A Method of Emergency Volunteer Team Internal Participation in Rescue Decision-Making Considering Psychological Behavior

Jie BAI; Shengqun CHEN

doi:10.21078/JSSI-2023-0079

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Journal of Systems Science and Information ›› 2024, Vol. 12 ›› Issue (1) : 64-80. DOI: 10.21078/JSSI-2023-0079

A Method of Emergency Volunteer Team Internal Participation in Rescue Decision-Making Considering Psychological Behavior

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Abstract

A method for internal participation in rescue decision-making of emergency volunteer teams considering psychological behavior is proposed to address the time sequence of rescue tasks. Firstly, the problem of multi-tasking and multi-operation within the emergency volunteer team is described. Secondly, considering that task leaders are influenced by behavioral and psychological factors in the evaluation, the required time for the job is used as a reference point, and the expected time that volunteers can complete the job is used as an attribute value. The task leader's prospect satisfaction value for each volunteer is calculated based on prospect theory, and the perceived utility values of disappointment theory and regret theory are calculated to measure the task leader's satisfaction with each volunteer. Furthermore, a multilayer coded genetic algorithm is used to construct an optimization model for emergency volunteer decision-making with the objective of maximizing the satisfaction value. Finally, the feasibility and effectiveness of this method are illustrated by an example analysis. The result shows that the efficiency of rescue tasks can be improved through decision optimization within the volunteer team.

Key words

emergency volunteers / rescue task / multi-layer coding genetic algorithm / satisfaction value / psychological behavior

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Jie BAI , Shengqun CHEN. A Method of Emergency Volunteer Team Internal Participation in Rescue Decision-Making Considering Psychological Behavior. Journal of Systems Science and Information, 2024, 12(1): 64-80 https://doi.org/10.21078/JSSI-2023-0079

1 Introduction

In recent years, various major disaster events have occurred frequently, resulting in significant casualties and property damage. After a sudden disaster, emergency rescue work requires a lot of human and material resources. The practice has proven that emergency volunteers play an important role in emergencies^{[1, 2]}.

Scholars at home and abroad have conducted a series of studies on volunteer decision-making in post-disaster rescue. Sampson^[3] compared the differences between volunteer labor decision-making and traditional labor decision-making based on cost structure, objective function, and constraints. In response to the volunteer job problem in humanitarian organization relief, Falasca and Zobel^[4] developed a multi-objective optimization model considering the ability and willingness of volunteers, and finally obtained the optimal volunteer job scheme. Considering the preferences and skills of volunteers, Garcia, et al.^[5] used mixed integer planning to assign volunteers to tasks in disaster situations. Lodree and Davis^[6] presented a case study of volunteer integration after a disaster, which is the first academic study to analyze volunteer integration data. Given that the arrival and departure times of volunteers are uncertain, Mayorga, et al.^[7] established a multi-server queuing system with random server arrivals and discontinuations and used a continuous-time Markov decision process to obtain the optimal volunteer decision scheme. For the volunteer decision problem in post-disaster rescue, Abualkhair, et al.^[8] utilized a heuristic strategy to assign volunteers to parallel queues and determined the most effective job strategy under various experimental conditions through a large number of experiments. Considering that the arrival and departure times of volunteers are random, Paret, et al.^[9] established a multi-server queuing model and used a Markov decision process to generate the optimal volunteer job scheme. To address the decision problem of social forces participating in post-disaster relief, Li, et al.^[10] proposed an optimal decision model and solution algorithm based on the principles of "acting according to ability and proximity". Accounting for each volunteer's preferences, Gordon and Erkut^[11] set up a goal-planning model and generated a personnel grouping scheme using a spreadsheet-based decision support tool. The contribution of these studies is mainly to solve the decision-making problems of individual volunteers, rather than volunteer teams.

In fact, many volunteers participate in relief efforts in small groups (e.g., families, sports teams, religious groups, etc.)^[12], and in difficult situations, volunteers tend to be more sustained in team-based relief efforts. When emergencies come, the relevant relief departments often give priority to volunteer teams rather than individual volunteers. To this end, Chen, et al.^[13] designed a model to solve the matching problem between volunteer teams and rescue tasks. The model not only improves the satisfaction of bilateral participants, but also avoids decision bias due to lack of information. However, it only solves the decision-making problem of the volunteer team and does not take into account the decision-making issues between volunteers within the team. Therefore, this paper proposes a multi-task and multi-operation decision optimization method within a team of emergency volunteers.

The prospect theory, first proposed by Kahneman and Tversky^[14] in 1979, is an integrated theory of psychology and behavioral science. First applied in economics, prospect theory has been extended to several fields in recent years, such as asset allocation^[15], health domain^{[16, 17]}, portfolio insurance^[18], transportation management^{[19, 20]}, multi-attribute decision-making^[21–24], and emergency decision-making^{[25, 26]}. In terms of decision-making, Chen, et al.^[27] proposed a multi-attribute matching decision method for the decision-making problem considering the psychological expectations and perceptions of matching subjects. Fan, et al.^[28] suggested a decision analysis method based on cumulative prospect theory by taking into account the psychological factors of decision-makers and using their expectations of each attribute as a reference point. Zhang, et al.^[29] presented a gray multi-index risk decision-making method based on prospect theory for the multi-index risk decision-making problem. In the decision-making process^[30–32], typical psychological behaviors include disappointment theory and regret theory. To address the problem of uncertain decisions in which decision-makers have disappointing behavior, Bell^[33] proposed the disappointment theory. Disappointment theory^[34–38], as an important theory for studying typical psychological behaviors, has received the attention of many researchers and has yielded relatively rich research results. The regret theory was first proposed independently by Bell^[39], Loomes and Sugden^[40], respectively, and it is also an important theory of behavioral decision-making^[41–44]. Zhang, et al.^[45] presented a decision analysis method based on regret theory when considering the behavior of decision-makers. Lu^[46] put forward an emergency decision-making method based on regret theory to solve the problem of whether emergency plans have an impact on the evolution of emergency scenarios. Zhang^[47] proposed a method for selecting and adjusting emergency scenarios that considers regret and disappointment behaviors in response to the emergency decision-making problem. This paper calculates the task leader's satisfaction value for each volunteer based on the prospect theory, and calculates the perceived utility values of disappointment theory and regret theory, and uses the perceived utility to measure the satisfaction level of task managers with each volunteer. Further comparative analysis is conducted through prospect theory, regret theory, and disappointment theory. As the subject of evaluating the satisfaction value of volunteers, the task leader's evaluation is influenced by behavioral and psychological factors, so psychological behavior plays an important role in the decision-making process.

