Pairwise Comparison Matrix Research Articles

Identification of groundwater recharge potential zones in a study region of South Kerala

Groundwater is considered as a precious natural resource which serves as the main source of agriculture and domestic purposes. Kerala state is blessed with around 3000mm rainfall annually because of two prominent monsoon. But the available water is insufficient to meet the demand of people. Increase in population and water demand cause threat to overall water balance. Ground water resource must be managed well to overcome these problems. Ground water recharging is a major requirement for sustainable utilization of water resources. It also becomes highly relevant to assess the water recharge zones and to preserve water quality. This study proposes identification of suitable water recharge sites in Karamana river basin, Thiruvananthapuram, Kerala. Karamana river supplies majority of drinking water in Thiruvananthapuram district. Since its quality is deteriorating day by day, appropriate locations for recharging groundwater is identified using GIS technique. Various thematic maps like soil, slope, drainage, geomorphology and land utilization that affect the groundwater recharge is integrated and weighted overlay analysis is adopted to find the groundwater recharge potential map. Weights are assigned using Analytical Hierarchy Process (AHP) by constructing a pairwise comparison matrix. The result depicts the groundwater recharge potential zones which is divided into very high, high, moderate, low and very low potential areas.

Groundwater potential zones mapping by applying GIS, remote sensing and multi-criteria decision analysis in the Ghiss basin, northern Morocco

The Ghiss watershed, located in a Mediterranean semi-arid area, is currently experiencing a prolonged drought. The scarcity of potable surface water has driven the population and the government to intensify the exploration of groundwater resources. Conventional methods used for groundwater exploration are generally expensive, time-consuming and are limited in space. Therefore, we suggest with the present study the application of geospatial techniques (Geographical Information Systems (GIS) and Remote Sensing) and Multi-criteria decision analysis as a non-conventional and more accessible method of groundwater exploration in the Ghiss basin. Accordingly, eleven factors of high importance concerning the delineation of groundwater potential zones were weighted depending on their relative importance using the Analytical Hierarchy Process's (AHP) pairwise comparison matrix. The GIS-based analysis of multiple thematic layers (drainage density, lineament density, roughness, lithology, land use and land cover, elevation, curvature, topographic wetness index, topographic position index, rainfall and slope) has revealed that “poor” and “moderate” groundwater potential constitute respectively 7% (58.59 km2) and 55% (460.35 km2) of the area, while “good” and “very good” groundwater potential represent respectively 35% (292.95 km2) and only 3% (25.11 km2) of the area. Our model results were validated using depth to water level (DWL) data of the Ghiss watershed and this comparison showed an acceptable conformity (70%) with GWPZs mapped for the Ghiss basin. It was also determined that the degree of conformity to generated GWPZ models using fewer parameters is comparable to those using more parameters. Our results indicate that two parameters (Lineament Density and Lithology) were sufficient to obtain a similar conformity (68%) with depth to water level data.

An Application of Neutrosophic Set to Relative Importance Assignment in AHP

The paper addresses a new facet of problem regarding the application of AHP in the real world. There are occasions that decision makers are not certain about relative importance assignment in pairwise comparison. The decision makers think the relative importance is among a set of scales, each of which is associated with a different possibility degree. A Discrete Single Valued Neutrosophic Number (DSVNN) with specified degrees of truth, indeterminacy, and falsity is employed to represent each assignment by taking into account all possible scales according to the decision maker’s thought. Each DSVNN assignment is transformed into a crisp value via a deneutrosophication using a similarity-to-absolute-truth measure. The obtained crisp scales are input to a pairwise comparison matrix for further analysis. The proposed neutrosophic set-based relative importance assignment is another additional novelty of the paper, which is different from all prior studies focusing only on the definition of measurement scales. The presented assignment emulates the real-world approach of decision making in human beings which may consider more than one possibility. It is also shown herein that the single and crisp relative importance assignment in the original AHP by Saaty is just a special case of the proposed methodology. The sensitivity analysis informs that when decision makers have neither absolute truth nor falsity about a scale, the proposed methodology is recommended for obtaining reliable relative importance scale. The applicability of the proposed methodology to the real-world problem is shown through the investment in equity market.

