Multi-Criteria Optimization of Mechanized Earth Processes and Its Impact on Economic and Environmental Sustainability
2. Analysis of Factors and Machines Useful for Earth Processes
- Bulk soils taken by a shovel or loader;
- Bulk soils disconnected by a spade or loader;
- Pit soils disconnected by a picker, excavator;
- Crumbly soils disconnected by a wedge, excavator;
- Easy demolition consolidated soils disconnected by a ripper, large excavator, demolitions;
- Hard demolition consolidated soils disconnected by a hard ripper, demolitions;
- Very hard demolition consolidated soils disconnected by demolitions.
3. Scientific Methods Used
Multi-Criteria Optimization Method
- Each parameter is assigned a different severity expressed by the weight of the parameter;
- Deterioration of any parameter must lead to an increase in the value of the multi-optimization indicator;
- The indicator of optimization of individual parameters must be implemented in such a way as to eliminate the influence of the choice of units;
- The values of the optimization indicator of individual parameters should not grow above all limits (the resulting multi-optimization indicator will not be sensitive to the choice of weighting factors);
- We choose the value of the optimization indicator of individual parameters so that the best variant has the lowest value of this indicator (performance and productivity-reciprocal values).
- Definition of optimization indicators:
- Time indicator—TI (i):for i = 1 …. n, where:TI (i)—time indicator;Ti—total duration of the “i”th machine’s work;n—number of machines.
- Energy indicator—EI (i):for i = 1 … n, where:EI (i)—energy indicator;Ei—machine energy consumption;n—number of machines.
- Cost indicator—CI (i):for i = 1 … n, where:CI (i)—cost indicator;Ci—total cost of the “i”th machine´s work;n—number of machines.
- Definition of weighting factors:In our paper, we applied these weighting factors:
The sum of the weighting factors is equal to 100%.
- Weighting factor of time—WT as a percentage;
- Weighting factor of energy—WE as a percentage;
- Weighting factor of cost—WC as a percentage.
- Definition of multi-criteria optimization indicator—IMO(i):TI (i)—Time indicator;EI (i)—Energy indicator;CI (i)—Cost indicator;WT—Weighting factor of time (%);WE—Weighting factor of energy (%);WC—Weighting factor of cost (%).Note: the sum of the weighting factors is equal to 100%.
- The best variant (BV) of the machine set is determined by this formula:for i = 1 … n, where:IMOi—multi-criteria optimization indicator of “i”th machine.This method was applied in our paper in the model example.
4. The Proposal of the Machine Selection Optimizing (MSO) Method for Earth Processes Using Multi-Criteria Optimization with Software Support
- Definition of the construction problem and the final product of the construction processes:Description of activities: This phase includes the key definition of the construction problem and final product of mechanized earth processes and the definition of all important input data.
- Proposal of suitable machines or machines groups:Description of activities: In this phase, the main activity is the proposal of suitable machines for a given type of construction works. The criterion (the aspect of quality) is the usefulness of the machines to provide the defined earth product. Basic processes at this step are the analysis of the earth process and earth product; proposal of useful machines for the defined earth product; the selection of all necessary input data concerning the machines including information about technical parameters, cost, fuel consumption, etc. The output of this step is machines useful to realize the earth product.
- Assessment of machines in terms of required time:Description of activities: At this phase, all the proposed machines or machine groups are evaluated according to the time criterion. The first step is calculating the production rates of all proposed and useful machines, and then the duration of the process is calculated. Time is one of the key requirements of most investors. Basic processes at this step are the creation of a model of mechanized earth processes; the proposal of possible variants of machines for defined earth processes; the proposal of mathematical variables and creation of mathematical models for calculating the duration of mechanized earth processes; software calculation of the duration of work by selected machines; comparing selected machine variants to the time of work required.The output of this step is machines that fulfill the time requirement.
- Assessment of machines in terms of additional optimizing criteria:Description of activities: This phase includes all machines, that fulfill the time criterion evaluated according to additional optimizing criteria, for example, cost or energy aspects). Minimizing cost and the consumption of fuel of machines are very serious requirements of investors and the construction process suppliers. Basic processes at this step are the definition of mathematic variables concerning the optimization criteria (cost, energy); creation of mathematical models for calculation cost and energy consumption in the defined earth processes; software calculation of cost and energy consumption by the selected machines; comparing selected machine variants to cost and energy consumption results (the output from software). The output of this step and the optimal solution is the optimal machines from the point of cost and fuel consumption.The output of this step is a machine with minimal costs and energy consumption.
