#### Abstract

The increase in the frequency of extreme weather has caused the impact of natural disasters to become more extensive. Natural disasters reduce the effective storage capacity of reservoirs and affect their normal function. Reservoir dredging is a key issue in the management of water resources and is a complicated multiple-attribute decision-making (MADM) problem. The traditional assessment of dredging productivity has been performed using a labor productivity method to evaluate the related issues of dredging performance. However, the traditional labor productivity method only deals with the single-input/single-output evaluation factor for various forms of productivity. The traditional labor productivity method cannot address complicated MADM problems in the assessment of dredging productivity. To resolve the limitations of the traditional labor productivity method, this paper extended data envelopment analysis (DEA) and proposed a novel method for evaluating dredging productivity. The proposed method can handle various combinations of evaluation factors (single-input, multi-input, single-output, and multioutput). Three real cases of reservoir dredging are applied to verify the effectiveness of the proposed method. The simulation results show that the proposed method can be applied generally and correctly assesses the related issues of dredging performance.

#### 1. Introduction

Climate change has led to a rapid increase in the frequency of extreme weather events, enhancing the risk of natural disasters. According to the United Nations and other sources of official statistics, floods are the most common natural disaster and cause the most fatalities among various types of natural disasters. The main cause of flooding is high-intensity rainfall due to extreme weather. Today, extreme weather can cause heavy rain, and total rainfall has increased especially in areas that are affected by tropical cyclones.

Over the past 70 years, floods have risen to varying degrees in various parts of the world, accounting for 53% of the world’s victims of natural disasters and 42% of deaths due to such disasters [1]. Hills et al. [2] and Brown and Daigneault [3] indicated that engineering solutions, such as building dams, river dredging, and raising the heights of buildings and strengthening them, should be applied to prevent flood disasters. Daigneault et al. [4] reported 3 such methods: planting riparian buffers, upland afforestation, and river dredging. River dredging has the greatest overall benefits but is expensive. Jeong et al. [5] reported that reservoir sedimentation is a severe problem worldwide and that there is an annual decrease in global reservoir storage capacity of 1% due to reservoir deposition.

Reservoir dredging, an excavation activity that is usually performed underwater, is a key issue for the management of water resources. Dredging performance is evaluated by observation and the use of detailed records, and its indicators include the type of equipment, type of transport, transport distance, reoperation frequency, machine proficiency, earthwork conditions, and other ongoing projects. Many scholars have explored the issues that are related to dredging. For example, Jeong et al. [5] used a multicriteria decision analysis technique to develop a river dredging management model in Korea that assigns weights to various dredging-related factors, including dredging cost and the social and environmental impact, to solve the problem of river dredging. Nachtmann et al. [6] discussed problem definition and model formulation of optimal dredge fleet scheduling to improve the efficiency of dredging projects that were undertaken by the US Army Corps of Engineers (USACE). This approach can be used by decision-makers to increase the productivity of dredging machines. Christian and Xie [7] indicated that appropriate planning and scheduling significantly reduce wait times and other delays, rendering earthworks more efficient and reducing the risk of cost overruns.

Dredging performance (productivity) is one of the main research topics in construction engineering and management science. Dredging involves the transportation of large amounts of earth, requiring the consideration of transportation methods and combinations of complex machinery. Therefore, reservoir dredging is a complicated multiple-attribute decision-making (MADM) problem. The traditional method for assessing dredging productivity uses a labor productivity method to evaluate the related issues of dredging performance. Thomas et al. [8] defined productivity as “the work hour (WH) required to complete a unit of work” and stated that research on productivity should focus on labor-intensive work, repetitive work, and important crew work. The traditional labor productivity method is simple and widely used in many areas, such as role of the fabricator in labor productivity [9], the effects of heat stress on construction labor productivity [10], and quantifying schedule risk in construction projects [11]. However, the traditional labor productivity method only deals with the single-input/single-output evaluation factor of various forms of productivity.

The data envelopment analysis (DEA) method can effectively solve complicated MADM problems. The DEA method was first proposed by Charnes et al. [12] as a mathematical programming method to evaluate the relative efficiency of decision-making units (DMUs) with multiple inputs and outputs variables. Although some papers have used the DEA method to solve productivity-related issues, no research utilized this method to deal with the evaluation of dredging productivity [13–17]. This paper extends the DEA method to propose a novel dredging productivity evaluation method, solving the issues that are related to the evaluation of dredging productivity. The author aggregated data on the work area conditions that are encountered by the army in Taiwan when building reservoirs and dredging rivers, comparing the difference between the proposed method and the traditional labor productivity method about equipment dispatch decisions. These findings would serve as a reference for dredging task scheduling and equipment allocation by the military.

