Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2019 / Article

Research Article | Open Access

Volume 2019 |Article ID 5130835 | 22 pages | https://doi.org/10.1155/2019/5130835

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

Academic Editor: Caroline Mota
Received22 Aug 2018
Revised04 Dec 2018
Accepted09 Jan 2019
Published21 Jan 2019

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 [1317]. 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.

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

4. Case Study

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

4.1. Case 1: Nanhua Reservoir

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

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


Work dayHydraulic excavator (SL-330) (A)Hydraulic excavator (320B) (B)Daily trucks (C)Daily dredging (m3) (D)

115981668
215981683
3231001701
4231001702
5141001700
615991696
723981665
8241001701
9151011716
10151011720
1124911706
1224931717
1315941729
1415951737
1525961747
1625981759
1716991770
18161001782
19251011792
20251021798
21161041826
22161061855
23251071871
24261081895
25261101925
26261121950
27261141985
28261172041
29261202093
30261162089
31261132083
32261092076
33261062067
34261032058
35261002047
3626972036
3726942024
3826922012
3926891999
4026871986
4126851973
4226831959
4326811946
4426791932
4526781918
4626761905
4726741891
4826731877
4926711863
5026701850
5126681836
5226671823
5326661809
5426651796

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.


Work dayInputOutputOutput/Input
Convert to single inputDaily dredging (M3)Daily dredging productivity

10.42216683950.526
20.42216833986.053
30.54517013118.500
40.54517023120.333
50.32317005259.375
60.42816963960.000
70.53316653121.875
80.65717012590.754
90.44017163896.422
100.44017203905.505
110.60217062833.792
120.61417172795.773
130.39817294344.442
140.40417374299.075
150.74317472349.905
160.75617592328.088
170.53917703281.461
180.54517823267.000
190.77417922316.031
200.78017982305.725
210.57018263205.213
220.58218553188.281
230.81018712309.589
240.92718952043.627
250.93919252049.194
260.95219502049.363
270.96419852059.906
280.98220412078.796
291.00020932093.000
300.97620892140.901
310.95820832175.285
320.93320762224.286
330.91520672258.642
340.89720582294.392
350.87920472329.345
360.86120362365.775
370.84220242402.590
380.83020122423.212
390.81219992461.455
400.80019862482.500
410.78819732504.192
420.77619592525.273
430.76419462548.333
440.75219322570.806
450.74519182572.927
460.73319052597.727
470.72118912621.975
480.71518772624.619
490.70318632649.957
500.69718502654.348
510.68518362680.885
520.67918232685.670
530.67318092689.054
540.66717962694.000

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.


Work dayInputOutput
Hydraulic excavator (SL-330)Hydraulic excavator (320B)Daily trucksConvert into a single-inputDaily dredging (M3)

10.0000.6670.6000.4221668
20.0000.6670.6000.4221683
31.0000.0000.6360.5451701
41.0000.0000.6360.5451702
50.0000.3330.6360.3231700
60.0000.6670.6180.4281696
71.0000.0000.6000.5331665
81.0000.3330.6360.6571701
90.0000.6670.6550.4401716
100.0000.6670.6550.4401720
111.0000.3330.4730.6021706
121.0000.3330.5090.6141717
130.0000.6670.5270.3981729
140.0000.6670.5450.4041737
151.0000.6670.5640.7431747
161.0000.6670.6000.7561759
170.0001.0000.6180.5391770
180.0001.0000.6360.5451782
191.0000.6670.6550.7741792
201.0000.6670.6730.7801798
210.0001.0000.7090.5701826
220.0001.0000.7450.5821855
231.0000.6670.7640.8101871
241.0001.0000.7820.9271895
251.0001.0000.8180.9391925
261.0001.0000.8550.9521950
271.0001.0000.8910.9641985
281.0001.0000.9450.9822041
291.0001.0001.0001.0002093
301.0001.0000.9270.9762089
311.0001.0000.8730.9582083
321.0001.0000.8000.9332076
331.0001.0000.7450.9152067
341.0001.0000.6910.8972058
351.0001.0000.6360.8792047
361.0001.0000.5820.8612036
371.0001.0000.5270.8422024
381.0001.0000.4910.8302012
391.0001.0000.4360.8121999
401.0001.0000.4000.8001986
411.0001.0000.3640.7881973
421.0001.0000.3270.7761959
431.0001.0000.2910.7641946
441.0001.0000.2550.7521932
451.0001.0000.2360.7451918
461.0001.0000.2000.7331905
471.0001.0000.1640.7211891
481.0001.0000.1450.7151877
491.0001.0000.1090.7031863
501.0001.0000.0910.6971850
511.0001.0000.0550.6851836
521.0001.0000.0360.6791823
531.0001.0000.0180.6731809
541.0001.0000.0000.6671796

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.


