Landslide susceptibility mapping in the Damrei Romel area, Cambodia using frequency ratio and logistic regression models

This study applied, tested and compared a probability model, a frequency ratio and statistical model, a logistic regression to Damre Romel area, Cambodia, using a geographic information system. For landslide susceptibility mapping, landslide locations were identified in the study area from interpretation of aerial photographs and field surveys, and a spatial database was constructed from topographic maps, geology and land cover. The factors that influence landslide occurrence, such as slope, aspect, curvature and distance from drainage were calculated from the topographic database. Lithology and distance from lineament were extracted and calculated from the geology database. Land cover was classified from Landsat TM satellite imagery. The relationship between the factors and the landslides was calculated using frequency ratio and logistic regression models. The relationships, frequency ratio and logistic regression coefficient were overlaid to make landslide susceptibility map. Then the landslide susceptibility map was compared with known landslide locations and tested. As the result, the frequency ratio model (86.97%) and the logistic regression (86.37%) had high and similar prediction accuracy. The landslide susceptibility map can be used to reduce hazards associated with landslides and to land cover planning.     

Predictive landslide susceptibility mapping using spatial information in the Pechabun area of Thailand

For predictive landslide susceptibility mapping, this study applied and verified probability model, the frequency ratio and statistical model, logistic regression at Pechabun, Thailand, using a geographic information system (GIS) and remote sensing. Landslide locations were identified in the study area from interpretation of aerial photographs and field surveys, and maps of the topography, geology and land cover were constructed to spatial database. The factors that influence landslide occurrence, such as slope gradient, slope aspect and curvature of topography and distance from drainage were calculated from the topographic database. Lithology and distance from fault were extracted and calculated from the geology database. Land cover was classified from Landsat TM satellite image. The frequency ratio and logistic regression coefficient were overlaid for landslide susceptibility mapping as each factor’s ratings. Then the landslide susceptibility map was verified and compared using the existing landslide location. As the verification results, the frequency ratio model showed 76.39% and logistic regression model showed 70.42% in prediction accuracy. The method can be used to reduce hazards associated with landslides and to plan land cover.     

Quantitative landslide susceptibility mapping at Pemalang area,Indonesia

For quantitative landslide susceptibility mapping, this study applied and verified a frequency ratio, logistic regression, and artificial neural network models to Pemalang area, Indonesia, using a Geographic Information System (GIS). Landslide locations were identified in the study area from interpretation of aerial photographs, satellite imagery, and field surveys; a spatial database was constructed from topographic and geological maps. The factors that influence landslide occurrence, such as slope gradient, slope aspect, curvature of topography, and distance from stream, were calculated from the topographic database. Lithology was extracted and calculated from geologic database. Using these factors, landslide susceptibility indexes were calculated by frequency ratio, logistic regression, and artificial neural network models. Then the landslide susceptibility maps were verified and compared with known landslide locations. The logistic regression model (accuracy 87.36%) had higher prediction accuracy than the frequency ratio (85.60%) and artificial neural network (81.70%) models. The models can be used to reduce hazards associated with landslides and to land-use planning.     

Landslide hazard mapping at Selangor, Malaysia using frequency ratio and logistic regression models

The aim of this study is to evaluate the landslide hazards at Selangor area, Malaysia, using Geographic Information System (GIS) and Remote Sensing. Landslide locations of the study area were identified from aerial photograph interpretation and field survey. Topographical maps, geological data, and satellite images were collected, processed, and constructed into a spatial database in a GIS platform. The factors chosen that influence landslide occurrence were: slope, aspect, curvature, distance from drainage, lithology, distance from lineaments, land cover, vegetation index, and precipitation distribution. Landslide hazardous areas were analyzed and mapped using the landslide-occurrence factors by frequency ratio and logistic regression models. The results of the analysis were verified using the landslide location data and compared with probability model. The comparison results showed that the frequency ratio model (accuracy is 93.04%) is better in prediction than logistic regression (accuracy is 90.34%) model.     

