Research on Optimization of Medical Waste Emergency Disposal Transportation Network for Public Health Emergencies in the Context of Intelligent Transportation

Abstract

In order to build a more comprehensive emergency disposal and transportation network system for medical waste, it is necessary to consider various uncertain factors and data characteristics. Therefore, in the context of intelligent transportation, this article considers the uncertainty of the quantity and regional population density of infectious medical waste generation as well as the emergency disposal of infectious medical waste under multi-cycle and multi-objective conditions, and it constructs a multi-cycle emergency disposal logistics network optimization model for infectious medical waste under uncertain conditions. Through deterministic transformation of the model and data mining of the medical waste disposal logistics network in Wuhan, China, the multi-objective model under uncertain conditions was also solved and sensitivity analyzed using the MOPSO-NSGA2 intelligent algorithm, verifying the effectiveness and superiority of the algorithm.

1. Introduction

With the application and development of science and technology in transportation systems, intelligent transportation systems have gradually become an effective means to solve transportation problems in sudden public events. Faced with sudden public safety incidents, the question is how to utilize technologies such as cloud computing, big data, mobile internet, artificial intelligence, and related intelligent algorithms to achieve multi-dimensional improvement and all-round innovation in road traffic management, road traffic transportation, traffic information services, and other businesses in order to achieve the optimal state of traffic flow, pedestrian flow, and logistics in the transportation network. This issue will become the direction of the future innovative development of the intelligent transportation industry.

The serious impact of public health emergencies on the economy and society, lives, and property safety has aroused great attention in all countries in the world, which seek to improve the emergency management system of public health emergencies. In recent years, China has made great efforts to improve its medical service and security capacity while investing a lot of money in infrastructure construction. By the end of 2019, health expenditure has exceeded 6 trillion CNY. By the end of 2020, China had more than one million health units, and its bed utilization rate exceeded 84.2% [1]. However, as health indicators have increased, there have been problems. For example, the amount of newly added medical waste keeps rising every year, and after medical supplies are used, due to the differences in uses, contacts, and machines, part of medical waste is still highly harmful, will cause damage to both the human body and the environment, and is thus a large risk factor [2]. If it is not disposed of harmlessly and in time, or if it is mixed with household waste or even illegally reused, this waste will pose a great threat. At the end of 2019, COVID-19 broke out, and it then spread around the world. The spread of the epidemic and the explosive growth of confirmed patients led to a rapid increase in the production of medical waste [3]. The production of medical waste in China has exceeded 3000 t per day since March 2020, and the disposal load of medical waste is far higher than before the epidemic. With the regular development of epidemic prevention and control, the safety problems caused by medical waste disposal have attracted wide attention. In this case, the economic and social significance of studying the emergency disposal of medical waste in public health emergencies is becoming more and more evident.

Due to the impact of the COVID-19 epidemic, the total amount of medical waste that is generated has increased significantly, but there is currently limited research on the emergency disposal of medical waste. Therefore, it is imperative to study the optimization of the transportation network for medical waste disposal in public health emergencies. In summary, in the context of intelligent transportation, this article applies data mining technology and intelligent algorithms to study the optimization plan of the medical waste emergency disposal transportation network in the event of sudden public health events. Based on the research in this article, the effective disposal and transportation of medical waste can maximize the protection of citizens’ health, which is of great significance for ecological protection and stable economic development.

2. Literature Review

Under the influence of the COVID-19 pandemic, domestic and foreign scholars have conducted much research on the emergency disposal of medical waste over the last few years. Maalouf et al. selected Lebanon [4], India [5], Bangladesh [6], Japan [7], China, and other countries in order to evaluate the production of medical waste within a specific period of time. Le et al. [8] used the Likert scale to conduct a questionnaire survey among 742 medical workers to determine the influencing factors related to infection risk. Saeed et al. [9] calculated infection risk by considering multiple factors, such as infection risk probability, the exposure of the surrounding population, and the amount of infectious medical waste. At present, the treatment technologies for medical waste include high-temperature steam, microwave disinfection, chemical disinfection, rotary kiln incineration, pyrolysis incineration, and so on [10]. Yatsunthea et al. [11] investigated a small power plant using medical waste as incineration fuel, and they calculated the disposal cost of medical waste in Thailand based on the example. Zhao et al. [12] quantitatively analyzed the environmental impact and the key factors of three mobile disposal modes, namely, incineration disposal vehicle, mobile steam microwave sterilization equipment, and joint disposal with municipal solid waste, and they believed that the third mode is more favorable to the environment. Govindan et al. [13] established a dual-objective mixed integer linear programming model for medical waste management during the COVID-19 pandemic.

For the emergency handling of public health emergencies, domestic and foreign scholars have constructed single objective or multi-objective models from the perspective of certainty and uncertainty, respectively, in order to optimize logistics network decision-making. From the perspective of certainty, Shadkam et al. [14] built an optimized linear programming model of the medical waste logistics network that has been generated by vaccination with the goal of minimizing costs during the COVID-19 pandemic. He et al. [15] built a three-layer medical waste recycling network with the goal of minimizing the total recovery cost, and they adopted a genetic algorithm, system dynamics, and other methods in order to construct and solve the model. Gao et al. [16] built a transportation route optimization network model with maximum efficiency, adopted the improved greedy ant colony algorithm to solve the problem, and compared the solution with the basic ant colony algorithm, the genetic algorithm, and the particle swarm optimization algorithm to prove the effectiveness of the model. Nathalie et al. [17] took into account the deprivation cost caused by the victims’ inability to obtain emergency supplies in time in an emergency event in order to build a facility location model. From the perspective of uncertainty, Huo et al. [18] built a multi-cycle logistics network model of medical waste under fuzzy environment with minimum economic cost and maximum social benefit. Zhou et al. [19] used the expected value formula of triangular fuzzy number to de-fuzzily fuzzy demand, thereby constructing the site-allocation model of emergency facilities. In addition, some scholars took into account the uncertainty of factors, such as production quantity and demand, and they adopted methods like possibility theory, fuzzy theory, grey set theory, and rough set theory to solve the problem [20,21].

Through the analysis of medical waste management at home and abroad, it can be found that the whole process management is advocated in the management of medical waste at home and abroad, and can finally achieve the purpose of standardized management. However, the current research on medical waste in China is mainly from the perspective of regulatory authorities, production units, or centralized disposal units, and there is scant literature on the medical waste emergency disposal logistics network from an all-round perspective. Therefore, this paper takes public health emergencies as the background, and it considers the uncertainty of the quantity and the population density of infectious medical waste, constructing a multi-agent medical waste emergency disposal logistics network structure and adopting the multi-objective optimization model and an intelligent algorithm in order to solve the problem. The paper thereby obtains research conclusions and policy suggestions on optimizing the medical waste emergency disposal logistics network under public health emergencies.

3. Analysis and Handling Methods of Uncertain Factors

3.1. Analysis of Uncertain Factors

3.1.1. Quantity of Infectious Medical Waste Generated

The spread of the epidemic—i.e., the increase in confirmed and asymptomatic infections—has led to a significant generation of medical waste. However, due to the varying degrees of infection and the varying complications of each patient, it is difficult to determine the amount of medical waste that is generated. The collection time and the quantity of medical waste are also uncertain. The factors that affect the collection of medical waste include the cost of organizing collection, the participation awareness of medical waste generators, the waste classification awareness of designated institutions, and the degree of attention paid to various micro and small medical waste generation points. Due to the diverse environments in which medical waste is generated, the packaging, transportation, and treatment technologies used in the collection process can also greatly affect the quality of medical waste recycling.

3.1.2. Population Density

Population density is an important factor in calculating the risk of infection. The population density in traditional risk models is generally given a certain value based on past experience. However, there is significant uncertainty in population density itself. On the one hand, accurate statistics of population density are difficult, and on the other hand, high population mobility leads to dynamic changes in population density. The uncertainty of population density can affect the accuracy of infectious risk assessment.

3.2. Methods for Handling Uncertain Factors

According to the generation mechanism of uncertain factors, most people use the theories of fuzzy numbers, interval numbers, or random numbers to deal with uncertain factors. When studying the uncertainty of the medical waste emergency disposal logistics network in this section, we consider setting the uncertain parameters in the model as fuzzy numbers. Commonly used fuzzy variables include equipotential fuzzy variables, triangular fuzzy variables, trapezoidal fuzzy variables, exponential distribution, and normal distribution fuzzy variables. Triangular fuzzy numbers have the advantages of being intuitive and easy to understand, and they can well express the fuzzy states of decision-makers in emergency situations when they are pessimistic, normal, and optimistic about the estimated values.

