Optimization of Surgery Scheduling Problems Based on Prescriptive

Analytics

ao Lopes

1 a

, Gonc¸alo Vieira

1 b

, Rita Veloso

, Susana Ferreira

, Maria Salazar

and Manuel Filipe Santos

1 c

Department of Information Systems, University of Minho, Guimar

aes, Portugal

Centro Hospitalar Universit

ario de Santo Ant

onio (CHUdSA), Portugal

Keywords:

Prescriptive Analytics, Surgery Scheduling Problems.

Abstract:

Surgery scheduling plays a crucial role in modern healthcare systems, ensuring efﬁcient use of resources, min-

imising patient waiting times and improving organisations’ operational performance. Additionally, healthcare

faces enormous challenges, with a general modernisation of all clinical and administrative processes expected,

requiring organisations to keep up with the latest advances in Information Technology. The scheduling of surg-

eries is a crucial sector for the good functioning of hospitals, and the management of waiting lists is directly

related to this process, which has seen the COVID-19 pandemic cause a signiﬁcant increase in waiting times

in some specialities. Surgery scheduling is considered a highly complex problem, inﬂuenced by numerous

factors such as resource availability, operating shifts, patient priorities and scheduling restrictions, putting sig-

niﬁcant challenges to healthcare providers. In this research, in collaboration with one of the leading hospitals

in Portugal, the Centro Hospitalar Universit

ario de Santo Ant

onio (CHUdSA), we propose an approach based

on Prescriptive Analytics, using optimisation algorithms to evaluate their performance in the management

of the operating room. The results allow identifying the feasibility of this approach, taking into account the

number of surgeries to be scheduled and surgical spaces in a time perspective, prevailing the priority of each

surgery in the waiting list.

1 INTRODUCTION

Over the last few years, we have witnessed a grow-

ing concern for the quality of Healthcare provided

to citizens. Organisations are increasingly seeking

more efﬁciency, with stronger investments in Artiﬁ-

cial Intelligence (van Hartskamp et al., 2019), seek-

ing to assist health professionals in making increas-

ingly complex and demanding decisions (G

org

u and

Pickl, 2013). A system capable of improving, assess-

ing and preventing future scenarios becomes a focal

topic in hospital development due to organisational

objectives that each entity needs to meet and the in-

creasingly precise treatment that must be provided to

patients (Briganti and Le Moine, 2020). Alongside

this, there is a belief that the immense volume of data

in a Hospital should be better utilised. The existence

of organisational and clinical data allocated in Hos-

pital Databases makes Healthcare an area with enor-

https://orcid.org/0000-0001-7854-8293

https://orcid.org/0009-0004-2635-105X

https://orcid.org/0000-0002-5441-3316

mous potential for the application of Intelligent Sys-

tems, capable of improving the clinical follow-up pro-

vided to patients and managing the different organi-

sational processes inherent to any clinical speciality

(Jayaratne et al., 2019).

The Surgical Scheduling Problem (SSP) is one

of the most debated issues in hospital management.

The COVID-19 pandemic aggravated this process, as

many specialities interrupted their normal functioning

to respond more efﬁciently to other critical patients,

increasing the number of patients waiting for a va-

cancy to perform the surgeries they need. This needs

to be rethought, as the old scheduling processes have

already resulted in long waiting lists, making it crucial

to develop strategies that can mitigate waiting times

and ﬁnancial losses for these organisations.

In cooperation with the Centro Hospitalar Univer-

sit

ario de Santo Ant

onio (CHUdSA), a study was car-

ried out to understand the feasibility of a more au-

tonomous solution, according to the intervention of

each hospital manager. The aim is to codify the ex-

isting restrictions in this process and implement opti-

474

Lopes, J., Vieira, G., Veloso, R., Ferreira, S., Salazar, M. and Santos, M.

Optimization of Surgery Scheduling Problems Based on Prescriptive Analytics.

DOI: 10.5220/0012131700003541

In Proceedings of the 12th International Conference on Data Science, Technology and Applications (DATA 2023), pages 474-479

ISBN: 978-989-758-664-4; ISSN: 2184-285X

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

misation algorithms that solve the increase in waiting

lists and associated costs. This study covers the en-

tire research process, from identifying and codifying

constraints to selecting and developing optimisation

algorithms, allowing a general understanding of the

viability of this approach.