Fuzzy Extension of Simplified variant of AHP

A class of methods for ranking a finite set of objects based on a multiplicative matrix of pairwise comparisons, when the comparison results are expressed by fuzzy values, is considered. A fuzzy extension of the simplified version of the AHP, which was introduced by the author earlier, is proposed. In this extension, the elements of the matrix of pairwise comparisons can be type 1 or type 2 fuzzy numbers.

Utilization of AHP-MAUT Method to Determine the Country of Exhibition Abroad in Batik Hatta Boutique

This research was conducted with the aim of helping decide the destination country for overseas exhibitions at the Batik Hatta Boutique. By knowing all the data and information of a country, boutique owners can decide which country to visit in the batik exhibition. Because if you attend the cast in all countries, there will be overruns in costs. The methods used are AHP and MAUT. The AHP method is used as a weighting using a linguistic value scale. Weights are obtained from the pairwise comparison matrix between two elements of all elements that occur at the same hierarchical level. The MAUT method is used to determine the importance of each alternative for the ranking process. The results of this study indicate that Cambodia was chosen as the location to be visited for the batik exhibition. The results of the validation using the Spearman Rank correlation comparison obtained a value of 0.951 meaning that this method can be used as a decision making.

Evaluation of Erosion Susceptibility of Godrahav Basin (Artvin) Using Geo-environmental Factors

This study aimed to produce the erosion susceptibility map of the Godrahav basin by using the Analytic Hierarchy Process (AHP) method. Godrahav stream basin, located within the borders of Artvin province in the Eastern Black Sea Region, covers an area of approximately 5310.12 hectares. In order to produce the erosion susceptibility map of the study area, 11 geo-environmental criteria which are effective in the formation of erosion (slope, aspect, profile curvature, drainage density, distance to drainage network, topographic wetness index (TWI), stream power index (SPI), slope length and slope steepness factor (LS), normalized difference vegetation index (NDVI), land use and lithology) were taken into account. The AHP method was used to determine the weights of the criteria. Similar studies in the literature and expert opinions were used to determine the importance of the criteria with respect to each other and to create the pairwise comparison matrix. According to the results obtained, it was determined that the erosion susceptibility was low in 4.9% of the basin, medium in 9.57% and high in 5.58% of the basin. The areas with high erosion susceptibility in the study area consist of agricultural and unproductive forest areas and lands with high slope. In order to reduce the risk of erosion, detailed studies and soil protection measures should be taken in these areas.

Pairwise comparisons matrix decomposition into approximation and orthogonal component using Lie theory

This paper examines the use of Lie group and Lie Algebra theory to construct the geometry of pairwise comparisons matrices. The Hadamard product (also known as coordinatewise, coordinate-wise, elementwise, or element-wise product) is analyzed in the context of inconsistency and inaccuracy by the decomposition method.The two designed components are the approximation and orthogonal components. The decomposition constitutes the theoretical foundation for the multiplicative pairwise comparisons.

Efficient vectors for simple perturbed consistent matrices

In the Analytic Hierarchy process, a method used in Decision Making, it may be important to approximate a pairwise comparison matrix (PC matrix) by a consistent one. In this context, the notion of efficient vector for a PC matrix arises. In this paper we describe all efficient vectors for an n×n comparison pairwise matrix obtained from a consistent one by perturbing one entry above the main diagonal, and the corresponding reciprocal entry. As a consequence, we give a simple proof of the result obtained by K. Ábele-Nagy and S. Bozóki (2016) that states that the principal eigenvector of a simple perturbed consistent matrix is efficient. In addition, we consider a set of non-efficient vectors associated with the simple perturbed consistent matrix and describe all the efficient vectors that dominate each vector in that set.

Materials selection criteria weighting method using analytic hierarchy process (AHP) with simplest questionnaire and modifying method of inconsistent pairwise comparison matrix