5. Application and Verification of This Optimal Method into a Model Example of Surface Excavation
6. Multi-Criteria Optimization of Mechanized Earth Processes
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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|Type of Machine||1.||2.||3.||4.||5.||6.||7.||8.||9.||10.||11.||12.||13.|
|Characteristics of minerals, category of workability|
(Slovak standard STN 73 30 50)
|Watery earth||CS 1||S 2||S||CS||CS|
category No. 1–2
category No. 3–4
category No. 4–5
|Modest workability, rock, category No. 5–6||CS||CS||CS|
|Hard workability, rock,|
category No. 6–7
|Types of excavations|
|Surface grading, depth 0.5 m||S||CS||CS||CS||S||S||S||S|
|Location of excavation area|
|Type of Machine||Convenient Transportation Distance in Meters|
|Dump truck||More then 1000|
|Types of Machines|
|N.||Construction Symbol||Software Symbol||Mathematical Variable||Unit of Measure||Mathematical Model||Note|
|01.||VBS||VBS (i)||Volume of scraper bed||m3||Input data|
|02.||LS||LS||The average distance of excavation scraper transport||m||Input data|
|03.||TFS||TFS (i)||Fixed scraper cycle time||s||Input data|
|04.||VTS||VTS (i)||Scraper speed during disconnecting, transport and loading processes||km/h−1||Input data|
|05.||VES||VES (i)||Scraper speed with empty bed||km/h−1||Input data|
|06.||CWES||CWES||Coefficient of scraper work efficiency||-||Input data|
|07.||BCS||BCS||Earth bulk coefficient||-|
|08.||PRS||PRS (i)||Scraper production rate||m3 h−1||PR = 1000.1.6.7/|
(3/3.6 + 2/4 + 2/5)
|PR = 1000.VBS.CWES.BCS/(TFS/3.6 + LS/VTS + LS/VES)|
|09.||VS||VS||Total volume of scraper earthwork||m3||Input data|
|10.||TW||TW (i)||Total duration of the scraper’s work||h||TW = 09/08||TW = VS/PRS|
|11.||HS||HS||Shift duration in hours||h/shift||Input data (8, 10, 12, 14, 16 h)|
|12.||TWS||TWS (i)||Scraper operating time during the shift||h/shift||TW = 0.6.11||TW = 0.6.HS|
|13.||FCWS||FCWS (i)||Scraper fuel consumption during operating mode||l.h−1||Input data from scraper producer|
|14.||TRS||TRS (i)||Scraper time with empty body (bed)||h/shift||TW = 0.4.11||TW = 0.4.HS|
|15.||FCRS||FCRS (i)||Fuel consumption of the scraper during transport with an empty body (bed)||l.h−1||Input data from scraper producer|
|16.||NS||NS||Number of shifts||shift||NS = 10/11||NS = TW/HS|
|17.||CFS||CFS (i)||Total fuel consumption of the scraper||l|
(liters of diesel)
|CFS = 16(12.13 + 14.15)||CFS = NS(TWS.FCWS + TRS.FCRS)|
|18.||CRS||CRS (i)||The cost of scraper renting||€/day||Input data from renting company|
|19.||CSS||CSS (i)||The daily cost of a scraper’s driver’s salary||EUR/day||Input data from construction company|
|20.||CMS||CMS (i)||Scraper´s daily maintenance costs||EUR/day||Input data from construction company|
|21.||PDS||PDS||Price of diesel per 1 L for scraper||EUR/l||Input data|
|22.||DCS||DCS (i)||Daily cost of scraper diesel||EUR/shift||DSF = (17/16).21||DSF = (CFD/|
|23.||TCFS||TCFS (i)||Total fixed costs (wages, oils, diesel, daily maintenance) of the scraper||EUR/day||TCFD = 19 + 20 + 22||TCFD = CSS + CMS + DCS|
|24.||TCS||TCS (i)||Total cost of the scraper||EUR||TCS = (18 + 23)16||TC = (CRS + TCFS)NS|
|N.||Construction Symbol||Software Symbol||Mathematical Variable||Unit of Measure||Mathematical Model||Mi|
(i = 1, 2, 3, …, 10)
|1.||T||T(i)||Total duration of the machine work||H|
|2.||E||E(i)||Machine energy consumption||L (liters of diesel)|
|3.||C||C(i)||Total cost of the machine work||EUR|
|4.||TI||TI(i)||Time indicator||-||TI(i) = T(i)/SUM T(i)|
i = 1…10
|5.||EI||E(i)||Energy indicator||-||EI(i) = E(i)/SUM E(i)|
i = 1…10
|6.||CI||C(i)||Cost indicator||-||CI(i) = C(i)/SUM C(i)|
i = 1…10
|7.||WT||WT||Weighting factor of time||-||Input (0–100%)|
the same for all variants
|8.||WE||WE||Weighting factor of energy||-||Input (0–100%)|
the same for all variants
|9.||WC||WC||Weighting factor of total cost||-||Input (0–100%)|
the same for all variants
|10.||IMO(i)||IMO(i)||Indicator of multi optimization||-||IMO(i) = (T(i).(WT(i) + E(i).WE + CI(i).WC).10−2|
|11.||Best variant||BV||BV = min(IMO(i)|
i = 1, 2, 3, …, 10
11 = min(10)
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Gašparík, J.; Motyčka, V.; Šťastný, P.; Szalayová, S. Multi-Criteria Optimization of Mechanized Earth Processes and Its Impact on Economic and Environmental Sustainability. Sustainability 2022, 14, 78. https://doi.org/10.3390/su14010078
Gašparík J, Motyčka V, Šťastný P, Szalayová S. Multi-Criteria Optimization of Mechanized Earth Processes and Its Impact on Economic and Environmental Sustainability. Sustainability. 2022; 14(1):78. https://doi.org/10.3390/su14010078Chicago/Turabian Style
Gašparík, Jozef, Vít Motyčka, Patrik Šťastný, and Sylvia Szalayová. 2022. "Multi-Criteria Optimization of Mechanized Earth Processes and Its Impact on Economic and Environmental Sustainability" Sustainability 14, no. 1: 78. https://doi.org/10.3390/su14010078