2 PROBLEM DEFINITION

2.1 Surgical Scheduling Problem

Room planning is a task that needs to be addressed in

many ﬁelds. A notable ﬁeld in healthcare is planning

operation rooms for surgeries. Cost containment and

reduction have become one of the primary goals in

healthcare management, with hospital managers and

professionals trying to understand each factor that in-

cludes the total cost of providing better services. Op-

erating Rooms (OR) are one of the areas that have

been gathering considerable attention since it is the

most critical cost centre and consumes a large propor-

tion of the Hospital’s total expenses. As a result, they

offer the potential for signiﬁcant cost-saving, and the

Surgery Scheduling Problem (SSP) has been studied

over the years and generated a variety of approaches

and heuristics (Visintin et al., 2017).

Based on these concepts, the SSP consists of as-

signing operations to a time interval so that surgery is

only scheduled once, at a given time, and never over-

laps with another (Agnetis et al., 2014). Despite the

different development approaches, with very diverse

implementations in the type of algorithms, there are

different perspectives obtained from the time scale

and the surrounding constraints, evidencing the in-

existence of standard approaches to the problem of

SSP that effectively prove its effectiveness compared

to hospital management carried out nowadays. As a

reﬂection, this problem still presents a scarcity of ac-

curate proposals that may allow the establishment of

standard rules and guidelines to manage this hospital

process. In order to deﬁne the bases for the devel-

opment of a decision support system, a research was

designed to prove the effectiveness of different opti-

mization algorithms in the conception of an approach

with common restrictions to different specialties, aim-

ing at a more global solution to the different health

organizations.

2.2 Optimization Algorithms

Currently, there is a growing trend in the adoption

of computational tools based on optimization meth-

ods. According to Cortez (Cortez, 2014), opti-

mization methods are divided into three main cate-

gories: Blind Search (BS), Local Search (LS) and

Population-Based Search (PBS). BS assumes the ex-

haustion of all alternatives, ensuring that all solutions

are tested. It has an easy implementation, but its feasi-

bility differs signiﬁcantly if the search space is contin-

uous or too large (Luke, 2012). LS is the most mod-

ern category of optimization and is based on new solu-

tions that are generated from existing solutions. Sev-

eral methods focus on a local neighbourhood through

a given initial solution and use previous searches to

guide the next one. PBS presents a new approach to

optimization algorithms, using a set of candidate so-

lutions instead of a single (Delen, 2019).

3 RESEARCH METHODOLOGY

Two methodologies were followed: Design Science

Research (DSR) as a research methodology, pro-

viding the necessary guidelines, and Cross-Industry

Standard Process for Data Mining (CRISP-DM). DSR

consists of 6 phases: 1. Identifying the problem and

motivation; 2. Deﬁning objectives of the solution;

3. Design and development; 4. Demonstration; 5.

Evaluation; 6. Communication (Peffers et al., 2007).

For Data Mining (DM) projects was chosen CRISP-

DM, providing a global perspective on the life cycle

of a data mining project. Includes 6 phases: 1. Busi-

ness Understanding; 2. Data Understanding; 3. Data

Preparation; 4. Modelling; 5. Evaluation; 6. Deploy-

ment (Azevedo and Santos, 2009). Figure 1 repre-

sents the crossover between these two methodologies.

4 DATA UNDERSTANDING

For the development of this study, surgeries scheduled

in a time interval were considered, as well as the exist-

ing shifts. Two new attributes were developed directly

related to shifts: the total time associated to an oper-

ating room and an occupation time with the related

time history as a control parameter. Only the medi-

cal speciality Obesity was considered. Each surgery

involves the execution of all necessary procedures.

Additionally, an estimated time is used, associated to

each type of surgery, using the interquartile mean, ob-

tained through the history of the times related to the

performance of that surgery by ICD10 code in the last

three years. The period under consideration is based

on the non-consideration of atypical restrictions, such

as the period between 2020 and 2021, associated to

the COVID-19 pandemic. The CHUdSA provided all

data.