The analytic hierarchy process has been widely used to determine subjective weights of materials selection criteria in materials selection using multi-criteria decision-making. However, the analytic hierarchy process has some drawbacks: it is difficult to construct a pairwise comparison matrix and meet the consistency requirement. First, we propose a new simplest questionnaire to perform the pairwise comparison without confusion, conventionally and easily. Next, we propose an improved modifying method for inconsistent pairwise comparison matrix according to the following principles: (1) the elements of the reconstructed pairwise comparison matrix should be nine-point scales, (2) the number and modifying the amount of the modified elements should be as small as possible and (3) the deviation between the original and reconstructed pairwise comparison matrixes should be as small as possible. The outline of the proposed modifying method is as follows: (1) calculate the consistency ration decrements of all the pairwise comparison matrixes reconstructed by modifying every element of the original pairwise comparison matrix to the lower and upper adjacent nine-point scales and (2) find the element with the maximum consistency ratio decrement and modify it to the lower or upper adjacent scale. To illustrate the effectiveness, we apply the proposed methods to determine the criteria weights for selecting the best phase change material used in a solar domestic hot water system, and apply the proposed modifying method to some examples from the published papers, and compare the performances with some previous methods. The simplest questionnaire and improved modifying method help materials designers and engineers to apply the analytic hierarchy process method in materials design and optimization problems, much more actively.

Analisis technology contribution coefficient (TCC) di UKM Gazal Makmur

Technology is an important aspect for the success of an industry. Gazal Makmur UKM is an UKM that processes cassava into chips in Gazal Hamlet, Kotaanyar Village, Kotaanyar District, Probolinggo Regency. This study aims to calculate the value of the technology component contribution coefficient (TCC) and determine the priority of technology component development in Gazal Makmur SMEs. The method used in this study is the technometric method, namely the technology assessment method used to evaluate the contribution of technology components and the pairwise comparison matrix approach. The measured technology components include technoware (production equipment), humanware (human resource capabilities), infoware (information tools), and orgaware (organizational tools). The results of this study indicate that the contribution of the Orgaware component is the highest in Gazal Makmur SMEs (0.578), then humanware (0.467), humanware (0.252), and the smallest is technoware (0.0.244). The TCC value for Gazal Makmur SMEs is 0.418. The results of this calculation show that these SMEs have a TCC value below 0.7 and above 0.3, meaning that it can be concluded that these SMEs are classified as having a semi-modern level of technology with a reasonable technology category for the SME scale. Improving the quality of Gazal Makmur cassava chips SMEs starts from the orgaware component then humanware, infoware and finally orgaware.

Efficiency of the principal eigenvector of some triple perturbed consistent matrices

In this paper we study the efficiency of the principal eigenvector of a pairwise comparison matrix obtained from a consistent one by perturbing three entries above the main diagonal, and the corresponding reciprocal entries, in a way that there is a submatrix of size 2 containing three of the perturbed entries and not containing a diagonal entry. Our approach uses the characterization of vector efficiency based on the strongly connection of a certain digraph associated with the matrix. By imposing some conditions on the magnitudes of the perturbations, we identify a class of matrices for which the principal eigenvector is efficient. This class is the union of two subclasses such that the digraph of all the matrices in the same subclass contains a common cycle with all vertices. The matrices we analyse include the simple perturbed consistent matrices, as well as a subfamily of the double perturbed consistent matrices, whose principal eigenvector efficiency has been studied in the literature. For completeness, we also include some examples of triple perturbed matrices for which the principal eigenvector is not efficient. Explicit expressions for the characteristic polynomial and the principal eigenvector of the triple perturbed consistent matrices we consider are also given.

Constrained Eigenvalue Minimization of Incomplete Pairwise Comparison Matrices by Nelder-Mead Algorithm

Pairwise comparison matrices play a prominent role in multiple-criteria decision-making, particularly in the analytic hierarchy process (AHP). Another form of preference modeling, called an incomplete pairwise comparison matrix, is considered when one or more elements are missing. In this paper, an algorithm is proposed for the optimal completion of an incomplete matrix. Our intention is to numerically minimize a maximum eigenvalue function, which is difficult to write explicitly in terms of variables, subject to interval constraints. Numerical simulations are carried out in order to examine the performance of the algorithm. The results of our simulations show that the proposed algorithm has the ability to solve the minimization of the constrained eigenvalue problem. We provided illustrative examples to show the simplex procedures obtained by the proposed algorithm, and how well it fills in the given incomplete matrices.

