a novel method for evaluating dredging productivity using

Research ArticleA Novel Method for Evaluating Dredging Productivity Using aData 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, Taiwan2Institute of Engineering Science and Technology, National Kaohsiung University of Science and Technology 811, Taiwan3Department of Management Sciences, R.O.C. Military Academy, Kaohsiung 830, Taiwan

Correspondence should be addressed to Kuei-Hu Chang; [email protected]

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.

The increase in the frequency of extreme weather has caused the impact of natural disasters to become more extensive. Naturaldisasters reduce the effective storage capacity of reservoirs and affect their normal function. Reservoir dredging is a key issue inthe management of water resources and is a complicated multiple-attribute decision-making (MADM) problem. The traditionalassessment of dredging productivity has been performedusing a labor productivitymethod to evaluate the related issues of dredgingperformance. However, the traditional labor productivity method only deals with the single-input/single-output evaluation factorfor various forms of productivity. The traditional labor productivity method cannot address complicated MADM problems in theassessment of dredging productivity. To resolve the limitations of the traditional labor productivity method, this paper extendeddata envelopment analysis (DEA) and proposed a novel method for evaluating dredging productivity. The proposed method canhandle various combinations of evaluation factors (single-input, multi-input, single-output, and multioutput). Three real cases ofreservoir dredging are applied to verify the effectiveness of the proposed method. The simulation results show that the proposedmethod 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 frequencyof extreme weather events, enhancing the risk of natu-ral disasters. According to the United Nations and othersources of official statistics, floods are the most commonnatural disaster and cause the most fatalities among vari-ous types of natural disasters. The main cause of floodingis high-intensity rainfall due to extreme weather. Today,extreme weather can cause heavy rain, and total rainfall hasincreased especially in areas that are affected by tropical cy-clones.

Over the past 70 years, floods have risen to varyingdegrees in various parts of the world, accounting for 53% ofthe world’s victims of natural disasters and 42% of deaths dueto such disasters [1]. Hills et al. [2] and Brown and Daigneault[3] indicated that engineering solutions, such as buildingdams, river dredging, and raising the heights of buildingsand strengthening them, should be applied to prevent flood

disasters. Daigneault et al. [4] reported 3 such methods:planting riparian buffers, upland afforestation, and riverdredging. River dredging has the greatest overall benefitsbut is expensive. Jeong et al. [5] reported that reservoirsedimentation is a severe problem worldwide and that thereis an annual decrease in global reservoir storage capacity of1% due to reservoir deposition.

Reservoir dredging, an excavation activity that is usuallyperformed underwater, is a key issue for the managementof water resources. Dredging performance is evaluated byobservation and the use of detailed records, and its indicatorsinclude the type of equipment, type of transport, trans-port distance, reoperation frequency, machine proficiency,earthwork conditions, and other ongoing projects. Manyscholars have explored the issues that are related to dredging.For example, Jeong et al. [5] used a multicriteria decisionanalysis technique to develop a river dredging managementmodel in Korea that assigns weights to various dredging-related factors, including dredging cost and the social and

HindawiMathematical Problems in EngineeringVolume 2019, Article ID 5130835, 22 pageshttps://doi.org/10.1155/2019/5130835

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2 Mathematical Problems in Engineering

environmental impact, to solve the problem of river dredg-ing. Nachtmann et al. [6] discussed problem definitionand model formulation of optimal dredge fleet schedulingto improve the efficiency of dredging projects that wereundertaken by the US Army Corps of Engineers (USACE).This approach can be used by decision-makers to increasethe productivity of dredging machines. Christian and Xie[7] indicated that appropriate planning and scheduling sig-nificantly reduce wait times and other delays, renderingearthworks more efficient and reducing the risk of cost over-runs.

Dredging performance (productivity) is one of the mainresearch topics in construction engineering and manage-ment science. Dredging involves the transportation of largeamounts of earth, requiring the consideration of trans-portation methods and combinations of complex machinery.Therefore, reservoir dredging is a complicated multiple-attribute decision-making (MADM)problem.The traditionalmethod for assessing dredging productivity uses a laborproductivitymethod to evaluate the related issues of dredgingperformance. Thomas et al. [8] defined productivity as “thework hour (WH) required to complete a unit of work” andstated that research on productivity should focus on labor-intensive work, repetitive work, and important crew work.The traditional labor productivity method is simple andwidely used in many areas, such as role of the fabricator inlabor productivity [9], the effects of heat stress on construc-tion labor productivity [10], and quantifying schedule riskin construction projects [11]. However, the traditional laborproductivity method only deals with the single-input/single-output evaluation factor of various forms of productiv-ity.

The data envelopment analysis (DEA) method can effec-tively solve complicated MADMproblems.TheDEAmethodwas first proposed by Charnes et al. [12] as a mathematicalprogramming method to evaluate the relative efficiency ofdecision-making units (DMUs) with multiple inputs andoutputs variables. Although some papers have used the DEAmethod to solve productivity-related issues, no researchutilized this method to deal with the evaluation of dredgingproductivity [13–17]. This paper extends the DEA method topropose a novel dredging productivity evaluation method,solving the issues that are related to the evaluation of dredgingproductivity. The author aggregated data on the work areaconditions that are encountered by the army in Taiwanwhen building reservoirs and dredging rivers, comparing thedifference between the proposed method and the traditionallabor productivity method about equipment dispatch deci-sions. These findings would serve as a reference for dredg-ing task scheduling and equipment allocation by the mili-tary.

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

2. Literature Review

2.1. Traditional Dredging Productivity. Dredging perfor-mance must cover many aspects, mainly including fourfactors: productivity, quality, safety, and timeliness. Mostimportantly, productivity must be at an appropriate level.Overall productivity usually depends on the productivityof the workers and machinery. It is generally believed thatproductivity is the ratio of “output” to “input” in unit time.As shown in [18]

Productivity = Total OutputTotal Input Resources (1)

Dredging work is often done using a combination ofmultiple operations, and traditional productivity calculationmethods can only solve the problem of single input–singleoutput.