For the triangular fuzzy number $\overline{D}=\left(d_1,d_2,d_3\right)$ and satisfies $d_1⩽d_2⩽d_3$, the expression for ${\mu }_{\overline{D}}(x)$ is:

$${\mu }_{\overline{D}}(x)=\{\begin{array}{cc}0,& x<d_1\\ \frac{x-d_1}{d_2-d_1},& d_1<x⩽d_2\\ \frac{d_3-x}{d_3-d_2},& d_2<x⩽d_3\\ 0,& x⩾d_3\end{array}$$

(1)

The left function satisfied when the membership function $\mu \frac{L}{D}\left(x\right)=\frac{x-d_1}{d_2-d_1}$ is $x\in (d_1,d_2)$, and the right function satisfied when the membership function $\mu \frac{R}{D}(x)=\frac{d_3-x}{d_3-d_2}$ is $x\in (d_2,d_3)$, as shown in Figure 1.

To effectively avoid the influence of fuzzy uncertain parameters, the Fuzzy Chance Constrained Programming (FCCP) method should be adopted.

This paper considers minimizing both the economic cost and the infectious risk of medical waste during emergency disposal. Therefore, for the minimization problem, using probability as a measure, $Pos\{\cdot \}$ represents the probability of time occurrence in $\{\cdot \}$, which is generally expressed as:

$$s.t.\hspace{1em}\begin{array}{l}\min \overline{f}\hfill \\ Pos\{f(x,\xi )\le f\}\ge \alpha \hfill \\ Pos\{g,(x,\xi )\le 0,i=1,2,\cdots ,q\}\ge \beta \hfill \end{array}$$

(2)

Among them, $\alpha$ and $\beta$ are the confidence levels predetermined by the decision-maker, $\alpha ,\beta \in (0,1)$. $i$ represent the i-th constraint condition in the planning model, $x$ represents the decision variable, and $\xi$ represents the fuzzy variable.

4. Multi-Objective Optimization Model under Uncertain Conditions

Each medical waste generation point within a given research area will generate a certain amount of infectious medical waste (IMW) per day. Infectious medical waste generation points (IMWGN) are concentrated in sealed packaging garbage bags and turnover boxes to specialized temporary storage points, which are then transported by special transfer vehicles to the Infectious Medical Waste Treatment Center (IMWTC). IMW will produce slag, fly ash, adsorbed dioxins, and other residues after being incinerated in a rotary kiln. According to regulations, slag can be transported to designated domestic waste sanitary landfills (DWSL) after treatment, while fly ash, adsorbed dioxins, and other residues need to be transported to specialized hazardous waste landfills (HWL) for treatment.

In order to cope with the large amount of medical waste generated in a short period of time, on the one hand, the processing efficiency and capacity of IMWTC can be improved through technological upgrading, and, on the other hand, the original noninfectious medical waste treatment center (NMWTC) that also uses rotary kiln incineration technology can be technically transformed in order to have the ability to handle IMW and to obtain a temporary license for operation. If processing capacity is not increased in a timely manner, it will lead to a large amount of IMW piling up in temporary storage points of IMWTC, resulting in storage costs and accompanied by certain infectious risks. Therefore, in this paper, the uncertainty of the quantity of infectious medical waste production and regional population density as well as the emergency disposal of infectious medical waste under the conditions of multi-cycle and multi-objective were considered, and the multi-cycle emergency disposal logistics network optimization model of infectious medical waste under uncertain conditions was constructed.

4.1. Model Assumptions

The model in this paper is based on the following assumptions: (1) All IMW transported from the production center to the processing center will be processed. (2) Special medical waste transfer trucks are used for transport, but there is still a certain risk of infection and spread. (3) There is a linear relationship between road transportation cost and distance and IMW quantity, and transport risk is linear with distance, population exposure, and IMW number. (4) All of the treatment facilities and landfills have certain fixed operating costs once they are put into use, and technical upgrading or technological transformation will not change the fixed operating costs. Moreover, both treatment centers and landfills have processing capacity limitations and capacity limitations. (5) IMWTC can improve its processing capacity through technology upgrading, but it has a certain cost, and NMWTC can process IMW after technical transformation and obtain the temporary license certificate to deal with IMW. (6) If the number of IMW transported to the processing center exceeds the processing capacity of the processing center, temporary storage is required, which will incur temporary storage cost and infectivity risk. (7) Residue, fly ash, adsorbed dioxins, and other residues from IMW treated by the treatment center do not contain infectious substances. (8) IMW must be processed by the treatment center before it can be transported to a landfill site for burial. (9) The locations of all of the points in the disposal network are known.

4.2. Model Construction

4.2.1. Symbol Description

$$G=\left\{i|i=1,2,\cdots ,I\right\} \mathrm{represents} \mathrm{all} \mathrm{IMWGN}.$$

$$T=\left\{j|j=1,2,\cdots ,J\right\} \mathrm{represents} \mathrm{all} \mathrm{IMWTC}.$$

$$N=\left\{m|m=1,2,\cdots ,M\right\} \mathrm{represents} \mathrm{all} \mathrm{NMWTC}.$$

$$D=\left\{p|p=1,2,\cdots ,P\right\} \mathrm{represents} \mathrm{all} \mathrm{DWSL}.$$

$$H=\left\{k|k=1,2,\cdots ,K\right\} \mathrm{represents} \mathrm{all} \mathrm{HWL}.$$

4.2.2. Parameters Description

$w_i$ represents the number of IMWs generated in $i$.

$uncc$ represents the unit collection cost of IMW in $i$.

$untc$ represents the unit shipping cost of IMW.

$Tunp{c}_j, Nunp{c}_m$ represent the unit processing cost of IMW at $j, m$.

$Tuns{c}_j, Nuns{c}_m$ represent the unit temporary storage cost of IMW at $j, m$.

$Dul{c}_p, Hul{c}_k$ represent the unit landfill cost at $p$ and the unit landfill cost at $k$ for the slag and hazardous waste, respectively, which is generated by the treatment of IMW.

$suntc, fautc$ represent the unit transportation cost of handling slag and hazardous waste generated by IMW, respectively.

$Tfo{c}_j, Nfo{c}_m, Dfo{c}_p, Hfo{c}_k$ represent the fixed operating cost of $j, m, p, k$.

${et{c}^{\prime }}_j, {nt{c}^{\prime }}_m$ represent the cost of technology upgrade and technological transformation for $j, m$, respectively.

$td$ represents transportation distance.

$p{w}_j$ represents the number of IMW in $j$ that are not upgraded.

$\tilde{p}t{w}_j$ represents the number of IMW that $j$ upgrades to increase.

$\tilde{n}p{w}_m$ represents the number of IMW processed by $m$ after technical modification.

$\dot{T}p{c}_j, \dot{N}p{c}_m, \dot{D}p{c}_p, \dot{H}p{c}_k$ represent the processing capability and capacity limit of $j, m, p, k$.

$\tilde{t}jp{c}_j$ indicates the improved processing capability of $j$ after the technology upgrade.

$\eta , \theta$ represent the unit coefficient of slag and hazardous waste generated by IMW;

$no{b}_i$ represents the number of beds owned by $i$.

${\phi }_i$ represents bed utilization rates of $i$.

$bimwgc$ represents the coefficient of IMW production.

$cir, tir$ represent the probability of infection risk occurring during collection and transport, respectively.

$Tsi{r}_j, Nsi{r}_m, Tpi{r}_j, Npi{r}_m$ represent the probability of infection risk occurring during the temporary storage and handling of $j, m$.

$cpe, tpe$ represent population exposure during collection and transportation, respectively.

$Tsi{r}_j, Nsp{e}_m, Tpp{e}_j, Npp{e}_m$ represent human exposure during the temporary storage and handling in $j, m$;

$cer, ter$ represent the effect radius of infection during collection and transportation, respectively.

$Tse{r}_j, Nse{r}_m, Tpe{r}_j, Npe{r}_m$ represent the effect radius of infection during temporary storage and handling of $j, m$.

$cpd, tpd$ represent the population density during collection and transportation, respectively.

$Tsp{d}_j, Nsp{d}_m,Tpp{d}_j, Npp{d}_m$ represent the population density during temporary storage and processing of $j, m$.

