room and the main room to the

hallways. In this work, we optimize the placement of

the furniture, light sources, and doorways to lower the

risk of patient fall.

Borrowing notation from the constraint satisfac-

tion problem literature, we formalize the input to our

method as three sets: X = {x

,...,x

}, a set of

n variable objects (e.g., furniture, lights sources, and

doors) for the room; D = {D

,...,D

}, a set of

domains that are deﬁned for each variable in X ; and

C , a set of constraints deﬁned over the variables in

X , where each constraint may relate any subset of the

variables.

For each object x

in X , we parameterize its place-

ment in the hospital room as the conﬁguration vector

∈ D

. We then parameterize the layout of the entire

hospital room as the vector 



 = [d

,...,d

]

, the

concatenation of the conﬁguration vectors for each of

the objects in X .

At a high level, the goal of the method is to deter-

mine a speciﬁc layout 



 of the hospital room that re-

spects each constraint in C , while minimizing a func-

tion that relates 



 to the risk of patient falls.

3.2 Quantifying Fall Risk

To evaluate a speciﬁc room layout we build on the

fall risk assessment model proposed in (Novin et al.,

2020) in which the overall fall risk distribution of a

room is calculated as a function of a set of factors

Optimizing Hospital Room Layout to Reduce the Risk of Patient Falls

extrinsic to the patient taken from previous studies of

hospital fall risk. This fall risk model considers both

static and dynamic factors affected by the room con-

ﬁguration and provides two levels of fall risk eval-

uation: (1) A room baseline evaluation that is calcu-

lated solely from the static factors of: ﬂoor type, light-

ing condition, door operation, and the supporting or

hazardous effect of the surrounding objects (e.g. grab

bars, chair, medical stands, sofa, sink, toilet, and bed)

resulting in a risk distribution over the entire room;

and (2) Motion-based evaluation that considers pa-

tient ambulation deﬁned by dynamic gait properties

such as the turning angle and the type of activity such

as sit-to-stand, walk, turn, and stand-to-sit.

The input to this risk model includes details about

the room such as ﬂoor surface type as well as the room

layout deﬁning the lighting, locations and conﬁgura-

tions of all objects, and door placements. The output

is a risk distribution deﬁned as a value for each el-

ement of a grid map discretizing the hospital room,

r(



).

In the baseline layer of the model, each grid has a

base value of 1. Then, the value is modiﬁed based on

the distance to the closest supporting object as well

as lighting, ﬂooring, and door operation factors. For

the motion-based evaluation, the model uses a set of

pre-deﬁned scenarios such as the patient’s transitions

from bed to toilet and then predicts sample trajecto-

ries between objects for each scenario. Each grid cell

through which the simulated trajectory passes is inﬂu-

enced by the speciﬁc simulated activity, such as sit-to-

stand, and dynamic factors such as angular velocity

and turning angle.

As multiple trajectories are possible between two

target objects, the model generates and evaluates a

distribution of simulated patient trajectories. The dis-

tribution of the fall risk for the entire room is obtained

by combining the baseline and motion-based evalua-

tion risk proﬁles. To do so, the average of the baseline

fall risk factors and the fall risk of the points of the

trajectories/activities laying on each grid cell is calcu-

lated. The ﬁnal output is a risk value for each grid cell.

This can be visualized as a heat map over the hospital

room layout showing the distribution of fall risk val-

ues (e.g., see Fig. 1). These values correspond to the

percentage of increase or decrease in the risk of fall

for each grid cell. Values greater than 1.0 (red cells)

mean that there is high fall risk, and values less than

1.0 (blue cells) show that the fall risk is decreased.

See (Novin et al., 2020) for more details on the spe-

ciﬁc framework and contributing factors.

