# A Novel Method for Evaluating Dredging Productivity Using a Data Envelopment Analysis-Based Technique

Authors: Hsin-Hung Lai; Kuei-Hu Chang; Chien-Liang Lin
Journal: Mathematical Problems in Engineering
 (2019)

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## 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.


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## Body

## 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 Section2, 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](1)Productivity=TotalOutputTotalInputResourcesDredging 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]:(2)Efficiency=∑c=1gucyc0∑i=1mvixi0where uc and vi denote the output and input weights (intensity), respectively. yc0 and xi0 are the outputs c and inputs i 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 n industries or DMUs (the DMUs in this paper are dredging projects) of the same nature (homogeneous), where each DMU uses m input resources and produces g outputs. For DMU j, the number of input resources is xij and the number of outputs is ycj(c=1,…,g). To assess the efficiency of DMUk, the output/input ratio Pk can be used, which is expressed as a percentage efficiency (that is, 0≤Pk≤1). Herein, uck is the weight of the output term c and vik is the weight of the input term i. In their original model, fractional programming was used to obtain the input and output variable weights—namely, vik, vik, and Pk—as expressed by (3)Maximize:Pk=∑c=1guckYck∑i=1mvikXikuck,Yck,vik,Xik≥0,i=1,2,…,m,c=1,2,…,gSubject  to:∑c=1guckYcr∑i=1mvikXir≤1,r=1,2,…,Ruck≥ε≥0,c=1,2,…,gvik≥ε≥0,i=1,2,…,mwhere ε 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 (∑i=1mvikXik=1) and add this to the restriction condition. The limiting inequality of (3) is multiplied by ∑i=1mvikXik on both sides of the inequality, and the right-hand side is canceled to obtain the following:(4)Maximize:Pk=∑c=1guckYckSubject  to:∑i=1mvikXik=1∑c=1guckYcr-∑i=1mvikXir≤0,r=1,2,…,Ruck≥ε≥0,c=1,2,…,gvik≥ε≥0,i=1,2,…,mIn (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 uck and vik are obtained using (3). DMU efficiency values are not necessarily decided by the manager in advance.IfPk=1, the rated DMU is “efficient;” if Pk<1, 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.


## 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](1)Productivity=TotalOutputTotalInputResourcesDredging 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]:(2)Efficiency=∑c=1gucyc0∑i=1mvixi0where uc and vi denote the output and input weights (intensity), respectively. yc0 and xi0 are the outputs c and inputs i 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 n industries or DMUs (the DMUs in this paper are dredging projects) of the same nature (homogeneous), where each DMU uses m input resources and produces g outputs. For DMU j, the number of input resources is xij and the number of outputs is ycj(c=1,…,g). To assess the efficiency of DMUk, the output/input ratio Pk can be used, which is expressed as a percentage efficiency (that is, 0≤Pk≤1). Herein, uck is the weight of the output term c and vik is the weight of the input term i. In their original model, fractional programming was used to obtain the input and output variable weights—namely, vik, vik, and Pk—as expressed by (3)Maximize:Pk=∑c=1guckYck∑i=1mvikXikuck,Yck,vik,Xik≥0,i=1,2,…,m,c=1,2,…,gSubject  to:∑c=1guckYcr∑i=1mvikXir≤1,r=1,2,…,Ruck≥ε≥0,c=1,2,…,gvik≥ε≥0,i=1,2,…,mwhere ε 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 (∑i=1mvikXik=1) and add this to the restriction condition. The limiting inequality of (3) is multiplied by ∑i=1mvikXik on both sides of the inequality, and the right-hand side is canceled to obtain the following:(4)Maximize:Pk=∑c=1guckYckSubject  to:∑i=1mvikXik=1∑c=1guckYcr-∑i=1mvikXir≤0,r=1,2,…,Ruck≥ε≥0,c=1,2,…,gvik≥ε≥0,i=1,2,…,mIn (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 uck and vik are obtained using (3). DMU efficiency values are not necessarily decided by the manager in advance.IfPk=1, the rated DMU is “efficient;” if Pk<1, 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:(5)Nij=xij-min⁡xijmax⁡xij-min⁡xiji=1,2,…m;j=1,2,…,nwherexij is the number of dispatches per day ofith work day with respect tojth 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 Figure1.Figure 1
Flowchart of the proposed dredging productivity evaluation method.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 Figure2. It mainly provides the public water supply in Tainan and Kaohsiung districts, which also have sightseeing and tourism functions.Figure 2
Nanhua Reservoir dredging diagram.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 Table1.Table 1
2011 Nanhua Reservoir dredging record data.
Work day Hydraulic excavator (SL-330) (A) Hydraulic excavator (320B) (B) Daily trucks (C) Daily dredging (m3) (D) 1 1 5 98 1668 2 1 5 98 1683 3 2 3 100 1701 4 2 3 100 1702 5 1 4 100 1700 6 1 5 99 1696 7 2 3 98 1665 8 2 4 100 1701 9 1 5 101 1716 10 1 5 101 1720 11 2 4 91 1706 12 2 4 93 1717 13 1 5 94 1729 14 1 5 95 1737 15 2 5 96 1747 16 2 5 98 1759 17 1 6 99 1770 18 1 6 100 1782 19 2 5 101 1792 20 2 5 102 1798 21 1 6 104 1826 22 1 6 106 1855 23 2 5 107 1871 24 2 6 108 1895 25 2 6 110 1925 26 2 6 112 1950 27 2 6 114 1985 28 2 6 117 2041 29 2 6 120 2093 30 2 6 116 2089 31 2 6 113 2083 32 2 6 109 2076 33 2 6 106 2067 34 2 6 103 2058 35 2 6 100 2047 36 2 6 97 2036 37 2 6 94 2024 38 2 6 92 2012 39 2 6 89 1999 40 2 6 87 1986 41 2 6 85 1973 42 2 6 83 1959 43 2 6 81 1946 44 2 6 79 1932 45 2 6 78 1918 46 2 6 76 1905 47 2 6 74 1891 48 2 6 73 1877 49 2 6 71 1863 50 2 6 70 1850 51 2 6 68 1836 52 2 6 67 1823 53 2 6 66 1809 54 2 6 65 1796


#### 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.Table 2
Daily dredging productivity by the traditional dredging productivity method.
Work day Input Output Output/Input Convert to single input Daily dredging (M3) Daily dredging productivity 1 0.422 1668 3950.526 2 0.422 1683 3986.053 3 0.545 1701 3118.500 4 0.545 1702 3120.333 5 0.323 1700 5259.375 6 0.428 1696 3960.000 7 0.533 1665 3121.875 8 0.657 1701 2590.754 9 0.440 1716 3896.422 10 0.440 1720 3905.505 11 0.602 1706 2833.792 12 0.614 1717 2795.773 13 0.398 1729 4344.442 14 0.404 1737 4299.075 15 0.743 1747 2349.905 16 0.756 1759 2328.088 17 0.539 1770 3281.461 18 0.545 1782 3267.000 19 0.774 1792 2316.031 20 0.780 1798 2305.725 21 0.570 1826 3205.213 22 0.582 1855 3188.281 23 0.810 1871 2309.589 24 0.927 1895 2043.627 25 0.939 1925 2049.194 26 0.952 1950 2049.363 27 0.964 1985 2059.906 28 0.982 2041 2078.796 29 1.000 2093 2093.000 30 0.976 2089 2140.901 31 0.958 2083 2175.285 32 0.933 2076 2224.286 33 0.915 2067 2258.642 34 0.897 2058 2294.392 35 0.879 2047 2329.345 36 0.861 2036 2365.775 37 0.842 2024 2402.590 38 0.830 2012 2423.212 39 0.812 1999 2461.455 40 0.800 1986 2482.500 41 0.788 1973 2504.192 42 0.776 1959 2525.273 43 0.764 1946 2548.333 44 0.752 1932 2570.806 45 0.745 1918 2572.927 46 0.733 1905 2597.727 47 0.721 1891 2621.975 48 0.715 1877 2624.619 49 0.703 1863 2649.957 50 0.697 1850 2654.348 51 0.685 1836 2680.885 52 0.679 1823 2685.670 53 0.673 1809 2689.054 54 0.667 1796 2694.000


