Mathematical Problems in Engineering
Volume 2019 (2019), Article ID 5130835, 22 pages
https://doi.org/10.1155/2019/5130835

Research Article

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

Hsin-Hung Lai,1,2 Kuei-Hu Chang,³ and Chien-Liang Lin²

¹Department of Civil Engineering, R.O.C. Military Academy, Kaohsiung 830, Taiwan
²Institute of Engineering Science and Technology, National Kaohsiung University of Science and Technology 811, Taiwan
³Department of Management Sciences, R.O.C. Military Academy, Kaohsiung 830, Taiwan

Correspondence should be addressed to Kuei-Hu Chang; evenken2002@gmail.com

Received 22 August 2018; Revised 4 December 2018; Accepted 9 January 2019; Published 21 January 2019

Academic Editor: Caroline Mota

Copyright © 2019 Hsin-Hung Lai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

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

1. Introduction

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

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

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

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

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

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

2. Literature Review

2.1. Traditional Dredging Productivity

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

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

2.2. DEA

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

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

The CCR model is the standard mode of DEA. The efficiency of a DMU can be expressed as follows [22]:

where and denote the output and input weights (intensity), respectively. and are the outputs and inputs of the observed DMU.

Charnes et al. [12] developed the first-mode CCR model for DEA to deal with multi-input and multioutput problems using a linear programming solution. The CCR model considers a DEA input with industries or DMUs (the DMUs in this paper are dredging projects) of the same nature (homogeneous), where each DMU uses input resources and produces outputs. For DMU , the number of input resources is and the number of outputs is . To assess the efficiency of , the output/input ratio can be used, which is expressed as a percentage efficiency (that is, ). Herein, is the weight of the output term and is the weight of the input term . In their original model, fractional programming was used to obtain the input and output variable weights—namely, , , and —as expressed by

where is a very small positive number (10⁻⁴), called a non-Archimedean constant. First, the fractional programming model that is given by (3) is converted into a linear programming problem before it is solved. In (3), consider the denominator in the objective function to be equal to 1 () and add this to the restriction condition. The limiting inequality of (3) is multiplied by on both sides of the inequality, and the right-hand side is canceled to obtain the following:

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

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

3. Proposed DEA-Based Method

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

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

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

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

Step 3. Convert different input-output combinations into a single-input-single-output model.
Single-input-single-output model convert used the following normalized equation:

where is the number of dispatches per day of ith work day with respect to jth input resource.

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

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

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 Figure 2. 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 Table 1.

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 Table 2, 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
1796

Step 4. Use the DEA CCR model to analyze the efficiency of multi-input data (DMUs) for assessing dredging productivity.
The daily dredging productivity of Nanhua Reservoir was calculated using DEAP software. The results are shown in Table 4.

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 Table 4 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 Figure 4.

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 Table 5.

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 Table 7.

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 Table 8 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
0.632

Figure 5: Comparison of 2011 Cao Gongzhao I productivity curves.

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

4.3. Case 3: Cao Gongzhao II

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

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 Table 11.

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 Table 12 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
1.000

Figure 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 Table 12, the traditional dredging productivity calculations are divided by one-day high dredging productivity with the ingle input results of proposed method are the same. Therefore, it is proven that the traditional dredging productivity method is a special case of the proposed method.(2)Under the condition that the dredging area and conditions are the same, the calculation results by the traditional dredging productivity method for Cao Gongzhao II (as shown by the red line in Figure 6) were divided by one-day high dredging productivity, which is the same with the results of the proposed method (green line shown).

5. Conclusions

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

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

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

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

Data Availability

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

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

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

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