Landslide susceptibility analysis in the Hoa Binh province of Vietnam using statistical index and logistic regression

The purpose of this study is to evaluate and compare the results of applying the statistical index and the logistic regression methods for estimating landslide susceptibility in the Hoa Binh province of Vietnam. In order to do this, first, a landslide inventory map was constructed mainly based on investigated landslide locations from three projects conducted over the last 10 years. In addition, some recent landslide locations were identified from SPOT satellite images, fieldwork, and literature. Secondly, ten influencing factors for landslide occurrence were utilized. The slope gradient map, the slope curvature map, and the slope aspect map were derived from a digital elevation model (DEM) with resolution 20 × 20 m. The DEM was generated from topographic maps at a scale of 1:25,000. The lithology map and the distance to faults map were extracted from Geological and Mineral Resources maps. The soil type and the land use maps were extracted from National Pedology maps and National Land Use Status maps, respectively. Distance to rivers and distance to roads were computed based on river and road networks from topographic maps. In addition, a rainfall map was included in the models. Actual landslide locations were used to verify and to compare the results of landslide susceptibility maps. The accuracy of the results was evaluated by ROC analysis. The area under the curve (AUC) for the statistical index model was 0.946 and for the logistic regression model, 0.950, indicating an almost equal predicting capacity.     

Ensemble-based landslide susceptibility maps in Jinbu area, Korea

Ensemble techniques were developed, applied and validated for the analysis of landslide susceptibility in Jinbu area, Korea using the geographic information system (GIS). Landslide-occurrence areas were detected in the study by interpreting aerial photographs and field survey data. Landslide locations were randomly selected in a 70/30 ratio for training and validation of the models, respectively. Topography, geology, soil and forest databases were also constructed. Maps relevant to landslide occurrence were assembled in a spatial database. Using the constructed spatial database, 17 landslide-related factors were extracted. The relationships between the detected landslide locations and the factors were identified and quantified by frequency ratio, weight of evidence, logistic regression and artificial neural network models and their ensemble models. The relationships were used as factor ratings in the overlay analysis to create landslide susceptibility indexes and maps. Then, the four landslide susceptibility maps were used as new input factors and integrated using the frequency ratio, weight of evidence, logistic regression and artificial neural network models as ensemble methods to make better susceptibility maps. All of the susceptibility maps were validated by comparison with known landslide locations that were not used directly in the analysis. As the result, the ensemble-based landslide susceptibility map that used the new landslide-related input factor maps showed better accuracy (87.11% in frequency ratio, 83.14% in weight of evidence, 87.79% in logistic regression and 84.54% in artificial neural network) than the individual landslide susceptibility maps (84.94% in frequency ratio, 82.82% in weight of evidence, 87.72% in logistic regression and 81.44% in artificial neural network). All accuracy assessments showed overall satisfactory agreement of more than 80%. The ensemble model was found to be more effective in terms of prediction accuracy than the individual model.     

Delineation of landslide hazard areas on Penang Island, Malaysia, by using frequency ratio, logistic regression, and artificial neural network models

This paper summarizes findings of landslide hazard analysis on Penang Island, Malaysia, using frequency ratio, logistic regression, and artificial neural network models with the aid of GIS tools and remote sensing data. Landslide locations were identified and an inventory map was constructed by trained geomorphologists using photo-interpretation from archived aerial photographs supported by field surveys. A SPOT 5 satellite pan sharpened image acquired in January 2005 was used for land-cover classification supported by a topographic map. The above digitally processed images were subsequently combined in a GIS with ancillary data, for example topographical (slope, aspect, curvature, drainage), geological (litho types and lineaments), soil types, and normalized difference vegetation index (NDVI) data, and used to construct a spatial database using GIS and image processing. Three landslide hazard maps were constructed on the basis of landslide inventories and thematic layers, using frequency ratio, logistic regression, and artificial neural network models. Further, each thematic layer’s weight was determined by the back-propagation training method and landslide hazard indices were calculated using the trained back-propagation weights. The results of the analysis were verified and compared using the landslide location data and the accuracy observed was 86.41, 89.59, and 83.55% for frequency ratio, logistic regression, and artificial neural network models, respectively. On the basis of the higher percentages of landslide bodies predicted in very highly hazardous and highly hazardous zones, the results obtained by use of the logistic regression model were slightly more accurate than those from the other models used for landslide hazard analysis. The results from the neural network model suggest the effect of topographic slope is the highest and most important factor with weightage value (1.0), which is more than twice that of the other factors, followed by the NDVI (0.52), and then precipitation (0.42). Further, the results revealed that distance from lineament has the lowest weightage, with a value of 0. This shows that in the study area, fault lines and structural features do not contribute much to landslide triggering.     