#### 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 Table2, use (5) to convert 3 inputs into a single-input-single-output model, as shown in Table 3.Table 3
3 inputs into a single-input-single-output model conversion.
Work day Input Output Hydraulic excavator (SL-330) Hydraulic excavator (320B) Daily trucks Convert into a single-input Daily dredging (M3) 1 0.000 0.667 0.600 0.422 1668 2 0.000 0.667 0.600 0.422 1683 3 1.000 0.000 0.636 0.545 1701 4 1.000 0.000 0.636 0.545 1702 5 0.000 0.333 0.636 0.323 1700 6 0.000 0.667 0.618 0.428 1696 7 1.000 0.000 0.600 0.533 1665 8 1.000 0.333 0.636 0.657 1701 9 0.000 0.667 0.655 0.440 1716 10 0.000 0.667 0.655 0.440 1720 11 1.000 0.333 0.473 0.602 1706 12 1.000 0.333 0.509 0.614 1717 13 0.000 0.667 0.527 0.398 1729 14 0.000 0.667 0.545 0.404 1737 15 1.000 0.667 0.564 0.743 1747 16 1.000 0.667 0.600 0.756 1759 17 0.000 1.000 0.618 0.539 1770 18 0.000 1.000 0.636 0.545 1782 19 1.000 0.667 0.655 0.774 1792 20 1.000 0.667 0.673 0.780 1798 21 0.000 1.000 0.709 0.570 1826 22 0.000 1.000 0.745 0.582 1855 23 1.000 0.667 0.764 0.810 1871 24 1.000 1.000 0.782 0.927 1895 25 1.000 1.000 0.818 0.939 1925 26 1.000 1.000 0.855 0.952 1950 27 1.000 1.000 0.891 0.964 1985 28 1.000 1.000 0.945 0.982 2041 29 1.000 1.000 1.000 1.000 2093 30 1.000 1.000 0.927 0.976 2089 31 1.000 1.000 0.873 0.958 2083 32 1.000 1.000 0.800 0.933 2076 33 1.000 1.000 0.745 0.915 2067 34 1.000 1.000 0.691 0.897 2058 35 1.000 1.000 0.636 0.879 2047 36 1.000 1.000 0.582 0.861 2036 37 1.000 1.000 0.527 0.842 2024 38 1.000 1.000 0.491 0.830 2012 39 1.000 1.000 0.436 0.812 1999 40 1.000 1.000 0.400 0.800 1986 41 1.000 1.000 0.364 0.788 1973 42 1.000 1.000 0.327 0.776 1959 43 1.000 1.000 0.291 0.764 1946 44 1.000 1.000 0.255 0.752 1932 45 1.000 1.000 0.236 0.745 1918 46 1.000 1.000 0.200 0.733 1905 47 1.000 1.000 0.164 0.721 1891 48 1.000 1.000 0.145 0.715 1877 49 1.000 1.000 0.109 0.703 1863 50 1.000 1.000 0.091 0.697 1850 51 1.000 1.000 0.055 0.685 1836 52 1.000 1.000 0.036 0.679 1823 53 1.000 1.000 0.018 0.673 1809 54 1.000 1.000 0.000 0.667 1796Step 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 Table4.Table 4
Dredging assessment results for the traditional dredging productivity assessment method and proposed method.
Work day Traditional dredging productivity method Proposed method Dredging productivity result Dredging productivity result/One-day high dredging productivity 1 input result 3 input result 1 3950.526 0.751 0.751 0.952 2 3986.053 0.758 0.758 0.961 3 3118.500 0.593 0.593 0.999 4 3120.333 0.593 0.593 1.000 5 5259.375 1.000 1.000 1.000 6 3960.000 0.753 0.753 0.965 7 3121.875 0.594 0.594 0.992 8 2590.754 0.493 0.493 0.920 9 3896.422 0.741 0.741 0.971 10 3905.505 0.743 0.743 0.973 11 2833.792 0.539 0.539 0.968 12 2795.773 0.532 0.532 0.964 13 4344.442 0.826 0.826 1.000 14 4299.075 0.817 0.817 1.000 15 2349.905 0.447 0.447 0.892 16 2328.088 0.443 0.443 0.890 17 3281.461 0.624 0.624 0.994 18 3267.000 0.621 0.621 0.994 19 2316.031 0.440 0.440 0.893 20 2305.725 0.438 0.438 0.892 21 3205.213 0.609 0.609 0.996 22 3188.281 0.606 0.606 1.000 23 2309.589 0.439 0.439 0.907 24 2043.627 0.389 0.389 0.853 25 2049.194 0.390 0.390 0.859 26 2049.363 0.390 0.390 0.863 27 2059.906 0.392 0.392 0.871 28 2078.796 0.395 0.395 0.885 29 2093.000 0.398 0.398 0.896 30 2140.901 0.407 0.407 0.909 31 2175.285 0.414 0.414 0.918 32 2224.286 0.423 0.423 0.931 33 2258.642 0.429 0.429 0.939 34 2294.392 0.436 0.436 0.947 35 2329.345 0.443 0.443 0.955 36 2365.775 0.450 0.450 0.963 37 2402.590 0.457 0.457 0.970 38 2423.212 0.461 0.461 0.973 39 2461.455 0.468 0.468 0.981 40 2482.500 0.472 0.472 0.984 41 2504.192 0.476 0.476 0.987 42 2525.273 0.480 0.480 0.989 43 2548.333 0.485 0.485 0.992 44 2570.806 0.489 0.489 0.995 45 2572.927 0.489 0.489 0.993 46 2597.727 0.494 0.494 0.996 47 2621.975 0.499 0.499 0.999 48 2624.619 0.499 0.499 0.996 49 2649.957 0.504 0.504 0.999 50 2654.348 0.505 0.505 0.997 51 2680.885 0.510 0.510 1.000 52 2685.670 0.511 0.511 1.000 53 2689.054 0.511 0.511 1.000 54 2694.000 0.512 0.512 1.000


#### 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 Table4 and Figure 3.Figure 3
Daily productivity by the traditional dredging productivity assessment method and proposed method.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 Figure4.Figure 4
Cao Gongzhao I dredging diagram.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 Table5.Table 5
2011 Cao Gongzhao I dredging record data.
Work day Hydraulic excavator (SL-330) (A) Hydraulic excavator (320B) (B) Daily trucks (C) Daily dredging (m3)(D) 1 2 7 79 1086 2 1 8 175 2936 3 1 8 385 6804 4 2 7 235 4147 5 2 7 178 3811 6 2 7 194 3763 7 2 7 353 6135 8 1 8 142 2087 9 1 8 194 4203 10 2 7 203 4565 11 2 7 292 4857 12 2 7 292 5280 13 2 7 193 3288 14 1 8 193 5367 15 1 8 296 5078 16 2 7 267 4569 17 2 7 275 4636 18 2 7 277 4650 19 2 7 302 5173 20 1 8 351 6055 21 2 7 427 7397 22 2 7 443 7741 23 2 7 409 7164 24 1 8 310 5431 25 2 7 333 5835 26 2 7 359 6290 27 2 7 443 7751 28 1 8 343 6007 29 1 8 403 7062 30 2 7 412 7210 31 2 7 423 7396 32 2 7 372 6510 33 2 7 421 7375 34 1 8 423 7410 35 2 7 422 7384 36 2 7 435 7620 37 2 7 437 7627 38 1 8 449 7841 39 2 7 449 7847 40 2 7 450 7866 41 2 7 434 7592 42 2 7 436 7625 43 1 8 426 7452 44 2 7 431 7540 45 2 7 440 7708 46 2 7 437 7643 47 1 8 383 6703 48 1 8 433 7580 49 1 8 436 7634 50 2 7 443 7754 51 2 7 435 7616 52 1 8 437 7643 53 2 7 433 7577 54 2 7 431 6754 55 2 7 443 7746 56 2 7 447 7752 57 1 8 10 400 58 1 8 10 400 59 2 7 303 5298 60 2 7 129 2266 61 2 7 40 686 62 2 7 252 5177 63 1 8 380 6651 64 1 8 355 6212 65 2 7 303 5298 66 2 7 129 2266


#### 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.Table 6
Daily dredging productivity by the traditional dredging productivity method.
Work day Input Output Output/Input Convert to single input Daily dredging (M3) Daily dredging productivity 1 0.386 79 2816.346 2 0.458 175 6405.818 3 0.617 385 11019.975 4 0.504 235 8231.639 5 0.461 178 8273.882 6 0.473 194 7960.192 7 0.593 353 10342.529 8 0.433 142 4816.154 9 0.473 194 8890.962 10 0.480 203 9519.431 11 0.547 292 8879.834 12 0.547 292 9653.186 13 0.472 193 6966.549 14 0.472 193 11371.493 15 0.550 296 9232.727 16 0.528 267 8652.912 17 0.534 275 8680.170 18 0.536 277 8681.754 19 0.555 302 9328.361 20 0.592 351 10233.803 21 0.649 427 11393.279 22 0.661 443 11704.605 23 0.636 409 11271.132 24 0.561 310 9687.730 25 0.578 333 10094.626 26 0.598 359 10523.194 27 0.661 443 11719.725 28 0.586 343 10257.749 29 0.631 403 11190.684 30 0.638 412 11303.088 31 0.646 423 11445.158 32 0.608 372 10714.713 33 0.645 421 11439.483 34 0.646 423 11466.823 35 0.645 422 11440.000 36 0.655 435 11628.208 37 0.657 437 11612.042 38 0.666 449 11774.881 39 0.666 449 11783.891 40 0.667 450 11799.000 41 0.655 434 11598.889 42 0.656 436 11622.402 43 0.648 426 11491.402 44 0.652 431 11559.582 45 0.659 440 11694.897 46 0.657 437 11636.401 47 0.616 383 10883.100 48 0.654 433 11593.975 49 0.656 436 11636.120 50 0.661 443 11724.261 51 0.655 435 11622.104 52 0.657 437 11636.401 53 0.654 433 11589.386 54 0.652 431 10354.564 55 0.661 443 11712.165 56 0.664 447 11667.777 57 0.333 10 1200.000 58 0.333 10 1200.000 59 0.555 303 9540.737 60 0.423 129 5350.841 61 0.356 40 1926.638 62 0.517 252 10020.000 63 0.614 380 10838.667 64 0.595 355 10445.656 65 0.555 303 9540.737 66 0.423 129 5350.841


#### 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 Table7.Table 7
Daily dredging productivity by the proposed method.
Work day Input Output Daily dredging productivity Hydraulic excavator (SL-330) Hydraulic excavator (320B) Daily trucks Daily dredging (M3) 1 input result 3 input result 1 2 7 79 1086 0.239 0.494 2 1 8 175 2936 0.543 0.603 3 1 8 385 6804 0.934 0.942 4 2 7 235 4147 0.698 0.762 5 2 7 178 3811 0.701 0.794 6 2 7 194 3763 0.675 0.756 7 2 7 353 6135 0.877 0.906 8 1 8 142 2087 0.408 0.529 9 1 8 194 4203 0.754 0.782 10 2 7 203 4565 0.807 0.898 11 2 7 292 4857 0.753 0.798 12 2 7 292 5280 0.818 0.868 13 2 7 193 3288 0.590 0.662 14 1 8 193 5367 0.964 1.000 15 1 8 296 5078 0.783 0.798 16 2 7 267 4569 0.733 0.787 17 2 7 275 4636 0.736 0.787 18 2 7 277 4650 0.736 0.786 19 2 7 302 5173 0.791 0.835 20 1 8 351 6055 0.867 0.878 21 2 7 427 7397 0.966 0.972 22 2 7 443 7741 0.992 0.994 23 2 7 409 7164 0.955 0.968 24 1 8 310 5431 0.821 0.836 25 2 7 333 5835 0.856 0.891 26 2 7 359 6290 0.892 0.920 27 2 7 443 7751 0.993 0.995 28 1 8 343 6007 0.869 0.881 29 1 8 403 7062 0.948 0.955 30 2 7 412 7210 0.958 0.969 31 2 7 423 7396 0.970 0.978 32 2 7 372 6510 0.908 0.932 33 2 7 421 7375 0.970 0.978 34 1 8 423 7410 0.972 0.976 35 2 7 422 7384 0.970 0.978 36 2 7 435 7620 0.986 0.99 37 2 7 437 7627 0.984 0.988 38 1 8 449 7841 0.998 1.000 39 2 7 449 7847 0.999 0.999 40 2 7 450 7866 1.000 1.000 41 2 7 434 7592 0.983 0.988 42 2 7 436 7625 0.985 0.989 43 1 8 426 7452 0.974 0.978 44 2 7 431 7540 0.980 0.985 45 2 7 440 7708 0.991 0.994 46 2 7 437 7643 0.986 0.990 47 1 8 383 6703 0.922 0.931 48 1 8 433 7580 0.983 0.986 49 1 8 436 7634 0.986 0.989 50 2 7 443 7754 0.994 0.996 51 2 7 435 7616 0.985 0.989 52 1 8 437 7643 0.986 0.989 53 2 7 433 7577 0.982 0.987 54 2 7 431 6754 0.878 0.883 55 2 7 443 7746 0.993 0.995 56 2 7 447 7752 0.989 0.990 57 1 8 10 400 0.102 0.360 58 1 8 10 400 0.102 0.360 59 2 7 303 5298 0.809 0.853 60 2 7 129 2266 0.453 0.632 61 2 7 40 686 0.163 0.617 62 2 7 252 5177 0.849 0.919 63 1 8 380 6651 0.919 0.927 64 1 8 355 6212 0.885 0.896 65 2 7 303 5298 0.809 0.853 66 2 7 129 2266 0.453 0.632