Work dayTraditional dredging productivity methodProposed method
Dredging productivity resultDredging productivity result/One-day high dredging productivity1 input result3 input result

13950.5260.7510.7510.952
23986.0530.7580.7580.961
33118.5000.5930.5930.999
43120.3330.5930.5931.000
55259.3751.0001.0001.000
63960.0000.7530.7530.965
73121.8750.5940.5940.992
82590.7540.4930.4930.920
93896.4220.7410.7410.971
103905.5050.7430.7430.973
112833.7920.5390.5390.968
122795.7730.5320.5320.964
134344.4420.8260.8261.000
144299.0750.8170.8171.000
152349.9050.4470.4470.892
162328.0880.4430.4430.890
173281.4610.6240.6240.994
183267.0000.6210.6210.994
192316.0310.4400.4400.893
202305.7250.4380.4380.892
213205.2130.6090.6090.996
223188.2810.6060.6061.000
232309.5890.4390.4390.907
242043.6270.3890.3890.853
252049.1940.3900.3900.859
262049.3630.3900.3900.863
272059.9060.3920.3920.871
282078.7960.3950.3950.885
292093.0000.3980.3980.896
302140.9010.4070.4070.909
312175.2850.4140.4140.918
322224.2860.4230.4230.931
332258.6420.4290.4290.939
342294.3920.4360.4360.947
352329.3450.4430.4430.955
362365.7750.4500.4500.963
372402.5900.4570.4570.970
382423.2120.4610.4610.973
392461.4550.4680.4680.981
402482.5000.4720.4720.984
412504.1920.4760.4760.987
422525.2730.4800.4800.989
432548.3330.4850.4850.992
442570.8060.4890.4890.995
452572.9270.4890.4890.993
462597.7270.4940.4940.996
472621.9750.4990.4990.999
482624.6190.4990.4990.996
492649.9570.5040.5040.999
502654.3480.5050.5050.997
512680.8850.5100.5101.000
522685.6700.5110.5111.000
532689.0540.5110.5111.000
542694.0000.5120.5121.000

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.

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

4.2. Case 2: Cao Gongzhao I

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

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


Work dayHydraulic excavator (SL-330) (A)Hydraulic excavator (320B) (B)Daily trucks (C)Daily dredging (m3)(D)

127791086
2181752936
3183856804
4272354147
5271783811
6271943763
7273536135
8181422087
9181944203
10272034565
11272924857
12272925280
13271933288
14181935367
15182965078
16272674569
17272754636
18272774650
19273025173
20183516055
21274277397
22274437741
23274097164
24183105431
25273335835
26273596290
27274437751
28183436007
29184037062
30274127210
31274237396
32273726510
33274217375
34184237410
35274227384
36274357620
37274377627
38184497841
39274497847
40274507866
41274347592
42274367625
43184267452
44274317540
45274407708
46274377643
47183836703
48184337580
49184367634
50274437754
51274357616
52184377643
53274337577
54274316754
55274437746
56274477752
571810400
581810400
59273035298
60271292266
612740686
62272525177
63183806651
64183556212
65273035298
66271292266

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.


Work dayInputOutputOutput/Input
Convert to single inputDaily dredging (M3)Daily dredging productivity

10.386792816.346
20.4581756405.818
30.61738511019.975
40.5042358231.639
50.4611788273.882
60.4731947960.192
70.59335310342.529
80.4331424816.154
90.4731948890.962
100.4802039519.431
110.5472928879.834
120.5472929653.186
130.4721936966.549
140.47219311371.493
150.5502969232.727
160.5282678652.912
170.5342758680.170
180.5362778681.754
190.5553029328.361
200.59235110233.803
210.64942711393.279
220.66144311704.605
230.63640911271.132
240.5613109687.730
250.57833310094.626
260.59835910523.194
270.66144311719.725
280.58634310257.749
290.63140311190.684
300.63841211303.088
310.64642311445.158
320.60837210714.713
330.64542111439.483
340.64642311466.823
350.64542211440.000
360.65543511628.208
370.65743711612.042
380.66644911774.881
390.66644911783.891
400.66745011799.000
410.65543411598.889
420.65643611622.402
430.64842611491.402
440.65243111559.582
450.65944011694.897
460.65743711636.401
470.61638310883.100
480.65443311593.975
490.65643611636.120
500.66144311724.261
510.65543511622.104
520.65743711636.401
530.65443311589.386
540.65243110354.564
550.66144311712.165
560.66444711667.777
570.333101200.000
580.333101200.000
590.5553039540.737
600.4231295350.841
610.356401926.638
620.51725210020.000
630.61438010838.667
640.59535510445.656
650.5553039540.737
660.4231295350.841

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.