Landslide susceptibility mapping by binary logistic regression, analytical hierarchy process, and statistical index models and assessment of their performances

The current research presents a detailed landslide susceptibility mapping study by binary logistic regression, analytical hierarchy process, and statistical index models and an assessment of their performances. The study area covers the north of Tehran metropolitan, Iran. When conducting the study, in the first stage, a landslide inventory map with a total of 528 landslide locations was compiled from various sources such as aerial photographs, satellite images, and field surveys. Then, the landslide inventory was randomly split into a testing dataset 70 % (370 landslide locations) for training the models, and the remaining 30 % (158 landslides locations) was used for validation purpose. Twelve landslide conditioning factors such as slope degree, slope aspect, altitude, plan curvature, normalized difference vegetation index, land use, lithology, distance from rivers, distance from roads, distance from faults, stream power index, and slope-length were considered during the present study. Subsequently, landslide susceptibility maps were produced using binary logistic regression (BLR), analytical hierarchy process (AHP), and statistical index (SI) models in ArcGIS. The validation dataset, which was not used in the modeling process, was considered to validate the landslide susceptibility maps using the receiver operating characteristic curves and frequency ratio plot. The validation results showed that the area under the curve (AUC) for three mentioned models vary from 0.7570 to 0.8520 $ ({\text{AUC}}_{\text{AHP}} = 75.70\;\% ,\;{\text{AUC}}_{\text{SI}} = 80.37\;\% ,\;{\text{and}}\;{\text{AUC}}_{\text{BLR}} = 85.20\;\% ) $ ( AUC AHP = 75.70 % , AUC SI = 80.37 % , and AUC BLR = 85.20 % ) . Also, plot of the frequency ratio for the four landslide susceptibility classes of the three landslide susceptibility models was validated our results. Hence, it is concluded that the binary logistic regression model employed in this study showed reasonably good accuracy in predicting the landslide susceptibility of study area. Meanwhile, the results obtained in this study also showed that the statistical index model can be used as a simple tool in the assessment of landslide susceptibility when a sufficient number of data are obtained.     

A comparative study on the landslide susceptibility mapping using logistic regression and statistical index models

The logistic regression and statistical index models are applied and verified for landslide susceptibility mapping in Daguan County, Yunnan Province, China, by means of the geographic information system (GIS). A detailed landslide inventory map was prepared by literatures, aerial photographs, and supported by field works. Fifteen landslide-conditioning factors were considered: slope angle, slope aspect, curvature, plan curvature, profile curvature, altitude, STI, SPI, and TWI were derived from digital elevation model; NDVI was extracted from Landsat ETM7; rainfall was obtained from local rainfall data; distance to faults, distance to roads, and distance to rivers were created from a 1:25,000 scale topographic map; the lithology was extracted from geological map. Using these factors, the landslide susceptibility maps were prepared by LR and SI models. The accuracy of the results was verified by using existing landslide locations. The statistical index model had a predictive rate of 81.02%, which is more accurate prediction in comparison with logistic regression model (80.29%). The models can be used to land-use planning in the study area.     

Manifestation of remote sensing data and GIS on landslide hazard analysis using spatial-based statistical models

This paper presents landslide hazard analysis at Cameron area, Malaysia, using a geographic information system (GIS) and remote sensing data. Landslide locations were identified from interpretation of aerial photographs and field surveys. Topographical and geological data and satellite images were collected, processed, and constructed into a spatial database using GIS and image processing. The factors chosen that influence landslide occurrence are topographic slope, topographic aspect, topographic curvature, and distance to rivers, all from the topographic database; lithology and distance to faults were taken from the geologic database; land cover from TM satellite image; the vegetation index value was taken from Landsat images; and precipitation distribution from meteorological data. Landslide hazard area was analyzed and mapped using the landslide occurrence factors by frequency ratio and bivariate logistic regression models. The results of the analysis were verified using the landslide location data and compared with the probabilistic models. The validation results showed that the frequency ratio model (accuracy is 89.25%) is better in prediction of landslide than bivariate logistic regression (accuracy is 85.73%) model.     