From the above literature, it is clear that the current research mainly focuses on the dispatch of scattered volunteers, with little emphasis on the dispatch of volunteer teams. This article studies how to coordinate work dispatch within volunteer teams and proposes a method of emergency volunteer team internal participation in rescue decision-making that considers psychological behavior.

The rest of the paper is organized as follows. Section 2 describes the problem of multi-tasking and multi-operation within a team of emergency volunteers and defines the associated notation. Section 3 proposes a method of decision optimization within a team of emergency volunteers to address this problem. This includes calculating the task leader's satisfaction value for each volunteer based on prospect theory, aiming at the maximum satisfaction value, and using the multi-layer coded genetic algorithm to construct a decision optimization model for emergency volunteers. Section 4 provides a case study for analysis, and Section 5 concludes the paper.

2 Description of the Problem

In emergency rescue, the issue of multiple tasks and multiple operations within the emergency volunteer team is proposed for operations where the rescue tasks have a time sequence.

2.1 Problem Formulation

Suppose a volunteer team agrees to accept requests for several rescue tasks, each with different jobs. As shown in Figure 1, the team has

m

volunteers to complete

n

tasks, and task

B_{j}

(

j = 1, 2, \dots, n

) has

l_{j}

jobs. The first job of task 1 is performed by volunteer

A_{1}

, the second job of task 1 is performed by volunteer

A_{m}

, and the

l

th job of task 1 is performed by volunteer

A_{2}

. The three digits in Figure 1 represent the decision-making situation of volunteers, for example, 101 represents the first job of task 1. 201 can be performed by Volunteer 2 or Volunteer 3, but ultimately can only be performed by one volunteer. The research object of this paper is how to solve the optimal decision-making scheme for multi-tasking and multi-operation for volunteers with different rescue capabilities and different times available for participation.

Figure 1 Multi-task and multi-job model within the volunteer team

Full size|PPT slide

2.2 Notations

The following symbols are used to indicate multi-tasking and multi-operation problems within a team of emergency volunteers:

A = {A_{i} | i = 1, 2, \dots, m}

denotes a collection of volunteers

A_{i}

B = {B_{j} | j = 1, 2, \dots, n}

denotes a collection of tasks

B_{j}

C = {C_{k} | k = 1, 2, \dots, l}

denotes a collection of jobs

C_{k}

H = {h_{j}^{k} | j = 1, 2, \dots, n, k = 1, 2, \dots, l}

represents the set of required times

h_{j}^{k}

for the jobs

C_{k}

in the task

B_{j}

P = {p_{i j}^{k} | i = 1, 2, \dots, m, j = 1, 2, \dots, n, k = 1, 2, \dots, l}

represents the set of expected time

p_{i j}^{k}

for the volunteer

A_{i}

to perform the jobs

C_{k}

in the task

B_{j}

T = {t_{i j}^{k} | i = 1, 2, \dots, m, j = 1, 2, \dots, n, k = 1, 2, \dots, l}

represents the set of actual time

t_{i j}^{k}

for the volunteer

A_{i}

to perform the jobs

C_{k}

in the task

B_{j}

F = {f_{i j}^{k} | i = 1, 2, \dots, m, j = 1, 2, \dots, n, k = 1, 2, \dots, l}

represents the set of completion time

f_{i j}^{k}

for the volunteer

A_{i}

to perform the jobs

C_{k}

in the task

B_{j}

D = {d_{i j}^{k} | i = 1, 2, \dots, m, j = 1, 2, \dots, n, k = 1, 2, \dots, l}

denotes the set of distances

d_{i j}^{k}

between

h_{j}^{k}

and

p_{i j}^{k}

L = {L (p_{i j}^{k}) | i = 1, 2, \dots, m, j = 1, 2, \dots, n, k = 1, 2, \dots, l}

denotes the set of profit and loss values

L (p_{i j}^{k})

p_{i j}^{k}

relative to

h_{j}^{k}

S = {S (p_{i j}^{k}) | i = 1, 2, \dots, m, j = 1, 2, \dots, n, k = 1, 2, \dots, l}

denotes the set of prospect satisfaction values

S (p_{i j}^{k})

of the task leader towards volunteer when the volunteers

A_{i}

perform the jobs

C_{k}

in the task

B_{j}

\bar{S} = {\bar{S} (p_{i j}^{k}) | i = 1, 2, \dots, m, j = 1, 2, \dots, n, k = 1, 2, \dots, l}

denotes the set of prospect satisfaction values

S (p_{i j}^{k})

normalized to

\bar{S} (p_{i j}^{k})

Hypothetical conditions:

1) At the same moment, one job of one task can be performed by only one volunteer.

2) At the same moment, a volunteer can only perform one job of one task.

3) Each job of each task is not allowed to be interrupted once it starts execution.

4) All tasks have the same priority among themselves.

5) Some tasks have sequential constraints on their jobs, while others have no sequential constraints on their jobs.

3 Decision-Making Method

A decision-making optimization method within an emergency volunteer team is proposed for the problem of multi-tasking and multi-operation within the emergency volunteer team. Calculate the satisfaction value of the task leader to each volunteer based on the required time for the job and the expected time that the volunteer can complete the job. A multi-layer coded genetic algorithm is used to construct an optimization model for emergency volunteer decision-making with the objective of maximizing the satisfaction value.

3.1 Solving Satisfaction Value Based on Prospect Theory

Prospect theory, as an integrated theory of psychology and behavioral sciences, can consider the influence of human behavioral and psychological factors in the decision-making process^[48]. As the subject of evaluating the satisfaction value of volunteers, the task leader's evaluation is influenced by behavioral and psychological factors. Therefore, in the problem of multi-tasking and multi-operation within emergency volunteer teams, it is not only of theoretical value but also of practical significance that the satisfaction value is solved by using prospect theory.