$Cfo, Cc, Cp, Cl, Ct, Ctu, Ctt, Cts$, respectively, represent the fixed operation cost, collection cost, processing cost, landfill cost, transportation cost, technology upgrade cost, technology transformation cost, and temporary storage cost in IMW disposal network.

$Rc, Rp, Rt, Rts$, respectively, represent the collection risk, processing risk, transportation risk, and temporary storage risk in IMW disposal network.

$C, R$ represent the total economic cost and total infectious risk of IMW disposal network, respectively.

4.2.3. Decision Variables

$$\tilde{e}t{t}_j=\{\begin{array}{l}1, \mathrm{Upgrade} \mathrm{j} \mathrm{technology}\hfill \\ 0, \mathrm{Otherwise} \hfill \end{array}$$

$$\tilde{n}t{t}_m=\{\begin{array}{l}1, \mathrm{Upgrade} \mathrm{m} \mathrm{technology}\hfill \\ 0, \mathrm{Otherwise} \hfill \end{array}$$

$$\widehat{p}t{t}_j=\{\begin{array}{ll}1,& \mathrm{The} \mathrm{number} \mathrm{of} \mathrm{IMW} \mathrm{shipped} \mathrm{to} \mathrm{the} \mathrm{disposal} \mathrm{center} \mathrm{is} \mathrm{greater} \\ & \mathrm{than} \mathrm{their} \mathrm{disposal} \mathrm{capacity} \mathrm{resulting} \mathrm{in} \mathrm{temporary} \mathrm{storage} \mathrm{costs}\\ 0,\hfill & \mathrm{Otherwise}\hfill \end{array}$$

$$\widehat{p}r{c}_j=\{\begin{array}{cc}1,\hfill & \mathrm{Temporary} \mathrm{storage} \mathrm{risk} \mathrm{caused} \mathrm{by} \mathrm{the} \mathrm{quantity} \mathrm{of} \mathrm{IMW} \mathrm{transported} \hfill \\ & \mathrm{to} \mathrm{the} \mathrm{disposal} \mathrm{center} \mathrm{j} \mathrm{exceeding} \mathrm{its} \mathrm{disposal} \mathrm{capacity}\hfill \\ 0,\hfill & \mathrm{Otherwise}\hfill \end{array}$$

$$\widehat{p}r{c}_j=\{\begin{array}{cc}1,\hfill & \mathrm{Temporary} \mathrm{storage} \mathrm{risk} \mathrm{caused} \mathrm{by} \mathrm{the} \mathrm{quantity} \mathrm{of} \mathrm{IMW} \mathrm{transported} \hfill \\ & \mathrm{to} \mathrm{the} \mathrm{disposal} \mathrm{center} \mathrm{j} \mathrm{exceeding} \mathrm{its} \mathrm{disposal} \mathrm{capacity}\hfill \\ 0,\hfill & \mathrm{Otherwise}\hfill \end{array}$$

$$\widehat{p}c{c}_m=\{\begin{array}{cc}1,\hfill & \mathrm{The} \mathrm{temporary} \mathrm{storage} \cos \mathrm{t} \mathrm{incurred} \mathrm{due} \mathrm{to} \mathrm{the} \mathrm{quantity} \mathrm{of} \mathrm{IMW}\hfill \\ & \mathrm{transported} \mathrm{to} \mathrm{the} \mathrm{disposal} \mathrm{center} \mathrm{m} \mathrm{exceeding} \mathrm{its} \mathrm{disposal} \mathrm{capacity}\hfill \\ 0,\hfill & \mathrm{Otherwise}\hfill \end{array}$$

$$\widehat{p}r{c}_m=\{\begin{array}{cc}1,\hfill & \mathrm{Temporary} \mathrm{storage} \mathrm{risk} \mathrm{caused} \mathrm{by} \mathrm{the} \mathrm{quantity} \mathrm{of} \mathrm{IMW} \mathrm{transported}\hfill \\ & \mathrm{to} \mathrm{the} \mathrm{disposal} \mathrm{center} \mathrm{m} \mathrm{exceeding} \mathrm{its} \mathrm{disposal} \mathrm{capacity}\hfill \\ 0,\hfill & \mathrm{Otherwise}\hfill \end{array}$$

4.2.4. Economic Cost

The economic cost involved in the multi-cycle disposal logistics network of infectious medical waste mainly includes the fixed operating cost $Cf{o}_t$, the collection cost $C{c}_t$, the treatment cost $C{p}_t$, the landfill cost $C{l}_t$, the transportation cost $C{t}_t$, the technology upgrade cost $Ct{u}_t$, the technical transformation cost $Ct{t}_t$ and the temporary storage cost $Ct{s}_t$:

$$\min C_t=\min (Cf{o}_t+C{c}_t+C{p}_t+C{l}_t+C{t}_t+Ct{u}_t+Ct{t}_t+Ct{s}_t)$$

(3)

where fixed operating cost $Cf{o}_t$ is expressed as:

$$Cf{o}_t={\displaystyle \sum _j{\displaystyle \sum _{t}T}}fo{c}_{jt}+{\displaystyle \sum _m{\displaystyle \sum _{t}N}}fo{c}_{m_t}\cdot \tilde{n}t{t}_{mt}+{\displaystyle \sum _p{\displaystyle \sum _{t}D}}fo{c}_{pt}+{\displaystyle \sum _k{\displaystyle \sum _{t}H}}fo{c}_{kt}$$

(4)

where collection cost $C{c}_t$ is expressed as:

$$Cc={\displaystyle \sum _i{\displaystyle \sum _t{w}_{it}}}\cdot uncc$$

(5)

where treatment cost $C{p}_t$ is expressed as:

$$C_{P_t}={\displaystyle \sum _j{\displaystyle \sum _t^{}Tun}}p{c}_j\cdot (p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \tilde{p}t{w}_{jt})+{\displaystyle \sum _m{\displaystyle \sum _{t}Nun}}p{c}_m\cdot \tilde{n}t{t}_{mt}\cdot \tilde{n}p{w}_{mt}$$

(6)

where landfill cost $C{l}_t$ is expressed as:

$$C{l}_t={\displaystyle \sum _i{w}_i}\cdot (\eta \cdot {\displaystyle \sum _{p}D}ul{c}_p+\theta \cdot {\displaystyle \sum _{k}H}ul{c}_k)$$

(7)

where transportation cost $C{t}_t$ is expressed as:

$$\begin{array}{ll}C{t}_t=& {\displaystyle \sum _j{\displaystyle \sum _t\left(p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \tilde{p}t{w}_{jt}\right)}}\cdot \left({\displaystyle \sum _{i}u}ntc\cdot t{d}_{jit}+\eta \cdot {\displaystyle \sum _{p}s}untc\cdot t{d}_{jpt}+\theta \cdot {\displaystyle \sum _{k}f}autc\cdot t{d}_{jkt}\right)+\\ & {\displaystyle \sum _m{\displaystyle \sum _t\tilde{n}}}t{t}_m\cdot \tilde{n}p{w}_m\cdot \left({\displaystyle \sum _{i}u}ntc\cdot t{d}_{imt}+\eta \cdot {\displaystyle \sum _{p}s}untc\cdot t{d}_{mpt}+\theta \cdot {\displaystyle \sum _{k}f}autc\cdot t{d}_{mkt}\right)\end{array}$$

(8)

where technology upgrade cost $Ct{u}_t$ is expressed as:

$$Ct{u}_t={\displaystyle \sum _j{\displaystyle \sum _i\tilde{e}t{t}_{jt}}}\cdot et{c}_j^{\prime }$$

(9)

where technical transformation cost $Ct{t}_t$ is expressed as:

$$Ct{t}_t={\displaystyle \sum _m{\displaystyle \sum _t\tilde{n}}}t{t}_{mt}\cdot nt{c}_m^{\prime }$$

(10)

where temporary storage cost $Ct{s}_t$ is expressed as:

$$\begin{array}{ll}Ct{s}_t=& \left({\displaystyle \sum _j{\displaystyle \sum _{t}T}}uns{c}_j\cdot \widehat{p}c{c}_{jt}\cdot \left(p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \tilde{p}t{w}_{jt}-\dot{T}p{c}_{{}_j}-\tilde{e}t{t}_{jt}\cdot \tilde{t}jp{c}_j\right)\right)\\ & +\left({\displaystyle \sum _m{\displaystyle \sum _{t}N}}uns{c}_m\cdot \widehat{p}c{c}_{mt}\cdot \tilde{n}t{t}_{mt}\cdot \left(\tilde{n}p{w}_{wt}-\dot{N}p{c}_m\right)\right)\end{array}$$