In our work we optimize a cost function designed

for this set of fall risk values that weighs different as-

pects of the distribution, as there are multiple poten-

Figure 2: Cost function parameters of the fall risk distribu-

tion, showing the median, maximum, and the area under the

high-risk tail. Parameter α is the cut-off value for the area

under the curve and the red region shows the area consid-

ered by the cost function.

tial aspects of the distribution that are relevant. For

example, if we deﬁne the cost function as the maxi-

mum fall risk in the room, the optimizer may focus

on reducing the risk of fall of the single worst grid

cell while the fall risk of the rest of the room re-

mains unacceptably high. On the other hand, if we

deﬁne the fall risk as the mean or median fall risk

over all the grid cells of the room, the algorithm may

reduce the mean or median while a few grid cell val-

ues may remain extremely high. Further, it may be the

case that the width of the high-risk tail of the distri-

bution is an important factor in assessing the overall

risk of a room, as it represents a set of high-risk ar-

eas. Each of these considerations relates the fall risk

distribution to a different objective. Thus, we deﬁne

a weighted combination of the median and the maxi-

mum of the fall risk distribution, as well as a metric of

the area under the high-risk tail of the distribution as

an aggregate representation of fall risk. The speciﬁc

weighting of these considerations can then be set by

the user based on their speciﬁc, clinically-motivated

preferences. In this work we treat this weighting as

input to our method.

Speciﬁcally, we deﬁne the cost function f (



) as:

f (



) =ω

median(r(



)) +ω

max(r(



))

+ ω



α − mean(r(



))

std(r(



))



(1)

where α is a user speciﬁed cut-off parameter that de-

termines where in the distribution to begin consider-

ing the area under the tail, as seen in Fig. 2. The third

term in Eq. 1 represents the aggregation of the grid

cells with risk values higher than α. The concept of

considering the area under the curve tail is a familiar

ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems

concept in ﬁnance risk management and is known as

the conditional value-at-risk (Rockafellar and Urya-

sev, 2002). Our ﬁnal cost function is then a function

of the median, mean, standard deviation, and maxi-

mum value of the fall risk distribution. Due to the dis-

cretization of the room and the random simulation of

patient movement in r(



), along with other factors,

f (



) is both highly non-linear and not differentiable.

This motivates our use of a gradient-free optimization

method when optimizing f (



).

3.3 Optimizing the Layout

In this work we leverage simulated annealing for op-

timizing f (



) as it is a well known stochastic iterative

optimization method for gradient and derivative free

cost functions such as f (



). At each iteration, a lay-

out nearby the current layout is generated at random

and its cost is evaluated. If it is an improvement over

the current layout it is accepted and becomes the cur-

rent layout for the next iteration. If it is worse, it may

still be accepted based on the Metropolis Probabil-

ity (Aarts and Korst, 1988; Van Laarhoven and Aarts,

1987; Metropolis et al., 1953):

Metropolis

= exp(

−∆c

κT

) (2)

where κ is the Boltzman constant and T is a “temper-

ature” value which decays over time according to a

cooling schedule and c stands for the cost value asso-

ciated with the layouts.

The temperature scheduling function we use in

our method is widely used and was ﬁrst introduced by

Kirkpatrick et al. in 1983 (Kirkpatrick et al., 1983),

= kT

i−1

(3)

where T

is the temperature at cycle i and is based

upon the previous cycle’s temperature, T

i−1

, and k is

a constant factor (0 < k < 1) controlling the rate of

temperature decay (Faber et al., 2005).

The algorithm, detailed in Alg. 1, begins with

an initial layout. It then improves upon this layout

for a set number of cycles, where the temperature

is decreased according to Eq. 3 between each cycle.

Within each cycle, the algorithm generates candidate

layouts, 



during a number of trials. In each trial,

the algorithm checks if the new candidate layout’s

cost value, c

is lower than the previously accepted

layout’s cost c

current

. If so, the system accepts the can-

didate layout for the next trial. However, if the cost

value of the candidate layout is higher than the pre-

viously accepted solution, the algorithm may still ac-

cept it depending on the acceptance probability de-

ﬁned by Eq. 2, enabling the algorithm to avoid local

minima.

Algorithm 1: Simulated Annealing for Hospital Room Op-

timization.

1: Initialization:

2: T

← initial temperature

3: k ← temperature decreasing factor

4: κ ← Boltzman constant

5: σ

← vector of standard deviations

6: numCycle ← number of cycles

7: numTrial ← number of trials per cycle

8: 



← initial room layout

9: 



current

← 



 the current layout

10: 



best

← 



 the best layout found

11: c

current

← f (



)  cost of current layout

12: c

best

← f (



)  cost of best layout found

13: for i = 1 to numCycle do

14: T

= kT

i−1

15: for j = 1 to numTrial do

16: 



← NearbyFeasLayout(



current

,σ

)

17: c

← f (



)

18: P = exp(

−c

current

κT

)

19: r ← generate a random number in (0, 1)

20: if c

< c

current

or r < P then

21: 



current

← 



22: c

current

← c

23: if c

current

< c

best

then

24: 



best

← 



current

25: c

best

← c

current

26: end if

27: end if

28: end for

29: end for

30: return 



best

As the algorithm progresses this acceptance prob-

ability decreases.