Using the required time

h_{j}^{k}

for the job as the reference point and the expected time

p_{i j}^{k}

that volunteers can complete the job as the attribute value. The size between the attribute value and the reference point is compared, and the profit and loss value of the attribute value

p_{i j}^{k}

relative to the reference point

h_{j}^{k}

is obtained by calculating the distance between the attribute value and the reference point. The specific calculation is as follows:

1) The size between the reference point

h_{j}^{k}

and the attribute value

p_{i j}^{k}

can be compared as follows:

\begin{aligned} x (p_{i j}^{k}) & = (p_{i j}^{k l o w} + p_{i j}^{k u p}) / 2, \\ i & = 1, 2, \dots, m, j = 1, 2, \dots, n, k = 1, 2, \dots, l . \end{aligned}

(1)

\begin{aligned} x (h_{j}^{k}) & = (h_{j}^{k l o w} + h_{j}^{k u p}) / 2, \\ j & = 1, 2, \dots, n, k = 1, 2, \dots, l . \end{aligned}

(2)

When

x (p_{i j}^{k}) > x (h_{j}^{k})

p_{i j}^{k} > h_{j}^{k}

. When

x (p_{i j}^{k}) < x (h_{j}^{k})

p_{i j}^{k} < h_{j}^{k}

2) The distance between the reference point

h_{j}^{k}

and the attribute value

p_{i j}^{k}

can be calculated as follows:

\begin{aligned} d_{i j}^{k} = \sqrt{\frac{1}{2} [(p_{i j}^{k l o w} - h_{j}^{k l o w})^{2} + (p_{i j}^{k u p} - h_{j}^{k u p})^{2}]} . \end{aligned}

(3)

3) The profit and loss value of the attribute value

p_{i j}^{k}

relative to the reference point

h_{j}^{k}

can be computed as follows:

\begin{aligned} L (p_{i j}^{k}) & = {\begin{cases} - d_{i j}^{k}, & p_{i j}^{k} \geq h_{j}^{k}, \\ d_{i j}^{k}, & p_{i j}^{k} < h_{j}^{k}, \end{cases} \\ i & = 1, 2, \dots, m, j = 1, 2, \dots, n, k = 1, 2, \dots, l . \end{aligned}

(4)

4) The prospect satisfaction value can be calculated as follows:

\begin{aligned} S (p_{i j}^{k}) & = {\begin{cases} - λ (- L (p_{i j}^{k}))^{β}, & p_{i j}^{k} \geq h_{j}^{k}, \\ L (p_{i j}^{k}))^{α}, & p_{i j}^{k} < h_{j}^{k}, \end{cases} \\ i & = 1, 2, \dots, m, j = 1, 2, \dots, n, k = 1, 2, \dots, l, \end{aligned}

(5)

where

λ = 2.25, α = β = 0.88

5) In order to eliminate the influence of different magnitudes on the calculation results, the prospect satisfaction values

S (p_{i j}^{k})

can be normalized as follows:

\begin{aligned} \bar{S} (p_{i j}^{k}) & = \frac{S (p_{i j}^{k}) - min (S (p_{i j}^{k}))}{max (S (p_{i j}^{k})) - min (S (p_{i j}^{k}))}, \\ i & = 1, 2, \dots, m, j = 1, 2, \dots, n, k = 1, 2, \dots, l . \end{aligned}

(6)

3.2 Constructing Decision-Making Optimization Model

When volunteers perform job

C_{k}

in the task

B_{j}

, the goal is to maximize the prospect satisfaction value of the task leader for each volunteer, so the objective function can be expressed as follows:

\begin{aligned} max {\bar{S} (p_{1 j}^{k}), \bar{S} (p_{2 j}^{k}), \dots, \bar{S} (p_{m j}^{k})}, \\ j = 1, 2, \dots, n, k = 1, 2, \dots, l . \end{aligned}

(7)

The constraints can be represented as follows:

\begin{aligned} f_{i j}^{k} - f_{i j}^{k - 1} \geq t_{i j}^{k}, \\ i = 1, 2, \dots, m, j = 1, 2, \dots, n, k = 1, 2, \dots, l . \end{aligned}

(8)

\begin{aligned} f_{i e}^{g} - f_{i j}^{k} \geq t_{i e}^{g}, \\ i = 1, 2, \dots, m, j = 1, 2, \dots, n, k = 1, 2, \dots, l . \end{aligned}

(9)

\begin{aligned} f_{i j}^{k} \geq t_{i j}^{k}, \\ i = 1, 2, \dots, m, j = 1, 2, \dots, n, k = 1, 2, \dots, l . \end{aligned}

(10)

f_{i j}^{k}

represents the completion time for the volunteer

A_{i}

to perform the jobs

C_{k}

in the task

B_{j}

t_{i j}^{k}

represents actual time for the volunteer

A_{i}

to perform the jobs

C_{k}

in the task

B_{j}

. Eq. (8) indicates that when jobs of the same task have sequential constraints, job

C_{k}

in the task

B_{j}

must be started after job

C_{k - 1}

is completed. Eq. (9) indicates that volunteer

A_{i}

can only start executing job

C_{g}

in the task

B_{e}

after executing job

C_{k}

in the task

B_{j}

. Eq. (10) represents that the completion time of any job cannot be less than its execution time.

3.3 Solving Decision-Making Optimization Model

Genetic algorithms, also known as GA (Genetic Algorithms), were proposed by Professor Holland of the University of Michigan in the United States, as a parallel stochastic search optimization method based on the genetic mechanism of nature and biological evolution^[49]. Generally, the genetic algorithm converts the value of the objective function into the fitness value of the chromosome, and the fitness value of the chromosome in this paper is the maximum prospective satisfaction value of the task leader for each volunteer. The genetic algorithm is an iterative process, each iteration will make the fitness of individuals in the population bigger and bigger, and finally gradually approach the approximate optimal solution of the problem. Therefore, in this paper, genetic algorithm is used to solve the volunteer decision problem.