(11)

4.2.5. Infection Risk

The infectious risks involved in the multi-cycle disposal logistics network of infectious medical waste mainly include the collection risk $R{c}_t$, the treatment risk $R{p}_t$, the transportation risk $R{t}_t$ and the temporary storage risk $Rt{s}_t$:

$$min{R}_t=\min (R{c}_t+R{p}_t+R{t}_t+Rt{s}_t)$$

(12)

where collection risk $R{c}_t$ is expressed as:

$$R{c}_t=\sum _i\sum _t{w}_{it}\cdot cir\cdot cpe$$

(13)

where treatment risk $R{p}_t$ is expressed as:

$$R{p}_t={\displaystyle \sum _j{\displaystyle \sum _t(p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \tilde{p}t{w}_{jt})}}\cdot Tpi{r}_j\cdot Tpp{e}_j+{\displaystyle \sum _m{\displaystyle \sum _t\tilde{n}t{t}_{mt}}}\cdot \tilde{n}p{w}_{wt}\cdot Npi{r}_{mt}\cdot Np{p}_m$$

(14)

where transportation risk $R{t}_t$ is expressed as:

$$R{t}_t={\displaystyle \sum _{i}t}ir\cdot tpe\cdot ({\displaystyle \sum _j{\displaystyle \sum _{t}t}}{d}_{ijt}\cdot (p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \tilde{p}t{w}_{jt})+{\displaystyle \sum _m{\displaystyle \sum _{t}t}}{d}_{imt}\cdot \tilde{n}t{t}_{mt}\cdot \tilde{n}p{w}_{mt})$$

(15)

where temporary storage risk $Rt{s}_t$ is expressed as:

$$\begin{array}{ll}Rt{s}_t& =({\displaystyle \sum _j{\displaystyle \sum _{t}T}}si{r}_j\cdot Tsp{e}_j\cdot \widehat{p}r{c}_{jt}\cdot (p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \tilde{p}t{w}_{jt}-\dot{T}p{c}_j-\tilde{e}t{t}_{jt}\cdot \tilde{t}jp{c}_j))\\ & +({\displaystyle \sum _m{\displaystyle \sum _{t}N}}si{r}_m\cdot Nsp{e}_m\cdot \widehat{p}r{c}_{mt}\cdot (\tilde{n}p{w}_{mt}-\dot{N}p{c}_m))\end{array}$$

(16)

4.2.6. Constraints

$${\displaystyle \sum _i{\displaystyle \sum _t{w}_{it}}}={\displaystyle \sum _j{\displaystyle \sum _t(p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \widehat{p}t{w}_{jt})}}+{\displaystyle \sum _m{\displaystyle \sum _t\tilde{n}}}t{t}_{mt}\cdot \tilde{n}p{w}_{mt} \forall i\in G,j\in T,m\in N$$

(17)

$${\displaystyle \sum _j{\displaystyle \sum _m\eta }}\cdot (p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \tilde{p}t{w}_{jt}+\tilde{n}t{t}_{mt}\cdot \tilde{n}p{w}_{mt})\le {\displaystyle \sum _p\dot{D}}p{c}_p \forall j\in T,m\in N,p\in D$$

(18)

$${\displaystyle \sum _j{\displaystyle \sum _m\theta }}\cdot (p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \tilde{p}t{w}_{jt}+\tilde{n}{t}_{mt}\cdot \tilde{n}p{w}_{mt})\le {\displaystyle \sum _k\dot{H}}p{c}_p \forall j\in T,m\in N,k\in H$$

(19)

$${\displaystyle \sum _i{\displaystyle \sum _t{w}_{it}}}={\displaystyle \sum _i{\displaystyle \sum _t{\phi }_{it}}}\cdot no{b}_{it}\cdot bimwgc \forall i\in G$$

(20)

$$cpe={(cer)}^2\cdot \pi \cdot cpd$$

(21)

$$tpe=2\cdot ter\cdot td\cdot tpd$$

(22)

$$Tsp{e}_j={(Tse{r}_j)}^2\cdot \pi \cdot Tsp{d}_j \forall j\in T$$

(23)

$$Nsp{e}_m={(Nse{r}_m)}^2\cdot \pi \cdot Nsp{d}_m \forall m\in N$$

(24)

$$Tpp{e}_j={(Tpe{r}_j)}^2\cdot \pi \cdot Tpp{d}_j \forall j\in T$$

(25)

$$Npp{e}_m={(Npe{r}_m)}^2\cdot \pi \cdot Npp{d}_m \forall m\in N$$

(26)

$$\tilde{e}t{t}_{jt},\tilde{n}t{t}_{mt},\widehat{p}c{c}_{jt},\widehat{p}r{c}_{jt},\widehat{p}c{c}_{mt},\widehat{p}r{c}_{mt}\in \left[0,1\right] \forall j\in T,m\in N$$

(27)

$$w_{it},p{w}_{jt},\tilde{p}t{w}_{jt},\tilde{n}p{w}_{mt}\ge 0 \forall i\in G,j\in T,m\in N$$

(28)

Equation (17) represents the flow equilibrium constraint of the objective function. All of the IMWs that are generated at the production point will be transported to the treatment center for incineration. Equations (18) and (19) represent capacity constraints. None of the incinerated waste in a landfill shall exceed the capacity limit of the facility. Equation (20) shows that the number of IMWs generated is equal to the number of beds at the generating point, the bed utilization rate, and the bed IMW generation coefficient. Equations (21), (22), (23), (24), (25), and (26), respectively, represent population exposure during collection, transportation, temporary storage, and processing. Equations (27) and (28) represent decision variable constraints.

4.3. Deterministic Transformation

Due to the randomness and uncertainty of the quantity of infectious medical waste generated and the regional population density, the model constructed in this paper is a fuzzy mathematical model, and it therefore requires deterministic transformation. The specific idea is to use the opportunity constrained programming transformation method in order to determine the model, and then to use the theory of deterministic programming to solve the model. Using triangular fuzzy numbers to handle uncertain factors, the determined model can be obtained as follows:

$$\begin{array}{l}\min C_t\ge {\displaystyle \sum _j{\displaystyle \sum _{t}Tfo{c}_{jt}}}+{\displaystyle \sum _m{\displaystyle \sum _{t}Nfo{c}_{mt}}}\cdot \tilde{n}t{t}_{mt}+{\displaystyle \sum _p{\displaystyle \sum _{t}D}fo{c}_{pt}}+{\displaystyle \sum _k{\displaystyle \sum _{t}Hfo{c}_{kt}}}\\ +{\displaystyle \sum _i{\displaystyle \sum _t((}}1-\alpha )\cdot w_{it}^L+\alpha \cdot w_{it}^M)\cdot uncc+{\displaystyle \sum _j{\displaystyle \sum _t\tilde{e}}}t{t}_j\cdot et{c}_j^{\prime }+{\displaystyle \sum _m{\displaystyle \sum _t\tilde{n}}}t{t}_{mt}\cdot nt{c}_m^{\prime }\\ +{\displaystyle \sum _i((}1-\alpha )\cdot w_{it}^L+\alpha \cdot w_{it}^M)\cdot (\eta \cdot {\displaystyle \sum _{p}D}ul{c}_p+\theta \cdot {\displaystyle \sum _{k}H}ul{c}_k)\\ +{\displaystyle \sum _j{\displaystyle \sum _t(p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \tilde{p}t{w}_{jt})}}\cdot ({\displaystyle \sum _{i}u}ntc\cdot t{d}_{ijt}+\eta \cdot {\displaystyle \sum _{p}s}untc\cdot t{d}_{jpt}+\theta \cdot {\displaystyle \sum _{k}fautc}\cdot t{d}_{jkt})\\ +{\displaystyle \sum _m{\displaystyle \sum _t\tilde{n}}}t{t}_m\cdot \tilde{n}p{w}_m\cdot ({\displaystyle \sum _{i}u}ntc\cdot t{d}_{imt}+\eta \cdot {\displaystyle \sum _{p}s}untc\cdot t{d}_{mpt}+\theta \cdot {\displaystyle \sum _{k}fau}tc\cdot t{d}_{mkt})\\ +({\displaystyle \sum _j{\displaystyle \sum _{t}T}}uns{c}_j\cdot \widehat{p}c{c}_j\cdot (p{w}_{jt}+\widehat{e}t{t}_{jt}\cdot \tilde{p}t{w}_{jt}-\dot{T}p{c}_j-\tilde{e}t{t}_{jt}\cdot \tilde{t}jp{c}_j))\\ +({\displaystyle \sum _m{\displaystyle \sum _{t}N}}uns{c}_m\cdot \widehat{p}c{c}_{mt}\cdot \tilde{n}t{t}_m\cdot (\tilde{n}p{w}_{mt}-\dot{N}p{c}_m))\end{array}$$