Wind farm site selection considering turbulence intensity

Selecting a suitable site is a critical step in wind energy projects. In this regard, using appropriate decision criteria plays a significant role. Turbulence intensity is one of the main characteristics of airflow that affects the power production and lifespan of wind turbines. Therefore, it is considered as a wind site selection criterion in this paper.The present paper formulates the effect of turbulence on both power production and lifespan of wind turbines via an equivalent wind power density (WPDeq) function, to use it in the wind site selection process. To implement the proposed methodology, 88 wind sites in Iran have been studied. The results reveal the significant effect of turbulence on the site selection process as some sites have changed their rank up to 8 grades considering turbulence intensity in the siting process.To consider the turbulence intensity as an independent criterion to use it in multi-criteria decision-making methods, its relative importance (weight) have to be calculated. Sensitivity analysis shows that, on average, the relative importance of turbulence intensity over wind power density can be approximated as 1/5. Researchers can quickly consider turbulence intensity in siting process incorporating its weight in the pairwise comparison matrix of multi-criteria decision–making.

On a Maximum Eigenvalue of Third-Order Pairwise Comparison Matrix in Analytic Hierarchy Process and Convergence of Newton\u2019s Method

Nowadays, the analytic hierarchy process is an established method of multiple criteria decision making in the field of Operations Research. Pairwise comparison matrix plays a crucial role in the analytic hierarchy process. The principal (maximum magnitude) eigenvalue of the pairwise comparison matrix can be utilized for measuring the consistency of the decision maker’s judgment. The simple transformation of the maximum magnitude eigenvalue is known to be Saaty’s consistency index. In this short note, we shed light on the characteristic polynomial of a pairwise comparison matrix of third order. We will show that the only real-number root of the characteristic equation is the maximum magnitude eigenvalue of the third-order pairwise comparison matrix. The unique real-number root appears in the area where it is greater than 3, which is equal to the order of the matrix. By applying usual Newton’s method to the characteristic polynomial of the third-order pairwise comparison matrix, we see that the sequence generated from the initial value of 3 always converges to the maximum magnitude eigenvalue.

An Integrated Multi Criteria Decision Making Model for Evaluating Park-and-Ride Facility Location Issue: A Case Study for Cuenca City in Ecuador

A park-and-ride (P&R) system is a set of facilities where private vehicle users can transfer to public transport to continue their journey. The main advantage of the system is decreasing the congestion in the central business district. This paper aims to analyze the most significant factors related to a Park-and-Ride facility location by adopting a combined model of Analytic Hierarchy Process (AHP) and Best Worst Method (BWM). The integrated model is applicable for complex problems, which can be structured as a hierarchy with at least one 5 × 5 pairwise comparison matrix (PCM) (or bigger). Applying AHP for at least 5 × 5 PCM may generate inconsistent matrices, which may cause a loss of reliable information. As a solution for this gap, we conducted BWM, which generates more consistent comparisons compared to the AHP approach. Moreover, the model requires fewer comparisons compared to the classic AHP approach. That is the main reason of adopting the AHP-BWM model to evaluate Park-and-Ride facility location factors for a designed two-level hierarchical structure. As a case study, a real-world complex decision-making process was selected to evaluate the Park-and-Ride facility location problem in Cuenca city, Ecuador. The result shows that the application of multi-criteria methods becomes a planning tool for experts when designing a P&R system.