The main operations of the genetic algorithm include selection, crossover, and mutation. Since these several operations give the genetic algorithm the ability to keep moving towards the goal, however, these operations are probabilistic and as the search progresses more good individuals are generated, gradually approaching the optimal solution of the problem^[49]. In this article, a multilayer coded genetic algorithm is used to solve the volunteer decision problem in the following steps:

1) Individual code

The chromosome coding method adopts integer coding, the coding of this chromosome mainly consists of two parts. The first layer is the order of execution of all tasks, and the second layer is the volunteer serial number corresponding to each job of the task. As shown in Figure 2, this individual expresses the order of execution of two tasks that are both performed twice corresponding to three volunteers. Among them, the first four digits indicate the execution order of tasks, which is task 2

\to

task 1

\to

task 1

\to

task 2 in order. Five to eight digits indicate volunteers, which is volunteer 3

\to

volunteer 1

\to

volunteer 2

\to

volunteer 1 in order.

Figure 2 Chromosome structure

Full size|PPT slide

2) Adaptation value

In this paper, the chromosome adaptation value based on multi-level coding genetic algorithm is the maximum prospect satisfaction value of the task leader for each volunteer. The adaptation value is calculated as follows:

\begin{aligned} f i t & = max {\bar{S} (p_{1 j}^{k}), \bar{S} (p_{2 j}^{k}), \dots, \bar{S} (p_{m j}^{k})}, \\ j & = 1, 2, \dots, n, k = 1, 2, \dots, l . \end{aligned}

(11)

3) Select operation

The selection operation adopts the roulette wheel method (i.e., the proportional method of adaptation), and the selection is made according to the probability of individual adaptation values. The higher the adaptation value, the greater the probability of being selected. The larger the prospect satisfaction value in this paper, the more likely the volunteer is to be selected.

4) Crossover operation

The crossover operation is performed by randomly selecting two chromosomes from the population and then randomly choosing the crossover position for the crossover. The operation is as follows: If the crossover position is 5, the crossover will be performed from the initial position to the crossover position. The schematic diagram of individual exchange crossover is shown in Figure 3.

Figure 3 Schematic diagram of individual exchange and crossover

Full size|PPT slide

5) Mutation operation

The mutation operation was performed by randomly selecting mutant individuals from the population, selecting two positions for each individual and swapping the corresponding volunteer serial numbers, as shown below, with crossover positions 2 and 4. The schematic diagram of individual variation is shown in Figure 4.

Figure 4 Schematic diagram of individual variation

Full size|PPT slide

4 Simulation Analysis

The method proposed in this paper is illustrated by an arithmetic example analysis using a typhoon disaster as an example. Suppose that after a typhoon disaster occurs in a certain place, 10 volunteers of a volunteer team need to complete 8 tasks such as accident rescue, personnel rescue and order maintenance. Among them, task 1 and task 5 go through 7 jobs, task 2, task 6 and task 7 go through 10 jobs, task 3 and task 8 go through 8 jobs and 8 jobs in task 8 are unordered, and task 4 goes through 9 jobs.

The volunteers available for each job are shown in Table 1. The content of the first row and the first column is {2, 3, 4}, indicating that the volunteers available for the first job of task 1 are volunteers 2, 3, and 4. The content of the second row and the second column is 7, indicating that the volunteer available for the second job of task 2 is Volunteer 7. The choice of volunteers varies depending on the occupation, age and gender of the volunteers.

Table 1 Optional volunteers for jobs

	Task 1	Task 2	Task 3	Task 4	Task 5	Task 6	Task 7	Task 8
Job 1	{2, 3, 4}	8	2	{3, 5, 7, 9}	6	9	6	{7, 9}
Job 2	1	7	{2, 4, 7}	8	8	{3, 8}	5	1
Job 3	6	{5, 6}	5	{4, 6}	{2, 4, 9}	{2, 4}	5	1
Job 4	{3, 8}	4	1	3	9	7	{4, 7}	{3, 6}
Job 5	{4, 8}	7	2	2	1	8	{2, 3}	6
Job 6	9	{1, 4}	4	8	{4, 6}	{2, 5, 8}	3	{5, 8}
Job 7	6	{4, 5}	{1, 6}	3	4	9	{3, 7}	{1, 3}
Job 8		4	{2, 5}	{2, 4, 7, 8, 9}		{1, 9}	5	10
Job 9		{2, 6, 9}		{5, 9}		9	{2, 5}
Job 10		{3, 7}				{1, 6}	10

The required time for each job is shown in Table 2. The content of the first row and the first column is [9, 10], indicating that the required time for the first job of task 1 is 9 to 10 hours, where [9, 10] represents the interval. The content of the second row and the second column is [2, 5], indicating that the required time for the second job of task 2 is 2 to 5 hours.

Table 2 Required time for each job

	Task 1	Task 2	Task 3	Task 4	Task 5	Task 6	Task 7	Task 8
Job 1	[9, 10]	[4, 9]	[2, 6]	[3, 5]	[5, 6]	[6, 8]	[7, 9]	[8, 8]
Job 2	[2, 6]	[2, 5]	[5, 9]	[1, 4]	[4, 5]	[5, 6]	[6, 8]	[7, 8]
Job 3	[1, 8]	[8, 9]	[2, 3]	[4, 5]	[5, 7]	[4, 7]	[7, 9]	[2, 4]
Job 4	[5, 6]	[3, 8]	[2, 5]	[3, 4]	[4, 6]	[2, 6]	[7, 7]	[3, 9]
Job 5	[6, 10]	[7, 8]	[4, 6]	[6, 7]	[3, 5]	[3, 5]	[6, 7]	[2, 8]
Job 6	[4, 5]	[1, 9]	[6, 8]	[3, 9]	[6, 7]	[7, 9]	[7, 8]	[8, 9]
Job 7	[3, 6]	[6, 7]	[2, 7]	[3, 8]	[4, 5]	[6, 8]	[5, 7]	[7, 8]
Job 8		[9, 10]	[4, 9]	[5, 6]		[6, 6]	[1, 7]	[7, 9]
Job 9		[2, 3]		[7, 8]		[7, 9]	[6, 8]
Job 10		[6, 7]				[6, 9]	[8, 9]

The expected time for each volunteer is shown in Table 3. The content of the first row and the first column is (9, [1, 10], [2, 9]), which means that the volunteers available for the first job of task 1 are volunteers 2, 3, and 4, and the time to select volunteer 2 is 9 hours, the time to select volunteer 3 is 1 to 10 hours, and the time to select volunteer 4 is 2 to 9 hours. The content of the second row and the second column is [1, 5], indicating that the time available for volunteer 7 in the second job of task 2 is 1 to 5 hours. Due to the influence of volunteers' personality, ability and specialty and other factors, the time for each volunteer to perform the task is different.