(29)

$$\begin{array}{l}\min R_t\ge {\displaystyle \sum _i{\displaystyle \sum _t((}}1-\alpha )\cdot w_{it}^L+\alpha \cdot w_{it}^M)\cdot cir\cdot cpe\\ +{\displaystyle \sum _j{\displaystyle \sum _t(p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \widehat{p}t{w}_{jt})}}\cdot Tpi{r}_j\cdot Tpp{e}_j+{\displaystyle \sum _m{\displaystyle \sum _t\tilde{n}}}t{t}_{mt}\cdot \tilde{n}p{w}_{mt}\cdot Npi{r}_m\cdot Npp{e}_m\\ +{\displaystyle \sum _{i}t}ir\cdot tpe\cdot ({\displaystyle \sum _j{\displaystyle \sum _{t}t}}{d}_{ijt}\cdot (p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \widehat{p}t{w}_{jt})+{\displaystyle \sum _m{\displaystyle \sum _{t}t}}{d}_{imt}\cdot \tilde{n}t{t}_{mt}\cdot \tilde{n}p{w}_{mt})\\ ({\displaystyle \sum _j{\displaystyle \sum _{t}Ti}}s{r}_j\cdot Tsp{e}_j\cdot \widehat{p}r{c}_{jt}\cdot (p{w}_{jt}+\tilde{e}t{t}_j\cdot \tilde{p}t{w}_{jt}-\dot{T}p{c}_j-\tilde{e}t{t}_{jt}\cdot \tilde{t}jp{c}_j))\\ +({\displaystyle \sum _m{\displaystyle \sum _{t}Nsi{r}_m}}\cdot Nsp{e}_m\cdot \widehat{p}r{c}_{mt}\cdot (\tilde{n}p{w}_{mt}-\dot{N}p{c}_m))\end{array}$$

(30)

$${\displaystyle \sum _i{\displaystyle \sum _t(1-\alpha )}}\cdot w_{it}^L+\alpha \cdot w_{it}^M)\ge {\displaystyle \sum _j{\displaystyle \sum _t(p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \tilde{p}t{w}_{jt})}}+{\displaystyle \sum {\displaystyle \sum _m\tilde{n}t}}{t}_{mt}\cdot \tilde{p}{w}_{mt} \forall i\in G,j\in T,m\in N$$

(31)

$${\displaystyle \sum _j{\displaystyle \sum _m\eta }}\cdot (p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \tilde{p}t{w}_{jt}+\tilde{n}t{t}_{mt}\cdot \tilde{n}p{w}_{mt})\le {\displaystyle \sum _p\dot{D}}p{c}_p \forall j\in T,m\in N,p\in D$$

(32)

$${\displaystyle \sum _j{\displaystyle \sum _m\theta }}\cdot (p{w}_{jt}+\tilde{e}t{t}_{jt}\cdot \tilde{p}t{w}_{jt}+\tilde{n}t{t}_{mt}\cdot \tilde{n}p{w}_{mt})\le {\displaystyle \sum _k\dot{H}}p{c}_p \forall j\in T,m\in N,k\in H$$

(33)

$${\displaystyle \sum _i{\displaystyle \sum _t((}}1-\alpha )\cdot w_{it}^L+\alpha \cdot w_{it}^M)\ge {\displaystyle \sum _i{\displaystyle \sum _t{\phi }_t}}\cdot no{b}_{it}\cdot bimwgc \forall i\in G$$

(34)

$$cpe={(cer)}^2\cdot \pi \cdot ((1-\beta )\cdot cp{d}^R+\beta \cdot cp{d}^M)$$

(35)

$$tpe=2\cdot ter\cdot td\cdot ((1-\beta )\cdot tp{d}^R+\beta \cdot tp{d}^M)$$

(36)

$$Tsp{e}_j={(Tse{r}_j)}^2\cdot \pi \cdot ((1-\beta )\cdot Tsp{d}_j^R+\beta \cdot Tsp{d}_j^M) \forall j\in T$$

(37)

$$Nsp{e}_m={(Nse{r}_m)}^2\cdot \pi \cdot ((1-\beta )\cdot Nsp{d}_m^R+\beta \cdot Nsp{d}_m^M) \forall m\in N$$

(38)

$$Tpp{e}_j={(Tpe{r}_j)}^2\cdot \pi \cdot ((1-\beta )\cdot Tpp{d}_j^R+\beta \cdot Tpp{d}_j^M) \forall j\in T$$

(39)

$$Npp{e}_m={(Npe{r}_m)}^2\cdot \pi \cdot ((1-\beta )\cdot Npp{d}_m^R+\beta \cdot Npp{d}_m^M) \forall m\in N$$

(40)

4.4. Algorithm Design

In the study of logistics network optimization, a non-dominant genetic algorithm (NSGA2) with elite strategy in multi-objective evolutionary algorithm (MOEA) is often used. Based on NSGA, a fast non-dominant sorting method is proposed to reduce the complexity of the algorithm. At the same time, an elite strategy is introduced in order to select the top-ranked individuals after the merging of parent-child populations as the new populations. However, the NSGA2 algorithm has the characteristic of a slow search speed, so this paper introduces the particle swarm optimization algorithm with fast computing speed in order to combine the two algorithms and for them to complement each other. The mixture of these two algorithms can make up for the shortcomings of both while preserving their respective advantages, and this is more conducive to the overall optimization effect of the emergency disposal logistics optimization network. The specific process of the improved hybrid algorithm MOPSO-NSGA2 is shown in Figure 2.

The basic steps of the NSGA2 MOPSO hybrid algorithm are as follows:

Step 1: Initialize particles

Initialize the speed and position of all of the particles. Calculate the objective function of all of the particles and store the non-inferior solutions in an external archive to form a Pareto solution set.

Step 2: Determine individual and group optima

Due to the initialization process, the individual optimization of each particle is its own. The optimal selection method for the group is to use dense distance sorting, and for convenience during initialization selection, it can also be randomly selected from the Pareto solution set.

Step 3: Update inertia weights

Inertia weight is an important parameter of the particle swarm optimization algorithm, which is related to the algorithm’s local and global search capabilities. At each iteration, the inertia weight is updated according to the following formula:

$$X_i^{(k)}=\frac{1}{x_{\max }-x_{\min }}\frac{1}{D}{\displaystyle \sum _{d=1}^D|g_d^{(k)}-x_{id}^{(k)}|}$$

(41)

$$w_i^{(k)}=w_{\mathrm{start}}-(w_{\mathrm{start}}-w_{end}){(X_i^{(k)}-1)}^2$$

(42)

where $D$ is the dimension of the solution space, $w_i^{(k)}$ is the inertia weight of the $i$ particle at time $k$, $w_{\mathrm{start}}$ and $w_{end}$ refer to the initial and ending values of $w$, respectively, and $x_{\max }$ and $x_{\min }$ represent the maximum and minimum values of the particle position variables, respectively.

Step 4: Update the velocity and position of particles

Update the position and the velocity of particles in the population, and then search for the optimal solution under the guidance of $Gb$ and $Pb$. Among them, the position update formula is similar to the single objective particle swarm optimization algorithm:

$$v_{id}^{(k+1)}=w{v}_{id}^{(k)}+c_1{r}_1(p_{id}^{(k)}-x_{id}^{(k)})+c_2{r}_2(g_d^{(k)}-x_{id}^{(k)})$$

(43)

$$x_{id}^{(k+1)}=x_{id}^{(k)}+v_{id}^{(k+1)}$$

(44)

where $w$ is the inertia weight, $c_1$ and $c_2$ are the acceleration factor, $r_1$ and $r_2$ are a random number of $(0,1)$, $p_{id}^{(k)}$ is the d-th dimensional component of the optimal position vector of the $i$ particle at time $k$, and $g_d^{(k)}$ is the d-th dimensional component in the optimal position vector of the population at time $k$.

Step 5: Calculate the fitness value of particles

Based on the objective function, obtain the fitness function of the particle swarm optimization algorithm.

Step 6: Iteration termination judgment

By analogy, determine whether the iteration requirements are met. If they are met, output the result. If not, return to step 3.

Step 7: Initialize the population

Use the offspring population generated by the MOPSO algorithm iteration as the initialization population of the NSGA2 algorithm.

Step 8: Fast non-dominated sorting

Among all individuals in the initial population, the dominance relationship is first used to determine the dominance attributes between each individual in the population. $Na$ is used to represent the number of dominant solutions $a$, and $Sa$ is used to represent the set of solutions dominated by dominant solutions $a$. Initialize the hierarchical level to $rank1$, determine all individuals of $Na=0$ in the population, and set these individuals as $rank1$. Subsequently, based on the set of all of the individuals controlled by $Sa$, the individuals of $Na=0$ at this time are searched for, and these individuals are stored in a new set as a hierarchical level, $rank2$, by analogy until all individuals have obtained a non-dominated ranking level.

Step 9: Crowding distance

Crowding distance is an indicator of the density at the midpoint of the Pareto front. It is generally believed that the sparser the distribution of solutions, the better, and this is because if the distribution of solutions becomes tighter, after cross mutation, the solution that can be searched for is still near the previous tight interval. The calculation formula for crowding distance is as follows:

$$Dc={\displaystyle \sum _{q=1}^s\frac{\left|f_q^{t+1}-f_q^{t-1}\right|}{f_q^{\max }-f_q^{\min }}}$$

(45)

Among them, $Dc$ represents the crowding distance, and $s$ represents the s-th objective function value of individual $t$. $f_q^{t+1}$, $f_q^{t-1}$ represent the values of individuals $t+1$ and $t-1$ on the q-th objective function, where $f_q^{\max }$, $f_q^{\min }$ are the maximum and minimum values of the q-th objective function.

Step 10: Elite Selection Strategy

The role of selection strategy is to select excellent individuals from the population for the next step of cross mutation operation, generating a new generation of offspring population. This algorithm adopts a binary tournament selection strategy based on crowding comparison operator and non-dominated ranking.

Step 11: Cross and mutation operations

Using simulated binary for crossover operation, assuming that the parents of two genes are $P_{1j}$ and $P_{2j}$, then:

$${\overline{P}}_{1j}=0.5\cdot \left[\left(1+{\varphi }_j\right)\cdot P_{1j}+\left(1-{\varphi }_j\right)\cdot P_{2j}\right]$$

(46)

$${\overline{P}}_{2j}=0.5\cdot \left[\left(1-{\varphi }_j\right)\cdot P_{1j}+\left(1+{\varphi }_j\right)\cdot P_{2j}\right]$$

(47)

Among them:

$$\mathsf{\Delta }j=\{\begin{array}{c}{\left(2u_j\right)}^{\frac{1}{\varphi +1}}\hspace{1em}\hspace{1em},u_j<0.5\\ {\left[1-2\cdot \left(1-u_j\right)\right]}^{\frac{1}{\varphi +1}},\mathrm{otherwise}\end{array}$$

(48)

Similarly, using simulated binary for mutation operations, assuming that the parent of a gene is $P_{3j}$, then:

$${\overline{P}}_{3j}=P_{3j}+\mathsf{\Delta }j$$

(49)

Among them:

$$\mathsf{\Delta }j=\{\begin{array}{c}{\left(2u_j\right)}^{\frac{1}{\varphi +1}}\hspace{1em}\hspace{1em},u_j<0.5\\ {\left[1-2\cdot \left(1-u_j\right)\right]}^{\frac{1}{\varphi +1}},\mathrm{otherwise}\end{array}$$

(50)

Step 12: Termination Rules

When the number of generated offspring reaches the maximum number of iterations $Gen$ of the rule, the algorithm stops.

This paper mainly introduces the changes brought by mixing the NSGA2 and MOPSO algorithms. In terms of initializing population, this paper uses the particle swarm optimization algorithm in the first stage to conduct preliminary optimization of the multi-objective problem, which is characterized by fast optimization speed and high search efficiency, and it obtains the population that has evolved to a certain extent. Then, the hybrid algorithm enters the second stage, and it takes the output results of the particle swarm optimization algorithm as part of the initial population of the NSGA2 algorithm so as to improve the overall quality of the initial population of NSGA2 algorithm, with the purpose of optimizing the initial population of the NSGA2 algorithm. In order to increase the richness of the initial population in the second stage, individuals preliminarily optimized by the particle swarm optimization algorithm were mixed with those generated by random initialization in the second stage to expand the population size of the NSGA2 algorithm, and subsequent iterative optimization was then carried out, as shown in Figure 3.

Local search is the process of searching in the vicinity of some individual in the hope of producing a better individual and participating in the evolution of the population as a future parent. In this paper, three methods of gene fragment reversal, gene location exchange, and gene location preposition were used in order to conduct a local search for selected individuals. The local search combined with multiple strategies improved the richness and diversity, and the advantage of these local search strategies was that they would not produce illegal solutions. These three strategies all randomly select the changed positions. Even if the same strategy is used for the same chromosome, there is still a high probability of getting different chromosome ordering ways.

5. Model Solving

5.1. Example Description

Before the epidemic, there was only one medical waste disposal institution in Wuhan, China, with a daily disposal capacity of only 50 t, far from meeting the demand for disposal capacity during the epidemic. In order to safely and effectively dispose of medical waste, Wuhan has simultaneously taken measures such as building new disposal facilities, upgrading existing facilities, coordinating disposal, and putting a large number of mobile medical waste disposal facilities into operation.

5.2. Data Preparation

Through the use of data mining technology to collect relevant data from Wuhan, in February 2020, there were a total of 40 infectious medical waste-generating institutions, including 27 designated hospitals, 11 shelter hospitals, and temporary hospitals in Huoshen Mountain and Leishen Mountain. The specific distribution and the number of beds are shown in

Table 1. Medical waste generating institutions and number of beds in Wuhan.

Serial Number	Generating Mechanism	Number of Beds	Serial Number	Generating Mechanism	Number of Beds
1	Wuhan Huoshenshan Hospital	1000	21	Wuhan Red Cross Society Hospital	300
2	Wuhan Huoshenshan Hospital	1500	22	Wuhan United Hospital	1200
3	Wuhan Gymnasium (Tongkou District)	305	23	Tongji Medical College, Huazhong University of Science and Technology	110
4	Wuhan International Convention & Exhibition Center	1800	24	Wuhan Central Hospital (Houhu Hospital District)	1500
5	Wuhan Economic & Technological Development Zone	1100	25	Wuhan Third Hospital	570
6	Wuhan living room	2000	26	PLA Central Theater Command General Hospital	1800
7	Wuhan Hongshan Gymnasium	800	27	Wuhan Fifth hospital medical association	910
8	Dahuashan Outdoor Sports Center	1000	28	East Hospital of Wuhan University People’s Hospital	800
9	Jiangan District National Fitness Center	1000	29	Hubei Hospital of Integrated Traditional Chinese and Western Medicine	1035
10	Optics Valley Science and Technology Exhibition Center	1000	30	Tianyou Hospital Affiliated to Wuhan University of Science and Technology	1035
11	Shek Pai Ling Vocational High School	800	31	Wuhan Sixth Hospital	1200
12	International Expo Center (Hanyang District)	1000	32	Wuhan Hospital of Chinese Medicine	500
13	Hubei Huangpi No. 1 Middle School	300	33	672 Orthopedic Hospital of Integrated Chinese and Western Medicine	500
14	Wuhan Jinyintan Hospital	900	34	Wuhan Huangpi Traditional Chinese Medicine Hospital	500
15	Wuhan Pulmonary Hospital	499	35	Jiangxia District Hospital of Traditional Chinese Medicine	400
16	Wuhan Hankou Hospital	808	36	Wuhan Xinzhou Hospital of Traditional Chinese Medicine	300
17	Wuhan Wuchang Hospital	889	37	Bauhinia Hospital	1000
18	Wuhan Fifth Hospital	600	38	Wuhan Hannan Hospital of Traditional Chinese Medicine	220
19	Wuhan Seventh Hospital	305	39	Caidian District People’s Hospital	1290
20	Wuhan Ninth Hospital	600	40	Hubei Maternal and Child Health Hospital	350

.

Huoshenshan, Leishenshan Temporary Hospital, and 11 makeshift hospitals were equipped with a total of 39 mobile medical waste incineration and disposal facilities, with a daily processing capacity of more than 70 t, which can basically achieve “daily clearance”. Therefore, in the subsequent calculation process, only the emergency disposal of medical waste generated by 27 designated hospitals is discussed in order to simplify the calculation process. Given the shortage of beds during the outbreak, the bed occupancy rate is 100%. The three cycles selected in this paper are 22 February, 23 February, and 24 February, respectively. The fuzzy numbers of IMW production in the three cycles are shown in

Table 2. Fuzzy number of infectious medical waste produced by designated hospitals in Wuhan.

Serial Number	Fixed-Point Hospital	Fuzzy Number of Infectious Medical Waste Production/t
		First Period	Second Period	Third Period
G1	Wuhan Jinyintan Hospital	4.1/4.6/4.2	5.0/5.0/5.5	6.1/5.2/6.2
G2	Wuhan Pulmonary Hospital	2.5/2.6/2.9	2.0/2.8/2.3	2.7/2.9/2.1
G3	Wuhan Hankou Hospital	3.9/4.2/4.5	4.1/4.5/4.2	4.7/4.7/4.6
G4	Wuhan Wuchang Hospital	4.1/4.6/4.7	4.9/4.9/5.0	5.1/5.2/5.2
G5	Wuhan Fifth Hospital	3.1/3.1/2.9	3.0/3.3/3.9	3.4/3.5/3.4
G6	Wuhan Seventh Hospital	1.4/1.6/1.5	1.3/1.7/1.1	1.7/1.8/2.1
G7	Wuhan Ninth Hospital	3.0/3.1/3.5	2.7/3.3/3.3	3.1/3.5/4.1
G8	Wuhan Red Cross Society Hospital	1.1/1.5/0.9	1.2/1.7/1.3	0.8/1.7/1.2
G9	Wuhan United Hospital	5.5/6.2/6.2	6.1/6.6/6.2	7.1/7.0/7.2
G10	Tongji Medical College, Huazhong University of Science and Technology	0.1/0.6/0.3	0.3/0.6/0.7	0.6/0.6/1.1
G11	Wuhan Central Hospital (Houhu Hospital District)	7.0/7.7/7.7	7.1/8.3/7.7	8.8/8.7/8.7
G12	Wuhan Third Hospital	1.2/2.9/2.2	3.1/3.1/3.5	3.4/3.3/3.9
G13	PLA Central Theater Command General Hospital	9.2/9.3/9.8	9.9/9.9/9.5	9.1/10.5/9.6
G14	Wuhan Fifth Hospital Medical Association	4.1/4.7/4.2	4.3/5.0/5.1	5.1/5.3/5.2
G15	East Hospital of Wuhan University People’s Hospital	4.1/4.1/4.5	4.5/4.4/4.1	4.3/4.6/4.8
G16	Hubei Hospital of Integrated Traditional Chinese and Western Medicine	5.5/5.3/5.1	5.2/5.7/5.4	5.1/6.0/6.1
G17	Tianyou Hospital Affiliated to Wuhan University of Science and Technology	5.1/5.3/5.2	5.7/5.7/5.3	6.2/6.0/6.5
G18	Wuhan Sixth Hospital	5.4/6.2/5.9	6.1/6.6/6.3	5.9/7.0/7.1
G19	Wuhan Hospital of Chinese Medicine	2.1/2.6/2.6	2.5/2.8/2.7	2.9/2.9/2.5
G20	672 Orthopedic Hospital of Integrated Chinese and Western Medicine	1.5/2.6/2.1	1.8/2.8/2.9	2.7/2.9/3.0
G21	Wuhan Huangpi Traditional Chinese Medicine Hospital	1.1/2.6/2.1	2.9/2.8/3.1	3.5/2.9/2.9
G22	Jiangxia District Hospital of Traditional Chinese Medicine	1.5/2.1/2.3	2.2/2.2/2.8	3.1/2.3/2.6
G23	Wuhan Xinzhou Hospital of Traditional Chinese Medicine	1.4/1.5/1.1	1.5/1.7/1.4	0.9/1.7/1.3
G24	Bauhinia Hospital	4.8/5.2/5.1	5.5/5.5/5.9	5.1/5.8/5.6
G25	Wuhan Hannan Hospital of Traditional Chinese Medicine	0.2/1.1/0.9	1.4/1.2/1.5	1.1/1.3/1.9
G26	Caidian District People’s Hospital	6.0/6.6/6.3	7.4/7.1/7.8	7.3/7.5/8.0
G27	Hubei Maternal and Child Health Hospital	1.1/1.8/1.5	0.7/1.9/2.1	2.0/2.0/2.4

. The unit collection cost at the production point is 800 CNY/t, and the probability of infection risk occurring in the collection process is 6 × 10⁻⁴. The effect radius of infection risk at each production point is 2 km.

Before the epidemic, there was only one qualified IMW disposal enterprise in Wuhan, namely, Wuhan Hanzi Environmental Protection Engineering Co., LTD. (No. T) (Wuhan, China), which had two medical waste treatment lines, and which could handle 50 t in a single day. After the outbreak, medical waste production surged, and the company increased its disposal capacity by increasing furnace temperatures and extending working hours.

After the outbreak of the epidemic, the Wuhan municipal government quickly started construction of the second medical waste disposal center, the Qianzishan Circular Economic Industrial Park Medical Waste Treatment Plant (No. NT1) project, in Wuhan City on 9 February 2020. The project has built three 10 t/d high-temperature cooking processing lines and three 10 t/d pyrolytic gasification processing lines, and the total disposal capacity of medical waste is 60 t/d. Since the industrial hazardous waste incineration facility is similar to the medical waste incineration device in principle, Wuhan Beihu Yunfeng Environmental Protection Technology Co., LTD. (No. NT2) (Wuhan, China) transforms the existing industrial hazardous waste incineration facility for the emergency treatment of medical waste after approval by the environmental protection authorities. After the transformation, the daily disposal capacity of medical waste of Beihu Yunfeng Company (Wuhan, China) is stable at about 15 t.

The medical waste disposed by the treatment center will produce various hazardous waste, such as incinerator slag, fly ash, and the adsorption of dioxins. The slag shall be transported to Hankou North Waste Incineration Power Plant (D1) for incineration and landfill treatment, while the hazardous waste shall be sent to the Hazardous Waste Landfill (D2) under Wuhan Xinhong Environmental Engineering Co., LTD. (Wuhan, China) for treatment. The nodes of the Wuhan infectious medical waste emergency disposal network are shown in Figure 4.

Population density is an important consideration in the calculation of infection risk. Population density itself has a large uncertainty, and the uncertainty of population density will affect the accuracy of infection risk assessment. Urban population density can be divided into five grades: extremely densely populated area (Ⅰ), dense area (Ⅱ), medium area (Ⅲ), rare area (Ⅳ), and extremely sparse area (Ⅴ). The classification standards are shown in

Table 3. Classification of urban population density and triangular fuzzy number.

Grade	Characteristic	Corresponding Triangular Fuzzy Number
Extremely densely populated area (Ⅰ)	>10,000 people per square kilometer	11,250/20,000/2850
Densely populated area (Ⅱ)	5000–10,000 people per square kilometer	5500/7500/9500
Medium population area (Ⅲ)	1000–5000 people per square kilometer	1250/3000/4800
Sparsely populated area (Ⅳ)	500–1000 people per square kilometer	600/750/900
Very sparsely populated area (Ⅴ)	<500 people per square kilometer	0/500/750

.

Table 4. Relevant data of infectious medical waste treatment center.

Processing Center	Processing Capacity (t/d)	Fixed Operating Cost (Ten Thousand CNY)	Cost of Technology Upgrade (Ten Thousand CNY)	Unit Processing Cost (Ten Thousand CNY/t)	Unit Temporary Storage Cost (Ten Thousand CNY/t)	Infectious Risk Probability	Effect Radius (km)
T	50	30	50	0.15	0.20	3.6 × 10−5	2.5

shows the relevant parameters of infectious medical waste treatment centers, including cost, infection risk, etc. The data were obtained according to the public information of the Wuhan government and the relevant literature.

The existing treatment center has two medical waste treatment lines with a daily processing capacity of 50 t. Based on the technology upgrade, the daily processing capacity can be increased to 70 t. The relevant parameters of the temporary medical waste treatment center are shown in

Table 5. Relevant data of temporary medical waste treatment center.

Processing Center	Processing Capacity (t/d)	Fixed Operating Cost (Ten Thousand CNY)	Cost of Technological Transformation (Ten Thousand CNY)	Infectious Risk Probability	Effect Radius (km)
NT1	60	70	100	3.6 × 10−5	2.5
NT2	15	20	30	3.6 × 10−5	2.5

. If the IMW shipped to the processing center exceeds the processing capacity of the day, it can be temporarily stored in the processing center, but the processing must be completed within 48 h.

After incineration of infectious medical waste in the treatment center, the production coefficients of slag and hazardous waste are 6% and 2%, respectively. The relevant parameters of the landfill site are shown in

Table 6. Landfill-related data.

Landfill	Treatment Type	Processing Capacity (t/d)	Fixed Operating Cost (Ten Thousand CNY/Cycle)	Unit Landfill Cost (Ten Thousand CNY/t)
D1	Household garbage	200	20	0.1
D2	Hazardous waste	100	30	0.15

.

Special medical waste transfer vehicles are used in the transportation process, and the unit transportation cost is 100 CNY/(t·km), The infectious risk probability of medical waste leakage caused by vehicle accidents during transportation is 4 × 10⁻⁷ and the effect radius is 1 km. After incineration of IMW in the treatment center, the unit transportation cost of the slag and the hazardous waste generated is 50 CNY/(t·km), 75 CNY/(t·km). The number of the population was 100, the number of iterations was 100, and the crossover probability and the mutation probability were 0.7 and 0.3, respectively.

5.3. Calculation Result

5.3.1. Algorithm Performance

In this paper, the MOPSO-NSGA2 algorithm was compiled by Matlab R2014b in order to simulate and compare the calculation results of the NSGA2 algorithm. The confidence level of the triangular fuzzy number of IMW and population density is 0.9. After 100 population iterations, the spatial distribution of the Pareto solution set is shown in Figure 5.

It can be seen from Figure 5 that the convergence of the Pareto optimal solution set obtained by the improved hybrid algorithm is obviously better than that of the NSGA2 algorithm, and it is closer to the real Pareto frontier. It is preliminarily confirmed that the improved MOPSO-NSGA2 algorithm has more obvious optimization performance when solving multi-objective problems. In addition, this paper also uses convergence index GD, distribution index SP, Pareto optimal solution number, and algorithm operation time in order to compare the performance of the MOPSO, the NSGA2, and the improved hybrid algorithm more scientifically. The results are shown in

Table 7. Performance comparison of the three optimization algorithms.

Algorithm	Convergence Index	Distributive Index	Pareto Number of Optimal Solutions	Algorithm Operation Time (s)
MOPSO	0.005135	0.091873	49	54
NSGA2	0.004486	0.062588	63	31
MOPSO-NSGA2	0.003991	0.053129	61	27

.

In conclusion, the solution set of the improved hybrid algorithm is better than that of the single algorithm, which also shows the feasibility and the effectiveness of the MOPSO-NSGA2 algorithm to solve the decision optimization problem of the multi-objective emergency disposal network.

5.3.2. Multi-period and Multi-objective

The optimization results of each target in each cycle after iteration of the improved hybrid algorithm are shown in

Table 8. Optimal calculation results of the mixed algorithm for each target in each period.

Period	Minimum Economic Cost	Minimal Risk of Infection	Multi-Objective Optimization
First period	(301.25, 1781.84)	(354.23, 1590.35)	(327.50, 1683.91)
Second period	(325.73, 1865.20)	(394.68, 1629.97)	(375.00, 1698.24)
Third period	(372.51, 1803.77)	(412.56, 1688.42)	(398.89, 1755.73)
Multiperiodic summation	(999.49, 5450.81)	(1161.47, 4908.74)	(1101.39, 5137.88)
Single period	(1028.44, 5523.61)	(1224.52, 5108.30)	(1181.52, 5392.13)

.

From the perspective of multi cycle, the economic cost and infectious risk involved in multi cycle are lower than that of single cycle. The reason is that considering only a single cycle, the transportation route and the facility location scheme of IMW emergency disposal are fixed, and the decision scheme of distribution, transportation, and treatment cannot be flexibly adjusted according to the actual production and the recovery amount of IMW, which results in a certain waste of resources and an increased risk of infection. To sum up, it is a better option to consider multi-cycle decision-making in the emergency handling logistics network of IMW.

From the perspective of multi-objective analysis, the economic cost of the multi-objective optimal combination of the IMW emergency response model was higher than that of the single objective considering only the economic cost, and it was lower than that under the condition of the optimal infection risk. Similarly, the infection risk of the multi-objective optimal combination was higher than that of the single objective considering only the infection risk, and it was lower than that of the optimal economic cost. In conclusion, the emergency response of IMWs in complex public health events should consider multiple objectives at the same time in order to avoid losing them.

5.3.3. Emergency Disposal Plan

In the case of multi cycle and multi objective, based on the uncertainty of IMW production volume and population density, the MOPSO-NSGA2 solved the IMW emergency disposal logistics network in Wuhan City, and the final optimal result was a 110.13 million CNY economic cost and a 5137.88 infection risk. The optimal routing scheme of IMW emergency handling transportation corresponding to this solution is shown in Figure 6, Figure 7 and Figure 8.

In the first cycle, IMWs were transported to the existing clinical Waste Treatment Centre T and the temporary Clinical Waste Treatment Centre NT1, respectively, for treatment. The treated residue was transported to landfills in D1 and D2, respectively. In the second cycle, IMWs were still transported to T and NT1, but at this point, the processing capacity of T is improved by technological upgrades. In the third cycle, the existing processing centers T, NT1, and NT2 were all put into use.

5.3.4. Sensitivity Analysis

In order to make the model a more realistic depiction of the scene, the confidence level of the triangular fuzzy quantity based on the medical waste production quantity proposed in this paper is analyzed. The optimal economic cost and the infection risk at different confidence levels are shown in Figure 9.

It can be seen that with the increase in confidence level, the optimal economic cost and the infection risk will increase, and that the decision-making body or the decision-maker should act according to the actual situation. At the same time, under different confidence levels, the emergency disposal plans of medical waste in each cycle did not change, and this further verified the stability of the logistics network that has been constructed in this paper.

6. Conclusions

In this paper, considering the uncertainty of medical waste production quantity and population density, a multi-cycle and multi-objective logistics network model of medical waste emergency disposal under uncertain conditions is constructed. Through the deterministic transformation of the model based on the case of medical waste disposal in Wuhan, MOPSO-NSGA2 hybrid algorithm was used to solve the multi-objective model under the uncertain conditions and the sensitivity analysis, which verified the effectiveness and the superiority of the algorithm and obtained the medical waste emergency disposal logistics network decision-making model in a complex reality. The results are as follows: (1) This paper optimizes the existing NSGA2 algorithm. In order to overcome the slow search speed of the NSGA2 algorithm, particle swarm optimization with fast computing speed is introduced in order to combine the two algorithms and to complement each other. By comparing the convergence, the distribution, the number of Pareto optimal solutions, and the operation time of the hybrid algorithm with the single algorithm, the superiority of the hybrid algorithm is further verified. (2) The optimization results of each target in each cycle after iteration of the improved hybrid algorithm were compared. From the perspective of multi-cycle analysis, the economic cost and the infectivity risk involved in the multi-cycle model were lower than the cost in the single-cycle one. From the perspective of multi-objective analysis, at the same time, a variety of goals more suitable for real life should be considered in order to avoid losing. (3) Through MOPSO-NSGA2 solving the Wuhan IMW emergency disposal logistics network, the final optimal result was an economic cost of 110.139 million CNY and an infectious risk of 5137.88. In the first cycle, IMW is transported to T and NT1, respectively, for processing. In the second cycle, IMWs are still transported to T and NT1, but at this time, the processing capacity of T is improved by technological upgrading. In the third cycle, the existing processing centers T, NT1, and NT2 were all put into use. (4) The confidence level of triangular fuzzy quantity of medical waste production was analyzed. As the confidence level increases, both the optimal economic cost and the risk of infection increase. Under different confidence levels, the emergency disposal plans of medical waste in each cycle did not change, which further verified the stability of the logistics network constructed in this paper.