SUSTAINABLE DESIGN OPTIMIZATION TOOL FOR PROTOTYPICAL BUILDINGS IN HOT ARID CLIMATE USING ANALYTICAL HIERARCHY PROCESS

New Building Information Modelling (BIM) – enabled performance metrics are gaining importance in Building Performance Simulation (BPS). However, scarce work was published featuring holistic metricsfor prototypical designs in hot arid climate. Thus, this research presents a BIM-enabled sustainable early-design decision support tool, whose optimizationvariables are building orientation and Window-to-Wall Ratio (WWR). The mode’s objective is reaching optimum building Sustainability Combined Score (SCS); the holistic value of performance parameters considered by the user. To demonstrate the methodology, the daylighting and thermal comfort metrics areconsidered: (1) Day-Lit Area (DLA); (2) Daylight Autonomy (DA); (3) Mean Daylight Factor (µDF); (4) Useful Daylight Index (UDI); (5) Temperature Discomfort Hours (TDH); and (6) Humidity Discomfort Hours (HDH).BIM simulation is carried out for various combinations of building orientations and WWR, metrics are converted into percentages then into criteria scores based upon expert-determined criteria rating scales. Next, using the Analytical Hierarchy Process (AHP), Criteria Relative Weights (CRW’s) are determined, using a Pairwise Comparison Matrix (PCM). SCS’s are computed for each scenario, as a function of criteria scores and CRW’s. The verification of the AHP Module is done arithmetically using consistency indices. After screening all valid scenarios considering site constraints, accessibility and design codes, the scenario with optimum SCS is obtained. Three cases of prototypical designs, comprising a school building, a civil defense facility and a congregational building are presented. All cases are located in the hot desert climate ofQatar. The validation of the SCS Module output is carried out using expert survey. اکتسب قياس معدلات أداء المنشآت باستخدام نمذجة معلومات البناء زخما کبيرا في کل من التصميم المعماري المستدام ومحاکاة البناء، وبالرغم من ذلک، قلما نشر من أبحاث تتناول معدلات مجمعة لقياس أداء المنشآت، ولاسيما فيما يتعلق بالتصميمات النمطية في المناطق ذات المناخ الصحراوي الجاف، ومن هذا المنطلق، يقدم هذا البحث أداة مبتکرة لدعم اتخاذ القرار ,والوصول لأفضل المعدلات أثناء مرحلة التصميم المبدئي، حيث تتماشى تلک الأداة المقترحة مع نظم نمذجة معلومات البناء، کما تعتمد تلک الأطروحة على تحليلالحالات الممکنة للمتغيرين:زاوية توجيه المنشأ ونسبة النوافذ إلى الحوائط، بهدف التوصل إلى أفضل قيمة للدرجة الکلية للاستدامة، والتي تمثل قيمة موحدة لکافة مؤشرات الأداء المختارة من قبل المستخدم. وبغرض عرض تلک الأطروحة، تم الاعتماد على هذه المجموعة من مؤشرات أداء الإضاءة الطبيعية والراحة الحرارية: (1) المساحة المضاءة طبيعيا، (2) متوسط معامل الإضاءة الطبيعية ، (3) استقلالية الإضاءة الطبيعية، (4) مؤشر الإضاءة الطبيعية، (5) ساعات درجة الحرارة السنوية غير المستوفاة، (6) ساعات الرطوبة النسبية غير المستوفاة. يتم إذا القيام بالمحاکاة المعتمدة على نمذجة معلومات البناء لکل من السيناريوهات الممکنة لزاوية توجيه المبنى مع نسبة النوافذ إلى الحوائط، ويتم تحويل مخرجات تلک الخطوة، وهي القياسات المنفصلة، إلى نسب مئوية، يتم تحويلها بدروها إلى درجات قياسية استنادا إلى مقياس تم تحديده بواسطة ورشة عمل ضمت مجموعة من الخبراء، وهکذا فإنه باستخدام طريقة التحليل الهرمي يتم التوصل إلى الأوزان النسبية لمعدلات الأداء المختارة، وذلک بتطبيق مصفوفة المقارنة الثنائية على تلک المعدلات، وبناء على ذلک يتم تقدير القيم الخاصة بالدرجة الکلية للاستدامة، والتي تعتمد بالأساس على الدرجات القياسية والأوزان النسبيةلمعدلات الأداء، کما يتم التحقق من منظومة التحليل الهرمي رياضيا باستخدام مؤشرات الاتساق، وبالإضافة إلى ذلک، فبعد إتمام عملية التدقيق لکل سيناريو مقترح - من حيث زاوية التوجيه ونسبة النوافذ إلى الحوائط- في ضوءطبيعة الموقع وأکواد البناء المحلية وغيرها من خصائص المشروع، وقد تم تناول ثلاثة مشروعات ذات تصميمات نمطية، تشمل مبنى تعليميا ومنشأة للدفاع المدني ودارا للعبادة، کأمثلة لتطبيق الأداة المقترحة، تقع کلها في المنطقة المناخية الصحراوية الحارة بدولةقطر، مع عرض النتائج التي تم التوصل إليها، وقد تم التحقق من المنظومة الخاصة بدرجة الاستدامة الکلية بواسطة استقصاء موجه إلى نخبة من المعماريين المتخصصين في مجال الاستدامة ونمذجة معلومات البناء، وتم التوصل بالأخير إلى أن المنشآت ذات المساحات الکبيرة عکست دقة أکثر في عملية محاکاة مؤشرات الاستدامة، وأظهرت قدرا أکبر من التأثر بالتغيير في القيم المدخلة من زاوية توجيه المنشأ أو نسبة النوافذ إلى الحوائط، مقارنة بالمنشآت الأصغر مساحة التي لم تتأثر نتائجهابنفس عند تغيير قيم المتغيرات.