2.2. DEA. Charnes et al. [12] initially proposed the DEAmethod as a mathematical programming method to evaluatethe relative efficiency of decision-making units (DMUs)(first-mode CCR model). Since then, many scholars haveapplied the DEAmethod to address decision-making-relatedissues. For example, Sowunmi et al. [19] used framework ofstochastic frontier analysis of the DEA method to considerenvironmentally detrimental inputs and traditional produc-tion inputs to estimate the efficiency of fishing operationsin sand dredging and non-dredging areas. Widiarto et al.[20] used DEA to assess the efficiency of microfinanceinstitutions and analyze the choice of loan methods in not-for-profit microfinance institutions. Fan et al. [21] evaluatedthe ecoefficiency of industrial parks in China using the DEAmodel, applying park resources, industrial structure, envi-ronmental policy, and scale of development as the indicatorsthat affect ecological efficiency to reflect the characteristics ofecoefficiency of sustainable development.

DEA is a method of measuring the relative efficiencies ofa group of DMUs that use multiple inputs to produce mul-tiple outputs. This nonparametric technique was originallyconceived to analyze a set of units. Because the DEA methodcan 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-worldproblems.

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

Efficiency =∑𝑔𝑐=1 𝑢𝑐𝑦𝑐0∑𝑚𝑖=1 V𝑖𝑥𝑖0

(2)

where 𝑢𝑐 and V𝑖 denote the output and input weights (inten-sity), respectively. 𝑦𝑐0 and 𝑥𝑖0 are the outputs 𝑐 and inputs 𝑖 ofthe observed DMU.

Charnes et al. [12] developed the first-mode CCR modelfor DEA to deal with multi-input and multioutput prob-lems using a linear programming solution. The CCR modelconsiders a DEA input with 𝑛 industries or DMUs (theDMUs in this paper are dredging projects) of the same nature

Mathematical Problems in Engineering 3

(homogeneous), where each DMU uses 𝑚 input resourcesand produces 𝑔 outputs. For DMU 𝑗, the number of inputresources is 𝑥𝑖𝑗 and the number of outputs is 𝑦𝑐𝑗 (𝑐 =1, . . . , 𝑔). To assess the efficiency of DMU𝑘, the output/inputratio 𝑃𝑘 can be used, which is expressed as a percentageefficiency (that is, 0 ≤ 𝑃𝑘 ≤ 1). Herein, 𝑢𝑘𝑐 is the weight ofthe output term 𝑐 and V𝑘𝑖 is the weight of the input term 𝑖.In their original model, fractional programming was used toobtain the input and output variable weights—namely, V𝑘𝑖 , V

𝑘𝑖 ,

and 𝑃𝑘—as expressed by

Maximize: 𝑃𝑘 =∑𝑔𝑐=1 𝑢

𝑘𝑐𝑌𝑘𝑐

∑𝑚𝑖=1 V𝑘𝑖𝑋𝑘𝑖

𝑢𝑘𝑐 , 𝑌𝑘𝑐 , V𝑘𝑖 , 𝑋𝑘𝑖 ≥ 0,

𝑖 = 1, 2, . . . , 𝑚, 𝑐 = 1, 2, . . . , 𝑔

Subject to:∑𝑔𝑐=1 𝑢

𝑘𝑐𝑌𝑟𝑐

∑𝑚𝑖=1 V𝑘𝑖𝑋𝑟𝑖≤ 1, 𝑟 = 1, 2, . . . , 𝑅

𝑢𝑘𝑐 ≥ 𝜀 ≥ 0, 𝑐 = 1, 2, . . . , 𝑔

V𝑘𝑖 ≥ 𝜀 ≥ 0, 𝑖 = 1, 2, . . . , 𝑚

(3)

where 𝜀 is a very small positive number (10−4), called anon-Archimedean constant. First, the fractional program-ming model that is given by (3) is converted into a linearprogramming problem before it is solved. In (3), considerthe denominator in the objective function to be equal to 1(∑𝑚𝑖=1 V

𝑘𝑖𝑋𝑘𝑖 = 1) and add this to the restriction condition. The

limiting inequality of (3) is multiplied by ∑𝑚𝑖=1 V𝑘𝑖𝑋𝑘𝑖 on both

sides of the inequality, and the right-hand side is canceled toobtain the following:

Maximize: 𝑃𝑘 =𝑔

∑𝑐=1

𝑢𝑘𝑐𝑌𝑘𝑐

Subject to:𝑚

∑𝑖=1

V𝑘𝑖𝑋𝑘𝑖 = 1

𝑔

∑𝑐=1

𝑢𝑘𝑐𝑌𝑟𝑐 −𝑚

∑𝑖=1

V𝑘𝑖𝑋𝑟𝑖 ≤ 0, 𝑟 = 1, 2, . . . , 𝑅

𝑢𝑘𝑐 ≥ 𝜀 ≥ 0, 𝑐 = 1, 2, . . . , 𝑔

V𝑘𝑖 ≥ 𝜀 ≥ 0, 𝑖 = 1, 2, . . . , 𝑚

(4)

In (3), the limit is the ratio of “actual output” to “actualinput” of each DMU; the value of that ratio is between 0 and 1.The optimal values of 𝑢𝑘𝑐 and V

𝑘𝑖 are obtained using (3). DMU

efficiency values are not necessarily decided by the managerin advance.

If 𝑃𝑘 = 1, the rated DMU is “efficient;” if 𝑃𝑘 < 1, therated DMU is “not efficient.” As in (4), each DMU mustuse its input and output as the objective function once, andthe inputs and outputs of other DMUs are considered to berestricted. Therefore, using this method for a comparison of

relative efficiency, the efficiency can be estimated in a fair andobjective manner.