In this way, the method generates better and better

layouts over time, iteratively improving the layouts

with respect to our cost function, returning the best

layout found at the conclusion of the method’s execu-

tion.

3.4 Generating Feasible Layouts

When generating both a random initial feasible room

layout (Alg. 1 line 8) and nearby feasible layouts

(Alg. 1 line 16, NearbyFeasLayout) during the ex-

ecution of the optimization, it is important that the

layouts are feasible, i.e., satisfy all of the constraints

in the constraint set C . In both cases, we employ a

random sampling with backtracking approach. Dur-

ing the generation of the initial room layout we sam-

ple uniformly at random from each variable’s domain.

When generating nearby layouts to an existing layout,

Optimizing Hospital Room Layout to Reduce the Risk of Patient Falls

we sample each variable’s conﬁguration from a nor-

mal distribution centered around the existing layout’s

conﬁguration and with standard deviation deﬁned for

each variable (σ

in Alg. 1). To ensure the constraints

are satisﬁed during this process we leverage a back-

tracking search method (Karumanchi, 2018). Back-

tracking chooses values for one variable at a time,

checking for constraint satisfaction as variables are

assigned. The method re-samples when a variable as-

signment violates constraints, and backtracks to re-

assign previous variables when a variable has no le-

gal values left to assign, or when a maximum num-

ber of iterations are reached or a maximum time has

elapsed while attempting to assign that variable. In

this way, backtracking recursively returns to previ-

ously assigned values, changing their assignments to

satisfy the constraints.

Figure 3 shows an example of backtracking dur-

ing the placement of an object in the hospital room.

In Fig. 3a, the algorithm attempts to place one of the

objects that is required to be in the bathroom, but be-

cause of the placement of the previous objects, it was

not able to do so. The method backtracks and con-

siders other placements for previously placed objects

(Fig 3b). Finally, it successfully places the objects

in the room while satisfying the constraints (Fig 3c).

Figure 4 depicts the overall ﬂow of the backtracking

algorithm.

The constraints in C ensure that the hospital room

layouts generated by our method maintain functional-

ity based on architectural regulation. The constraints

depend on the objects to be placed within the room

and can be deﬁned over a single object, such as re-

quiring certain types of furniture to be adjacent to a

wall and requiring a light to be placed in the bound-

aries of the room, or multiple objects such as ensuring

that there exists a minimum clearance on both sides

of a bed. Our method takes the constraint set as an

input and makes no assumptions about the properties

of the constraint functions, such as differentiability,

other than to require that the constraint functions re-

turn a boolean value indicating whether a speciﬁc lay-

out violates or satisﬁes the constraints. The speciﬁc

constraints we use in our experiments are described

in Sec. 4.

4 IMPLEMENTATION AND

EXPERIMENTAL RESULTS

To assess the performance of the proposed model, we

optimize the interior conﬁguration of two common ty-

pologies of hospital rooms: inboard rooms and out-

board rooms. In the inboard architecture, the bath-

(a) Unsuccessful object placement

(b) Multiple object placement trials

Figure 3: Object placement procedure. (a) Previously

placed objects prevent feasible placement of a subsequent

object. (b) Backtracking changes the placement of previ-

ously placed objects. (c) All objects are placed in a way that

satisﬁes the constraints.

ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems

Figure 4: A ﬂowchart of the backtracking method.

Figure 5: Schematic of the hospital room. Blue lines are

permissible hallway door placements for outboard rooms

and red lines show the permissible hallway door placement

walls for inboard rooms.

room is located near the entry of the room and next

to hallways. In the outboard room, the bathroom is

placed along the exterior wall of the room (see Fig. 5).

In this paper, we demonstrate the efﬁcacy of our op-

timization method on a representative sample room

from each of these room types using dimensions and

shapes used in real hospitals.

4.1 Implementation Details

For both the inboard and outboard room experiments

we deﬁne X to include: furniture consisting of a sofa,

the patient bed, a patient chair, a visitor chair, a mo-

bile medical stand, a toilet, and a sink; a ceiling light

for both the main room and the bathroom; and a door

connecting the bathroom to the main room and the

main room to the hallway (see Fig. 5).