Metode Analytical Hierarchy Process (AHP) untuk Pemilihan Media Sosial Pemasaran Songket Sambas

Songket Sambas (Kain Lunggi) is a gold thread cloth typical of the culture of the Sambas people. The Sambas songket craftsmen have used social media a lot in marketing their products. The selection of the right social media in product marketing can help increase sales of Sambas songket. It can be the key to success in expanding Sambas songket sales to various regions. This study aims to apply the Analytical Hierarchy Process (AHP) method in the selection of social media that is widely used as the right Sambas songket marketing media. In this study, the AHP method was used as a method for decision making. In determining the pairwise comparison matrix, Sambas songket craftsmen were involved. The criteria used are age range (C1), gender (C2), number of users (C3), level of popularity (C4). From this study, we have the value of Facebook is 0.82, Instagram is 0.60, Youtube is 0.06, Twitter is 0.04. The final priority result of the right social media to use with the first order is Facebook.

On the similarity between ranking vectors in the pairwise comparison method

There are many priority deriving methods for pairwise comparison (PC) matrices. It is known that when these matrices are consistent all these methods result in the same priority vector. However, when they are inconsistent, the results may vary. The presented work formulates an estimation of the difference between priority vectors in the two most popular ranking methods: the eigenvalue method and the geometric mean method. The estimation provided refers to the inconsistency of the PC matrix. Theoretical considerations are accompanied by Monte Carlo experiments showing the discrepancy between the values of both methods.

A Decision Analysis Model for the Brand Experience of Branded Apps Using Consistency Fuzzy Linguistic Preference Relations

Branded apps are not only an important platform for enterprises and customers to have real-time interactions and communicate marketing messages, but also a new business model that encourages value co-creation between the two. In order to explore the impact of branded apps on customers, this study constructs a fuzzy multi-criteria decision making (FMCDM) analysis model, and it uses consistent fuzzy linguistic preference relations (CFLPR) to set up a symmetric pairwise comparison matrix, which greatly reduces the complexity and error rate of calculations. Empirical research findings show that brand experience attributes and the influence of brand experience on customer loyalty and satisfaction can be more accurately measured. As a consequence of this study, we show that, among the brand experience facets of two retail chain branded apps, behavioral experience is the most favored, while affective experience is the least favored. Furthermore, brand attachment and active participation should be strengthened to enhance customer loyalty. Through the analytical model employed in this study, enterprises can regularly monitor changes in the brand experience preferences of branded app users and evaluate app performance to flexibly adjust mobile device-based marketing campaigns and strategies. It can also aid enterprises in using mobile devices effectively to improve customer loyalty and address the issue of diminishing brand loyalty.

A comprehensive framework based on GIS-AHP for the installation of solar PV farms in Kahramanmaraş, Turkey

Solar photovoltaic (PV) technologies receive investment, support, and incentives despite their apparent high costs. In terms of renewable energy policies and spatial planning, site selection for solar PV farms is a critical issue. A novel comprehensive framework for assessing the site suitability of solar PV farms is proposed, which considers the preservation of natural, ecological conservation, and cultural areas. The framework combines a Geographical Information System (GIS) with layers of satellite-derived data for energy resources as well as locally collected data, and the Multi Criteria Decision Making (MCDM) method based on the Analytic Hierarchy Process (AHP). In the GIS environment, maps belonging to fourteen sub-criteria of the three main criteria (Geography, Climate and Location) for Kahramanmaraş, Turkey were obtained, as well as suitability map derived from their weighted sum. The AHP method generates the appropriate weight for each input criteria using a pairwise comparison matrix. GHI, aspect, distance from power line network, land use/cover, annual average temperature, and others were found as the most necessary sub-criteria, respectively. According to the findings, 9.62% of study area very low, 20.15% is low, 22.51% is moderate, 23.98% is high and 23.74% is very high, and 26% is unsuitable for solar PV farms. Based on the results, the northern districts of the study region were determined to be the most suitable for the construction of solar PV farms. When existing five PV farms' location selection decisions were examined, it was observed that the investment outcomes were consistent with the results of the study. The proposed framework is projected to minimize the cost, time, and resources used on the construction of solar PV farms.