#### 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 Table8 and Figure 5.Table 8
The dredging assessment results for Cao Gongzhao I.
Work day Traditional dredging productivity method Proposed method Dredging productivity result Dredging productivity result/One-day high dredging productivity 1 input result 3 input result 1 2816.346 0.239 0.239 0.494 2 6405.818 0.543 0.543 0.603 3 11019.975 0.934 0.934 0.942 4 8231.639 0.698 0.698 0.762 5 8273.882 0.701 0.701 0.794 6 7960.192 0.675 0.675 0.756 7 10342.529 0.877 0.877 0.906 8 4816.154 0.408 0.408 0.529 9 8890.962 0.754 0.754 0.782 10 9519.431 0.807 0.807 0.898 11 8879.834 0.753 0.753 0.798 12 9653.186 0.818 0.818 0.868 13 6966.549 0.590 0.590 0.662 14 11371.493 0.964 0.964 1.000 15 9232.727 0.783 0.783 0.798 16 8652.912 0.733 0.733 0.787 17 8680.170 0.736 0.736 0.787 18 8681.754 0.736 0.736 0.786 19 9328.361 0.791 0.791 0.835 20 10233.803 0.867 0.867 0.878 21 11393.279 0.966 0.966 0.972 22 11704.605 0.992 0.992 0.994 23 11271.132 0.955 0.955 0.968 24 9687.730 0.821 0.821 0.836 25 10094.626 0.856 0.856 0.891 26 10523.194 0.892 0.892 0.920 27 11719.725 0.993 0.993 0.995 28 10257.749 0.869 0.869 0.881 29 11190.684 0.948 0.948 0.955 30 11303.088 0.958 0.958 0.969 31 11445.158 0.970 0.970 0.978 32 10714.713 0.908 0.908 0.932 33 11439.483 0.970 0.970 0.978 34 11466.823 0.972 0.972 0.976 35 11440.000 0.970 0.970 0.978 36 11628.208 0.986 0.986 0.990 37 11612.042 0.984 0.984 0.988 38 11774.881 0.998 0.998 1.000 39 11783.891 0.999 0.999 0.999 40 11799.000 1.000 1.000 1.000 41 11598.889 0.983 0.983 0.988 42 11622.402 0.985 0.985 0.989 43 11491.402 0.974 0.974 0.978 44 11559.582 0.980 0.980 0.985 45 11694.897 0.991 0.991 0.994 46 11636.401 0.986 0.986 0.990 47 10883.100 0.922 0.922 0.931 48 11593.975 0.983 0.983 0.986 49 11636.120 0.986 0.986 0.989 50 11724.261 0.994 0.994 0.996 51 11622.104 0.985 0.985 0.989 52 11636.401 0.986 0.986 0.989 53 11589.386 0.982 0.982 0.987 54 10354.564 0.878 0.878 0.883 55 11712.165 0.993 0.993 0.995 56 11667.777 0.989 0.989 0.990 57 1200.000 0.102 0.102 0.360 58 1200.000 0.102 0.102 0.360 59 9540.737 0.809 0.809 0.853 60 5350.841 0.453 0.453 0.632 61 1926.638 0.163 0.163 0.617 62 10020.000 0.849 0.849 0.919 63 10838.667 0.919 0.919 0.927 64 10445.656 0.885 0.885 0.896 65 9540.737 0.809 0.809 0.853 66 5350.841 0.453 0.453 0.632Figure 5
Comparison of 2011 Cao Gongzhao I productivity curves.Based on the results of Table8 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 Table9.Table 9
2012 Cao Gongzhao II dredging record data.
Work day Hydraulic excavator (SL-330) (A) Hydraulic excavator (320B) (B) Daily trucks (C) Daily dredging (m3)(D) 1 3 10 13 320 2 3 10 9 6012 3 2 13 10 6210 4 2 13 8 8033 5 2 14 8 8217 6 3 14 7 8210 7 3 15 6 8858 8 3 14 7 10423 9 3 14 7 10713 10 3 14 7 10785 11 3 14 7 10634 12 3 14 7 10220 13 3 14 7 12031 14 3 14 7 12523 15 3 14 8 12666 16 3 14 8 12804 17 3 14 9 14181 18 3 16 11 8091 19 3 15 9 14518 20 3 15 8 14312 21 3 14 8 15270 22 3 13 8 15373 23 3 13 8 15413 24 3 14 9 16211 25 3 15 7 16503 26 3 14 7 16366 27 2 13 8 17005 28 2 13 7 17832 29 2 13 4 16527 30 2 13 7 16583 31 2 13 6 15589 32 2 13 6 15056 33 1 12 3 15037 34 1 11 4 16142 35 1 9 2 15861 36 1 7 1 4916 37 1 5 3 5057 38 1 1 2 3775


#### 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.Table 10
Daily dredging productivity of Cao Gongzhao II by the traditional dredging productivity method.
Work day Input Output Output/Input Convert to single input Daily dredging (M3) Daily dredging productivity 1 0.867 320 369.231 2 0.756 6012 7957.059 3 0.683 6210 9087.805 4 0.628 8033 12795.929 5 0.650 8217 12641.538 6 0.789 8210 10407.042 7 0.783 8858 11308.085 8 0.789 10423 13212.254 9 0.789 10713 13579.859 10 0.789 10785 13671.127 11 0.789 10634 13479.718 12 0.789 10220 12954.930 13 0.789 12031 15250.563 14 0.789 12523 15874.225 15 0.817 12666 15509.388 16 0.817 12804 15678.367 17 0.844 14181 16793.289 18 0.944 8091 8566.941 19 0.867 14518 16751.538 20 0.839 14312 17060.662 21 0.817 15270 18697.959 22 0.794 15373 19350.629 23 0.794 15413 19400.979 24 0.844 16211 19197.237 25 0.811 16503 20346.164 26 0.789 16366 20745.634 27 0.628 17005 27087.611 28 0.600 17832 29720.000 29 0.517 16527 31987.742 30 0.600 16583 27638.333 31 0.572 15589 27242.913 32 0.572 15056 26311.456 33 0.300 15037 50123.333 34 0.306 16142 52828.364 35 0.206 15861 77161.622 36 0.133 4916 36870.000 37 0.144 5057 35010.000 38 0.028 3775 135900.000


#### 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 Table11.Table 11
Daily dredging productivity of Cao Gongzhao II by the proposed method.
Work day Input Output Daily dredging productivity Hydraulic excavator (SL-330) Hydraulic excavator (320B) Daily trucks Daily dredging (M3) 1 input result 3 input result 1 3 10 13 320 0.003 0.015 2 3 10 9 6012 0.059 0.275 3 2 13 10 6210 0.067 0.257 4 2 13 8 8033 0.094 0.332 5 2 14 8 8217 0.093 0.320 6 3 14 7 8210 0.077 0.294 7 3 15 6 8858 0.083 0.301 8 3 14 7 10423 0.097 0.373 9 3 14 7 10713 0.100 0.383 10 3 14 7 10785 0.101 0.386 11 3 14 7 10634 0.099 0.381 12 3 14 7 10220 0.095 0.366 13 3 14 7 12031 0.112 0.431 14 3 14 7 12523 0.117 0.448 15 3 14 8 12666 0.114 0.453 16 3 14 8 12804 0.115 0.458 17 3 14 9 14181 0.124 0.507 18 3 16 11 8091 0.063 0.261 19 3 15 9 14518 0.123 0.493 20 3 15 8 14312 0.126 0.486 21 3 14 8 15270 0.138 0.546 22 3 13 8 15373 0.142 0.582 23 3 13 8 15413 0.143 0.583 24 3 14 9 16211 0.141 0.580 25 3 15 7 16503 0.150 0.560 26 3 14 7 16366 0.153 0.586 27 2 13 8 17005 0.199 0.704 28 2 13 7 17832 0.219 0.738 29 2 13 4 16527 0.235 0.684 30 2 13 7 16583 0.203 0.686 31 2 13 6 15589 0.200 0.645 32 2 13 6 15056 0.194 0.623 33 1 12 3 15037 0.369 0.940 34 1 11 4 16142 0.389 1.000 35 1 9 2 15861 0.568 1.000 36 1 7 1 4916 0.271 0.470 37 1 5 3 5057 0.258 1.000 38 1 1 2 3775 1.000 1.000


#### 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 Table12 and Figure 6.Table 12
The dredging assessment results for Cao Gongzhao II.
Work day Traditional dredging productivity method Proposed method Dredging productivity result Dredging productivity result/One-day high dredging productivity 1 input result 3 input result 1 369.231 0.003 0.003 0.015 2 7957.059 0.059 0.059 0.275 3 9087.805 0.067 0.067 0.257 4 12795.929 0.094 0.094 0.332 5 12641.538 0.093 0.093 0.320 6 10407.042 0.077 0.077 0.294 7 11308.085 0.083 0.083 0.301 8 13212.254 0.097 0.097 0.373 9 13579.859 0.100 0.100 0.383 10 13671.127 0.101 0.101 0.386 11 13479.718 0.099 0.099 0.381 12 12954.930 0.095 0.095 0.366 13 15250.563 0.112 0.112 0.431 14 15874.225 0.117 0.117 0.448 15 15509.388 0.114 0.114 0.453 16 15678.367 0.115 0.115 0.458 17 16793.289 0.124 0.124 0.507 18 8566.941 0.063 0.063 0.261 19 16751.538 0.123 0.123 0.493 20 17060.662 0.126 0.126 0.486 21 18697.959 0.138 0.138 0.546 22 19350.629 0.142 0.142 0.582 23 19400.979 0.143 0.143 0.583 24 19197.237 0.141 0.141 0.580 25 20346.164 0.150 0.150 0.560 26 20745.634 0.153 0.153 0.586 27 27087.611 0.199 0.199 0.704 28 29720.000 0.219 0.219 0.738 29 31987.742 0.235 0.235 0.684 30 27638.333 0.203 0.203 0.686 31 27242.913 0.200 0.200 0.645 32 26311.456 0.194 0.194 0.623 33 50123.333 0.369 0.369 0.940 34 52828.364 0.389 0.389 1.000 35 77161.622 0.568 0.568 1.000 36 36870.000 0.271 0.271 0.470 37 35010.000 0.258 0.258 1.000 38 135900.000 1.000 1.000 1.000Figure 6
Comparison of 2012 Cao Gongzhao II productivity curves.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 Table12, 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 Figure6) were divided by one-day high dredging productivity, which is the same with the results of the proposed method (green line shown).