Work dayInputOutputDaily dredging productivity
Hydraulic excavator (SL-330)Hydraulic excavator (320B)Daily trucksDaily dredging (M3)1 input result3 input result

1277910860.2390.494
21817529360.5430.603
31838568040.9340.942
42723541470.6980.762
52717838110.7010.794
62719437630.6750.756
72735361350.8770.906
81814220870.4080.529
91819442030.7540.782
102720345650.8070.898
112729248570.7530.798
122729252800.8180.868
132719332880.5900.662
141819353670.9641.000
151829650780.7830.798
162726745690.7330.787
172727546360.7360.787
182727746500.7360.786
192730251730.7910.835
201835160550.8670.878
212742773970.9660.972
222744377410.9920.994
232740971640.9550.968
241831054310.8210.836
252733358350.8560.891
262735962900.8920.920
272744377510.9930.995
281834360070.8690.881
291840370620.9480.955
302741272100.9580.969
312742373960.9700.978
322737265100.9080.932
332742173750.9700.978
341842374100.9720.976
352742273840.9700.978
362743576200.9860.99
372743776270.9840.988
381844978410.9981.000
392744978470.9990.999
402745078661.0001.000
412743475920.9830.988
422743676250.9850.989
431842674520.9740.978
442743175400.9800.985
452744077080.9910.994
462743776430.9860.990
471838367030.9220.931
481843375800.9830.986
491843676340.9860.989
502744377540.9940.996
512743576160.9850.989
521843776430.9860.989
532743375770.9820.987
542743167540.8780.883
552744377460.9930.995
562744777520.9890.990
5718104000.1020.360
5818104000.1020.360
592730352980.8090.853
602712922660.4530.632
6127406860.1630.617
622725251770.8490.919
631838066510.9190.927
641835562120.8850.896
652730352980.8090.853
662712922660.4530.632

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.


Work dayTraditional dredging productivity methodProposed method
Dredging productivity resultDredging productivity result/One-day high dredging productivity1 input result3 input result

12816.3460.2390.2390.494
26405.8180.5430.5430.603
311019.9750.9340.9340.942
48231.6390.6980.6980.762
58273.8820.7010.7010.794
67960.1920.6750.6750.756
710342.5290.8770.8770.906
84816.1540.4080.4080.529
98890.9620.7540.7540.782
109519.4310.8070.8070.898
118879.8340.7530.7530.798
129653.1860.8180.8180.868
136966.5490.5900.5900.662
1411371.4930.9640.9641.000
159232.7270.7830.7830.798
168652.9120.7330.7330.787
178680.1700.7360.7360.787
188681.7540.7360.7360.786
199328.3610.7910.7910.835
2010233.8030.8670.8670.878
2111393.2790.9660.9660.972
2211704.6050.9920.9920.994
2311271.1320.9550.9550.968
249687.7300.8210.8210.836
2510094.6260.8560.8560.891
2610523.1940.8920.8920.920
2711719.7250.9930.9930.995
2810257.7490.8690.8690.881
2911190.6840.9480.9480.955
3011303.0880.9580.9580.969
3111445.1580.9700.9700.978
3210714.7130.9080.9080.932
3311439.4830.9700.9700.978
3411466.8230.9720.9720.976
3511440.0000.9700.9700.978
3611628.2080.9860.9860.990
3711612.0420.9840.9840.988
3811774.8810.9980.9981.000
3911783.8910.9990.9990.999
4011799.0001.0001.0001.000
4111598.8890.9830.9830.988
4211622.4020.9850.9850.989
4311491.4020.9740.9740.978
4411559.5820.9800.9800.985
4511694.8970.9910.9910.994
4611636.4010.9860.9860.990
4710883.1000.9220.9220.931
4811593.9750.9830.9830.986
4911636.1200.9860.9860.989
5011724.2610.9940.9940.996
5111622.1040.9850.9850.989
5211636.4010.9860.9860.989
5311589.3860.9820.9820.987
5410354.5640.8780.8780.883
5511712.1650.9930.9930.995
5611667.7770.9890.9890.990
571200.0000.1020.1020.360
581200.0000.1020.1020.360
599540.7370.8090.8090.853
605350.8410.4530.4530.632
611926.6380.1630.1630.617
6210020.0000.8490.8490.919
6310838.6670.9190.9190.927
6410445.6560.8850.8850.896
659540.7370.8090.8090.853
665350.8410.4530.4530.632

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.