Landslide susceptibility analysis and its verification using likelihood ratio, logistic regression, and artificial neural network models: case study of Youngin, Korea

The likelihood ratio, logistic regression, and artificial neural networks models are applied and verified for analysis of landslide susceptibility in Youngin, Korea, using the geographic information system. From a spatial database containing such data as landslide location, topography, soil, forest, geology, and land use, the 14 landslide-related factors were calculated or extracted. Using these factors, landslide susceptibility indexes were calculated by likelihood ratio, logistic regression, and artificial neural network models. Before the calculation, the study area was divided into two sides (west and east) of equal area, for verification of the models. Thus, the west side was used to assess the landslide susceptibility, and the east side was used to verify the derived susceptibility. The results of the landslide susceptibility analysis were verified using success and prediction rates. The verification results showed satisfactory agreement between the susceptibility map and the existing data on landslide locations.     

GIS-based landslide susceptibility mapping with probabilistic likelihood ratio and spatial multi-criteria evaluation models (North of Tehran,Iran)

The aim of this study is to produce landslide susceptibility mapping by probabilistic likelihood ratio (PLR) and spatial multi-criteria evaluation (SMCE) models based on geographic information system (GIS) in the north of Tehran metropolitan, Iran. The landslide locations in the study area were identified by interpretation of aerial photographs, satellite images, and field surveys. In order to generate the necessary factors for the SMCE approach, remote sensing and GIS integrated techniques were applied in the study area. Conditioning factors such as slope degree, slope aspect, altitude, plan curvature, profile curvature, surface area ratio, topographic position index, topographic wetness index, stream power index, slope length, lithology, land use, normalized difference vegetation index, distance from faults, distance from rivers, distance from roads, and drainage density are used for landslide susceptibility mapping. Of 528 landslide locations, 70 % were used in landslide susceptibility mapping, and the remaining 30 % were used for validation of the maps. Using the above conditioning factors, landslide susceptibility was calculated using SMCE and PLR models, and the results were plotted in ILWIS-GIS. Finally, the two landslide susceptibility maps were validated using receiver operating characteristic curves and seed cell area index methods. The validation results showed that area under the curve for SMCE and PLR models is 76.16 and 80.98 %, respectively. The results obtained in this study also showed that the probabilistic likelihood ratio model performed slightly better than the spatial multi-criteria evaluation. These landslide susceptibility maps can be used for preliminary land use planning and hazard mitigation purpose.     

Frequency ratio model based landslide susceptibility mapping in lower Mae Chaem watershed, Northern Thailand

The purpose of this study is to produce a landslide susceptibility map for the lower Mae Chaem watershed, northern Thailand using a Geographic Information System (GIS) and remotely sensed images. For this purpose, past landslide locations were identified from satellite images and aerial photographs accompanied by the field surveys to create a landslide inventory map. Ten landslide-inducing factors were used in the susceptibility analysis: elevation, slope angle, slope aspect, lithology, distance from lineament, distance from drainage, precipitation, soil texture, land use/land cover (LULC), and NDVI. The first eight factors were prepared from their associated database while LULC and NDVI maps were generated from Landsat-5 TM images. Landslide susceptibility was analyzed and mapped using the frequency ratio (FR) model that determines the level of correlation between locations of past landslides and the chosen factors and describes it in terms of frequency ratio index. Finally, the output map was validated using the area under the curve (AUC) method where the success rate of 80.06% and the prediction rate of 84.82% were achieved. The obtained map can be used to reduce landslide hazard and assist with proper planning of LULC in the future.     

RS & GIS-based landslide susceptibility mapping of the Balason River basin,Darjeeling Himalaya,using logistic regression (LR) model

The present study deals with the preparation of a landslide susceptibility map of the Balason River basin, Darjeeling Himalaya, using a logistic regression model based on Geographic Information System and Remote Sensing. The landslide inventory map was prepared with a total of 295 landslide locations extracted from various satellite images and intensive field survey. Topographical maps, satellite images, geological, geomorphological, soil, rainfall and seismic data were collected, processed and constructed into a spatial database in a GIS environment. The chosen landslide-conditioning factors were altitude, slope aspect, slope angle, slope curvature, geology, geomorphology, soil, land use/land cover, normalised differential vegetation index, drainage density, lineament number density, distance from lineament, distance to drainage, stream power index, topographic wetted index, rainfall and peak ground acceleration. The produced landslide susceptibility map satisfied the decision rules and ?2 Log likelihood, Cox &; Snell R-Square and Nagelkerke R-Square values proved that all the independent variables were statistically significant. The receiver operating characteristic curve showed that the prediction accuracy of the landslide probability map was 96.10%. The proposed LR method can be used in other hazard/disaster studies and decision-making.     