## 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 Figure2. It mainly provides the public water supply in Tainan and Kaohsiung districts, which also have sightseeing and tourism functions.Figure 2
Nanhua Reservoir dredging diagram.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 Table1.Table 1
2011 Nanhua Reservoir dredging record data.
Work day Hydraulic excavator (SL-330) (A) Hydraulic excavator (320B) (B) Daily trucks (C) Daily dredging (m3) (D) 1 1 5 98 1668 2 1 5 98 1683 3 2 3 100 1701 4 2 3 100 1702 5 1 4 100 1700 6 1 5 99 1696 7 2 3 98 1665 8 2 4 100 1701 9 1 5 101 1716 10 1 5 101 1720 11 2 4 91 1706 12 2 4 93 1717 13 1 5 94 1729 14 1 5 95 1737 15 2 5 96 1747 16 2 5 98 1759 17 1 6 99 1770 18 1 6 100 1782 19 2 5 101 1792 20 2 5 102 1798 21 1 6 104 1826 22 1 6 106 1855 23 2 5 107 1871 24 2 6 108 1895 25 2 6 110 1925 26 2 6 112 1950 27 2 6 114 1985 28 2 6 117 2041 29 2 6 120 2093 30 2 6 116 2089 31 2 6 113 2083 32 2 6 109 2076 33 2 6 106 2067 34 2 6 103 2058 35 2 6 100 2047 36 2 6 97 2036 37 2 6 94 2024 38 2 6 92 2012 39 2 6 89 1999 40 2 6 87 1986 41 2 6 85 1973 42 2 6 83 1959 43 2 6 81 1946 44 2 6 79 1932 45 2 6 78 1918 46 2 6 76 1905 47 2 6 74 1891 48 2 6 73 1877 49 2 6 71 1863 50 2 6 70 1850 51 2 6 68 1836 52 2 6 67 1823 53 2 6 66 1809 54 2 6 65 1796


### 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.Table 2
Daily dredging productivity by the traditional dredging productivity method.
Work day Input Output Output/Input Convert to single input Daily dredging (M3) Daily dredging productivity 1 0.422 1668 3950.526 2 0.422 1683 3986.053 3 0.545 1701 3118.500 4 0.545 1702 3120.333 5 0.323 1700 5259.375 6 0.428 1696 3960.000 7 0.533 1665 3121.875 8 0.657 1701 2590.754 9 0.440 1716 3896.422 10 0.440 1720 3905.505 11 0.602 1706 2833.792 12 0.614 1717 2795.773 13 0.398 1729 4344.442 14 0.404 1737 4299.075 15 0.743 1747 2349.905 16 0.756 1759 2328.088 17 0.539 1770 3281.461 18 0.545 1782 3267.000 19 0.774 1792 2316.031 20 0.780 1798 2305.725 21 0.570 1826 3205.213 22 0.582 1855 3188.281 23 0.810 1871 2309.589 24 0.927 1895 2043.627 25 0.939 1925 2049.194 26 0.952 1950 2049.363 27 0.964 1985 2059.906 28 0.982 2041 2078.796 29 1.000 2093 2093.000 30 0.976 2089 2140.901 31 0.958 2083 2175.285 32 0.933 2076 2224.286 33 0.915 2067 2258.642 34 0.897 2058 2294.392 35 0.879 2047 2329.345 36 0.861 2036 2365.775 37 0.842 2024 2402.590 38 0.830 2012 2423.212 39 0.812 1999 2461.455 40 0.800 1986 2482.500 41 0.788 1973 2504.192 42 0.776 1959 2525.273 43 0.764 1946 2548.333 44 0.752 1932 2570.806 45 0.745 1918 2572.927 46 0.733 1905 2597.727 47 0.721 1891 2621.975 48 0.715 1877 2624.619 49 0.703 1863 2649.957 50 0.697 1850 2654.348 51 0.685 1836 2680.885 52 0.679 1823 2685.670 53 0.673 1809 2689.054 54 0.667 1796 2694.000


### 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 Table2, use (5) to convert 3 inputs into a single-input-single-output model, as shown in Table 3.Table 3
3 inputs into a single-input-single-output model conversion.
Work day Input Output Hydraulic excavator (SL-330) Hydraulic excavator (320B) Daily trucks Convert into a single-input Daily dredging (M3) 1 0.000 0.667 0.600 0.422 1668 2 0.000 0.667 0.600 0.422 1683 3 1.000 0.000 0.636 0.545 1701 4 1.000 0.000 0.636 0.545 1702 5 0.000 0.333 0.636 0.323 1700 6 0.000 0.667 0.618 0.428 1696 7 1.000 0.000 0.600 0.533 1665 8 1.000 0.333 0.636 0.657 1701 9 0.000 0.667 0.655 0.440 1716 10 0.000 0.667 0.655 0.440 1720 11 1.000 0.333 0.473 0.602 1706 12 1.000 0.333 0.509 0.614 1717 13 0.000 0.667 0.527 0.398 1729 14 0.000 0.667 0.545 0.404 1737 15 1.000 0.667 0.564 0.743 1747 16 1.000 0.667 0.600 0.756 1759 17 0.000 1.000 0.618 0.539 1770 18 0.000 1.000 0.636 0.545 1782 19 1.000 0.667 0.655 0.774 1792 20 1.000 0.667 0.673 0.780 1798 21 0.000 1.000 0.709 0.570 1826 22 0.000 1.000 0.745 0.582 1855 23 1.000 0.667 0.764 0.810 1871 24 1.000 1.000 0.782 0.927 1895 25 1.000 1.000 0.818 0.939 1925 26 1.000 1.000 0.855 0.952 1950 27 1.000 1.000 0.891 0.964 1985 28 1.000 1.000 0.945 0.982 2041 29 1.000 1.000 1.000 1.000 2093 30 1.000 1.000 0.927 0.976 2089 31 1.000 1.000 0.873 0.958 2083 32 1.000 1.000 0.800 0.933 2076 33 1.000 1.000 0.745 0.915 2067 34 1.000 1.000 0.691 0.897 2058 35 1.000 1.000 0.636 0.879 2047 36 1.000 1.000 0.582 0.861 2036 37 1.000 1.000 0.527 0.842 2024 38 1.000 1.000 0.491 0.830 2012 39 1.000 1.000 0.436 0.812 1999 40 1.000 1.000 0.400 0.800 1986 41 1.000 1.000 0.364 0.788 1973 42 1.000 1.000 0.327 0.776 1959 43 1.000 1.000 0.291 0.764 1946 44 1.000 1.000 0.255 0.752 1932 45 1.000 1.000 0.236 0.745 1918 46 1.000 1.000 0.200 0.733 1905 47 1.000 1.000 0.164 0.721 1891 48 1.000 1.000 0.145 0.715 1877 49 1.000 1.000 0.109 0.703 1863 50 1.000 1.000 0.091 0.697 1850 51 1.000 1.000 0.055 0.685 1836 52 1.000 1.000 0.036 0.679 1823 53 1.000 1.000 0.018 0.673 1809 54 1.000 1.000 0.000 0.667 1796Step 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 Table4.Table 4
Dredging assessment results for the traditional dredging productivity assessment method and proposed method.
Work day Traditional dredging productivity method Proposed method Dredging productivity result Dredging productivity result/One-day high dredging productivity 1 input result 3 input result 1 3950.526 0.751 0.751 0.952 2 3986.053 0.758 0.758 0.961 3 3118.500 0.593 0.593 0.999 4 3120.333 0.593 0.593 1.000 5 5259.375 1.000 1.000 1.000 6 3960.000 0.753 0.753 0.965 7 3121.875 0.594 0.594 0.992 8 2590.754 0.493 0.493 0.920 9 3896.422 0.741 0.741 0.971 10 3905.505 0.743 0.743 0.973 11 2833.792 0.539 0.539 0.968 12 2795.773 0.532 0.532 0.964 13 4344.442 0.826 0.826 1.000 14 4299.075 0.817 0.817 1.000 15 2349.905 0.447 0.447 0.892 16 2328.088 0.443 0.443 0.890 17 3281.461 0.624 0.624 0.994 18 3267.000 0.621 0.621 0.994 19 2316.031 0.440 0.440 0.893 20 2305.725 0.438 0.438 0.892 21 3205.213 0.609 0.609 0.996 22 3188.281 0.606 0.606 1.000 23 2309.589 0.439 0.439 0.907 24 2043.627 0.389 0.389 0.853 25 2049.194 0.390 0.390 0.859 26 2049.363 0.390 0.390 0.863 27 2059.906 0.392 0.392 0.871 28 2078.796 0.395 0.395 0.885 29 2093.000 0.398 0.398 0.896 30 2140.901 0.407 0.407 0.909 31 2175.285 0.414 0.414 0.918 32 2224.286 0.423 0.423 0.931 33 2258.642 0.429 0.429 0.939 34 2294.392 0.436 0.436 0.947 35 2329.345 0.443 0.443 0.955 36 2365.775 0.450 0.450 0.963 37 2402.590 0.457 0.457 0.970 38 2423.212 0.461 0.461 0.973 39 2461.455 0.468 0.468 0.981 40 2482.500 0.472 0.472 0.984 41 2504.192 0.476 0.476 0.987 42 2525.273 0.480 0.480 0.989 43 2548.333 0.485 0.485 0.992 44 2570.806 0.489 0.489 0.995 45 2572.927 0.489 0.489 0.993 46 2597.727 0.494 0.494 0.996 47 2621.975 0.499 0.499 0.999 48 2624.619 0.499 0.499 0.996 49 2649.957 0.504 0.504 0.999 50 2654.348 0.505 0.505 0.997 51 2680.885 0.510 0.510 1.000 52 2685.670 0.511 0.511 1.000 53 2689.054 0.511 0.511 1.000 54 2694.000 0.512 0.512 1.000


### 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 Table4 and Figure 3.Figure 3
Daily productivity by the traditional dredging productivity assessment method and proposed method.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.