We make a distinction between the furniture ob-

jects that are required to be placed against the wall

for functionality (the patient bed, sofa, sink, and toi-

let) and the furniture objects that are allowed to be

placed freely throughout the inside of the room (the

patient chair, visitor chair, and mobile medical stand).

Each of the furniture objects that can be placed freely

inside the room have domains that include two po-

sition values, representing the x and y location, and

an orientation value, i.e., R

× (S)

. The lights have

domains that include the position values but not ori-

entation, R

. For both the furniture objects required to

be placed against the wall and the doors we implicitly

represent this using a domain deﬁned by a single real

value associated with the object’s location along a pa-

rameterized representation of the walls unwrapped as

a line (See Fig. 6 for an example).

We deﬁne our constraints based on architec-

tural guidelines(Ramsey, 2007; Neufert and Neufert,

2012). We require certain objects to be placed in spe-

ciﬁc sub-rooms as well as clearance values around

certain types of objects. These are detailed in Table 1.

The clearance value constraints are designed to

ensure functional use by an average size adult, how-

ever we recognize that additional considerations such

as those deﬁned by the American’s with Disabilities

Act (ADA) may have different requirements. Further,

we require a feasible layout to have one light in the

bathroom area and one light in the main room. We re-

quire the bathroom door to connect the bathroom and

main room and the main door to connect the main

room and the hallway. We also require that no ob-

jects’ geometries overlap in the x, y plane, with the

exception of the lights which are placed on the ceiling

and as such do not collide with objects placed on the

ﬂoor. Moreover, the algorithm places each object in

the correct sub-room (see Table 1). For example, the

bed must be placed in the main room. For objects that

can be positioned in either room, such as the cabinets

or sink, the user speciﬁes in which room the object

should be placed.

The difference between the outboard and inboard

room typology manifests in the constraint associated

with the door connecting the patient living area to the

hallway. In an inboard room, this door must be placed

on one of the two walls shared by the bathroom, and

in an outboard room it must be placed on one of the

two walls not shared by the bathroom (see Fig. 5).

The trajectories that we use when calculating the

fall risk (see Sec. 3.2) are: ambulation from the bed to

the patient chair, from the bed to the toilet, and from

the bed to the main door. We set the parameters in

Eq. 1 with α chosen to be 95% of the max(r(



)) value

and ω

= ω

= 0.33.

The initial temperature value in our simulated an-

nealing is chosen to be 10, k is set to 0.8, κ is set

to 1, numCycles is set to 25, and numTrials is set to

30 based on a heuristic analysis of our cycles’ accep-

Optimizing Hospital Room Layout to Reduce the Risk of Patient Falls

Figure 6: Sampling a point on the walls of the room for objects that are constrained to be against the walls. We unwrap the

walls of the room into a single line, sample a point on the line and then ﬁnd the coordinates of the sampled point in the original

space with the walls in their original 2D geometry.

Table 1: Clearance constraints for objects placed in the rooms along with the rooms the object belongs to.

Object Bed Sofa & Chairs Toilet Sink

Clearance constraint 0.4m, both sides 0.35m, front 0.4m, front 0.35m, front

Sub-room constraint Main room Main room Bathroom Bathroom

Table 2: Values of σ

. Parameters σ

and σ

are the position of the object inside the room. σ

theta

stands for the orientation

values. Parameter σ

shows the standard deviation value for the objects that are attached to a wall.

Objects Main room Bathroom

Furniture (generic) 1m 1m 30

◦

- 0.5m 0.5m 30

◦

Furniture (against wall) - - - 5m - - - 1m

Lights 1m 1m - - 1m 1m - -

Doors - - - 4m - - - 2m

tance rates (as in (Szu and Hartley, 1987) and (Duque-

Ant

on, 1997)). The values in σ

depends on the spe-

ciﬁc object and their corresponding sub-room. Table 2

shows the set values for σ

. During initial and near-by

room generation, our timeout to initiate backtracking

is set at 5 seconds.

For both the inboard and outboard room typolo-

gies we use the room geometry shown in Figs 1, 9,

and 10.