Optimization of Surgery Scheduling Problems Based on Prescriptive Analytics

475

Figure 1: Crossover of Methodologies.

5 MODELING

The approach developed by the team takes into ac-

count the operational needs of CHUdSA, seeking to

strike a balance between patient typology and prior-

ity with providing the best patient care. In this sense,

hospital administrators must consider several factors

when performing surgical planning, such as the shifts

available to allocate a patient, the number of shifts

and professionals available, and the ability to perform

new admissions, always seeking to reduce the wait-

ing list for surgery. Based on a set of basic rules used

in any speciality and to model a solution for the PSS,

we consider, for this study, a surgical area of a hos-

pital, composed of S operating rooms, a ﬁnite hori-

zon of periods H, in days, and a set N of selected

patients waiting to have their surgeries scheduled.

Each patient in {1, ..., N} has a type of surgery per

ICD10 code and thus has an estimated time associ-

ated with that surgery. This time includes the duration

of the surgery and an additional time for cleaning and

pre-surgical preparation. Regarding operating rooms,

each one speciﬁes the day and the operating room.

Additionally, it was considered that all surgeons could

be assigned to surgery. Thus, minimizing the number

of surgeries exceeding the Guaranteed Maximum Re-

sponse Time (GMRT) is the primary goal of the op-

timization. This deﬁnition translates into wanting to

obtain a solution capable of providing surgeries in a

shorter timeframe to patients while reducing the mon-

etary costs to the hospital inherent to paying signiﬁ-

cant ﬁnes for performing surgeries after the deadline.

The design considerations for this approach are:

1. There is a prioritized patient list for surgeries. Pa-

tient priority is deﬁned based on medical and wait-

ing time factors.

2. The hospital contains a speciﬁc set of ORs. Each

one is unique and specially adapted for certain

types of interventions.

3. A surgery that is programmed after its deadline

earns a penalty depending on your priority.

4. After a scheduling proposal performed by the

algorithms has been deﬁned, the surgeries not

scheduled remain on the waiting list for the next

scheduling. The increase in waiting days for

surgery makes these surgeries seen as priorities to

be planned in future proposals;

5. Each surgery also has information regarding the

time required to perform necessary procedures,

such as cleaning room and preparing it.

The typical structure of these solutions is based on

three main code sectors: Initial Solution (IS), Evalu-

ation Function (EF) and Objective Function (OF), in

this order.

1. IS is a ﬁrst representation of the problem in a

coding process. Ensures an initial guess, often

called a ”starting point” for the algorithm (Gan-

domi et al., 2013);

2. The deﬁnition of EF translates to evaluating a pos-

sible solution in the context of the problem to be

maximised or minimised. The function allows

different solutions to be compared, providing a

ranking or a quality measure score (Michalewicz

et al., 2006);

3. The OF is composed by the optimisation algo-

rithms. The implementation depends on the type

of algorithms to be deployed (blind search, local

search, population-based search, multi-objective

search) (Cortez, 2014).

The Initial Solution (IS) was obtained in random

or sequential slots through the list of specialised surg-

eries by assigning one slot to each input surgery. It

is implemented by the ﬁrst ﬁt method (Brent, 1989)

and obtained by assigning surgeries in available slots,

respecting the time constraints associated with each

surgery and the existing turnovers with the addition

of multiple surgeries to a given slot.

The performance is evaluated by a function devel-

oped for this purpose. Each solution considers the as-

signed surgeries by specifying a penalty (p) obtained

in a surgery (represented mathematically as follows):

DATA 2023 - 12th International Conference on Data Science, Technology and Applications

476

pt =

∑

i=1

(1)

The OF was developed considering two local op-

timisation algorithms:

1. Hill Climbing (HC) is a local optimization method

that climbs a hill until a local optimum is found,

adopting consecutive searches for new solutions

within the neighbourhood of the current solution,

adopting a new solution if it is better than the

previous one (Balan, 2022). Hill Climbing (HC)

implementation was retrieved and adapted from

(Cortez, 2014) and can be perceived by the fol-

lowing function:

hclimbing(par, f n, change, control, type) (2)

The input variables are presented as follows:

• The initial solution (par);

• The evaluation function (fn) that evaluates the

total penalty of the allocated surgeries;

• A change function (change), responsible for

generating the next candidate, creating minor

disturbances in the initial solution by swapping

surgeries between different slots, and evaluat-

ing if this was proﬁtable;

• The variable control is a list that indicates the

number of interactions to execute and the infor-

mation to collect throughout the solution;

• A last variable (type) indicates the main goal:

minimisation.