Table 3 Expected time for each volunteer to complete the job

	Task 1	Task 2	Task 3	Task 4	Task 5	Task 6	Task 7	Task 8
Job 1	9, [1, 10], [2, 9]	[3, 8]	[2, 3]	[3, 6], [3, 5], [3, 4], [3, 8]	[4, 5]	[5, 7]	[7, 9]	[7, 8], [8, 9]
Job 2	[5, 6]	[1, 5]	[2, 9], [2, 8], [2, 7]	[3, 5]	[3, 5]	[1, 6], [5, 6]	[6, 8]	[2, 7]
Job 3	[3, 9]	[7, 9], [5, 9]	[3, 6]	[3, 4], [3, 8]	5, 6, [4, 5]	[5, 6], [6, 9]	[6, 7]	[1, 8]
Job 4	[4, 9], [3, 10]	[3, 9]	[2, 9]	[3, 6]	[4, 5]	[5, 8]	[5, 7], 7	[5, 8], [7, 8]
Job 5	[3, 4], [3, 7]	[6, 9]	[2, 4]	[3, 8]	[4, 7]	[5, 10]	[5, 7], [6, 7]	[6, 9]
Job 6	[4, 5]	[4, 9], [6, 10]	[1, 8]	[3, 4]	[4, 5], [4, 8]	[6, 7], [5, 8], [5, 9]	[6, 7]	[4, 8], [1, 8]
Job 7	[5, 7]	[4, 10], [1, 8]	[1, 4], [2, 9]	[3, 9]	[4, 6]	[5, 7]	[6, 8], [5, 7]	[7, 8], [3, 8]
Job 8		[3, 9]	[2, 7], [3, 9]	[3, 8], [4, 9], [3, 5], [3, 9], [3, 7]		[5, 6], [3, 8]	[6, 7]	[3, 9]
Job 9		[3, 4], [1, 7], [2, 8]		[3, 6], [3, 10]		[2, 7]	[3, 7], [6, 7]
Job 10		[1, 8], [1, 6]				[5, 8], [1, 6]	[4, 8]

4.1 Solving Process

According to the above Eqs. (1)~(6), the satisfaction values of task leaders for each volunteer were found out, as shown in Table 4. The content of the first row and the first column is {0.17, 0.35, 0.31}, which means that the volunteers available for the first job of task 1 are volunteers 2, 3, and 4, and the satisfaction value for volunteer 2 is 0.17, for volunteer 3 is 0.35, and for volunteer 4 is 0.31. The content of the second row and the second column is 0.26, indicating that the satisfaction value of volunteer 7 for the second job of task 2 is 0.26.

Table 4 Satisfaction values of task leaders to each volunteer

	Task 1	Task 2	Task 3	Task 4	Task 5	Task 6	Task 7	Task 8
Job 1	{0.17, 0.35, 0.31}	0.14	0.21	{0.09, 0.11, 0.15, 0.04}	0.15	0.14	0.11	{0.14, 0.1}
Job 2	0.02	0.26	{0.19, 0.16, 0.14}	0.11	0.18	{0.27, 0.06}	0.07	0.28
Job 3	0.05	{0.15, 0.2}	0.06	{0.16, 0.04}	{0.17, 0.07, 0.18}	{0.07, 0.06}	0.17	0.04
Job 4	{0.04, 0.02}	0.07	0.03	0.07	0.14	0.03	{0.16, 0.09}	{0.05, 0.04}
Job 5	{0.17, 0.23}	0.08	0.2	0.19	0.06	0.02	{0.13, 0.09}	0.04
Job 6	0.11	{0.04, 0.04}	0.25	0.26	{0.2, 0.16}	{0.17, 0.16, 0.17}	0.14	{0.22, 0.31}
Job 7	0.05	{0.05, 0.26}	{0.21, 0.06}	0.06	0.08	0.14	{0.07, 0.09}	{0.1, 0.22}
Job 8		0.28	{0.19, 0.13}	{0.05, 0.04, 0.18, 0.03, 0.17}		{0.13, 0.21}	0.01	0.22
Job 9		{0.09, 0.05, 0.02}		{0.24, 0.24}		0.26	{0.2, 0.12}
Job 10		{0.26, 0.26}				{0.14, 0.28}	0.22

The basic parameters of the algorithm are as follows: The number of populations is 40, the maximum number of iterations is 50, the crossover probability is 0.8, and the variation probability is 0.6.

The changing trend of population fitness values based on prospect theory is shown in Figure 5.

Figure 5 Variation of population fitness values based on prospect theory

Full size|PPT slide

It can be seen from Figure 5: As the number of iterations increases, the envelope of the population fitness values tends to stabilize. After 50 iterations, the fitness value of the population tends to 1.9. The change of population mean tends to be stable in the 12th generation, which indicates that the multilayer coded genetic algorithm can effectively solve the scheduling problem of volunteers and rescue tasks.

The Gantt chart of volunteer decision-making based on prospect theory is shown in Figure 6.

Figure 6 Gantt chart of volunteer decision-making based on prospect theory

Full size|PPT slide

The three digits in Figure 6 represent the decision-making situation of the volunteers, for example, 401 indicates the first job of task 4. The row from top to bottom of the matrix in the figure shows the order in which each volunteer performs the task. For instance, the second row indicates the order in which the 9th volunteer performs the task, and 601 indicates the first job of task 6.

4.2 Comparison and Analysis

In the decision-making process, typical psychological behaviors include disappointment theory and regret theory. The disappointment theory was first proposed by Bell^[33]. The basic idea of disappointment theory is that the decision-maker will compare the actual decision result with the expectation, and when the actual decision result is smaller than the expectation, the decision-maker will feel disappointed. On the contrary, it will feel pleasure. Regret theory was first put forward independently by Bell^[39], Loomes and Sugden^[40], respectively. The basic idea of regret theory is that decision-makers will compare their actual situation with the one they might have been in, and when they find that choosing other alternative options would result in better results, decision-makers will feel regret. Conversely, they will feel happy. The following is a comparative analysis between prospect theory and these two theories.

The changing trend of population fitness values based on disappointment theory is shown in Figure 7.