3. Proposed DEA-Based Method

The possibility of extreme climate changes due to thegreenhouse effect and rises in sea water temperature in the21st century is growing rapidly. Extreme weather, includ-ing typhoons, causes serious river and reservoir earthrockflow problems, which dredging can alleviate. However, riveror reservoir dredging is a complicated multiple-attributedecision-making (MADM) problem.The traditional methodof calculating dredging productivity can only deal withthe problem of single input–single output. But, dredgingis a systematic problem, influenced by the complexity ofmultiple inputs and multiple outputs. To effectively solvethis issue of dredging, this paper used the DEA CCR modelto effectively handle the dredging MADM problem. Theadvantages of the DEA method can handle the complexmulti-input–multioutput problems for assessing dredgingissues.

Theprocedure of the proposedDEA-basedmethod in thispaper comprises five steps.

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

Step 2. Consider the number of each type of instrumentas input and earthwork as output. For example, hydraulicexcavators and trucks are the input resources, and dredgingproductivity is the total output results.

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

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

𝑁𝑖𝑗 =[𝑥𝑖𝑗 −min (𝑥𝑖𝑗)]

max (𝑥𝑖𝑗) −min (𝑥𝑖𝑗)

(𝑖 = 1, 2, . . . 𝑚; 𝑗 = 1, 2, . . . , 𝑛)

(5)

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

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

The flowchart of the novel dredging productivity evalua-tion method is shown in Figure 1.

Step 5. Analyze the dredging productivity evaluation resultsand provide suggestions.

4. Case Study

To verify the feasibility and effectiveness of the proposedmethod and demonstrate that the traditional method of


Step 1.

Step 2.

Step 3.

Step 4.

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

Use the DEA CCR model to analyze the efficiency of multi-input data (DMUs) for

assessing dredging productivity.

Convert different input-output combinations into a single-input-single-output model.

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

Observe and record the daily number of machines, earthwork output, and working

area status of the dredging work area.

Figure 1: Flowchart of the proposed dredging productivity evaluation method.

Figure 2: Nanhua Reservoir dredging diagram.

calculating dredging productivity is a special case of theproposed method, this paper will apply three practicaldredging cases (Nanhua Reservoir, Cao Gongzhao I, andCao Gongzhao II) from sites in Taiwan to calculate dredgingproductivity.

4.1. Case 1: Nanhua Reservoir. Nanhua Reservoir is locatedeast of Yushan Village, Nanhua District, Tainan City, Taiwan.The Nanhua Reservoir was built in 1988 and completed in1994; 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 watersupply in Tainan and Kaohsiung districts, which also havesightseeing and tourism functions.

In the dredging case of Nanhua Reservoir, we collecteddata for 54 working days from April 8 to May 31, 2011.The input items include the number of dispatches per dayfor hydraulic excavators (SL-330 and 320B) and trucks, and

the output is the amount of earthwork output, as shown inTable 1.

4.1.1. Solution by the Traditional Dredging Productivity Assess-ment Method. The traditional dredging productivity assess-ment method is based mainly on calculations by the laborproductivity method [8]. However, the labor productivitymethod can only solve the single-input–single-output prob-lem and cannot solve the multi-input–multioutput problem.In fact, dredging is a multi-input–multioutput MADM prob-lem. Formultiple input variables, we used (5) to convert theminto a single input variable. The daily dredging productivity iscalculated by the traditional dredging productivity method,as shown in Table 2.

4.1.2. Solution by the Proposed Method. The proposed dredg-ing productivity evaluation method can handle differentcombinations of evaluation factors (single-input, multi-input, single-output, andmultioutput) for dredging data. Thefollowing steps describe the proposed method.

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

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

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


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 16682 1 5 98 16833 2 3 100 17014 2 3 100 17025 1 4 100 17006 1 5 99 16967 2 3 98 16658 2 4 100 17019 1 5 101 171610 1 5 101 172011 2 4 91 170612 2 4 93 171713 1 5 94 172914 1 5 95 173715 2 5 96 174716 2 5 98 175917 1 6 99 177018 1 6 100 178219 2 5 101 179220 2 5 102 179821 1 6 104 182622 1 6 106 185523 2 5 107 187124 2 6 108 189525 2 6 110 192526 2 6 112 195027 2 6 114 198528 2 6 117 204129 2 6 120 209330 2 6 116 208931 2 6 113 208332 2 6 109 207633 2 6 106 206734 2 6 103 205835 2 6 100 204736 2 6 97 203637 2 6 94 202438 2 6 92 201239 2 6 89 199940 2 6 87 198641 2 6 85 197342 2 6 83 195943 2 6 81 194644 2 6 79 193245 2 6 78 191846 2 6 76 190547 2 6 74 189148 2 6 73 187749 2 6 71 186350 2 6 70 185051 2 6 68 1836


Table 1: Continued.

Work day Hydraulic excavator (SL-330) (A) Hydraulic excavator (320B) (B) Daily trucks (C) Daily dredging (m3) (D)52 2 6 67 182353 2 6 66 180954 2 6 65 1796

Table 2: Daily dredging productivity by the traditional dredging productivity method.

Work day Input Output Output/InputConvert to single input Daily dredging (M3) Daily dredging productivity

1 0.422 1668 3950.5262 0.422 1683 3986.0533 0.545 1701 3118.5004 0.545 1702 3120.3335 0.323 1700 5259.3756 0.428 1696 3960.0007 0.533 1665 3121.8758 0.657 1701 2590.7549 0.440 1716 3896.42210 0.440 1720 3905.50511 0.602 1706 2833.79212 0.614 1717 2795.77313 0.398 1729 4344.44214 0.404 1737 4299.07515 0.743 1747 2349.90516 0.756 1759 2328.08817 0.539 1770 3281.46118 0.545 1782 3267.00019 0.774 1792 2316.03120 0.780 1798 2305.72521 0.570 1826 3205.21322 0.582 1855 3188.28123 0.810 1871 2309.58924 0.927 1895 2043.62725 0.939 1925 2049.19426 0.952 1950 2049.36327 0.964 1985 2059.90628 0.982 2041 2078.79629 1.000 2093 2093.00030 0.976 2089 2140.90131 0.958 2083 2175.28532 0.933 2076 2224.28633 0.915 2067 2258.64234 0.897 2058 2294.39235 0.879 2047 2329.34536 0.861 2036 2365.77537 0.842 2024 2402.59038 0.830 2012 2423.21239 0.812 1999 2461.45540 0.800 1986 2482.50041 0.788 1973 2504.19242 0.776 1959 2525.27343 0.764 1946 2548.33344 0.752 1932 2570.806


Table 2: Continued.