5 RESULTS AND DISCUSSION

We studied the performance of our optimization al-

gorithm in reducing the risk of fall in two room ty-

pologies. We perform ten optimization runs for each

room typology. The average time required for each

optimization run was (2.4359 ± 0.8453) × 10

sec-

onds (≈ 7 hours). In Fig. 7 we plot the cost value

of the layout being considered at each iteration (each

trial of each cycle), i.e., c

current

, averaged over the ten

runs. As can be seen, the simulated annealing algo-

rithm rapidly explores the parameter space early in

the runs, escaping many local minima, however as the

run progresses the algorithm settles upon low cost lay-

outs.

In Fig. 8 we plot the cost value of the best lay-

out found up until that iteration in the optimization,

i.e., c

best

, averaged over the ten runs. The average

Figure 7: The cost value for the layout during the optimiza-

tion iterations for the inboard room type (blue) and the out-

board room type (red). The shaded regions show the corre-

sponding standard deviation of each cost value.

starting cost value for the randomly initialized in-

board rooms and outboard rooms were 5.04±0.4 and

4.67±0.65, respectively. After optimization, the low-

est cost value for the generated rooms for the inboard

type was 3.42 ± 0.08 and 3.36±0.07 for the outboard

type. This represents a reduction of 40% for the in-

board room and 42% for the outboard room. We also

evaluated the risk-of-fall-based cost value of a tradi-

tional hospital room layout, as depicted in Fig. 1a.

The cost value of the traditional layout was found

to be 4.1 ± 0.27. Compared with the traditional lay-

ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems

Figure 8: The cost value for the best layout found up to a

given iteration under our method for the inboard room type

(blue) and the outboard room type (red). We also plot the

value associated with the traditional layout for reference.

The shaded regions represent the corresponding standard

deviation.

out, our optimized layouts achieve a cost reduction of

18.05%. To evaluate the statistical difference between

the traditional room cost value, and the starting cost

values and the ﬁnal cost values for the generated room

typologies, we applied the two sample Kolmogorov-

Smirnov test (K-S test), a statistical test designed to

determine if two continuous or discrete distributions

are signiﬁcantly different (Chakravarti et al., 1967).

We examined the similarity between the distributions

in ﬁve cases: 1) inboard: the cost values of the ini-

tial randomized layouts vs the cost values of the ﬁnal

layouts, 2) outboard: cost values of the initial random-

ized layouts vs cost values of the ﬁnal layouts, 3) the

ﬁnal cost values of the optimized inboard rooms vs

the ﬁnal cost values of the optimized outboard rooms,

4) the ﬁnal cost values of the optimized inboard rooms

vs the cost values of the traditional room, and 5) the ﬁ-

nal cost values of the optimized outboard rooms vs the

cost values of the traditional room. In all ﬁve cases,

the null hypothesis was rejected at the 5% signiﬁ-

cance level. For the initial vs ﬁnal cost values for both

the inboard and outboard rooms, and the comparison

between the optimized inboard and outboard rooms

with the traditional room, the order of the asymptotic

p-value was 10

−5

with K-S score of 1. In rejecting

the null hypothesis for inboard vs outboard ﬁnal cost

values, the p−value was computed as 0.0310 with a

K-S score of 0.6, which indicates more similarity than

between the initial and ﬁnal layouts, but still signiﬁ-

cantly different. In Figs. 9 and 10, we show repre-

sentative inboard and outboard room layouts, both be-

fore and after optimization, as well as their associated

fall risk score heatmaps. In Fig. 1 we show the same

for the traditional layout. One potentially interesting

(a) Initial room layout (b) Final room layout

Figure 9: Outboard room layout evaluation and optimiza-

tion with respect to fall risk. (a) and (b) show schematics

of the outboard rooms generated by the algorithm. (a) is an

instance of the initial room layout and (b) shows the op-

timized room layout for one of the runs. (c) and (d) show

the corresponding heat map of the risk of fall as evaluated

by the fall risk model. Higher values on the color-bars of

ﬁgures (c) and (d) indicate higher risk of falls.

trend is the lower cost values found when optimiz-

ing the outboard rooms compared with the inboard

rooms. Looking at Fig. 5, placing the hallway door

on one of the further walls to the bathroom will place

the door in between the bed and the bathroom. This

results in trajectories with fewer sharp turns, which

decreases the risk of falls as deﬁned in the fall risk

model. This may also result from outboard walls be-

ing longer than the inboard walls for our room ge-

ometry, and hence, the algorithm has more options of

sampling points for door placement and potentially

more conﬁguration options.