Figure 7 Variation of population fitness values based on disappointment theory

Full size|PPT slide

It can be seen from Figure 7: As the number of iterations increases, the envelope of the population fitness values tends to stabilize. After 50 iterations, the fitness value of the population tends to 10.1. The change of population mean tends to be stable in the 22nd generation.

The changing trend of population fitness values based on regret theory is shown in Figure 8.

Figure 8 Variation of population fitness values based on regret theory

Full size|PPT slide

It can be seen from Figure 8: As the number of iterations increases, the envelope of the population fitness values tends to stabilize. After 50 iterations, the fitness value of the population tends to 9.9. The change of population mean tends to be stable in the 16th generation.

As can be seen from Figure 5, Figure 7 and Figure 8, the change of population mean based on prospect theory tends to be stable in the 12th generation, the change of population mean based on disappointment theory tends to be stable in the 22nd generation, and the change of population mean based on regret theory tends to be stable in the 16th generation. It shows that the population fitness value based on the prospect theory converges faster, which can optimally solve the decision-making problems within the volunteer team.

The Gantt chart of volunteer decision-making based on disappointment theory is shown in Figure 9.

Figure 9 Gantt chart of volunteer decision-making based on disappointment theory

Full size|PPT slide

The matrix in Figure 9 represents the order in which each volunteer performs the tasks from top to bottom of each row. For example, the third row represents the order in which the 8th volunteer performs the task, and 201 indicates the first job of task 2.

The Gantt chart of volunteer decision-making based on regret theory is shown in Figure 10.

Figure 10 Gantt chart of volunteer decision-making based on regret theory

Full size|PPT slide

The row from top to bottom of the matrix in Figure 10 shows the order in which each volunteer performs the task. For instance, the fifth row stands for the order in which the 6th volunteer performs the task, and 501 indicates the first job of task 5.

5 Conclusions

This paper proposed an approach for the emergency volunteer team to participate in rescue decision-making within the team, considering psychological behavior, in response to the problem of decision-making within the volunteer team and the operational situation where rescue tasks have a time sequence. Considering that task leaders are influenced by behavioral and psychological factors in the evaluation, the required time for the job is used as a reference point, and the expected time that volunteers can complete the job is used as an attribute value. The task leader's prospect satisfaction value for each volunteer is calculated based on prospect theory, and the perceived utility values of disappointment theory and regret theory are calculated to measure the task leader's satisfaction with each volunteer.

The proposed method has several advantages. First, this article studies how to coordinate task dispatch within volunteer teams and proposes an optimization method for multi-task and multi-operation decision-making within emergency volunteer teams. Second, the model was solved by a multilayer coded genetic algorithm, and the feasibility and effectiveness of the method were illustrated by the analysis of arithmetic examples, providing theoretical guidance for the rescue work. Third, it can be seen from Figure 5, Figure 7 and Figure 8 that the population fitness value based on the prospect theory converges faster, which can optimally solve the decision-making problems within the volunteer team.

Although the results obtained in this study are promising and reveal the potential of the proposed emergency volunteer team's internal participation in rescue decision-making, the limitations should be noted. First, the data in this article is hypothetical, not real data. Second, the comparative analysis section did not provide more quantitative results. Finally, the study aims to maximize the satisfaction of the task leader with the volunteers to achieve the decision-making of the volunteer team, without considering the two-way choice between the volunteer team and the rescue task. Therefore, further research is needed in the future.

References

Publishing order | Descend order by publishing year | Descend order by cited within

1	Zhang S W. Research on optimization decision-making of emergency scheduling for rescue teams under large-scale geological disasters. Wuhan: China University of Geosciences, 2018. Cited in this article [1]

2	Zhang Q, Ai X Y. How to build a coordinated mechanism for voluntary service participation in emergency managementin the new era. Chinese Public Administration, 2020, (10): 147- 152. Cited in this article [1]

3	Sampson S E. Optimization of volunteer labor jobs. Journal of Operations Management, 2006, 24 (4): 363- 377. https://doi.org/10.1016/j.jom.2005.05.005 Cited in this article [1]

4	Falasca M, Zobel C. An optimization model for volunteer jobs in humanitarian organizations. Socio-Economic Planning Sciences, 2012, 46 (4): 250- 260. https://doi.org/10.1016/j.seps.2012.07.003 Cited in this article [1]

5	Garcia C, Rabadi G, Handy F. Dynamic resource allocation and coordination for high-load crisis volunteer management. Journal of Humanitarian Logistics and Supply Chain Management, 2018, 8 (4): 533- 556. https://doi.org/10.1108/JHLSCM-02-2018-0019 Cited in this article [1]

6	Lodree E J, Davis L B. Empirical analysis of volunteer convergence following the 2011 tornado disaster in Tuscaloosa, Alabama. Natural Hazards, 2016, 84 (2): 1109- 1135. https://doi.org/10.1007/s11069-016-2477-8 Cited in this article [1]

7	Mayorga M E, Lodree E J, Wolczynski J. The optimal job of spontaneous volunteers. Journal of the Operational Research Society, 2017, 68 (9): 1106- 1116. https://doi.org/10.1057/s41274-017-0219-2 Cited in this article [1]

8	Abualkhair H, Lodree E J, Davis L B. Managing volunteer convergence at disaster relief centers. International Journal of Production Economics, 2020, 220, 107399. https://doi.org/10.1016/j.ijpe.2019.05.018 Cited in this article [1]

9	Paret K E, Mayorga M E, Lodree E J. Assigning spontaneous volunteers to relief efforts under uncertainty in task demand and volunteer availability. Omega, 2021, 99, 102228. https://doi.org/10.1016/j.omega.2020.102228 Cited in this article [1]

10	Li Y, Li Z, Zhang L L. Dispatch model of social forces for disaster relief based on improved simulated annealing algorithm. Journal of Safety Science and Technology, 2021, 17 (2): 27- 33. Cited in this article [1]

11	Gordon L, Erkut E. Improving volunteer scheduling for the Edmonton Folk Festival. Interfaces, 2004, 34 (5): 367- 376. https://doi.org/10.1287/inte.1040.0097 Cited in this article [1]