45 0.745 1918 2572.92746 0.733 1905 2597.72747 0.721 1891 2621.97548 0.715 1877 2624.61949 0.703 1863 2649.95750 0.697 1850 2654.34851 0.685 1836 2680.88552 0.679 1823 2685.67053 0.673 1809 2689.05454 0.667 1796 2694.000

Rela

tive e

ffici

ency

Work day

2011 Nanhua Reservoir productivity curve comparison 2011 Nanhua Reservoir productivity curve comparison

Traditional method productivity Proposed method (1 input)Proposed method (3 input)

6000.00

5000.00

4000.00

3000.00

2000.00

1000.00

0.00 0.00

0.20

0.40

0.60

0.80

1.00

1.20

Rela

tive e

ffici

ency

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

Work day

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

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

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

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

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

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

The daily dredging productivity of Nanhua Reservoir wascalculated using DEAP software. The results are shown inTable 4.

4.1.3. Comparison and Discussion. We calculated the dredg-ing assessment results for 1-input-1-output and 3-input-1-output in order to compare the traditional dredging pro-ductivity assessment method with the proposed dredgingproductivity evaluation method. The results are shown inTable 4 and Figure 3.

As verified by Nanhua Reservoir, we obtain the followingconclusions:

(1) Dredging is an MADM problem that may includesingle-input–single-output and multi-input–mul-tioutput. The traditional dredging productivitymethod can only calculate the single-input–single-output problem.The proposed dredging productivityevaluation method can calculate the dredgingproductivity of single-input–single-output, multiple-input–single-output, single-input–multiple-output,and multi-input–multioutput. Therefore, it is proventhat the traditional dredging productivity method isa special case of the proposed method.

(2) The calculation results of traditional dredging pro-ductivity, divided by one-day high dredging pro-ductivity with the single input results of proposedmethod, are the same. This result implies that theproposed method can solve more complex problemsof dredging productivity.


Table 3: 3 inputs into a single-input-single-output model conversion.

Work day Input OutputHydraulic 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 16682 0.000 0.667 0.600 0.422 16833 1.000 0.000 0.636 0.545 17014 1.000 0.000 0.636 0.545 17025 0.000 0.333 0.636 0.323 17006 0.000 0.667 0.618 0.428 16967 1.000 0.000 0.600 0.533 16658 1.000 0.333 0.636 0.657 17019 0.000 0.667 0.655 0.440 171610 0.000 0.667 0.655 0.440 172011 1.000 0.333 0.473 0.602 170612 1.000 0.333 0.509 0.614 171713 0.000 0.667 0.527 0.398 172914 0.000 0.667 0.545 0.404 173715 1.000 0.667 0.564 0.743 174716 1.000 0.667 0.600 0.756 175917 0.000 1.000 0.618 0.539 177018 0.000 1.000 0.636 0.545 178219 1.000 0.667 0.655 0.774 179220 1.000 0.667 0.673 0.780 179821 0.000 1.000 0.709 0.570 182622 0.000 1.000 0.745 0.582 185523 1.000 0.667 0.764 0.810 187124 1.000 1.000 0.782 0.927 189525 1.000 1.000 0.818 0.939 192526 1.000 1.000 0.855 0.952 195027 1.000 1.000 0.891 0.964 198528 1.000 1.000 0.945 0.982 204129 1.000 1.000 1.000 1.000 209330 1.000 1.000 0.927 0.976 208931 1.000 1.000 0.873 0.958 208332 1.000 1.000 0.800 0.933 207633 1.000 1.000 0.745 0.915 206734 1.000 1.000 0.691 0.897 205835 1.000 1.000 0.636 0.879 204736 1.000 1.000 0.582 0.861 203637 1.000 1.000 0.527 0.842 202438 1.000 1.000 0.491 0.830 201239 1.000 1.000 0.436 0.812 199940 1.000 1.000 0.400 0.800 198641 1.000 1.000 0.364 0.788 197342 1.000 1.000 0.327 0.776 195943 1.000 1.000 0.291 0.764 194644 1.000 1.000 0.255 0.752 193245 1.000 1.000 0.236 0.745 191846 1.000 1.000 0.200 0.733 190547 1.000 1.000 0.164 0.721 189148 1.000 1.000 0.145 0.715 187749 1.000 1.000 0.109 0.703 186350 1.000 1.000 0.091 0.697 1850


Table 3: Continued.

Work day Input OutputHydraulic excavator (SL-330) Hydraulic excavator (320B) Daily trucks Convert into a single-input Daily dredging (M3)

51 1.000 1.000 0.055 0.685 183652 1.000 1.000 0.036 0.679 182353 1.000 1.000 0.018 0.673 180954 1.000 1.000 0.000 0.667 1796

Table 4: Dredging assessment results for the traditional dredging productivity assessment method and proposed method.