6 CONCLUSION AND FUTURE

WORK

In this work, we presented a method that built upon

a patient fall-risk model and presented a gradient-free

optimization method, based on simulated annealing,

to reduce the risk of patient falls in hospital rooms

by optimizing the conﬁgurations of objects inside the

room. We evaluated our method on two room ty-

Optimizing Hospital Room Layout to Reduce the Risk of Patient Falls

(a) Initial room layout

(b) Final room layout

(d) Final risk heatmap

Figure 10: Inboard room layout evaluation and optimization

with respect to fall risk. (a) and (b) show schematics of the

inboard rooms generated by the algorithm. (a) is an instance

of the initial room layout and (b) shows the optimized room

layout for one of the runs. (c) and (d) show the correspond-

ing heat map of the risk of fall as evaluated by the fall risk

model. Higher values on the color-bars of ﬁgures (c) and (d)

indicate higher risk of falls.

pologies, inboard and outboard, with common hospi-

tal room objects utilized in both. The algorithm opti-

mized the layout of the rooms with respect to a cost

function that was deﬁned based on the distribution of

the patient fall risk in the rooms, which considered

both static factors associated with the object place-

ments in the room as well as the kinematics and dy-

namics of simulated patient trajectories.

Our method leverages constraints based on object

functionality and architectural guidelines used for fa-

cility layout planning. We demonstrated results, aver-

aging ten runs for each room type, showing signiﬁcant

improvement with respect to our patient fall-risk cost

metric compared to both random initial room layouts

and traditional hospital room layouts.

We chose simulated annealing as a canonical opti-

mization option for complex gradient-free problems

such as ours and intend the results to demonstrate

the feasibility of utilizing optimization in the problem

domain. However we recognize that many other op-

timization methods may be applicable and intend to

investigate the use of other methods such as genetic

algorithms, particle swarms, gray wolf optimizer, etc,

in the future. Further, we intend to investigate the use

of other metrics deﬁned over the fall-risk distribution

beyond the weighted metric presented in this work.

We will incorporate expert feedback from hospital de-

signers, architects, and healthcare providers into the

optimization loop. This feedback will be used to en-

hance the fall risk model and optimization method to

improve our result and achieve a functional, safe room

layout.

We will also conduct human subject studies to

evaluate the result of optimized room layouts in re-

ducing the risk of patient falls in a simulated hospi-

tal room. While our method and the fall-risk model it

builds upon are speciﬁc to hospital room layouts, our

method may have applications in reducing falls in at-

risk populations outside of healthcare settings as well.

These other environments include assisted living, and

long-term care facilities, and homes of individuals at

high risk of falls.

We believe that this work takes signiﬁcant steps

toward demonstrating the feasibility of optimizing the

layout of hospital rooms in order to reduce the risk of

patient falls and improve patient outcomes.

ACKNOWLEDGMENT

This project was supported by grant number

R18HS025606 from the Agency for Healthcare Re-

search and Quality (AHRQ). The content is solely the

responsibility of the authors and does not necessarily

represent the ofﬁcial views of the Agency for Health-

care Research and Quality.

REFERENCES

Aarts, E. and Korst, J. (1988). Simulated annealing and

boltzmann machines.

Ahonen, H., de Alvarenga, A. G., and Amaral, A. R. (2014).

Simulated annealing and tabu search approaches for

the corridor allocation problem. European Journal of

Operational Research, 232(1):221–233.

Alert, S. E. (2015). Preventing falls and fall-related injuries

in health care facilities. The Joint Commission, 55:1–

Araghi, S. K. and Stouffs, R. (2015). Exploring cellular au-

tomata for high density residential building form gen-

eration. Automation in Construction, 49:152–162.

Aranda-Gallardo, M., Morales Asencio, J. M., Canca-

Sanchez, J. C., Mora-Banderas, A. M., Moya-Suarez,

A. B., and for preventing falls in Hospital Costa del

Sol, G. (2013). Instruments for assessing the risk of

falls in acute hospitalized patients: a systematic review

protocol. Journal of Advanced Nursing, 69(1):185–

193.

ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems

Baykaso

glu, A. and Gindy, N. N. (2001). A simulated an-

nealing algorithm for dynamic layout problem. Com-

puters & Operations Research, 28(14):1403–1426.