Evaluation of the consistency of landslide susceptibility mapping: a case study from the Kankai watershed in east Nepal

GIS-based landslide susceptibility maps for the Kankai watershed in east Nepal are developed using the frequency ratio method and the multiple linear regression technique. The maps are derived from comparing observed landslides with possible causative factors: slope angle, slope aspect, slope curvature, relative relief, distance from drainage, land use, geology, distance from faults and mean annual rainfall. The consistency of the maps is evaluated using landslide density analysis, success rate analysis and spatially agreed area approach. The first two analyses produce almost identical quantitative results, whereas the last approach is able to reveal spatial differences between the maps and also to improve predictions in the agreed high landslide-susceptible area.     

Landslide susceptibility mapping using certainty factor, index of entropy and logistic regression models in GIS and their comparison at Mugling�CNarayanghat road section in Nepal Himalaya

Landslide susceptibility maps are vital for disaster management and for planning development activities in the mountainous country like Nepal. In the present study, landslide susceptibility assessment of Mugling?CNarayanghat road and its surrounding area is made using bivariate (certainty factor and index of entropy) and multivariate (logistic regression) models. At first, a landslide inventory map was prepared using earlier reports and aerial photographs as well as by carrying out field survey. As a result, 321 landslides were mapped and out of which 241 (75?%) were randomly selected for building landslide susceptibility models, while the remaining 80 (25?%) were used for validating the models. The effectiveness of landslide susceptibility assessment using GIS and statistics is based on appropriate selection of the factors which play a dominant role in slope stability. In this case study, the following landslide conditioning factors were evaluated: slope gradient; slope aspect; altitude; plan curvature; lithology; land use; distance from faults, rivers and roads; topographic wetness index; stream power index; and sediment transport index. These factors were prepared from topographic map, drainage map, road map, and the geological map. Finally, the validation of landslide susceptibility map was carried out using receiver operating characteristic (ROC) curves. The ROC plot estimation results showed that the susceptibility map using index of entropy model with AUC value of 0.9016 has highest prediction accuracy of 90.16?%. Similarly, the susceptibility maps produced using logistic regression model and certainty factor model showed 86.29 and 83.57?% of prediction accuracy, respectively. Furthermore, the ROC plot showed that the success rate of all the three models performed more than 80?% accuracy (i.e. 89.15?% for IOE model, 89.10?% for LR model and 87.21?% for CF model). Hence, it is concluded that all the models employed in this study showed reasonably good accuracy in predicting the landslide susceptibility of Mugling?CNarayanghat road section. These landslide susceptibility maps can be used for preliminary land use planning and hazard mitigation purpose.     

Application of weights-of-evidence and certainty factor models and their comparison in landslide susceptibility mapping at Haraz watershed, Iran

The main goal of this study was to investigate the application of the weights-of-evidence and certainty factor approaches for producing landslide susceptibility maps of a landslide-prone area (Haraz) in Iran. For this purpose, the input layers of the landslide conditioning factors were prepared in the first stage. The landslide conditioning factors considered for the study area were slope gradient, slope aspect, altitude, lithology, land use, distance from streams, distance from roads, distance from faults, topographic wetness index, stream power index, stream transport index and plan curvature. For validation of the produced landslide susceptibility maps, the results of the analyses were compared with the field-verified landslide locations. Additionally, the receiver operating characteristic curves for all the landslide susceptibility models were constructed and the areas under the curves were calculated. The landslide locations were used to validate results of the landslide susceptibility maps. The verification results showed that the weights-of-evidence model (79.87%) performed better than certainty factor (72.02%) model with a standard error of 0.0663 and 0.0756, respectively. According to the results of the area under curve evaluation, the map produced by weights-of-evidence exhibits satisfactory properties.     