Work dayTraditional dredging productivity method Proposed method

Dredging productivity result Dredging productivity result/One-dayhigh dredging productivity 1 input result 3 input result

1 3950.526 0.751 0.751 0.9522 3986.053 0.758 0.758 0.9613 3118.500 0.593 0.593 0.9994 3120.333 0.593 0.593 1.0005 5259.375 1.000 1.000 1.0006 3960.000 0.753 0.753 0.9657 3121.875 0.594 0.594 0.9928 2590.754 0.493 0.493 0.9209 3896.422 0.741 0.741 0.97110 3905.505 0.743 0.743 0.97311 2833.792 0.539 0.539 0.96812 2795.773 0.532 0.532 0.96413 4344.442 0.826 0.826 1.00014 4299.075 0.817 0.817 1.00015 2349.905 0.447 0.447 0.89216 2328.088 0.443 0.443 0.89017 3281.461 0.624 0.624 0.99418 3267.000 0.621 0.621 0.99419 2316.031 0.440 0.440 0.89320 2305.725 0.438 0.438 0.89221 3205.213 0.609 0.609 0.99622 3188.281 0.606 0.606 1.00023 2309.589 0.439 0.439 0.90724 2043.627 0.389 0.389 0.85325 2049.194 0.390 0.390 0.85926 2049.363 0.390 0.390 0.86327 2059.906 0.392 0.392 0.87128 2078.796 0.395 0.395 0.88529 2093.000 0.398 0.398 0.89630 2140.901 0.407 0.407 0.90931 2175.285 0.414 0.414 0.91832 2224.286 0.423 0.423 0.93133 2258.642 0.429 0.429 0.93934 2294.392 0.436 0.436 0.94735 2329.345 0.443 0.443 0.95536 2365.775 0.450 0.450 0.96337 2402.590 0.457 0.457 0.97038 2423.212 0.461 0.461 0.973


Table 4: Continued.



39 2461.455 0.468 0.468 0.98140 2482.500 0.472 0.472 0.98441 2504.192 0.476 0.476 0.98742 2525.273 0.480 0.480 0.98943 2548.333 0.485 0.485 0.99244 2570.806 0.489 0.489 0.99545 2572.927 0.489 0.489 0.99346 2597.727 0.494 0.494 0.99647 2621.975 0.499 0.499 0.99948 2624.619 0.499 0.499 0.99649 2649.957 0.504 0.504 0.99950 2654.348 0.505 0.505 0.99751 2680.885 0.510 0.510 1.00052 2685.670 0.511 0.511 1.00053 2689.054 0.511 0.511 1.00054 2694.000 0.512 0.512 1.000

Figure 4: Cao Gongzhao I dredging diagram.

4.2. Case 2: Cao Gongzhao I. Cao Gongzhao was built in1919, across the areas of Pingtung and Kaohsiung, Taiwan. Itis one of the important sources of irrigation water for earlyfarmland in Taiwan. TheCaoGongzhao I dredging work areahas a width of 800 meters, length of 500 meters, and an areaof 40 hectares. The depth of digging is 2.5 meters, and theplanned dredging volume is 1 million cubic meters, as shownin Figure 4.

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

4.2.1. Solution by the Traditional Dredging Productivity Assess-ment 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 shownin Table 6.

4.2.2. Solution by the Proposed Method (Cao Gongzhao I).Using the DEA CCR model, the daily dredging productivityfor Cao Gongzhao I is calculated; the results are shown inTable 7.

4.2.3. Comparison and Discussion. We calculate the dredgingassessment results for 1-input-1-output and 3-input-1output tocompare the dredging assessment results for Cao GongzhaoI which is between the traditional and the proposed dredgingproductivity evaluation methods. See Table 8 and Figure 5.

Based on the results of Table 8 and Figure 5, the calcu-lation results of traditional dredging productivity, dividedby one-day high dredging productivity with the single inputresults of proposed method, are the same. Therefore, thetraditional dredging productivity assessment method can beviewed as a special case of the novel dredging productivityevaluation method.

4.3. Case 3: Cao Gongzhao II. Phase 1 dredging was imple-mented at Cao Gongzhao in 2011, and the second phase ofdredgingwas carried out in the same region in 2012, for a totalof 38 days. The records are shown in Table 9.

4.3.1. Solution by the Traditional Dredging Productivity Assess-ment Method (Cao Gongzhao II). The multi-input variablesfor Cao Gongzhao II were transformed into a single inputquantity. Use (1) and (5) to calculated daily dredging produc-tivity, as shown in Table 10.


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 10862 1 8 175 29363 1 8 385 68044 2 7 235 41475 2 7 178 38116 2 7 194 37637 2 7 353 61358 1 8 142 20879 1 8 194 420310 2 7 203 456511 2 7 292 485712 2 7 292 528013 2 7 193 328814 1 8 193 536715 1 8 296 507816 2 7 267 456917 2 7 275 463618 2 7 277 465019 2 7 302 517320 1 8 351 605521 2 7 427 739722 2 7 443 774123 2 7 409 716424 1 8 310 543125 2 7 333 583526 2 7 359 629027 2 7 443 775128 1 8 343 600729 1 8 403 706230 2 7 412 721031 2 7 423 739632 2 7 372 651033 2 7 421 737534 1 8 423 741035 2 7 422 738436 2 7 435 762037 2 7 437 762738 1 8 449 784139 2 7 449 784740 2 7 450 786641 2 7 434 759242 2 7 436 762543 1 8 426 745244 2 7 431 754045 2 7 440 770846 2 7 437 764347 1 8 383 670348 1 8 433 758049 1 8 436 763450 2 7 443 775451 2 7 435 7616


Table 5: Continued.

Work day Hydraulic excavator (SL-330) (A) Hydraulic excavator (320B) (B) Daily trucks (C) Daily dredging (m3)(D)52 1 8 437 764353 2 7 433 757754 2 7 431 675455 2 7 443 774656 2 7 447 775257 1 8 10 40058 1 8 10 40059 2 7 303 529860 2 7 129 226661 2 7 40 68662 2 7 252 517763 1 8 380 665164 1 8 355 621265 2 7 303 529866 2 7 129 2266

Table 6: Daily dredging productivity by the traditional dredging productivity method.


1 0.386 79 2816.3462 0.458 175 6405.8183 0.617 385 11019.9754 0.504 235 8231.6395 0.461 178 8273.8826 0.473 194 7960.1927 0.593 353 10342.5298 0.433 142 4816.1549 0.473 194 8890.96210 0.480 203 9519.43111 0.547 292 8879.83412 0.547 292 9653.18613 0.472 193 6966.54914 0.472 193 11371.49315 0.550 296 9232.72716 0.528 267 8652.91217 0.534 275 8680.17018 0.536 277 8681.75419 0.555 302 9328.36120 0.592 351 10233.80321 0.649 427 11393.27922 0.661 443 11704.60523 0.636 409 11271.13224 0.561 310 9687.73025 0.578 333 10094.62626 0.598 359 10523.19427 0.661 443 11719.72528 0.586 343 10257.74929 0.631 403 11190.68430 0.638 412 11303.08831 0.646 423 11445.158


Table 6: Continued.


32 0.608 372 10714.71333 0.645 421 11439.48334 0.646 423 11466.82335 0.645 422 11440.00036 0.655 435 11628.20837 0.657 437 11612.04238 0.666 449 11774.88139 0.666 449 11783.89140 0.667 450 11799.00041 0.655 434 11598.88942 0.656 436 11622.40243 0.648 426 11491.40244 0.652 431 11559.58245 0.659 440 11694.89746 0.657 437 11636.40147 0.616 383 10883.10048 0.654 433 11593.97549 0.656 436 11636.12050 0.661 443 11724.26151 0.655 435 11622.10452 0.657 437 11636.40153 0.654 433 11589.38654 0.652 431 10354.56455 0.661 443 11712.16556 0.664 447 11667.77757 0.333 10 1200.00058 0.333 10 1200.00059 0.555 303 9540.73760 0.423 129 5350.84161 0.356 40 1926.63862 0.517 252 10020.00063 0.614 380 10838.66764 0.595 355 10445.65665 0.555 303 9540.73766 0.423 129 5350.841

Table 7: Daily dredging productivity by the proposed method.

Work day Input Output Daily dredging productivityHydraulic excavator (SL-330) Hydraulic excavator (320B) Daily trucks Daily dredging (M3) 1 input result 3 input result

1 2 7 79 1086 0.239 0.4942 1 8 175 2936 0.543 0.6033 1 8 385 6804 0.934 0.9424 2 7 235 4147 0.698 0.7625 2 7 178 3811 0.701 0.7946 2 7 194 3763 0.675 0.7567 2 7 353 6135 0.877 0.9068 1 8 142 2087 0.408 0.5299 1 8 194 4203 0.754 0.78210 2 7 203 4565 0.807 0.898


Table 7: Continued.


11 2 7 292 4857 0.753 0.79812 2 7 292 5280 0.818 0.86813 2 7 193 3288 0.590 0.66214 1 8 193 5367 0.964 1.00015 1 8 296 5078 0.783 0.79816 2 7 267 4569 0.733 0.78717 2 7 275 4636 0.736 0.78718 2 7 277 4650 0.736 0.78619 2 7 302 5173 0.791 0.83520 1 8 351 6055 0.867 0.87821 2 7 427 7397 0.966 0.97222 2 7 443 7741 0.992 0.99423 2 7 409 7164 0.955 0.96824 1 8 310 5431 0.821 0.83625 2 7 333 5835 0.856 0.89126 2 7 359 6290 0.892 0.92027 2 7 443 7751 0.993 0.99528 1 8 343 6007 0.869 0.88129 1 8 403 7062 0.948 0.95530 2 7 412 7210 0.958 0.96931 2 7 423 7396 0.970 0.97832 2 7 372 6510 0.908 0.93233 2 7 421 7375 0.970 0.97834 1 8 423 7410 0.972 0.97635 2 7 422 7384 0.970 0.97836 2 7 435 7620 0.986 0.9937 2 7 437 7627 0.984 0.98838 1 8 449 7841 0.998 1.00039 2 7 449 7847 0.999 0.99940 2 7 450 7866 1.000 1.00041 2 7 434 7592 0.983 0.98842 2 7 436 7625 0.985 0.98943 1 8 426 7452 0.974 0.97844 2 7 431 7540 0.980 0.98545 2 7 440 7708 0.991 0.99446 2 7 437 7643 0.986 0.99047 1 8 383 6703 0.922 0.93148 1 8 433 7580 0.983 0.98649 1 8 436 7634 0.986 0.98950 2 7 443 7754 0.994 0.99651 2 7 435 7616 0.985 0.98952 1 8 437 7643 0.986 0.98953 2 7 433 7577 0.982 0.98754 2 7 431 6754 0.878 0.88355 2 7 443 7746 0.993 0.99556 2 7 447 7752 0.989 0.99057 1 8 10 400 0.102 0.36058 1 8 10 400 0.102 0.36059 2 7 303 5298 0.809 0.85360 2 7 129 2266 0.453 0.632


Table 7: Continued.


61 2 7 40 686 0.163 0.61762 2 7 252 5177 0.849 0.91963 1 8 380 6651 0.919 0.92764 1 8 355 6212 0.885 0.89665 2 7 303 5298 0.809 0.85366 2 7 129 2266 0.453 0.632

Table 8: The dredging assessment results for Cao Gongzhao I.



1 2816.346 0.239 0.239 0.4942 6405.818 0.543 0.543 0.6033 11019.975 0.934 0.934 0.9424 8231.639 0.698 0.698 0.7625 8273.882 0.701 0.701 0.7946 7960.192 0.675 0.675 0.7567 10342.529 0.877 0.877 0.9068 4816.154 0.408 0.408 0.5299 8890.962 0.754 0.754 0.78210 9519.431 0.807 0.807 0.89811 8879.834 0.753 0.753 0.79812 9653.186 0.818 0.818 0.86813 6966.549 0.590 0.590 0.66214 11371.493 0.964 0.964 1.00015 9232.727 0.783 0.783 0.79816 8652.912 0.733 0.733 0.78717 8680.170 0.736 0.736 0.78718 8681.754 0.736 0.736 0.78619 9328.361 0.791 0.791 0.83520 10233.803 0.867 0.867 0.87821 11393.279 0.966 0.966 0.97222 11704.605 0.992 0.992 0.99423 11271.132 0.955 0.955 0.96824 9687.730 0.821 0.821 0.83625 10094.626 0.856 0.856 0.89126 10523.194 0.892 0.892 0.92027 11719.725 0.993 0.993 0.99528 10257.749 0.869 0.869 0.88129 11190.684 0.948 0.948 0.95530 11303.088 0.958 0.958 0.96931 11445.158 0.970 0.970 0.97832 10714.713 0.908 0.908 0.93233 11439.483 0.970 0.970 0.97834 11466.823 0.972 0.972 0.97635 11440.000 0.970 0.970 0.978


Table 8: Continued.



36 11628.208 0.986 0.986 0.99037 11612.042 0.984 0.984 0.98838 11774.881 0.998 0.998 1.00039 11783.891 0.999 0.999 0.99940 11799.000 1.000 1.000 1.00041 11598.889 0.983 0.983 0.98842 11622.402 0.985 0.985 0.98943 11491.402 0.974 0.974 0.97844 11559.582 0.980 0.980 0.98545 11694.897 0.991 0.991 0.99446 11636.401 0.986 0.986 0.99047 10883.100 0.922 0.922 0.93148 11593.975 0.983 0.983 0.98649 11636.120 0.986 0.986 0.98950 11724.261 0.994 0.994 0.99651 11622.104 0.985 0.985 0.98952 11636.401 0.986 0.986 0.98953 11589.386 0.982 0.982 0.98754 10354.564 0.878 0.878 0.88355 11712.165 0.993 0.993 0.99556 11667.777 0.989 0.989 0.99057 1200.000 0.102 0.102 0.36058 1200.000 0.102 0.102 0.36059 9540.737 0.809 0.809 0.85360 5350.841 0.453 0.453 0.63261 1926.638 0.163 0.163 0.61762 10020.000 0.849 0.849 0.91963 10838.667 0.919 0.919 0.92764 10445.656 0.885 0.885 0.89665 9540.737 0.809 0.809 0.85366 5350.841 0.453 0.453 0.632

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 3202 3 10 9 60123 2 13 10 62104 2 13 8 80335 2 14 8 82176 3 14 7 82107 3 15 6 88588 3 14 7 104239 3 14 7 1071310 3 14 7 10785


Table 9: Continued.

Work day Hydraulic excavator (SL-330) (A) Hydraulic excavator (320B) (B) Daily trucks (C) Daily dredging (m3)(D)11 3 14 7 1063412 3 14 7 1022013 3 14 7 1203114 3 14 7 1252315 3 14 8 1266616 3 14 8 1280417 3 14 9 1418118 3 16 11 809119 3 15 9 1451820 3 15 8 1431221 3 14 8 1527022 3 13 8 1537323 3 13 8 1541324 3 14 9 1621125 3 15 7 1650326 3 14 7 1636627 2 13 8 1700528 2 13 7 1783229 2 13 4 1652730 2 13 7 1658331 2 13 6 1558932 2 13 6 1505633 1 12 3 1503734 1 11 4 1614235 1 9 2 1586136 1 7 1 491637 1 5 3 505738 1 1 2 3775

Table 10: Daily dredging productivity of Cao Gongzhao II by the traditional dredging productivity method.


1 0.867 320 369.2312 0.756 6012 7957.0593 0.683 6210 9087.8054 0.628 8033 12795.9295 0.650 8217 12641.5386 0.789 8210 10407.0427 0.783 8858 11308.0858 0.789 10423 13212.2549 0.789 10713 13579.85910 0.789 10785 13671.12711 0.789 10634 13479.71812 0.789 10220 12954.93013 0.789 12031 15250.56314 0.789 12523 15874.22515 0.817 12666 15509.38816 0.817 12804 15678.367


Table 10: Continued.


17 0.844 14181 16793.28918 0.944 8091 8566.94119 0.867 14518 16751.53820 0.839 14312 17060.66221 0.817 15270 18697.95922 0.794 15373 19350.62923 0.794 15413 19400.97924 0.844 16211 19197.23725 0.811 16503 20346.16426 0.789 16366 20745.63427 0.628 17005 27087.61128 0.600 17832 29720.00029 0.517 16527 31987.74230 0.600 16583 27638.33331 0.572 15589 27242.91332 0.572 15056 26311.45633 0.300 15037 50123.33334 0.306 16142 52828.36435 0.206 15861 77161.62236 0.133 4916 36870.00037 0.144 5057 35010.00038 0.028 3775 135900.000

Work day

Cao Gongzhao productivity curve comparison Cao Gongzhao productivity curve comparison

Traditional method productivity Proposed method (1 input)Proposed method (3 input)

1.20

1.00

0.80

0.60

0.40

0.20

0.00

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65

0.00

2000.00

4000.00

6000.00

8000.00

10000.00

12000.00

14000.00

Rela

tive e

ffici

ency

Work day

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65

Rela

tive e

ffici

ency

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

4.3.2. Solution by the Proposed Method (Cao Gongzhao II).Using the DEA CCR model, the daily dredging productivityfor Cao Gongzhao II is calculated; the results are shown inTable 11.

4.3.3. Comparison and Discussion. The dredging assessmentresults of Cao Gongzhao II by the traditional dredging pro-ductivity assessment method and the proposed method areshown in Table 12 and Figure 6.

The dredging case of Cao Gongzhao II yields the follow-ing conclusions:

(1) The traditional dredging productivity method canonly calculate the single-input–single-output prob-lem. The proposed dredging productivity evalua-tion method can calculate the dredging productivityof multi-input–multioutput problem. Based on theresults of Table 12, the traditional dredging productiv-ity calculations are divided by one-day high dredging


Table 11: Daily dredging productivity of Cao Gongzhao II by the proposed method.