Work dayHydraulic excavator (SL-330) (A)Hydraulic excavator (320B) (B)Daily trucks (C)Daily dredging (m3)(D)

131013320
231096012
3213106210
421388033
521488217
631478210
731568858
8314710423
9314710713
10314710785
11314710634
12314710220
13314712031
14314712523
15314812666
16314812804
17314914181
18316118091
19315914518
20315814312
21314815270
22313815373
23313815413
24314916211
25315716503
26314716366
27213817005
28213717832
29213416527
30213716583
31213615589
32213615056
33112315037
34111416142
3519215861
361714916
371535057
381123775

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.


Work dayInputOutputOutput/Input
Convert to single inputDaily dredging (M3)Daily dredging productivity

10.867320369.231
20.75660127957.059
30.68362109087.805
40.628803312795.929
50.650821712641.538
60.789821010407.042
70.783885811308.085
80.7891042313212.254
90.7891071313579.859
100.7891078513671.127
110.7891063413479.718
120.7891022012954.930
130.7891203115250.563
140.7891252315874.225
150.8171266615509.388
160.8171280415678.367
170.8441418116793.289
180.94480918566.941
190.8671451816751.538
200.8391431217060.662
210.8171527018697.959
220.7941537319350.629
230.7941541319400.979
240.8441621119197.237
250.8111650320346.164
260.7891636620745.634
270.6281700527087.611
280.6001783229720.000
290.5171652731987.742
300.6001658327638.333
310.5721558927242.913
320.5721505626311.456
330.3001503750123.333
340.3061614252828.364
350.2061586177161.622
360.133491636870.000
370.144505735010.000
380.0283775135900.000

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.


Work dayInputOutputDaily dredging productivity
Hydraulic excavator (SL-330)Hydraulic excavator (320B)Daily trucksDaily dredging (M3)1 input result3 input result

1310133200.0030.015
2310960120.0590.275
32131062100.0670.257
4213880330.0940.332
5214882170.0930.320
6314782100.0770.294
7315688580.0830.301
83147104230.0970.373
93147107130.1000.383
103147107850.1010.386
113147106340.0990.381
123147102200.0950.366
133147120310.1120.431
143147125230.1170.448
153148126660.1140.453
163148128040.1150.458
173149141810.1240.507
183161180910.0630.261
193159145180.1230.493
203158143120.1260.486
213148152700.1380.546
223138153730.1420.582
233138154130.1430.583
243149162110.1410.580
253157165030.1500.560
263147163660.1530.586
272138170050.1990.704
282137178320.2190.738
292134165270.2350.684
302137165830.2030.686
312136155890.2000.645
322136150560.1940.623
331123150370.3690.940
341114161420.3891.000
35192158610.5681.000
3617149160.2710.470
3715350570.2581.000
3811237751.0001.000

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.


Work day Traditional dredging productivity methodProposed method
Dredging productivity resultDredging productivity result/One-day high dredging productivity1 input result3 input result

1369.2310.0030.0030.015
27957.0590.0590.0590.275
39087.8050.0670.0670.257
412795.9290.0940.0940.332
512641.5380.0930.0930.320
610407.0420.0770.0770.294
711308.0850.0830.0830.301
813212.2540.0970.0970.373
913579.8590.1000.1000.383
1013671.1270.1010.1010.386
1113479.7180.0990.0990.381
1212954.9300.0950.0950.366
1315250.5630.1120.1120.431
1415874.2250.1170.1170.448
1515509.3880.1140.1140.453
1615678.3670.1150.1150.458
1716793.2890.1240.1240.507
188566.9410.0630.0630.261
1916751.5380.1230.1230.493
2017060.6620.1260.1260.486
2118697.9590.1380.1380.546
2219350.6290.1420.1420.582
2319400.9790.1430.1430.583
2419197.2370.1410.1410.580
2520346.1640.1500.1500.560
2620745.6340.1530.1530.586
2727087.6110.1990.1990.704
2829720.0000.2190.2190.738
2931987.7420.2350.2350.684
3027638.3330.2030.2030.686
3127242.9130.2000.2000.645
3226311.4560.1940.1940.623
3350123.3330.3690.3690.940
3452828.3640.3890.3891.000
3577161.6220.5680.5681.000
3636870.0000.2710.2710.470
3735010.0000.2580.2581.000
38135900.0001.0001.0001.000

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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