Landslide susceptibility mapping using LiDAR and DMC data: a case study in the Three Gorges area, China

The objective of this study is to map landslide susceptibility in Zigui segment of the Yangtze Three Gorges area that is known as one of the most landslide-prone areas in China by using data from light detection and ranging (LiDAR) and digital mapping camera (DMC). The likelihood ratio (LR) and logistic regression model (LRM) were used in this study. The work is divided into three phases. The first phase consists of data processing and analysis. In this phase, LiDAR and DMC data and geological maps were processed, and the landslide-controlling factors were derived such as landslide density, digital elevation model (DEM), slope angle, aspect, lithology, land use and distance from drainage. Among these, the landslide inventories, land use and drainage were constructed with both LiDAR and DMC data; DEM, slope angle and aspect were constructed with LiDAR data; lithology was taken from the 1:250,000 scale geological maps. The second phase is the logistic regression analysis. In this phase, the LR was applied to find the correlation between the landslide locations and the landslide-controlling factors, whereas the LRM was used to predict the occurrence of landslides based on six factors. To calculate the coefficients of LRM, 13,290,553 pixels was used, 29.5 % of the total pixels. The logical regression coefficients of landslide-controlling factors were obtained by logical regression analysis with SPSS 17.0 software. The accuracy of the LRM was 88.8 % on the whole. The third phase is landslide susceptibility mapping and verification. The mapping result was verified using the landslide location data, and 64.4 % landslide pixels distributed in “extremely high” zone and “high” zone; in addition, verification was performed using a success rate curve. The verification result show clearly that landslide susceptibility zones were in close agreement with actual landslide areas in the field. It is also shown that the factors that were applied in this study are appropriate; lithology, elevation and distance from drainage are primary factors for the landslide susceptibility mapping in the area, while slope angle, aspect and land use are secondary.     

Groundwater qanat potential mapping using frequency ratio and Shannon’s entropy models in the Moghan watershed,Iran

The purpose of current study is to produce groundwater qanat potential map using frequency ratio (FR) and Shannon's entropy (SE) models in the Moghan watershed, Khorasan Razavi Province, Iran. The qanat is basically a horizontal, interconnected series of underground tunnels that accumulate and deliver groundwater from a mountainous source district, along a water- bearing formation (aquifer), and to a settlement. A qanat locations map was prepared for study area in 2013 based on a topographical map at a 1:50,000-scale and extensive field surveys. 53 qanat locations were detected in the field surveys. 70 % (38 locations) of the qanat locations were used for groundwater potential mapping and 30 % (15 locations) were used for validation. Fourteen effective factors were considered in this investigation such as slope degree, slope aspect, altitude, topographic wetness index (TWI), stream power index (SPI), slope length (LS), plan curvature, profile curvature, distance to rivers, distance to faults, lithology, land use, drainage density, and fault density. Using the above conditioning factors, groundwater qanat potential map was generated implementing FR and SE models, and the results were plotted in ArcGIS. The predictive capability of frequency ratio and Shannon's entropy models were determined by the area under the relative operating characteristic curve. The area under the curve (AUC) for frequency ratio model was calculated as 0.8848. Also AUC for Shannon's entropy model was 0.9121, which depicts the excellence of this model in qanat occurrence potential estimation in the study area. So the Shannon's entropy model has higher AUC than the frequency ratio model. The produced groundwater qanat potential maps can assist planners and engineers in groundwater development plans and land use planning.     

Comparison of landslide susceptibility mapping methodologies for Koyulhisar,Turkey: conditional probability,logistic regression,artificial neural networks,and support vector machine

This case study presented herein compares the GIS-based landslide susceptibility mapping methods such as conditional probability (CP), logistic regression (LR), artificial neural networks (ANNs) and support vector machine (SVM) applied in Koyulhisar (Sivas, Turkey). Digital elevation model was first constructed using GIS software. Landslide-related factors such as geology, faults, drainage system, topographical elevation, slope angle, slope aspect, topographic wetness index, stream power index, normalized difference vegetation index, distance from settlements and roads were used in the landslide susceptibility analyses. In the last stage of the analyses, landslide susceptibility maps were produced from ANN, CP, LR, SVM models, and they were then compared by means of their validations. However, area under curve values obtained from all four methodologies showed that the map obtained from ANN model looks like more accurate than the other models, accuracies of all models can be evaluated relatively similar. The results also showed that the CP is a simple method in landslide susceptibility mapping and highly compatible with GIS operating features. Susceptibility maps can be easily produced using CP, because input process, calculation and output processes are very simple in CP model when compared with the other methods considered in this study.