1 3 10 13 320 0.003 0.0152 3 10 9 6012 0.059 0.2753 2 13 10 6210 0.067 0.2574 2 13 8 8033 0.094 0.3325 2 14 8 8217 0.093 0.3206 3 14 7 8210 0.077 0.2947 3 15 6 8858 0.083 0.3018 3 14 7 10423 0.097 0.3739 3 14 7 10713 0.100 0.38310 3 14 7 10785 0.101 0.38611 3 14 7 10634 0.099 0.38112 3 14 7 10220 0.095 0.36613 3 14 7 12031 0.112 0.43114 3 14 7 12523 0.117 0.44815 3 14 8 12666 0.114 0.45316 3 14 8 12804 0.115 0.45817 3 14 9 14181 0.124 0.50718 3 16 11 8091 0.063 0.26119 3 15 9 14518 0.123 0.49320 3 15 8 14312 0.126 0.48621 3 14 8 15270 0.138 0.54622 3 13 8 15373 0.142 0.58223 3 13 8 15413 0.143 0.58324 3 14 9 16211 0.141 0.58025 3 15 7 16503 0.150 0.56026 3 14 7 16366 0.153 0.58627 2 13 8 17005 0.199 0.70428 2 13 7 17832 0.219 0.73829 2 13 4 16527 0.235 0.68430 2 13 7 16583 0.203 0.68631 2 13 6 15589 0.200 0.64532 2 13 6 15056 0.194 0.62333 1 12 3 15037 0.369 0.94034 1 11 4 16142 0.389 1.00035 1 9 2 15861 0.568 1.00036 1 7 1 4916 0.271 0.47037 1 5 3 5057 0.258 1.00038 1 1 2 3775 1.000 1.000

productivity with the ingle input results of proposedmethod are the same. Therefore, it is proven that thetraditional dredging productivity method is a specialcase of the proposed method.

(2) Under the condition that the dredging area and con-ditions are the same, the calculation results by thetraditional dredging productivity method for CaoGongzhao 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 proposedmethod (green line shown).

5. Conclusions

In the 21st century, many earthrock flow disasters that arecaused by extreme climate have deeply affected many coun-tries and have caused a gradual decline in the supply of fresh-


Table 12: The dredging assessment results for Cao Gongzhao II.


Dredgingproductivity result

Dredging productivity result/One-dayhigh dredging productivity 1 input result 3 input result

1 369.231 0.003 0.003 0.0152 7957.059 0.059 0.059 0.2753 9087.805 0.067 0.067 0.2574 12795.929 0.094 0.094 0.3325 12641.538 0.093 0.093 0.3206 10407.042 0.077 0.077 0.2947 11308.085 0.083 0.083 0.3018 13212.254 0.097 0.097 0.3739 13579.859 0.100 0.100 0.38310 13671.127 0.101 0.101 0.38611 13479.718 0.099 0.099 0.38112 12954.930 0.095 0.095 0.36613 15250.563 0.112 0.112 0.43114 15874.225 0.117 0.117 0.44815 15509.388 0.114 0.114 0.45316 15678.367 0.115 0.115 0.45817 16793.289 0.124 0.124 0.50718 8566.941 0.063 0.063 0.26119 16751.538 0.123 0.123 0.49320 17060.662 0.126 0.126 0.48621 18697.959 0.138 0.138 0.54622 19350.629 0.142 0.142 0.58223 19400.979 0.143 0.143 0.58324 19197.237 0.141 0.141 0.58025 20346.164 0.150 0.150 0.56026 20745.634 0.153 0.153 0.58627 27087.611 0.199 0.199 0.70428 29720.000 0.219 0.219 0.73829 31987.742 0.235 0.235 0.68430 27638.333 0.203 0.203 0.68631 27242.913 0.200 0.200 0.64532 26311.456 0.194 0.194 0.62333 50123.333 0.369 0.369 0.94034 52828.364 0.389 0.389 1.00035 77161.622 0.568 0.568 1.00036 36870.000 0.271 0.271 0.47037 35010.000 0.258 0.258 1.00038 135900.000 1.000 1.000 1.000

water, making the exploitation of water resources a nationaleffort. Dredging is a key issue in the preservation of waterresources. Improving the preservation and application ofwater resources to ensure a plentiful freshwater supplythrough dredging is a topic that every country is studyingintently.

Dredging assessments primarily use productivity to rep-resent the effectiveness of dredging. The evaluation of dredg-ing also includes input variables, such as tools, trucks, andmanpower, and the complexity of the output results, suchas earthwork, flow rate, and water storage increase. Thetraditional dredging assessment method mainly uses work


Work day

2012 Cao Gongzhao productivity curve comparison 2012 Cao Gongzhao productivity curve comparison

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

Traditional method productivity

0.00

20000.00

40000.00

60000.00

80000.00

100000.00

120000.00

140000.00

160000.00

Rela

tive e

ffici

ency

0.00

0.20

0.40

0.60

0.80

1.00

1.20

Rela

tive e

ffici

ency

Work day

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

Proposed method (1 input)Proposed method (3 input)

Figure 6: Comparison of 2012 Cao Gongzhao II productivity curves.

force productivity to calculate the dredging performance [8].Although the traditional workforce productivity method issimple to calculate, this method can only deal with single-input variables and single-output outcomes and cannot solvemulti-input and -output multicriteria dredging decision-making problems.

To solve the related issue of dredging assessments, thispaper extended the DEA method to handle different com-binations of evaluation factors (single-input, multi-input,single-output, and multioutput). Three real cases of reservoirdredging were applied to verify the effectiveness of theproposed method. The simulation results show that the tra-ditional dredging productivity assessment can be viewed as aspecial case of the proposed dredging productivity evaluationmethod.Therefore, it is more appropriate to use the proposedmethod to calculate daily dredging productivity.

Subsequent studies can improve the risk assessment ofnatural and man-made factors, such as climate, machinery,earthwork conditions, the proficiency of operators, andmanagers’ methods; consider the subjective and objectiveweights of each evaluation factors of dredging to furtherexplore dredging topics. In terms of calculation methods,use different DEA model (such as network data envelopmentanalysis model, BBC model, and weighted slack-based Mea-sures model) to evaluate the dredging productivity.

Data Availability

The dredging productivity data used to support the findingsof 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 andTechnology, Taiwan, for financially supporting this research

under Contract nos. MOST 106-2410-H-145-001 and MOST107-2410-H-145-001.

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