2. Simulated Annealing (SA) implementation was

also adapted from (Cortez, 2014). In contrast to

HC, which adopts a ﬁxed value for this control

parameter, SA uses a variable temperature during

the search. The method starts with a high tem-

perature, gradually decreasing the control param-

eter until it reaches the minimum value or until the

set number of iterations is reached. The following

function represents the SA implementation:

simulated annealing( f unc, s0, niter, step) (3)

The input variables are presented as:

• The evaluation function (func) that evaluates

the total penalty, similar to HC;

• The initial solution (s0), also similar to HC;

• Maximum number of iterations (niter);

• Parameter to control the cooling speed of the

model (step).

6 EVALUATION AND

DEPLOYMENT

OR management by the CHUdSA can be classiﬁed by

the number of surgeries performed in each speciality

and the number of surgeries performed after the dead-

line. Such variables determine the total penalisation

of the hospital, translating into costs that it will have

to assume. Based on this, Table 1 represents a general

analysis of the existing data considering the special-

ity chosen (Obesity) for this study to understand the

relationship between the number of surgeries to be al-

located and the number of available vacancies. The

choice of this speciality takes into account the most

frequent scenario in which the number of surgeries

to be allocated is greater than the number of exist-

ing shifts. In this scenario, the optimisation of the

ORs must be extremely efﬁcient to achieve the great-

est number of surgeries with the existing resources.

Table 1: Analysis between number of surgeries and avail-

able ORs in Obesity.

Number of surgeries Number of Time Slots

198 122

The implementation of HC and SA algorithms

leads to a set of results presented in Tables 2 and 3.

Table 2: Final Results of Hill Climbing Algorithm.

Hill Climbing Algorithm Results

Penalty 0

Surgeries without Penalty 190

Surgeries with Penalty 0

Unscheduled surgeries 8

Table 3: Final Results of SA Algorithm.

SA Algorithm Results

Penalty 0

Surgeries without Penalty 164

Surgeries with Penalty 1

Unscheduled surgeries 33

It was also possible to understand the impact of

the algorithms on the scheduling of each surgery: the

HC schedules 98% of surgeries for a more recent

date, compared to the scheduling date performed by

CHUdSA. In SA, it was possible to obtain a more re-

cent date in 85% of surgeries.

To perform the deployment of this solution, an ap-

plication was developed, which allows testing the dif-

ferent algorithms according to a set of variables that

interfere directly with the type of scheduling propos-

als generated. In it, all the necessary information is

available for a professional to validate the scheduling

Optimization of Surgery Scheduling Problems Based on Prescriptive Analytics

477

proposals and conﬁrm a possible appointment. Figure

2 present the constitution of the ﬁnal prototype.

Figure 2: Prototype for visualisation of a scheduling pro-

posal.

The main objective of this prototype is to inte-

grate the ability to generate possible scheduling so-

lutions for the physicians responsible for performing

this process in each speciality. These should be able to

test potential alternatives, edit the ﬁnal solution, and

change the variables that directly inﬂuence the ability

to generate solutions (execution times, scheduling in-

tervals and desired efﬁciency), having them the ﬁnal

responsibility of submitting the ﬁnal proposal. Once

a solution is approved, data is sent to the clinical sys-

tem, as well as to the Database of the CHUdSA Busi-

ness Intelligence system (AIDA-BI), allowing hos-

pital professionals to consult the information at any

time, such as responsible physicians, schedules, pro-

cedures, users and operating rooms.

7 DISCUSSION

Through the implementation of these algorithms, a set

of results can be proven:

1. The penalty of automatic scheduling, according to

the described optimisation algorithms, proves the

feasibility of this approach as a response to the

SSP.