Bertsimas, D., Tsitsiklis, J., et al. (1993). Simulated anneal-

ing. Statistical science, 8(1):10–15.

Callis, N. (2016). Falls prevention: Identiﬁcation of predic-

tive fall risk factors. Applied nursing research, 29:53–

58.

Cameron, I. D., Gillespie, L. D., Robertson, M. C., Mur-

ray, G. R., Hill, K. D., Cumming, R. G., and Kerse, N.

(2012). Interventions for preventing falls in older peo-

ple in care facilities and hospitals. Cochrane database

of systematic reviews, (12).

Cern

y, V. (1985). Thermodynamical approach to the trav-

eling salesman problem: An efﬁcient simulation algo-

rithm. Journal of optimization theory and applica-

tions, 45(1):41–51.

Chakravarti, I. M., Laha, R. G., and Roy, J. (1967). Hand-

book of methods of applied statistics, volume 2. Wiley.

Choi, Y.-S., Lawler, E., Boenecke, C. A., Ponatoski, E. R.,

and Zimring, C. M. (2011). Developing a multi-

systemic fall prevention model, incorporating the

physical environment, the care process and technol-

ogy: a systematic review. Journal of advanced nurs-

ing, 67(12):2501–2524.

Clarke, H. D., Timm, V. L., Goldberg, B. R., and Hattrup,

S. J. (2012). Preoperative patient education reduces

in-hospital falls after total knee arthroplasty. Clinical

Orthopaedics and Related Research®, 470(1):244–

249.

Commission, J. et al. (2015). Preventing falls and fall-

related injuries in health care facilities. Sentinel Event

Alert, (55):1.

Donald, I., Pitt, K., Armstrong, E., and Shuttleworth, H.

(2000). Preventing falls on an elderly care rehabili-

tation ward. Clinical rehabilitation, 14(2):178–185.

Dowsland, K. A. and Thompson, J. (2012). Simulated

annealing. Handbook of natural computing, pages

1623–1655.

Duque-Ant

on, M. (1997). Constructing efﬁcient simulated

annealing algorithms. Discrete Applied Mathematics,

77(2):139–159.

Faber, R., Jockenh

ovel, T., and Tsatsaronis, G. (2005). Dy-

namic optimization with simulated annealing. Com-

puters & chemical engineering, 29(2):273–290.

Gal, R., Shapira, L., Ofek, E., and Kohli, P. (2014). Flare:

Fast layout for augmented reality applications. In

2014 IEEE International Symposium on Mixed and

Augmented Reality (ISMAR), pages 207–212. IEEE.

edira, K. (2013). Constraint satisfaction problems: csp

formalisms and techniques. John Wiley & Sons.

Hignett, S. and Masud, T. (2006). A review of environ-

mental hazards associated with in-patient falls. Er-

gonomics, 49(5-6):605–616.

Hsiao, H. (2016). Fall Prevention and Protection: Princi-

ples, Guidelines, and Practices. CRC Press.

Hughes, R. (2008). Patient safety and quality: An evidence-

based handbook for nurses, volume 3. Agency for

Healthcare Research and Quality Rockville, MD.

IKEA (2019). Ikea apps - ikea. https://www.ikea.com/

us/en/customer-service/mobile-apps/. (Accessed on

09/14/2020).

Jamali, N., Leung, R. K., and Verderber, S. (2020). A review

of computerized hospital layout modelling techniques

and their ethical implications. Frontiers of Architec-

tural Research.

Karumanchi, N. (2018). Algorithm Design Techniques: Re-

cursion, Backtracking, Greedy, Divide and Conquer,

and Dynamic Programming. CareerMonk Publica-

tions.

Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P. (1983).

Optimization by simulated annealing. Science,

220(4598):671–680.

Leaperr (2018). Autonomous ai interior design system.

https://www.builtworld.com/db/company/leaperrai.

(Accessed on 09/16/2020).

Liggett, R. S. (1985). Optimal spatial arrangement as a

quadratic assignment problem. In Design Optimiza-

tion, pages 1–40. Elsevier.

Lin, Q.-L., Liu, H.-C., Wang, D.-J., and Liu, L. (2015). In-

tegrating systematic layout planning with fuzzy con-

straint theory to design and optimize the facility lay-

out for operating theatre in hospitals. Journal of Intel-

ligent Manufacturing, 26(1):87–95.