## 4.1.1. 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.Table 2
Daily dredging productivity by the traditional dredging productivity method.
Work day Input Output Output/Input Convert to single input Daily dredging (M3) Daily dredging productivity 1 0.422 1668 3950.526 2 0.422 1683 3986.053 3 0.545 1701 3118.500 4 0.545 1702 3120.333 5 0.323 1700 5259.375 6 0.428 1696 3960.000 7 0.533 1665 3121.875 8 0.657 1701 2590.754 9 0.440 1716 3896.422 10 0.440 1720 3905.505 11 0.602 1706 2833.792 12 0.614 1717 2795.773 13 0.398 1729 4344.442 14 0.404 1737 4299.075 15 0.743 1747 2349.905 16 0.756 1759 2328.088 17 0.539 1770 3281.461 18 0.545 1782 3267.000 19 0.774 1792 2316.031 20 0.780 1798 2305.725 21 0.570 1826 3205.213 22 0.582 1855 3188.281 23 0.810 1871 2309.589 24 0.927 1895 2043.627 25 0.939 1925 2049.194 26 0.952 1950 2049.363 27 0.964 1985 2059.906 28 0.982 2041 2078.796 29 1.000 2093 2093.000 30 0.976 2089 2140.901 31 0.958 2083 2175.285 32 0.933 2076 2224.286 33 0.915 2067 2258.642 34 0.897 2058 2294.392 35 0.879 2047 2329.345 36 0.861 2036 2365.775 37 0.842 2024 2402.590 38 0.830 2012 2423.212 39 0.812 1999 2461.455 40 0.800 1986 2482.500 41 0.788 1973 2504.192 42 0.776 1959 2525.273 43 0.764 1946 2548.333 44 0.752 1932 2570.806 45 0.745 1918 2572.927 46 0.733 1905 2597.727 47 0.721 1891 2621.975 48 0.715 1877 2624.619 49 0.703 1863 2649.957 50 0.697 1850 2654.348 51 0.685 1836 2680.885 52 0.679 1823 2685.670 53 0.673 1809 2689.054 54 0.667 1796 2694.000


## 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 Table2, use (5) to convert 3 inputs into a single-input-single-output model, as shown in Table 3.Table 3
3 inputs into a single-input-single-output model conversion.
Work day Input Output Hydraulic excavator (SL-330) Hydraulic excavator (320B) Daily trucks Convert into a single-input Daily dredging (M3) 1 0.000 0.667 0.600 0.422 1668 2 0.000 0.667 0.600 0.422 1683 3 1.000 0.000 0.636 0.545 1701 4 1.000 0.000 0.636 0.545 1702 5 0.000 0.333 0.636 0.323 1700 6 0.000 0.667 0.618 0.428 1696 7 1.000 0.000 0.600 0.533 1665 8 1.000 0.333 0.636 0.657 1701 9 0.000 0.667 0.655 0.440 1716 10 0.000 0.667 0.655 0.440 1720 11 1.000 0.333 0.473 0.602 1706 12 1.000 0.333 0.509 0.614 1717 13 0.000 0.667 0.527 0.398 1729 14 0.000 0.667 0.545 0.404 1737 15 1.000 0.667 0.564 0.743 1747 16 1.000 0.667 0.600 0.756 1759 17 0.000 1.000 0.618 0.539 1770 18 0.000 1.000 0.636 0.545 1782 19 1.000 0.667 0.655 0.774 1792 20 1.000 0.667 0.673 0.780 1798 21 0.000 1.000 0.709 0.570 1826 22 0.000 1.000 0.745 0.582 1855 23 1.000 0.667 0.764 0.810 1871 24 1.000 1.000 0.782 0.927 1895 25 1.000 1.000 0.818 0.939 1925 26 1.000 1.000 0.855 0.952 1950 27 1.000 1.000 0.891 0.964 1985 28 1.000 1.000 0.945 0.982 2041 29 1.000 1.000 1.000 1.000 2093 30 1.000 1.000 0.927 0.976 2089 31 1.000 1.000 0.873 0.958 2083 32 1.000 1.000 0.800 0.933 2076 33 1.000 1.000 0.745 0.915 2067 34 1.000 1.000 0.691 0.897 2058 35 1.000 1.000 0.636 0.879 2047 36 1.000 1.000 0.582 0.861 2036 37 1.000 1.000 0.527 0.842 2024 38 1.000 1.000 0.491 0.830 2012 39 1.000 1.000 0.436 0.812 1999 40 1.000 1.000 0.400 0.800 1986 41 1.000 1.000 0.364 0.788 1973 42 1.000 1.000 0.327 0.776 1959 43 1.000 1.000 0.291 0.764 1946 44 1.000 1.000 0.255 0.752 1932 45 1.000 1.000 0.236 0.745 1918 46 1.000 1.000 0.200 0.733 1905 47 1.000 1.000 0.164 0.721 1891 48 1.000 1.000 0.145 0.715 1877 49 1.000 1.000 0.109 0.703 1863 50 1.000 1.000 0.091 0.697 1850 51 1.000 1.000 0.055 0.685 1836 52 1.000 1.000 0.036 0.679 1823 53 1.000 1.000 0.018 0.673 1809 54 1.000 1.000 0.000 0.667 1796Step 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 Table4.Table 4
Dredging assessment results for the traditional dredging productivity assessment method and proposed method.
Work day Traditional dredging productivity method Proposed method Dredging productivity result Dredging productivity result/One-day high dredging productivity 1 input result 3 input result 1 3950.526 0.751 0.751 0.952 2 3986.053 0.758 0.758 0.961 3 3118.500 0.593 0.593 0.999 4 3120.333 0.593 0.593 1.000 5 5259.375 1.000 1.000 1.000 6 3960.000 0.753 0.753 0.965 7 3121.875 0.594 0.594 0.992 8 2590.754 0.493 0.493 0.920 9 3896.422 0.741 0.741 0.971 10 3905.505 0.743 0.743 0.973 11 2833.792 0.539 0.539 0.968 12 2795.773 0.532 0.532 0.964 13 4344.442 0.826 0.826 1.000 14 4299.075 0.817 0.817 1.000 15 2349.905 0.447 0.447 0.892 16 2328.088 0.443 0.443 0.890 17 3281.461 0.624 0.624 0.994 18 3267.000 0.621 0.621 0.994 19 2316.031 0.440 0.440 0.893 20 2305.725 0.438 0.438 0.892 21 3205.213 0.609 0.609 0.996 22 3188.281 0.606 0.606 1.000 23 2309.589 0.439 0.439 0.907 24 2043.627 0.389 0.389 0.853 25 2049.194 0.390 0.390 0.859 26 2049.363 0.390 0.390 0.863 27 2059.906 0.392 0.392 0.871 28 2078.796 0.395 0.395 0.885 29 2093.000 0.398 0.398 0.896 30 2140.901 0.407 0.407 0.909 31 2175.285 0.414 0.414 0.918 32 2224.286 0.423 0.423 0.931 33 2258.642 0.429 0.429 0.939 34 2294.392 0.436 0.436 0.947 35 2329.345 0.443 0.443 0.955 36 2365.775 0.450 0.450 0.963 37 2402.590 0.457 0.457 0.970 38 2423.212 0.461 0.461 0.973 39 2461.455 0.468 0.468 0.981 40 2482.500 0.472 0.472 0.984 41 2504.192 0.476 0.476 0.987 42 2525.273 0.480 0.480 0.989 43 2548.333 0.485 0.485 0.992 44 2570.806 0.489 0.489 0.995 45 2572.927 0.489 0.489 0.993 46 2597.727 0.494 0.494 0.996 47 2621.975 0.499 0.499 0.999 48 2624.619 0.499 0.499 0.996 49 2649.957 0.504 0.504 0.999 50 2654.348 0.505 0.505 0.997 51 2680.885 0.510 0.510 1.000 52 2685.670 0.511 0.511 1.000 53 2689.054 0.511 0.511 1.000 54 2694.000 0.512 0.512 1.000


## 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 Table4 and Figure 3.Figure 3
Daily productivity by the traditional dredging productivity assessment method and proposed method.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 Figure4.Figure 4
Cao Gongzhao I dredging diagram.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 Table5.Table 5
2011 Cao Gongzhao I dredging record data.
Work day Hydraulic excavator (SL-330) (A) Hydraulic excavator (320B) (B) Daily trucks (C) Daily dredging (m3)(D) 1 2 7 79 1086 2 1 8 175 2936 3 1 8 385 6804 4 2 7 235 4147 5 2 7 178 3811 6 2 7 194 3763 7 2 7 353 6135 8 1 8 142 2087 9 1 8 194 4203 10 2 7 203 4565 11 2 7 292 4857 12 2 7 292 5280 13 2 7 193 3288 14 1 8 193 5367 15 1 8 296 5078 16 2 7 267 4569 17 2 7 275 4636 18 2 7 277 4650 19 2 7 302 5173 20 1 8 351 6055 21 2 7 427 7397 22 2 7 443 7741 23 2 7 409 7164 24 1 8 310 5431 25 2 7 333 5835 26 2 7 359 6290 27 2 7 443 7751 28 1 8 343 6007 29 1 8 403 7062 30 2 7 412 7210 31 2 7 423 7396 32 2 7 372 6510 33 2 7 421 7375 34 1 8 423 7410 35 2 7 422 7384 36 2 7 435 7620 37 2 7 437 7627 38 1 8 449 7841 39 2 7 449 7847 40 2 7 450 7866 41 2 7 434 7592 42 2 7 436 7625 43 1 8 426 7452 44 2 7 431 7540 45 2 7 440 7708 46 2 7 437 7643 47 1 8 383 6703 48 1 8 433 7580 49 1 8 436 7634 50 2 7 443 7754 51 2 7 435 7616 52 1 8 437 7643 53 2 7 433 7577 54 2 7 431 6754 55 2 7 443 7746 56 2 7 447 7752 57 1 8 10 400 58 1 8 10 400 59 2 7 303 5298 60 2 7 129 2266 61 2 7 40 686 62 2 7 252 5177 63 1 8 380 6651 64 1 8 355 6212 65 2 7 303 5298 66 2 7 129 2266