2. All implemented algorithms can offer improve-

ments in ORs management and organisation. Still,

HC is the algorithm that achieves better schedul-

ing capability;

3. The SA algorithm presents a higher than expected

number of unscheduled surgeries. This can be jus-

tiﬁed by the fact that SA does not include as a de-

termining factor the heuristic ability to establish

new solutions from the deﬁned number of itera-

tions but through a probabilistic value (tempera-

ture) determining the ability to ﬁnd new solutions.

Common to both algorithms is that certain surg-

eries have a minimum execution time greater than

the maximum time of an existing shift and, there-

fore, would never be scheduled in this optimisa-

tion process. By recommendation of CHUdSA

professionals, these surgeries are always treated

as exceptional cases and should be managed ac-

cording to speciﬁc internal procedures;

4. Modeling the ﬁrst solution with a surgery allo-

cation algorithm, taking into account the priority

and longevity of a surgery on a waiting list, repre-

sents an important improvement in the scheduling

process. The total penalty proves the possibility

of improving the management of surgeries in the

possible time-space;

5. Additionally, this implementation focused on AI-

based heuristics translates into a substantial im-

provement in the number of surgeries that are al-

located after the surgical limit. Thus, we can no-

tice a great capacity for improvement of OR man-

agement with a solution capable of optimising the

scheduling process in this speciality.

8 CONCLUSION AND FUTURE

WORK

The study of allocation and scheduling problems is

always considered to be of great complexity. Taking

this reality to healthcare, the responsibility to create

an effective solution is even more signiﬁcant since the

priority must always be the care provided to patients,

trying to pay attention to the existing resources and

the practices of good organisational management in-

creasingly important in the hospital context.

The developed approach offers a ﬁrst sketch of

what can be contemplated in an intelligent system to

support all the decisions made in SSP. Considering

a general constraints model for any hospital, imple-

menting optimization algorithms, and considering the

same constraints for generating the initial solution, it

was possible to prove the ability to ﬁnd better solu-

tions for surgical scheduling. The HC and SA algo-

rithms demonstrate the capacity to have a better oc-

cupation of the available ORs, with clear highlights

to HC, which allocates a signiﬁcant percentage of

surgeries (96%), always trying to considering as main

reference the scheduling limit without accumulating

penalties. The use of many iterations in the imple-

mented algorithms means a high computational load

and a waiting time for solutions, which is still impor-

tant in order to make it possible to ﬁnd the best alter-

natives within each scheduling scenario.

DATA 2023 - 12th International Conference on Data Science, Technology and Applications

478

Taking into account all the limitations found in

scheduling problems and the high level of organisa-

tional complexity that a hospital currently has, we

consider this approach a possible solution to SSP

problems, of which the organisation of surgeries on

time and the necessary cost control, crucial to opti-

mise all management processes, always prevail. SA

presents extremely satisfactory results, nullifying the

number of surgeries with a penalty, i.e., surgeries with

a scheduled date higher than the deadline. Further-

more, this algorithm provides a nearly optimal solu-

tion, reaching a stabilisation point after 100 iterations,

something that does not happen in the HC and that

may justify the fact that it does not allocate a greater

number of surgeries.

In the ﬁrst phase of this research, new perspec-

tives were obtained on how an approach based on AI

heuristics can translate into a solution capable of au-

tomating and improving this process. However, some

scenarios could be further explored as future work:

1. Testing this study in other healthcare specialities

will be the ﬁrst step to understanding if the suc-

cess of implementing this logic is well achieved

in different environments.

2. A deeper study on the nulliﬁcation of the schedul-

ing penalty may be equated. While the hospital

would like to pay the least amount of costs related

to surgeries scheduled after the deadline, it may

be pertinent to identify whether a proposal with

a higher penalty will better serve the hospital’s

scheduling interests.

3. A new constraint can be added, always consider-

ing that there are urgent cases to be executed. De-

spite in this study only surgeries from the waiting

list were considered, it is possible to complement

the scheduling constraints with an additional rule,

always leaving space in an OR for urgent cases;

4. Improving the efﬁciency of the optimization

method by exploring new models and their con-

ﬁgurations (only local search algorithms were ad-

dressed, but there is some scope for development

for population-based, blind search or even multi-

objective search algorithms).

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