The remainder of this article is organized as follows. In Section 2, we review the literature on the traditional dredging productivity and DEA methods. In Section 3, we propose a novel dredging productivity evaluation method using a data envelopment analysis-based technique. In Section 4, we examine 3 real cases of reservoir dredging to verify the effectiveness of the proposed method. Finally, in Section 5, we provide the conclusions and future work.

#### 2. Literature Review

##### 2.1. Traditional Dredging Productivity

Dredging performance must cover many aspects, mainly including four factors: productivity, quality, safety, and timeliness. Most importantly, productivity must be at an appropriate level. Overall productivity usually depends on the productivity of the workers and machinery. It is generally believed that productivity is the ratio of “output” to “input” in unit time. As shown in [18]

Dredging work is often done using a combination of multiple operations, and traditional productivity calculation methods can only solve the problem of single input–single output.

##### 2.2. DEA

Charnes et al. [12] initially proposed the DEA method as a mathematical programming method to evaluate the relative efficiency of decision-making units (DMUs) (first-mode CCR model). Since then, many scholars have applied the DEA method to address decision-making-related issues. For example, Sowunmi et al. [19] used framework of stochastic frontier analysis of the DEA method to consider environmentally detrimental inputs and traditional production inputs to estimate the efficiency of fishing operations in sand dredging and non-dredging areas. Widiarto et al. [20] used DEA to assess the efficiency of microfinance institutions and analyze the choice of loan methods in not-for-profit microfinance institutions. Fan et al. [21] evaluated the ecoefficiency of industrial parks in China using the DEA model, applying park resources, industrial structure, environmental policy, and scale of development as the indicators that affect ecological efficiency to reflect the characteristics of ecoefficiency of sustainable development.

DEA is a method of measuring the relative efficiencies of a group of DMUs that use multiple inputs to produce multiple outputs. This nonparametric technique was originally conceived to analyze a set of units. Because the DEA method can solve MADM problems with single-input–single-output, single-input–multioutput, or multi-input–multiple-output, this theoretical basis can be applied widely to real-world problems.

The CCR model is the standard mode of DEA. The efficiency of a DMU can be expressed as follows [22]:where and denote the output and input weights (intensity), respectively. and are the outputs and inputs of the observed DMU.

Charnes et al. [12] developed the first-mode CCR model for DEA to deal with multi-input and multioutput problems using a linear programming solution. The CCR model considers a DEA input with industries or DMUs (the DMUs in this paper are dredging projects) of the same nature (homogeneous), where each DMU uses input resources and produces outputs. For DMU , the number of input resources is and the number of outputs is . To assess the efficiency of , the output/input ratio can be used, which is expressed as a percentage efficiency (that is, ). Herein, is the weight of the output term and is the weight of the input term . In their original model, fractional programming was used to obtain the input and output variable weights—namely, , , and —as expressed by where is a very small positive number (10^{−4}), called a non-Archimedean constant. First, the fractional programming model that is given by (3) is converted into a linear programming problem before it is solved. In (3), consider the denominator in the objective function to be equal to 1 () and add this to the restriction condition. The limiting inequality of (3) is multiplied by on both sides of the inequality, and the right-hand side is canceled to obtain the following:

In (3), the limit is the ratio of “actual output” to “actual input” of each DMU; the value of that ratio is between 0 and 1. The optimal values of and are obtained using (3). DMU efficiency values are not necessarily decided by the manager in advance.

If , the rated DMU is “efficient;” if , the rated DMU is “not efficient.” As in (4), each DMU must use its input and output as the objective function once, and the inputs and outputs of other DMUs are considered to be restricted. Therefore, using this method for a comparison of relative efficiency, the efficiency can be estimated in a fair and objective manner.

#### 3. Proposed DEA-Based Method

The possibility of extreme climate changes due to the greenhouse effect and rises in sea water temperature in the 21st century is growing rapidly. Extreme weather, including typhoons, causes serious river and reservoir earthrock flow problems, which dredging can alleviate. However, river or reservoir dredging is a complicated multiple-attribute decision-making (MADM) problem. The traditional method of calculating dredging productivity can only deal with the problem of single input–single output. But, dredging is a systematic problem, influenced by the complexity of multiple inputs and multiple outputs. To effectively solve this issue of dredging, this paper used the DEA CCR model to effectively handle the dredging MADM problem. The advantages of the DEA method can handle the complex multi-input–multioutput problems for assessing dredging issues.

The procedure of the proposed DEA-based method in this paper comprises five steps.

*Step 1. *Observe and record the daily number of machines, earthwork output, and working area status of the dredging work area.

*Step 2. *Consider the number of each type of instrument as input and earthwork as output. For example, hydraulic excavators and trucks are the input resources, and dredging productivity is the total output results.

*Step 3. *Convert different input-output combinations into a single-input-single-output model.

Single-input-single-output model convert used the following normalized equation:

where is the number of dispatches per day of* i*th work day with respect to* j*th input resource.

*Step 4. *Use the DEA CCR model to analyze the efficiency of multi-input data (DMUs) for assessing dredging productivity.

The flowchart of the novel dredging productivity evaluation method is shown in Figure 1.

*Step 5. *Analyze the dredging productivity evaluation results and provide suggestions.

#### 4. Case Study

To verify the feasibility and effectiveness of the proposed method and demonstrate that the traditional method of calculating dredging productivity is a special case of the proposed method, this paper will apply three practical dredging cases (Nanhua Reservoir, Cao Gongzhao I, and Cao Gongzhao II) from sites in Taiwan to calculate dredging productivity.

##### 4.1. Case 1: Nanhua Reservoir

Nanhua Reservoir is located east of Yushan Village, Nanhua District, Tainan City, Taiwan. The Nanhua Reservoir was built in 1988 and completed in 1994; the reservoir catchment area is 104 square kilometers, and the reservoir capacity is 158.05 million cubic meters, as shown in Figure 2. It mainly provides the public water supply in Tainan and Kaohsiung districts, which also have sightseeing and tourism functions.

In the dredging case of Nanhua Reservoir, we collected data for 54 working days from April 8 to May 31, 2011. The input items include the number of dispatches per day for hydraulic excavators (SL-330 and 320B) and trucks, and the output is the amount of earthwork output, as shown in Table 1.

###### 4.1.1. Solution by the Traditional Dredging Productivity Assessment Method

The traditional dredging productivity assessment method is based mainly on calculations by the labor productivity method [8]. However, the labor productivity method can only solve the single-input–single-output problem and cannot solve the multi-input–multioutput problem. In fact, dredging is a multi-input–multioutput MADM problem. For multiple input variables, we used (5) to convert them into a single input variable. The daily dredging productivity is calculated by the traditional dredging productivity method, as shown in Table 2.

###### 4.1.2. Solution by the Proposed Method

The proposed dredging productivity evaluation method can handle different combinations of evaluation factors (single-input, multi-input, single-output, and multioutput) for dredging data. The following steps describe the proposed method.

*Step 1. *Observe and record the daily number of machines, earthwork output, and working area status of the dredging work area.

Many of the factors that affect Nanhua Reservoir’s dredging productivity include weather, transportation distance, earthwork conditions, road conditions, machine tools, and people’s feelings. After the assessment, the input variables were hydraulic excavators (SL-330, 320B) and trucks as the influential variables for the dredging productivity of Nanhua Reservoir.

*Step 2. *Consider the number of each type of instrument as input and earthwork as output.

The assessment of the productivity output of the assessment case was 1 earthwork (m3).

*Step 3. *Convert different input-output combinations into a single-input-single-output model.

Based on the results of Table 2, use (5) to convert 3 inputs into a single-input-single-output model, as shown in Table 3.

*Step 4. *Use the DEA CCR model to analyze the efficiency of multi-input data (DMUs) for assessing dredging productivity.

The daily dredging productivity of Nanhua Reservoir was calculated using DEAP software. The results are shown in Table 4.

###### 4.1.3. Comparison and Discussion

We calculated the dredging assessment results for 1-input-1-output and 3-input-1-output in order to compare the traditional dredging productivity assessment method with the proposed dredging productivity evaluation method. The results are shown in Table 4 and Figure 3.

As verified by Nanhua Reservoir, we obtain the following conclusions:(1)Dredging is an MADM problem that may include single-input–single-output and multi-input–multioutput. The traditional dredging productivity method can only calculate the single-input–single-output problem. The proposed dredging productivity evaluation method can calculate the dredging productivity of single-input–single-output, multiple-input–single-output, single-input–multiple-output, and multi-input–multioutput. Therefore, it is proven that the traditional dredging productivity method is a special case of the proposed method.(2)The calculation results of traditional dredging productivity, divided by one-day high dredging productivity with the single input results of proposed method, are the same. This result implies that the proposed method can solve more complex problems of dredging productivity.

##### 4.2. Case 2: Cao Gongzhao I

Cao Gongzhao was built in 1919, across the areas of Pingtung and Kaohsiung, Taiwan. It is one of the important sources of irrigation water for early farmland in Taiwan. The Cao Gongzhao I dredging work area has a width of 800 meters, length of 500 meters, and an area of 40 hectares. The depth of digging is 2.5 meters, and the planned dredging volume is 1 million cubic meters, as shown in Figure 4.