### 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.Table 6
Daily dredging productivity by the traditional dredging productivity method.
Work day Input Output Output/Input Convert to single input Daily dredging (M3) Daily dredging productivity 1 0.386 79 2816.346 2 0.458 175 6405.818 3 0.617 385 11019.975 4 0.504 235 8231.639 5 0.461 178 8273.882 6 0.473 194 7960.192 7 0.593 353 10342.529 8 0.433 142 4816.154 9 0.473 194 8890.962 10 0.480 203 9519.431 11 0.547 292 8879.834 12 0.547 292 9653.186 13 0.472 193 6966.549 14 0.472 193 11371.493 15 0.550 296 9232.727 16 0.528 267 8652.912 17 0.534 275 8680.170 18 0.536 277 8681.754 19 0.555 302 9328.361 20 0.592 351 10233.803 21 0.649 427 11393.279 22 0.661 443 11704.605 23 0.636 409 11271.132 24 0.561 310 9687.730 25 0.578 333 10094.626 26 0.598 359 10523.194 27 0.661 443 11719.725 28 0.586 343 10257.749 29 0.631 403 11190.684 30 0.638 412 11303.088 31 0.646 423 11445.158 32 0.608 372 10714.713 33 0.645 421 11439.483 34 0.646 423 11466.823 35 0.645 422 11440.000 36 0.655 435 11628.208 37 0.657 437 11612.042 38 0.666 449 11774.881 39 0.666 449 11783.891 40 0.667 450 11799.000 41 0.655 434 11598.889 42 0.656 436 11622.402 43 0.648 426 11491.402 44 0.652 431 11559.582 45 0.659 440 11694.897 46 0.657 437 11636.401 47 0.616 383 10883.100 48 0.654 433 11593.975 49 0.656 436 11636.120 50 0.661 443 11724.261 51 0.655 435 11622.104 52 0.657 437 11636.401 53 0.654 433 11589.386 54 0.652 431 10354.564 55 0.661 443 11712.165 56 0.664 447 11667.777 57 0.333 10 1200.000 58 0.333 10 1200.000 59 0.555 303 9540.737 60 0.423 129 5350.841 61 0.356 40 1926.638 62 0.517 252 10020.000 63 0.614 380 10838.667 64 0.595 355 10445.656 65 0.555 303 9540.737 66 0.423 129 5350.841


### 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 Table7.Table 7
Daily dredging productivity by the proposed method.
Work day Input Output Daily dredging productivity Hydraulic excavator (SL-330) Hydraulic excavator (320B) Daily trucks Daily dredging (M3) 1 input result 3 input result 1 2 7 79 1086 0.239 0.494 2 1 8 175 2936 0.543 0.603 3 1 8 385 6804 0.934 0.942 4 2 7 235 4147 0.698 0.762 5 2 7 178 3811 0.701 0.794 6 2 7 194 3763 0.675 0.756 7 2 7 353 6135 0.877 0.906 8 1 8 142 2087 0.408 0.529 9 1 8 194 4203 0.754 0.782 10 2 7 203 4565 0.807 0.898 11 2 7 292 4857 0.753 0.798 12 2 7 292 5280 0.818 0.868 13 2 7 193 3288 0.590 0.662 14 1 8 193 5367 0.964 1.000 15 1 8 296 5078 0.783 0.798 16 2 7 267 4569 0.733 0.787 17 2 7 275 4636 0.736 0.787 18 2 7 277 4650 0.736 0.786 19 2 7 302 5173 0.791 0.835 20 1 8 351 6055 0.867 0.878 21 2 7 427 7397 0.966 0.972 22 2 7 443 7741 0.992 0.994 23 2 7 409 7164 0.955 0.968 24 1 8 310 5431 0.821 0.836 25 2 7 333 5835 0.856 0.891 26 2 7 359 6290 0.892 0.920 27 2 7 443 7751 0.993 0.995 28 1 8 343 6007 0.869 0.881 29 1 8 403 7062 0.948 0.955 30 2 7 412 7210 0.958 0.969 31 2 7 423 7396 0.970 0.978 32 2 7 372 6510 0.908 0.932 33 2 7 421 7375 0.970 0.978 34 1 8 423 7410 0.972 0.976 35 2 7 422 7384 0.970 0.978 36 2 7 435 7620 0.986 0.99 37 2 7 437 7627 0.984 0.988 38 1 8 449 7841 0.998 1.000 39 2 7 449 7847 0.999 0.999 40 2 7 450 7866 1.000 1.000 41 2 7 434 7592 0.983 0.988 42 2 7 436 7625 0.985 0.989 43 1 8 426 7452 0.974 0.978 44 2 7 431 7540 0.980 0.985 45 2 7 440 7708 0.991 0.994 46 2 7 437 7643 0.986 0.990 47 1 8 383 6703 0.922 0.931 48 1 8 433 7580 0.983 0.986 49 1 8 436 7634 0.986 0.989 50 2 7 443 7754 0.994 0.996 51 2 7 435 7616 0.985 0.989 52 1 8 437 7643 0.986 0.989 53 2 7 433 7577 0.982 0.987 54 2 7 431 6754 0.878 0.883 55 2 7 443 7746 0.993 0.995 56 2 7 447 7752 0.989 0.990 57 1 8 10 400 0.102 0.360 58 1 8 10 400 0.102 0.360 59 2 7 303 5298 0.809 0.853 60 2 7 129 2266 0.453 0.632 61 2 7 40 686 0.163 0.617 62 2 7 252 5177 0.849 0.919 63 1 8 380 6651 0.919 0.927 64 1 8 355 6212 0.885 0.896 65 2 7 303 5298 0.809 0.853 66 2 7 129 2266 0.453 0.632


### 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 Table8 and Figure 5.Table 8
The dredging assessment results for Cao Gongzhao I.
Work day Traditional dredging productivity method Proposed method Dredging productivity result Dredging productivity result/One-day high dredging productivity 1 input result 3 input result 1 2816.346 0.239 0.239 0.494 2 6405.818 0.543 0.543 0.603 3 11019.975 0.934 0.934 0.942 4 8231.639 0.698 0.698 0.762 5 8273.882 0.701 0.701 0.794 6 7960.192 0.675 0.675 0.756 7 10342.529 0.877 0.877 0.906 8 4816.154 0.408 0.408 0.529 9 8890.962 0.754 0.754 0.782 10 9519.431 0.807 0.807 0.898 11 8879.834 0.753 0.753 0.798 12 9653.186 0.818 0.818 0.868 13 6966.549 0.590 0.590 0.662 14 11371.493 0.964 0.964 1.000 15 9232.727 0.783 0.783 0.798 16 8652.912 0.733 0.733 0.787 17 8680.170 0.736 0.736 0.787 18 8681.754 0.736 0.736 0.786 19 9328.361 0.791 0.791 0.835 20 10233.803 0.867 0.867 0.878 21 11393.279 0.966 0.966 0.972 22 11704.605 0.992 0.992 0.994 23 11271.132 0.955 0.955 0.968 24 9687.730 0.821 0.821 0.836 25 10094.626 0.856 0.856 0.891 26 10523.194 0.892 0.892 0.920 27 11719.725 0.993 0.993 0.995 28 10257.749 0.869 0.869 0.881 29 11190.684 0.948 0.948 0.955 30 11303.088 0.958 0.958 0.969 31 11445.158 0.970 0.970 0.978 32 10714.713 0.908 0.908 0.932 33 11439.483 0.970 0.970 0.978 34 11466.823 0.972 0.972 0.976 35 11440.000 0.970 0.970 0.978 36 11628.208 0.986 0.986 0.990 37 11612.042 0.984 0.984 0.988 38 11774.881 0.998 0.998 1.000 39 11783.891 0.999 0.999 0.999 40 11799.000 1.000 1.000 1.000 41 11598.889 0.983 0.983 0.988 42 11622.402 0.985 0.985 0.989 43 11491.402 0.974 0.974 0.978 44 11559.582 0.980 0.980 0.985 45 11694.897 0.991 0.991 0.994 46 11636.401 0.986 0.986 0.990 47 10883.100 0.922 0.922 0.931 48 11593.975 0.983 0.983 0.986 49 11636.120 0.986 0.986 0.989 50 11724.261 0.994 0.994 0.996 51 11622.104 0.985 0.985 0.989 52 11636.401 0.986 0.986 0.989 53 11589.386 0.982 0.982 0.987 54 10354.564 0.878 0.878 0.883 55 11712.165 0.993 0.993 0.995 56 11667.777 0.989 0.989 0.990 57 1200.000 0.102 0.102 0.360 58 1200.000 0.102 0.102 0.360 59 9540.737 0.809 0.809 0.853 60 5350.841 0.453 0.453 0.632 61 1926.638 0.163 0.163 0.617 62 10020.000 0.849 0.849 0.919 63 10838.667 0.919 0.919 0.927 64 10445.656 0.885 0.885 0.896 65 9540.737 0.809 0.809 0.853 66 5350.841 0.453 0.453 0.632Figure 5
Comparison of 2011 Cao Gongzhao I productivity curves.Based on the results of Table8 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.


## 4.2.1. 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.Table 6
Daily dredging productivity by the traditional dredging productivity method.
Work day Input Output Output/Input Convert to single input Daily dredging (M3) Daily dredging productivity 1 0.386 79 2816.346 2 0.458 175 6405.818 3 0.617 385 11019.975 4 0.504 235 8231.639 5 0.461 178 8273.882 6 0.473 194 7960.192 7 0.593 353 10342.529 8 0.433 142 4816.154 9 0.473 194 8890.962 10 0.480 203 9519.431 11 0.547 292 8879.834 12 0.547 292 9653.186 13 0.472 193 6966.549 14 0.472 193 11371.493 15 0.550 296 9232.727 16 0.528 267 8652.912 17 0.534 275 8680.170 18 0.536 277 8681.754 19 0.555 302 9328.361 20 0.592 351 10233.803 21 0.649 427 11393.279 22 0.661 443 11704.605 23 0.636 409 11271.132 24 0.561 310 9687.730 25 0.578 333 10094.626 26 0.598 359 10523.194 27 0.661 443 11719.725 28 0.586 343 10257.749 29 0.631 403 11190.684 30 0.638 412 11303.088 31 0.646 423 11445.158 32 0.608 372 10714.713 33 0.645 421 11439.483 34 0.646 423 11466.823 35 0.645 422 11440.000 36 0.655 435 11628.208 37 0.657 437 11612.042 38 0.666 449 11774.881 39 0.666 449 11783.891 40 0.667 450 11799.000 41 0.655 434 11598.889 42 0.656 436 11622.402 43 0.648 426 11491.402 44 0.652 431 11559.582 45 0.659 440 11694.897 46 0.657 437 11636.401 47 0.616 383 10883.100 48 0.654 433 11593.975 49 0.656 436 11636.120 50 0.661 443 11724.261 51 0.655 435 11622.104 52 0.657 437 11636.401 53 0.654 433 11589.386 54 0.652 431 10354.564 55 0.661 443 11712.165 56 0.664 447 11667.777 57 0.333 10 1200.000 58 0.333 10 1200.000 59 0.555 303 9540.737 60 0.423 129 5350.841 61 0.356 40 1926.638 62 0.517 252 10020.000 63 0.614 380 10838.667 64 0.595 355 10445.656 65 0.555 303 9540.737 66 0.423 129 5350.841


## 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 Table7.Table 7
Daily dredging productivity by the proposed method.
Work day Input Output Daily dredging productivity Hydraulic excavator (SL-330) Hydraulic excavator (320B) Daily trucks Daily dredging (M3) 1 input result 3 input result 1 2 7 79 1086 0.239 0.494 2 1 8 175 2936 0.543 0.603 3 1 8 385 6804 0.934 0.942 4 2 7 235 4147 0.698 0.762 5 2 7 178 3811 0.701 0.794 6 2 7 194 3763 0.675 0.756 7 2 7 353 6135 0.877 0.906 8 1 8 142 2087 0.408 0.529 9 1 8 194 4203 0.754 0.782 10 2 7 203 4565 0.807 0.898 11 2 7 292 4857 0.753 0.798 12 2 7 292 5280 0.818 0.868 13 2 7 193 3288 0.590 0.662 14 1 8 193 5367 0.964 1.000 15 1 8 296 5078 0.783 0.798 16 2 7 267 4569 0.733 0.787 17 2 7 275 4636 0.736 0.787 18 2 7 277 4650 0.736 0.786 19 2 7 302 5173 0.791 0.835 20 1 8 351 6055 0.867 0.878 21 2 7 427 7397 0.966 0.972 22 2 7 443 7741 0.992 0.994 23 2 7 409 7164 0.955 0.968 24 1 8 310 5431 0.821 0.836 25 2 7 333 5835 0.856 0.891 26 2 7 359 6290 0.892 0.920 27 2 7 443 7751 0.993 0.995 28 1 8 343 6007 0.869 0.881 29 1 8 403 7062 0.948 0.955 30 2 7 412 7210 0.958 0.969 31 2 7 423 7396 0.970 0.978 32 2 7 372 6510 0.908 0.932 33 2 7 421 7375 0.970 0.978 34 1 8 423 7410 0.972 0.976 35 2 7 422 7384 0.970 0.978 36 2 7 435 7620 0.986 0.99 37 2 7 437 7627 0.984 0.988 38 1 8 449 7841 0.998 1.000 39 2 7 449 7847 0.999 0.999 40 2 7 450 7866 1.000 1.000 41 2 7 434 7592 0.983 0.988 42 2 7 436 7625 0.985 0.989 43 1 8 426 7452 0.974 0.978 44 2 7 431 7540 0.980 0.985 45 2 7 440 7708 0.991 0.994 46 2 7 437 7643 0.986 0.990 47 1 8 383 6703 0.922 0.931 48 1 8 433 7580 0.983 0.986 49 1 8 436 7634 0.986 0.989 50 2 7 443 7754 0.994 0.996 51 2 7 435 7616 0.985 0.989 52 1 8 437 7643 0.986 0.989 53 2 7 433 7577 0.982 0.987 54 2 7 431 6754 0.878 0.883 55 2 7 443 7746 0.993 0.995 56 2 7 447 7752 0.989 0.990 57 1 8 10 400 0.102 0.360 58 1 8 10 400 0.102 0.360 59 2 7 303 5298 0.809 0.853 60 2 7 129 2266 0.453 0.632 61 2 7 40 686 0.163 0.617 62 2 7 252 5177 0.849 0.919 63 1 8 380 6651 0.919 0.927 64 1 8 355 6212 0.885 0.896 65 2 7 303 5298 0.809 0.853 66 2 7 129 2266 0.453 0.632


## 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 Table8 and Figure 5.Table 8
The dredging assessment results for Cao Gongzhao I.
Work day Traditional dredging productivity method Proposed method Dredging productivity result Dredging productivity result/One-day high dredging productivity 1 input result 3 input result 1 2816.346 0.239 0.239 0.494 2 6405.818 0.543 0.543 0.603 3 11019.975 0.934 0.934 0.942 4 8231.639 0.698 0.698 0.762 5 8273.882 0.701 0.701 0.794 6 7960.192 0.675 0.675 0.756 7 10342.529 0.877 0.877 0.906 8 4816.154 0.408 0.408 0.529 9 8890.962 0.754 0.754 0.782 10 9519.431 0.807 0.807 0.898 11 8879.834 0.753 0.753 0.798 12 9653.186 0.818 0.818 0.868 13 6966.549 0.590 0.590 0.662 14 11371.493 0.964 0.964 1.000 15 9232.727 0.783 0.783 0.798 16 8652.912 0.733 0.733 0.787 17 8680.170 0.736 0.736 0.787 18 8681.754 0.736 0.736 0.786 19 9328.361 0.791 0.791 0.835 20 10233.803 0.867 0.867 0.878 21 11393.279 0.966 0.966 0.972 22 11704.605 0.992 0.992 0.994 23 11271.132 0.955 0.955 0.968 24 9687.730 0.821 0.821 0.836 25 10094.626 0.856 0.856 0.891 26 10523.194 0.892 0.892 0.920 27 11719.725 0.993 0.993 0.995 28 10257.749 0.869 0.869 0.881 29 11190.684 0.948 0.948 0.955 30 11303.088 0.958 0.958 0.969 31 11445.158 0.970 0.970 0.978 32 10714.713 0.908 0.908 0.932 33 11439.483 0.970 0.970 0.978 34 11466.823 0.972 0.972 0.976 35 11440.000 0.970 0.970 0.978 36 11628.208 0.986 0.986 0.990 37 11612.042 0.984 0.984 0.988 38 11774.881 0.998 0.998 1.000 39 11783.891 0.999 0.999 0.999 40 11799.000 1.000 1.000 1.000 41 11598.889 0.983 0.983 0.988 42 11622.402 0.985 0.985 0.989 43 11491.402 0.974 0.974 0.978 44 11559.582 0.980 0.980 0.985 45 11694.897 0.991 0.991 0.994 46 11636.401 0.986 0.986 0.990 47 10883.100 0.922 0.922 0.931 48 11593.975 0.983 0.983 0.986 49 11636.120 0.986 0.986 0.989 50 11724.261 0.994 0.994 0.996 51 11622.104 0.985 0.985 0.989 52 11636.401 0.986 0.986 0.989 53 11589.386 0.982 0.982 0.987 54 10354.564 0.878 0.878 0.883 55 11712.165 0.993 0.993 0.995 56 11667.777 0.989 0.989 0.990 57 1200.000 0.102 0.102 0.360 58 1200.000 0.102 0.102 0.360 59 9540.737 0.809 0.809 0.853 60 5350.841 0.453 0.453 0.632 61 1926.638 0.163 0.163 0.617 62 10020.000 0.849 0.849 0.919 63 10838.667 0.919 0.919 0.927 64 10445.656 0.885 0.885 0.896 65 9540.737 0.809 0.809 0.853 66 5350.841 0.453 0.453 0.632Figure 5
Comparison of 2011 Cao Gongzhao I productivity curves.Based on the results of Table8 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 Table9.Table 9
2012 Cao Gongzhao II dredging record data.
Work day Hydraulic excavator (SL-330) (A) Hydraulic excavator (320B) (B) Daily trucks (C) Daily dredging (m3)(D) 1 3 10 13 320 2 3 10 9 6012 3 2 13 10 6210 4 2 13 8 8033 5 2 14 8 8217 6 3 14 7 8210 7 3 15 6 8858 8 3 14 7 10423 9 3 14 7 10713 10 3 14 7 10785 11 3 14 7 10634 12 3 14 7 10220 13 3 14 7 12031 14 3 14 7 12523 15 3 14 8 12666 16 3 14 8 12804 17 3 14 9 14181 18 3 16 11 8091 19 3 15 9 14518 20 3 15 8 14312 21 3 14 8 15270 22 3 13 8 15373 23 3 13 8 15413 24 3 14 9 16211 25 3 15 7 16503 26 3 14 7 16366 27 2 13 8 17005 28 2 13 7 17832 29 2 13 4 16527 30 2 13 7 16583 31 2 13 6 15589 32 2 13 6 15056 33 1 12 3 15037 34 1 11 4 16142 35 1 9 2 15861 36 1 7 1 4916 37 1 5 3 5057 38 1 1 2 3775


### 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.Table 10
Daily dredging productivity of Cao Gongzhao II by the traditional dredging productivity method.
Work day Input Output Output/Input Convert to single input Daily dredging (M3) Daily dredging productivity 1 0.867 320 369.231 2 0.756 6012 7957.059 3 0.683 6210 9087.805 4 0.628 8033 12795.929 5 0.650 8217 12641.538 6 0.789 8210 10407.042 7 0.783 8858 11308.085 8 0.789 10423 13212.254 9 0.789 10713 13579.859 10 0.789 10785 13671.127 11 0.789 10634 13479.718 12 0.789 10220 12954.930 13 0.789 12031 15250.563 14 0.789 12523 15874.225 15 0.817 12666 15509.388 16 0.817 12804 15678.367 17 0.844 14181 16793.289 18 0.944 8091 8566.941 19 0.867 14518 16751.538 20 0.839 14312 17060.662 21 0.817 15270 18697.959 22 0.794 15373 19350.629 23 0.794 15413 19400.979 24 0.844 16211 19197.237 25 0.811 16503 20346.164 26 0.789 16366 20745.634 27 0.628 17005 27087.611 28 0.600 17832 29720.000 29 0.517 16527 31987.742 30 0.600 16583 27638.333 31 0.572 15589 27242.913 32 0.572 15056 26311.456 33 0.300 15037 50123.333 34 0.306 16142 52828.364 35 0.206 15861 77161.622 36 0.133 4916 36870.000 37 0.144 5057 35010.000 38 0.028 3775 135900.000


### 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 Table11.Table 11
Daily dredging productivity of Cao Gongzhao II by the proposed method.
Work day Input Output Daily dredging productivity Hydraulic excavator (SL-330) Hydraulic excavator (320B) Daily trucks Daily dredging (M3) 1 input result 3 input result 1 3 10 13 320 0.003 0.015 2 3 10 9 6012 0.059 0.275 3 2 13 10 6210 0.067 0.257 4 2 13 8 8033 0.094 0.332 5 2 14 8 8217 0.093 0.320 6 3 14 7 8210 0.077 0.294 7 3 15 6 8858 0.083 0.301 8 3 14 7 10423 0.097 0.373 9 3 14 7 10713 0.100 0.383 10 3 14 7 10785 0.101 0.386 11 3 14 7 10634 0.099 0.381 12 3 14 7 10220 0.095 0.366 13 3 14 7 12031 0.112 0.431 14 3 14 7 12523 0.117 0.448 15 3 14 8 12666 0.114 0.453 16 3 14 8 12804 0.115 0.458 17 3 14 9 14181 0.124 0.507 18 3 16 11 8091 0.063 0.261 19 3 15 9 14518 0.123 0.493 20 3 15 8 14312 0.126 0.486 21 3 14 8 15270 0.138 0.546 22 3 13 8 15373 0.142 0.582 23 3 13 8 15413 0.143 0.583 24 3 14 9 16211 0.141 0.580 25 3 15 7 16503 0.150 0.560 26 3 14 7 16366 0.153 0.586 27 2 13 8 17005 0.199 0.704 28 2 13 7 17832 0.219 0.738 29 2 13 4 16527 0.235 0.684 30 2 13 7 16583 0.203 0.686 31 2 13 6 15589 0.200 0.645 32 2 13 6 15056 0.194 0.623 33 1 12 3 15037 0.369 0.940 34 1 11 4 16142 0.389 1.000 35 1 9 2 15861 0.568 1.000 36 1 7 1 4916 0.271 0.470 37 1 5 3 5057 0.258 1.000 38 1 1 2 3775 1.000 1.000


### 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 Table12 and Figure 6.Table 12
The dredging assessment results for Cao Gongzhao II.
Work day Traditional dredging productivity method Proposed method Dredging productivity result Dredging productivity result/One-day high dredging productivity 1 input result 3 input result 1 369.231 0.003 0.003 0.015 2 7957.059 0.059 0.059 0.275 3 9087.805 0.067 0.067 0.257 4 12795.929 0.094 0.094 0.332 5 12641.538 0.093 0.093 0.320 6 10407.042 0.077 0.077 0.294 7 11308.085 0.083 0.083 0.301 8 13212.254 0.097 0.097 0.373 9 13579.859 0.100 0.100 0.383 10 13671.127 0.101 0.101 0.386 11 13479.718 0.099 0.099 0.381 12 12954.930 0.095 0.095 0.366 13 15250.563 0.112 0.112 0.431 14 15874.225 0.117 0.117 0.448 15 15509.388 0.114 0.114 0.453 16 15678.367 0.115 0.115 0.458 17 16793.289 0.124 0.124 0.507 18 8566.941 0.063 0.063 0.261 19 16751.538 0.123 0.123 0.493 20 17060.662 0.126 0.126 0.486 21 18697.959 0.138 0.138 0.546 22 19350.629 0.142 0.142 0.582 23 19400.979 0.143 0.143 0.583 24 19197.237 0.141 0.141 0.580 25 20346.164 0.150 0.150 0.560 26 20745.634 0.153 0.153 0.586 27 27087.611 0.199 0.199 0.704 28 29720.000 0.219 0.219 0.738 29 31987.742 0.235 0.235 0.684 30 27638.333 0.203 0.203 0.686 31 27242.913 0.200 0.200 0.645 32 26311.456 0.194 0.194 0.623 33 50123.333 0.369 0.369 0.940 34 52828.364 0.389 0.389 1.000 35 77161.622 0.568 0.568 1.000 36 36870.000 0.271 0.271 0.470 37 35010.000 0.258 0.258 1.000 38 135900.000 1.000 1.000 1.000Figure 6
Comparison of 2012 Cao Gongzhao II productivity curves.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 Table12, 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 Figure6) were divided by one-day high dredging productivity, which is the same with the results of the proposed method (green line shown).


## 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.Table 10
Daily dredging productivity of Cao Gongzhao II by the traditional dredging productivity method.
Work day Input Output Output/Input Convert to single input Daily dredging (M3) Daily dredging productivity 1 0.867 320 369.231 2 0.756 6012 7957.059 3 0.683 6210 9087.805 4 0.628 8033 12795.929 5 0.650 8217 12641.538 6 0.789 8210 10407.042 7 0.783 8858 11308.085 8 0.789 10423 13212.254 9 0.789 10713 13579.859 10 0.789 10785 13671.127 11 0.789 10634 13479.718 12 0.789 10220 12954.930 13 0.789 12031 15250.563 14 0.789 12523 15874.225 15 0.817 12666 15509.388 16 0.817 12804 15678.367 17 0.844 14181 16793.289 18 0.944 8091 8566.941 19 0.867 14518 16751.538 20 0.839 14312 17060.662 21 0.817 15270 18697.959 22 0.794 15373 19350.629 23 0.794 15413 19400.979 24 0.844 16211 19197.237 25 0.811 16503 20346.164 26 0.789 16366 20745.634 27 0.628 17005 27087.611 28 0.600 17832 29720.000 29 0.517 16527 31987.742 30 0.600 16583 27638.333 31 0.572 15589 27242.913 32 0.572 15056 26311.456 33 0.300 15037 50123.333 34 0.306 16142 52828.364 35 0.206 15861 77161.622 36 0.133 4916 36870.000 37 0.144 5057 35010.000 38 0.028 3775 135900.000


## 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 Table11.Table 11
Daily dredging productivity of Cao Gongzhao II by the proposed method.
Work day Input Output Daily dredging productivity Hydraulic excavator (SL-330) Hydraulic excavator (320B) Daily trucks Daily dredging (M3) 1 input result 3 input result 1 3 10 13 320 0.003 0.015 2 3 10 9 6012 0.059 0.275 3 2 13 10 6210 0.067 0.257 4 2 13 8 8033 0.094 0.332 5 2 14 8 8217 0.093 0.320 6 3 14 7 8210 0.077 0.294 7 3 15 6 8858 0.083 0.301 8 3 14 7 10423 0.097 0.373 9 3 14 7 10713 0.100 0.383 10 3 14 7 10785 0.101 0.386 11 3 14 7 10634 0.099 0.381 12 3 14 7 10220 0.095 0.366 13 3 14 7 12031 0.112 0.431 14 3 14 7 12523 0.117 0.448 15 3 14 8 12666 0.114 0.453 16 3 14 8 12804 0.115 0.458 17 3 14 9 14181 0.124 0.507 18 3 16 11 8091 0.063 0.261 19 3 15 9 14518 0.123 0.493 20 3 15 8 14312 0.126 0.486 21 3 14 8 15270 0.138 0.546 22 3 13 8 15373 0.142 0.582 23 3 13 8 15413 0.143 0.583 24 3 14 9 16211 0.141 0.580 25 3 15 7 16503 0.150 0.560 26 3 14 7 16366 0.153 0.586 27 2 13 8 17005 0.199 0.704 28 2 13 7 17832 0.219 0.738 29 2 13 4 16527 0.235 0.684 30 2 13 7 16583 0.203 0.686 31 2 13 6 15589 0.200 0.645 32 2 13 6 15056 0.194 0.623 33 1 12 3 15037 0.369 0.940 34 1 11 4 16142 0.389 1.000 35 1 9 2 15861 0.568 1.000 36 1 7 1 4916 0.271 0.470 37 1 5 3 5057 0.258 1.000 38 1 1 2 3775 1.000 1.000


## 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 Table12 and Figure 6.Table 12
The dredging assessment results for Cao Gongzhao II.
Work day Traditional dredging productivity method Proposed method Dredging productivity result Dredging productivity result/One-day high dredging productivity 1 input result 3 input result 1 369.231 0.003 0.003 0.015 2 7957.059 0.059 0.059 0.275 3 9087.805 0.067 0.067 0.257 4 12795.929 0.094 0.094 0.332 5 12641.538 0.093 0.093 0.320 6 10407.042 0.077 0.077 0.294 7 11308.085 0.083 0.083 0.301 8 13212.254 0.097 0.097 0.373 9 13579.859 0.100 0.100 0.383 10 13671.127 0.101 0.101 0.386 11 13479.718 0.099 0.099 0.381 12 12954.930 0.095 0.095 0.366 13 15250.563 0.112 0.112 0.431 14 15874.225 0.117 0.117 0.448 15 15509.388 0.114 0.114 0.453 16 15678.367 0.115 0.115 0.458 17 16793.289 0.124 0.124 0.507 18 8566.941 0.063 0.063 0.261 19 16751.538 0.123 0.123 0.493 20 17060.662 0.126 0.126 0.486 21 18697.959 0.138 0.138 0.546 22 19350.629 0.142 0.142 0.582 23 19400.979 0.143 0.143 0.583 24 19197.237 0.141 0.141 0.580 25 20346.164 0.150 0.150 0.560 26 20745.634 0.153 0.153 0.586 27 27087.611 0.199 0.199 0.704 28 29720.000 0.219 0.219 0.738 29 31987.742 0.235 0.235 0.684 30 27638.333 0.203 0.203 0.686 31 27242.913 0.200 0.200 0.645 32 26311.456 0.194 0.194 0.623 33 50123.333 0.369 0.369 0.940 34 52828.364 0.389 0.389 1.000 35 77161.622 0.568 0.568 1.000 36 36870.000 0.271 0.271 0.470 37 35010.000 0.258 0.258 1.000 38 135900.000 1.000 1.000 1.000Figure 6
Comparison of 2012 Cao Gongzhao II productivity curves.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 Table12, 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 Figure6) 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.



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*Source: 5130835-2019-01-21.xml*