Mayo, N. E., Gloutney, L., and Levy, A. R. (1994). A

randomized trial of identiﬁcation bracelets to pre-

vent falls among patients in a rehabilitation hospi-

tal. Archives of physical medicine and rehabilitation,

75(12):1302–1308.

McKendall Jr, A. R., Shang, J., and Kuppusamy, S. (2006).

Simulated annealing heuristics for the dynamic facil-

ity layout problem. Computers & operations research,

33(8):2431–2444.

Merrell, P., Schkufza, E., Li, Z., Agrawala, M., and Koltun,

V. (2011). Interactive furniture layout using interior

design guidelines. ACM transactions on graphics

(TOG), 30(4):1–10.

Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N.,

Teller, A. H., and Teller, E. (1953). Equation of state

calculations by fast computing machines. The journal

of chemical physics, 21(6):1087–1092.

Neufert, E. and Neufert, P. (2012). Architects’ data. John

Wiley & Sons.

Nikolaev, A. G. and Jacobson, S. H. (2010). Simulated an-

nealing. In Handbook of metaheuristics, pages 1–39.

Springer.

Novin, R. S., Taylor, E., Hermans, T., and Merryweather, A.

(2020). Development of a novel computational model

for evaluating fall risk in patient room design. HERD:

Health Environments Research & Design Journal.

Palubeckis, G. (2015). Fast simulated annealing for single-

row equidistant facility layout. Applied Mathematics

and Computation, 263:287–301.

Planner5D (2011). Free 3d home planner — design a house

online: Planner5d. https://planner5d.com/. (Accessed

on 09/14/2020).

Ramsey, C. G. (2007). Architectural graphic standards.

John Wiley & Sons.

Optimizing Hospital Room Layout to Reduce the Risk of Patient Falls

Rismanchian, F. and Lee, Y. H. (2017). Process mining–

based method of designing and optimizing the lay-

outs of emergency departments in hospitals. HERD:

Health Environments Research & Design Journal,

10(4):105–120.

Rockafellar, R. T. and Uryasev, S. (2002). Conditional

value-at-risk for general loss distributions. Journal of

banking & ﬁnance, 26(7):1443–1471.

Romeijn, H. E. and Smith, R. L. (1994). Simulated anneal-

ing for constrained global optimization. Journal of

Global Optimization, 5(2):101–126.

S¸ ahin, R. (2011). A simulated annealing algorithm for solv-

ing the bi-objective facility layout problem. Expert

Systems with Applications, 38(4):4460–4465.

Seraﬁni, P. (1994). Simulated annealing for multi objective

optimization problems. In Multiple criteria decision

making, pages 283–292. Springer.

SpacemakerAI (2016). Spacemaker: a cloud-based ai soft-

ware. https://www.spacemakerai.com/. (Accessed on

09/14/2020).

Szu, H. and Hartley, R. (1987). Fast simulated annealing.

Physics letters A, 122(3-4):157–162.

Tideiksaar, R., Feiner, C. F., and Maby, J. (1993). Falls pre-

vention: the efﬁcacy of a bed alarm system in an acute-

care setting. The Mount Sinai Journal of Medicine,

New York, 60(6):522–527.

Tutenel, T., Bidarra, R., Smelik, R. M., and De Kraker, K. J.

(2009). Rule-based layout solving and its application

to procedural interior generation. In CASA Workshop

on 3D Advanced Media In Gaming And Simulation.

Van Laarhoven, P. J. and Aarts, E. H. (1987). Simulated

annealing. In Simulated annealing: Theory and appli-

cations, pages 7–15. Springer.

Willgoss, T. G., Yohannes, A. M., and Mitchell, D. (2010).

Review of risk factors and preventative strategies for

fall-related injuries in people with intellectual disabil-

ities. Journal of clinical nursing, 19(15-16):2100–

2109.

Wu, W., Fan, L., Liu, L., and Wonka, P. (2018). Miqp-

based layout design for building interiors. In Com-

puter Graphics Forum, volume 37, pages 511–521.

Wiley Online Library.

Yang, X.-S. (2014). Nature-inspired optimization algo-

rithms. Elsevier.

Zuo, X., Li, B., Huang, X., Zhou, M., Cheng, C., Zhao, X.,

and Liu, Z. (2019). Optimizing hospital emergency

department layout via multiobjective tabu search.

IEEE Transactions on Automation Science and Engi-

neering, 16(3):1137–1147.

ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems