Ambulance Vehicle Routing under Pandemic with Fuzzy Cooperative

Game via Smart Contracts

Alexander Smirnov and Nikolay Teslya

SPC RAS, 14

line, 39, St. Petersburg, Russia

Keywords: Decision Support, Optimization, Fuzzy Game, Pandemic, Smart Contacts, Transportation, Ambulance,

Vehicle.

Abstract: The pandemic caused by COVID-19 virus has posed a challenge for healthcare systems in many countries.

One of the important tasks facing after a sick person detection is the timely patient’s transportation to a

hospital. When making a decision on transportation to the hospital, it is necessary to account for many

parameters, including beds space availability, availability of hospital staff and medicines required by the

treatment protocol, diagnostic equipment on ambulance team, the distance to the hospital, ambulance vehicle

locations, as well as hospital and ambulance staff psychophysical state, and patient’s reaction to

hospitalization. Some of them can be gathered through smart city sources, like city databases or operational

systems, but most of them require access to medical services. It is proposed to consider hospitals as

participants of a cooperative game, whose overall goal is to ensure the maximum of cured patients. To describe

the psychophysical state of the personnel, as well as to ensure greater variability of the resulting solution, the

game parameters are proposed to be set using fuzzy sets and fuzzy logic. To implement the game rules, it is

proposed to use smart contracts in blockchain technology. The blockchain could also be used to provide access

to data from medical services, store and distribute the current state of hospitals, and save processing results

for later analysis and model refinement.

1 INTRODUCTION

Coronavirus pandemic has proven to be a major

challenge for healthcare systems in many countries.

One of the problems was the patient’s timely

hospitalization, given the limited number of

ambulance vehicles and bed space in hospitals.

When discussing the problem sources and

possible solutions, a large number of factors must be

considered (Patel et al., 2020); at that, four large

groups can be distinguished, associated with the main

actors: hospital, patient, ambulance, a dispatcher

(distribution center). Each of them, due to the

increased load, must constantly monitor the current

situation and promptly form a solution suitable for all

participants in the process (see Fig. 1) (Xiong et al.,

2020). The complexity of the problem of patient

distribution is the stochasticity of their admission and

a high rate of change in the operational situation.

High load causes an increased impact on the

psychological and emotional state of staff and

https://orcid.org/0000-0003-0619-8620

patients. This leads to distress increase and errors’

number increase during decision making that can

reduce the care speed and quality (Patel et al., 2020;

Xiong et al., 2020).

The paper proposes considering a narrower

problem associated with the patients’ hospitalization

under a pandemic. A methodology for using

information technologies to support decision-making

for ambulance vehicle routing during hospitalization

is proposed. It is based on the division of the problem

into two tasks: 1) making a decision on

hospitalization with the selection of an ambulance

vehicle and 2) the selection of a hospital to which the

patient must be transported with the selected vehicle.

For each task, several parameters are estimated that

describe both the quantitative characteristics of the

task, such as the availability of vacant places (beds)

in hospitals, the average transportation time, the

number of ambulance vehicles, the cost of treatment,

and the qualitative parameters associated with the

psychoemotional load on patients, dispatchers, and

medical staff.

538

Smirnov, A. and Teslya, N.

Ambulance Vehicle Routing under Pandemic with Fuzzy Cooperative Game via Smart Contracts.

DOI: 10.5220/0010455605380545

In Proceedings of the 7th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2021), pages 538-545

ISBN: 978-989-758-513-5

Figure 1: Decision making on ambulance vehicle routing for patient treatment.

The choice of a hospital is carried out through the

formation of a cooperative game in which hospitals

are participants. The cooperative game characteristic

function estimates benefit of cooperation as the

number of patients cured under the constraints

imposed by each participant under current conditions,

like, the supply of medicines, the availability of

equipment, the probability of successful treatment

and psycological state of medical staff. To take into

account the probabilistic characteristics and

psychological state of medical personnel, it is

proposed to use fuzzy logic and fuzzy sets.

To quickly track the current situation in this work,

it is proposed to use blockchain and smart contracts.

Blockchain capabilities allow to save patient medical

records and permit access to them only by authorized

staff. It is also possible to store the current state

according to the main parameters that can describe

the current situation. Smart contracts in the form of

decentralized applications can be used to compute the

outcome of the coalition game and support decision-

making during a hospitalization.

The paper is structured as follows. Section 2

describes the current state of research on the use of

information technology to support decision-making

in healthcare. Section 3 describes the decision-

making methodology for hospitalization under a

pandemic. Section 4 contains a description of

describes the hospitalization process as a fuzzy

cooperative game and the parameters that should be

taken into account when making an appropriate

decision. The work conclusion provides general

conclusions and directions for further work.

2 RELATED WORK

Currently, the application of information

technologies to healthcare is an active and promising

research area. The range of their applications is quite

wide: from storing medical records, containing all

parameters of a patient and her/his health history are

saved (Dalianis, 2018), to the use of artificial

intelligence for identifying diagnoses and searching

for medicines for a specific disease of a particular

patient (Topol, 2019; Yu et al., 2018).

It should also be noted that the use of information

technology in healthcare is focused on the processing

of information that is usually classified as personal

data and medical secrecy. This requires

corresponding levels of security for the subsystems

responsible for processing, storing, transferring, and

providing access to the information. In the event of an

epidemic, however, it is necessary to provide online

access to this information (Raskar et al., 2020). The

recent advanced studies suggest an application of the

distributed ledger technology based on the blockchain

concept to solve this problem, as well as smart

contracts technology that expands its capabilities. The

research efforts are focused on developing scalable

systems for collecting readings from sensors that

Smart city

Hospital

Ambulance

vehicle

Patient

Traffic

Population density

Pharmacies location

Hospital location

Free beds

Treatment protocols

Staff competences

Equipment

Dispatcher

center

Location

Staff competences

Equipment

Location

Disease symptoms

Other symptoms

Initial diagnosis

Patient transportation

Medical

diagnostics

center

Decision

Ambulance Vehicle Routing under Pandemic with Fuzzy Cooperative Game via Smart Contracts

539

monitor the patient's condition (Jamil et al., 2020;

Satamraju & Malarkodi, 2020), creating distributed

systems for accessing patient data during routine

examinations, and making diagnoses in case of illness

(Satamraju & Malarkodi, 2020; S. Wang et al., 2018;

Z. Wang et al., 2020).

It is also worth noting existing interdisciplinary

research combining the technologies of the Internet of

Things, supply chains, and the distributed ledger in

healthcare. Thus, in (Islam & Young Shin, 2020), a

system is proposed that collects data from patients

using unmanned aerial vehicles furnished with

special equipment. The collected data are encrypted

and moved to the nearest server, where they are

decrypted and put onto a medical record, access to

which is organized by calling functions of smart

contracts implemented using the Solidity language in

the Ethereum blockchain platform. This scheme

provides remote diagnostics using professional

equipment, with full protection of all patient’s

personal data from the measurement moment to the

medical doctor submission.

Another study suggests using blockchain to

control the vaccine supply chain (Yong et al., 2020).

Within the framework of the developed system, the

control of the stages from the creation of a vaccine to

its application by a doctor is provided. This enables

tracking the distribution process, covering the

population with the vaccine, and is compliant with the

conditions and terms of the vaccine transportation and

storage, which allows for avoiding negative

consequences caused by damage of the vaccine due

to any violation at any stage of delivery. Additionally,

the system includes a recommendation module based

on a neural network of the LSTM (long short-term

memory) model for assessing the vaccine demand

based on the results of the previous vaccination.

3 DECISION SUPPORT ON

AMBULANCE VEHICLE

ROUTING UNDER A

PANDEMIC

3.1 Common Requirements

Since the resources used to overcome the

consequences of epidemics are limited, it is assumed

that their distribution should be directed towards

solutions that are most effective in the current

situation. Agents (participants) form coalitions to use

these resources in which the competencies of each

agent correspond best to the particular problem being

solved. The contribution of each member of the

coalition is estimating as a payoff for task solving

based on the benefit that coalition will gain after

successful task solving. For example, in the case of

hospitalization task the benefit will be the ratio of

cured patients to the number of deaths. It is proposed

to evaluate the effectiveness of socially-oriented

decisions as to the ratio of funds spent on treatment to

potential losses from deaths, while it should be borne

in mind that losses significantly exceed any spent

funds.

The gain of the coalition in this case can be

estimated as the difference between the potential

losses and the funds spent. To motivate agents when

working in a coalition, the entire total payoff (or part

of it) can be distributed among them. This model

allows for applying fuzzy cooperative games to form

a coalition and distribute the payoff between the

members of the coalition. Fuzziness in this problem

allows for operating with fuzzy values of efficiency

and gain, which provides flexibility and variability of

the solutions obtained, as well as to account for

retrospective estimates of the level of uncertainty

distress among participants, including those arising

under the influence of competing for external

regulators of behavior.

3.2 Social and Psychological

Characteristics for Decision

Support

It is proposed to use a mathematical formalism to

describe human behavior. For example, in (Kleiner et

al., 2018), a model of psychological factors of

economic behavior is considered, that includes the

systemic structure of an agent (person), presented in

the work as a set of four interacting subsystems:

intentional (agent's intentions), anticipatory (agent's

expectations), cognitive (agent's perception of the

surrounding world) and functional (agent's behavior).

Analysis and compilation of behavior models are also

used to predict human actions, for example, in

tourism (Gretzel et al., 2015) and marketing (Stalidis

et al., 2015). In this case, the description can be based

on various formalizations, for instance, first-order

logic, description logic, classical algebraic formulas,

consistent with the proposed methodology.

In studies conducted in the context of the 2020

pandemic, it is noted that the incompleteness of a

threatening situation produces a major effect on

people, and the cumulative nature of the stress effect

is recorded (Xiong et al., 2020). Unfavorable

background factors for all participants in the decision-

making process are anxiety, fear of infection, forced

VEHITS 2021 - 7th International Conference on Vehicle Technology and Intelligent Transport Systems

540

isolation from family members (Shah et al., 2020),

anxiety, and depressive states increase (Montemurro,

2020). The behavior of patients is influenced by the

stress, fear, depression caused by the disease itself

and its severity; and by the stress associated,

according to foreign scientists, with a “health crisis”

(Garfin et al., 2020), which is largely due to the

dissemination of threatening, emotional, and

sometimes redundant information about an invisible

threat, which in isolation leads to the constant appeal

of people to its sources, doubts that in these

conditions one can count on a full and high-quality

medical service. Lack of protective equipment,

problems with adequate treatment, as well as a purely

human factor - fatigue, tension, anxiety, and

professional burnout of medical personnel (Li et al.,

2020; Mo et al., 2020; Montemurro, 2020), induce

negative emotional states in the hospitalized, attempts

to influence the decisions of medical personnel.

Decision-making by medical workers,

management personnel, operational workers is

carried out against a background of fatigue, stress,

and distress. Uncertainty distress has become a key

factor in the impact on medical staff in COVID-19

(Freeston et al., 2020). The uncertainty of the

diagnosis and prognosis of treatment is associated

with the lack of reliable and complete information

about the disease and the forms of its manifestation,

treatment methods, considering the individual

characteristics of patients. These features of the

diagnosis are the characteristic of the current situation

of a pandemic, in which the diagnosis is not always

defined timely, it is formulated vaguely and

unclearly, the disease manifests itself variably, and a

high variety of symptoms is demonstrated.

As several studies have shown (Buheji et al.,

2020), stress occurs when a person is sensitive to the

perception of environmental stimuli, while her/his

resources are aimed at correcting the impact of the

environment or changing it are insufficient. In the

context of the ongoing pandemic, methods are being

developed to express diagnostics of anxiety, states of

uncertainty in large samples, and attempts are being

made to assess the emotional state of individual social

groups or society as a whole (Ahorsu et al., 2020;

Pakpour & Griffiths, 2020).

Formalization of stress indicators requires high

variability with the possibility of states’ fuzzy

description. The most effective tool in this case is

fuzzy sets. Within the framework of the methodology,

fuzzy sets can be used together with the mathematical

apparatus of fuzzy logic and fuzzy cooperative

games, which provide the formalization of the patient

and doctor's state and also form constraints for the

optimization problem being solved.

The use of fuzzy logic and fuzzy cooperative

games in describing the interaction of coalition

participants is a relatively new approach that has

shown, however, its effectiveness in problems of

supply chain configuration (Sheremetov, 2009) and

coalition formation (Mohebbi & Li, 2015). From the

medical point of view, the apparatus of fuzzy logic

and cooperative games can be used to assess the

effectiveness of hospitals (Omrani et al., 2018). The

effectiveness in this work is assessed by many

parameters, including the number and quality of staff

(doctors, nurses, support staff), the number of beds,

the number of operations, costs of treatment and

maintenance, etc. The mechanism of coalition games

was used after the division of the country (in this

study, Iran) into separate regions according to

economic and demographic parameters, and the

assumption that each hospital works in cooperation

with other hospitals in the region. This allowed to

calculate the total gain for the region and track the

contribution of each hospital to the total gain.

4 FUZZY COOPERATIVE GAME

USAGE FOR AMBULANCE

VEHICLE ROUTING

To formulate the ambulance vehicle routing problem,

an analysis of open sources and official documents of

the Russian Ministry of Health was carried out.

According to the model, two related tasks can be

distinguished that must be solved during the

hospitalization process.

4.1 Initial Diagnosis

The first task is to determine the need for

hospitalization and the selection of the ambulance

vehicle from the vehicle pool (Fig. 2).

Figure 2: Initial call dispatching problem.

Upon receipt of a call from a patient, a short

Patient

Emergency

service

Ambulance

vehicle

call

assign

inspect

Ambulance Vehicle Routing under Pandemic with Fuzzy Cooperative Game via Smart Contracts

541

survey is conducted to estimate the probability of a

particular disease. The survey, beside questions to

identify the main symptoms, may contain questions

about concomitant diseases, gender, age, and recent

contacts. Additionally, the location of the patient and

his/her medical insurance is being specified.

After collecting the information, the dispatcher

service must estimate the need for hospitalization (at

least half of the symptoms of the disease has to be

confirmed). Then, based on the current demand and

availability, an ambulance is selected, which has the

necessary equipment and medicines for preliminary

examination and potential hospitalization.

As part of the developed methodology,

dispatchers are offered a decision support system

evaluating the need for hospitalization and selecting

an appropriate ambulance vehicle. The set of

parameters to be used for decision support includes:

Global Parameters:

▪ Healthcare system priorities;

▪ General epidemiological situation.

Information Gathered from the Dispatcher:

▪ Number of calls for a day;

▪ The average severity of patients who require

hospitalization;

▪ The average distance from the patient's location

to the hospital (ambulance service radius);

▪ Vacant beds in hospitals;

▪ Average queue time for ambulance

appointments in case of hospitalization.

Information from Ambulance Cars:

▪ Location;

▪ Staff quality (Average decision time, number of

errors (the patient returns to the place of

residence));

▪ Ambulance equipment (medical drugs, tools,

tests);

▪ Staff working time (fatigue level).

The problem of choosing an ambulance for

hospitalization is proposed to be formulated as a

choice problem. Moreover, if an ambulance is already

with the patient, then it is only necessary to solve the

problem of choosing a hospital. Otherwise, after

choosing a hospital, it is necessary to be guided by the

parameters listed above, as constraints in the selection

problem.

4.2 Hospital Selection

The second task is to choose the hospital, the patient

needs to be transported to (Fig. 3).

Figure 3: Process of patient transportation to hospital.

After an ambulance is assigned to a patient, the

ambulance staff is responsible for the state of the

patient. They need to conduct an initial examination

using their equipment and decide whether the patient

needs an urgent hospitalization or transportation to a

sorting center or for additional testing. For example,

in the case of COVID-19, computer tomography of

the lungs may be necessary to confirm the diagnosis

and the need for hospitalization.

When deciding on hospitalization, it is necessary

to choose a hospital that has vacant beds and all the

necessary equipment to treat the patient with the

given severity of the disease. For this purpose, it is

also necessary to contact the dispatcher, who, based

on the assessment of the current situation, decides on

the place of additional examination or hospitalization.

When solving this problem, it is also necessary to

consider many parameters, including:

Patient and Ambulance Parameters:

▪ Patient condition (Condition description sheet

(20 parameters and general assessment),

comorbidities, age);

▪ Location.

Dispatcher Parameters:

▪ Healthcare system priorities;

▪ Road traffic;

▪ Sorting and laboratory parameters;

▪ Service time for one patient;

▪ Service queue;

▪ Resources (tests, disinfectant materials);

▪ Free seats;

▪ Cleaning and disinfection time after service.

Hospital Parameters

▪ Service time for one patient;

▪ Queue length;

▪ Bed amount;

▪ Available treatment protocols and scripts;

▪ Available resources (medicines, equipment);

Ambulance vehicle

with patient

Emergency

service

Hospital

Sorting centre

and computer

tomography

request

assign

VEHITS 2021 - 7th International Conference on Vehicle Technology and Intelligent Transport Systems

542

▪ Bed quality (availability of additional functions

and/or equipment to ensure comfort and relief

of the patient's condition);

▪ Staff qualification and competences.

This problem is proposed to be formulated using

the formalism of a cooperative game. The hospitals in

the game are the players among whom it is needed to

assign patients. Also, the players are diagnostic

centers and distribution centers. A coalition can be

formed between hospitals (in the absence of full

compliance with the treatment protocol), between

hospitals, and diagnostic centers.

Let us introduce a formalization of the coalition

game for choosing a coalition of hospitals. Each of

the players    aims at providing patient care P

(transferring him from the "sick" state to the "healthy"

state), guided by the treatment protocol (strategy) 



using own resources



. Hospitals can form coalitions

to pool their resources to achieve a goal within

existing strategies. When solving a coalition game, a

set of coalition participants is formed, to which the

patient is assigned to (1). In this case, the coalitions

of one participant are possible if he has the necessary

resources to achieve the goal.





 





 





  



 











 





(1)

Where  is the coalition, 



is a characteristic

function that is calculated based on the the current

parameters  of patient    and player  of the

coalition , 



is the strategy of the player of the

coalition . It is proposed to formalize stress levels,

the psychological and physical state of hospital staff

and patients through linguistic variables such as 

   , where  is the name of the variable,  is the

set of values and their membership functions,  is the

carrier of the fuzzy set.

5 SMART CONTRACTS

UTILIZATION

When organizing the exchange of information within

the framework of the methodology, it is proposed to

use the capabilities of a distributed digital ledger. The

rationale for this decision is the need to provide

trusted access for various services to electronic health

records to speed up the exchange of information

about the patient's condition, to save the history of

changes in the state. Using the smart contract

mechanism, a distributed ledger can be configured to

control access to electronic health records.

Smart contracts are used as a distributed

application. The contracts implement the logic of

solving the coalition game. They take the current state

of the players as input and form a decision that is

stored in the distributed ledger. According to the

decision received, the appointment of the hospital is

carried out and, after approval by the dispatcher, the

process of transporting the patient to the hospital is

started.

Figure 4: Decision making through with fuzzy cooperative game via smart contracts.

Smart

city

Smart city

services

Ambulanc

e vehicle

service

Ambulanc

e vehicle

service

Ambulance

vehicle service

Patient

Dispatcher

center

Medical

diagnostics center

service

Medical

diagnostics center

service

Medical diagnostics

center service

Hospit

servic

Hospit

servic

Hospital

service

Distributed digital ledger

(Hyperledger Fabric)

Electronic Health Records

Free beds in Hospitals

Hospitals equipment, staff and drugs

Ambulance vehicles distribution

Ambulance vehicles equipment and staff

Current tasks

Fuzzy cooperative

game rules

Ambulance Vehicle Routing under Pandemic with Fuzzy Cooperative Game via Smart Contracts

543

The system for decision making on ambulance

vehicle routing is presented in Figure 4. Sources of

information about the current state of the system are

represented by services in the information space.

Each service is associated with a distributed ledger

and can transfer data through blocks in the ledger.

When requested by a patient, the dispatch center can

quickly receive current information and

recommendations on where to transport the patient.

The recommendation is formed by calling a smart

contract containing the rules of a cooperative game.

By placing contracts in the digital ledger, all blocks

can be accessed from a smart contract, which allows

to quickly get the current state of the system and form

a coalition composition that corresponds to maximum

benefit (to cure a sick person).

The Hyperledger Fabric platform is used to form

a distributed ledger (Androulaki et al., 2018). Its

choice is due to the possibility of forming separate

chains of blocks corresponding to hospitals or

electronic patient records. Using built-in capabilities

for the implementation of smart contracts, access

control to medical records can be controlled.

Complex contracts can also be implemented to

calculate the outcome of a coalition game.

The example of smart contract for core calculation

is presented at listing 1.

Listing 1: Example of a chaincode for coalition

calculation.

var hospitals []Hospital // Hospital

list

var patient Patient // Patients list

var K, K_prev // coalitions

func coalitionCalc(stub

shim.ChaincodeStubInterface, args

[]string) (string, error) {

hospitals[i], patient = args[i],

args[j]

for h in hospitals {

K = f(patient, h)

if K > K_prev

K = K_prev

}

stub.PutState(K)

}

Preliminary experiments had shown that

information exchange between coalition participants

through smart contracts requires about 20 ms for each

exchange transaction that includes information

transfer, store in digital ledger and sharing between

all coalition participants. The test stand had the

following configuration: CPU Intel i7 7700k, RAM

16 Gb, SSD M2, 240 Gb.

6 CONCLUSIONS

The work shows the formalization of the

transportation process using a fuzzy cooperative

game problem that takes into account the main

parameters of the hospitals and patients as the values

of the objective function, and the limitations of the

health care system as the limitations of the function.

The main impact on the proposed methodology is

concentrated on taking into account the economic

effect and human behavior with an increase in the

level of stress in the methodology. All parameters are

formalized with the fuzzy sets and their consideration

in the objective function is done using the fuzzy logic.

For the exchange of data on the current situation,

the use of a digital distributed ledger is proposed. The

decision of the target function and decision making,

in this case, can be implemented in the form of smart

contracts in the ledger. This approach ensures the

consistency and immutability of data in the decision-

making process and the accumulation of statistics for

subsequent objective analysis of the pandemic.

ACKNOWLEDGEMENTS

The reported study was funded by RFBR according

to the research project № 20-04-60054 and by

Russian State Research No. 0073-2019-0005.

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