12	Zayas-Cabán G, Lodree E J, Kaufman D L. Optimal control of parallel queues for managing volunteer convergence. Production and Operations Management, 2020, 29 (10): 2268- 2288. https://doi.org/10.1111/poms.13224 Cited in this article [1]

13	Chen S Q, Zhang L, Shi H L, et al. Two-sided matching model for assigning volunteer teams to relief tasks in the absence of sufficient information. Knowledge-Based Systems, 2021, 232, 107495. https://doi.org/10.1016/j.knosys.2021.107495 Cited in this article [1]

14	Kahneman D, Tversky A. Prospect theory: An analysis of decision under risk. Econometrica, 1979, 47 (2): 263- 291. https://doi.org/10.2307/1914185 Cited in this article [1]

15	Best M J, Grauer R R. Prospect theory and portfolio selection. Journal of Behavioral and Experimental Finance, 2016, 11, 13- 17. https://doi.org/10.1016/j.jbef.2016.05.002 Cited in this article [1]

16	Attema A E, Brouwer W B F, l'Haridon O. Prospect theory in the health domain: A quantitative assessment. Journal of health economics, 2013, 32 (6): 1057- 1065. https://doi.org/10.1016/j.jhealeco.2013.08.006 Cited in this article [1]

17	Attema A E, Brouwer W B F, l'Haridon O, et al. An elicitation of utility for quality of life under prospect theory. Journal of health economics, 2016, 48, 121- 134. https://doi.org/10.1016/j.jhealeco.2016.04.002 Cited in this article [1]

18	Dichtl H, Drobetz W. Portfolio insurance and prospect theory investors: Popularity and optimal design of capital protected financial products. Journal of Banking & Finance, 2011, 35 (7): 1683- 1697. Cited in this article [1]

19	Li X W. Decision-making method of highway network planning based on prospect theory. Procedia-Social and Behavioral Sciences, 2013, 96, 2042- 2050. https://doi.org/10.1016/j.sbspro.2013.08.230 Cited in this article [1]

20	Zhou L, Zhong S, Ma S, et al. Prospect theory based estimation of drivers' risk attitudes in route choice behaviors. Accident Analysis & Prevention, 2014, 73, 1- 11. Cited in this article [1]

21	Fan Z P, Zhang X, Chen F D, et al. Multiple attribute decision making considering aspiration-levels: A method based on prospect theory. Computers & Industrial Engineering, 2013, 65 (2): 341- 350. Cited in this article [1]

22	Wan S P, Zou W C, Dong J Y. Prospect theory based method for heterogeneous group decision making with hybrid truth degrees of alternative comparisons. Computers and Industrial Engineering, 2020, 141, 106285. https://doi.org/10.1016/j.cie.2020.106285

23	Wan S P, Zou W C, Dong J Y, et al. A probabilistic linguistic dominance score method considering individual semantics and psychological behavior of decision makers. Expert Systems with Applications, 2021, 184, 115372. https://doi.org/10.1016/j.eswa.2021.115372

24	Sun G S, Zhang W Y, Dong J Y, et al. Behavioral decision-making of key stakeholders in public-private partnerships: A hybrid method and benefit distribution study. Computer Modeling in Engineering & Sciences, 2023, 136 (3): 2895- 2934. Cited in this article [1]

25	Liu Y, Fan Z P, Zhang Y. Risk decision analysis in emergency response: A method based on cumulative prospect theory. Computers & Operations Research, 2014, 42, 75- 82. Cited in this article [1]

26	Wang L, Zhang Z X, Wang Y M. A prospect theory-based interval dynamic reference point method for emergency decision making. Expert Systems with Applications, 2015, 42 (23): 9379- 9388. https://doi.org/10.1016/j.eswa.2015.07.056 Cited in this article [1]

27	Chen X, Han J, Zhang X. Method for multiple attribute matching decision making considering matching body's psychological aspiration and perception. Control and Decision, 2014, 29 (11): 2027- 2033. Cited in this article [1]

28	Fan Z P, Chen F D, Zhang X. Method for hybrid multiple attribute decision making based on cumulative prospect theory. Journal of Systems Engineering, 2012, 27 (03): 295- 301. Cited in this article [1]

29	Zhang J, Dang Y G, Li X M. Grey multi-criteria risk decision-making method based on prospect theory. Computer Engineering and Applications, 2014, 50 (22): 7- 10. Cited in this article [1]

30	Zhang Z, Kou X Y, Palomares I, et al. Stable two-sided matching decision making with incomplete fuzzy preference relations: A disappointment theory-based approach. Applied Soft Computing, 2019, 84, 105730. https://doi.org/10.1016/j.asoc.2019.105730 Cited in this article [1]

31	Zhang Z, Gao J, Gao Y, et al. Two-sided matching decision making with multi-granular hesitant fuzzy linguistic term sets and incomplete criteria weight information. Expert Systems with Applications, 2021, 168, 114311. https://doi.org/10.1016/j.eswa.2020.114311

Zhang Z, Kou X Y, Yu W Y, et al. Consistency improvement for fuzzy preference relations with self-confidence: An application in two-sided matching decision making. Journal of the Operational Research Society, 2021, 72 (8): 1914- 1927.

https://doi.org/10.1080/01605682.2020.1748529

Cited in this article [1]

33	Bell D E. Disappointment in decision making under uncertainty. Operations Research, 1985, 33 (1): 1- 27. https://doi.org/10.1287/opre.33.1.1 Cited in this article [2]

34	Gul F. A theory of disappointment aversion. Econometrica, 1991, 59 (3): 667686. Cited in this article [1]

35	Grant S, Kajii A. AUSI expected utility: An anticipated utility theory of relative disappointment aversion. Journal of Economic Behavior & Organization, 1998, 37 (3): 277- 290.

36	Delquié P, Cillo A. Expectations, disappointment, and rank-dependent probability weighting. Theory and Decision, 2006, 60, 193- 206. https://doi.org/10.1007/s11238-005-4571-3

37	Delquié P, Cillo A. Disappointment without prior expectation: A unifying perspective on decision under risk. Journal of Risk and Uncertainty, 2006, 33, 197- 215. https://doi.org/10.1007/s11166-006-0499-4

38	Laciana C E, Weber E U. Correcting expected utility for comparisons between alternative outcomes: A unified parameterization of regret and disappointment. Journal of Risk and Uncertainty, 2008, 36, 1- 17. https://doi.org/10.1007/s11166-007-9027-4 Cited in this article [1]

39	Bell D E. Regret in decision making under uncertainty. Operations Research, 1982, 30 (5): 961- 981. https://doi.org/10.1287/opre.30.5.961 Cited in this article [2]

40	Loomes G, Sugden R. Regret theory: An alternative theory of rational choice under uncertainty. The Economic Journal, 1982, 92 (368): 805- 824. https://doi.org/10.2307/2232669 Cited in this article [2]

41	Zeelenberg M. Anticipated regret, expected feedback and behavioral decision making. Journal of Behavioral Decision Making, 1999, 12 (2): 93- 106. https://doi.org/10.1002/(SICI)1099-0771(199906)12:2<93::AID-BDM311>3.0.CO;2-S Cited in this article [1]

42	Humphrey S J. Feedback-conditional regret theory and testing regret-aversion in risky choice. Journal of Economic Psychology, 2004, 25 (6): 839- 857. https://doi.org/10.1016/j.joep.2003.09.004

43	Laciana C E, Weber E U. Correcting expected utility for comparisons between alternative outcomes: A unified parameterization of regret and disappointment. Journal of Risk and Uncertainty, 2008, 36, 1- 17. https://doi.org/10.1007/s11166-007-9027-4

44	Chorus C G. Regret theory-based route choices and traffic equilibria. Transportmetrica, 2012, 8 (4): 291- 305. https://doi.org/10.1080/18128602.2010.498391 Cited in this article [1]

45	Zhang X, Fan Z P, Chen F D. Method for risky multiple attribute decision making based on regret theory. Systems Engineering — Theory & Practice, 2013, 33 (9): 2313- 2320. Cited in this article [1]

46	Lu J. Study on the alternative selection method for emergency response based on regret theory. Shenyang: Northeastern University, 2013. Cited in this article [1]

47	Zhang H. Research on emergency plan selection and adjustment methods considering the behavior of regret and disappointment. Shenyang: Northeastern University, 2014. Cited in this article [1]

48	Zhang L W. Research on the optimization of vehicle routing problem based on prospect theory. Fuzhou: Fuzhou University, 2017. Cited in this article [1]

49	Liu M, Suo L Z. Flow job shop scheduling based on genetic algorithm. The Journal of New Industrialization, 2018, 8 (5): 75- 80. Cited in this article [2]

Funding

Fujian Provincial Social Science Foundation Project(FJ2023B052)

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Abstract
Key words
Cite this article
1 Introduction
2 Description of the Problem
2.1 Problem Formulation
Figure 1 Multi-task and multi-job model within the volunteer team
2.2 Notations
3 Decision-Making Method
3.1 Solving Satisfaction Value Based on Prospect Theory
3.2 Constructing Decision-Making Optimization Model
3.3 Solving Decision-Making Optimization Model
Figure 2 Chromosome structure
Figure 3 Schematic diagram of individual exchange and crossover
Figure 4 Schematic diagram of individual variation
4 Simulation Analysis
Table 1 Optional volunteers for jobs
Table 2 Required time for each job
Table 3 Expected time for each volunteer to complete the job
4.1 Solving Process
Table 4 Satisfaction values of task leaders to each volunteer
Figure 5 Variation of population fitness values based on prospect theory
Figure 6 Gantt chart of volunteer decision-making based on prospect theory
4.2 Comparison and Analysis
Figure 7 Variation of population fitness values based on disappointment theory
Figure 8 Variation of population fitness values based on regret theory
Figure 9 Gantt chart of volunteer decision-making based on disappointment theory
Figure 10 Gantt chart of volunteer decision-making based on regret theory
5 Conclusions
References
Funding

Received	Accepted	Published
2023-05-16	2023-08-28	2024-02-25
Issue Date
2024-02-28

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Abstract

Key words

Cite this article

1 Introduction

2 Description of the Problem

2.1 Problem Formulation

Figure 1 Multi-task and multi-job model within the volunteer team

2.2 Notations

3 Decision-Making Method

3.1 Solving Satisfaction Value Based on Prospect Theory

3.2 Constructing Decision-Making Optimization Model

3.3 Solving Decision-Making Optimization Model

Figure 2 Chromosome structure

Figure 3 Schematic diagram of individual exchange and crossover

Figure 4 Schematic diagram of individual variation

4 Simulation Analysis

Table 1 Optional volunteers for jobs

Table 2 Required time for each job

Table 3 Expected time for each volunteer to complete the job

4.1 Solving Process

Table 4 Satisfaction values of task leaders to each volunteer

Figure 5 Variation of population fitness values based on prospect theory

Figure 6 Gantt chart of volunteer decision-making based on prospect theory

4.2 Comparison and Analysis

Figure 7 Variation of population fitness values based on disappointment theory

Figure 8 Variation of population fitness values based on regret theory

Figure 9 Gantt chart of volunteer decision-making based on disappointment theory

Figure 10 Gantt chart of volunteer decision-making based on regret theory

5 Conclusions

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References

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Abstract

Key words

Cite this article

1 Introduction

2 Description of the Problem

2.1 Problem Formulation

Figure 1 Multi-task and multi-job model within the volunteer team

2.2 Notations

3 Decision-Making Method

3.1 Solving Satisfaction Value Based on Prospect Theory

3.2 Constructing Decision-Making Optimization Model

3.3 Solving Decision-Making Optimization Model

Figure 2 Chromosome structure

Figure 3 Schematic diagram of individual exchange and crossover

Figure 4 Schematic diagram of individual variation

4 Simulation Analysis

Table 1 Optional volunteers for jobs

Table 2 Required time for each job

Table 3 Expected time for each volunteer to complete the job

4.1 Solving Process

Table 4 Satisfaction values of task leaders to each volunteer

Figure 5 Variation of population fitness values based on prospect theory

Figure 6 Gantt chart of volunteer decision-making based on prospect theory

4.2 Comparison and Analysis

Figure 7 Variation of population fitness values based on disappointment theory

Figure 8 Variation of population fitness values based on regret theory

Figure 9 Gantt chart of volunteer decision-making based on disappointment theory

Figure 10 Gantt chart of volunteer decision-making based on regret theory

5 Conclusions

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References

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Footnotes

Funding