The case of Cao Gongzhao I has 66 days of dredging records. The input items include the number of dispatches per day for hydraulic excavators (SL-330 and 320B) and trucks, and the output is the amount of earthwork output, as shown in Table 5.

###### 4.2.1. Solution by the Traditional Dredging Productivity Assessment Method (Cao Gongzhao I)

Transform the multi-input variables of Cao Gongzhao I into a single input variable. Use (1) and (5) to calculate daily dredging productivity, as shown in Table 6.

###### 4.2.2. Solution by the Proposed Method (Cao Gongzhao I)

Using the DEA CCR model, the daily dredging productivity for Cao Gongzhao I is calculated; the results are shown in Table 7.

###### 4.2.3. Comparison and Discussion

We calculate the dredging assessment results for 1-input-1-output and 3-input-1output to compare the dredging assessment results for Cao Gongzhao I which is between the traditional and the proposed dredging productivity evaluation methods. See Table 8 and Figure 5.

Based on the results of Table 8 and Figure 5, the calculation results of traditional dredging productivity, divided by one-day high dredging productivity with the single input results of proposed method, are the same. Therefore, the traditional dredging productivity assessment method can be viewed as a special case of the novel dredging productivity evaluation method.

##### 4.3. Case 3: Cao Gongzhao II

Phase 1 dredging was implemented at Cao Gongzhao in 2011, and the second phase of dredging was carried out in the same region in 2012, for a total of 38 days. The records are shown in Table 9.

###### 4.3.1. Solution by the Traditional Dredging Productivity Assessment Method (Cao Gongzhao II)

The multi-input variables for Cao Gongzhao II were transformed into a single input quantity. Use (1) and (5) to calculated daily dredging productivity, as shown in Table 10.

###### 4.3.2. Solution by the Proposed Method (Cao Gongzhao II)

Using the DEA CCR model, the daily dredging productivity for Cao Gongzhao II is calculated; the results are shown in Table 11.

###### 4.3.3. Comparison and Discussion

The dredging assessment results of Cao Gongzhao II by the traditional dredging productivity assessment method and the proposed method are shown in Table 12 and Figure 6.

The dredging case of Cao Gongzhao II yields the following conclusions:(1)The traditional dredging productivity method can only calculate the single-input–single-output problem. The proposed dredging productivity evaluation method can calculate the dredging productivity of multi-input–multioutput problem. Based on the results of Table 12, the traditional dredging productivity calculations are divided by one-day high dredging productivity with the ingle input results of proposed method are the same. Therefore, it is proven that the traditional dredging productivity method is a special case of the proposed method.(2)Under the condition that the dredging area and conditions are the same, the calculation results by the traditional dredging productivity method for Cao Gongzhao II (as shown by the red line in Figure 6) were divided by one-day high dredging productivity, which is the same with the results of the proposed method (green line shown).

#### 5. Conclusions

In the 21st century, many earthrock flow disasters that are caused by extreme climate have deeply affected many countries and have caused a gradual decline in the supply of freshwater, making the exploitation of water resources a national effort. Dredging is a key issue in the preservation of water resources. Improving the preservation and application of water resources to ensure a plentiful freshwater supply through dredging is a topic that every country is studying intently.

Dredging assessments primarily use productivity to represent the effectiveness of dredging. The evaluation of dredging also includes input variables, such as tools, trucks, and manpower, and the complexity of the output results, such as earthwork, flow rate, and water storage increase. The traditional dredging assessment method mainly uses work force productivity to calculate the dredging performance [8]. Although the traditional workforce productivity method is simple to calculate, this method can only deal with single-input variables and single-output outcomes and cannot solve multi-input and -output multicriteria dredging decision-making problems.

To solve the related issue of dredging assessments, this paper extended the DEA method to handle different combinations of evaluation factors (single-input, multi-input, single-output, and multioutput). Three real cases of reservoir dredging were applied to verify the effectiveness of the proposed method. The simulation results show that the traditional dredging productivity assessment can be viewed as a special case of the proposed dredging productivity evaluation method. Therefore, it is more appropriate to use the proposed method to calculate daily dredging productivity.

Subsequent studies can improve the risk assessment of natural and man-made factors, such as climate, machinery, earthwork conditions, the proficiency of operators, and managers’ methods; consider the subjective and objective weights of each evaluation factors of dredging to further explore dredging topics. In terms of calculation methods, use different DEA model (such as network data envelopment analysis model, BBC model, and weighted slack-based Measures model) to evaluate the dredging productivity.

#### Data Availability

The dredging productivity data used to support the findings of this study are included within the article.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Acknowledgments

The authors would like to thank the Ministry of Science and Technology, Taiwan, for financially supporting this research under Contract nos. MOST 106-2410-H-145-001 and MOST 107-2410-H-145-001.