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MULTIPLE-CRITERIA MODEL FOR OPTIMAL OFF-ROAD VEHICLE SELECTION FOR PASSENGER TRANSPORTATION: BWM-COPRAS MODEL
Si Dragan S. Pamucar3, Lazar M. Savinb
ct University of Defence in Belgrade, Military Academy,
O Department of Logistics, Belgrade, Republic of Serbia,
o a e-mail: dragan.pamucar@va.mod.gov.rs, corresponding author, ^ ORCIDiD: http://orcid.org/0000-0001-8522-1942
^ b e-mail: Iazarsavin96@gmail.com, ^ ORCID iD: http://orcid.org/0000-0002-6121-936X
uj DOI: 10.5937/vojtehg68-22916; https://doi.org/10.5937/vojtehg68-22916
FIELD: Mathematics, Transport, Logistics < ARTICLE TYPE: Original scientific paper
ARTICLE LANGUAGE: English
Abstract:
Introduction/purpose: Adequate evaluation and choice of off-road vehicles used in performing various types of assignments is a very important factor ¡3 which affects user mobility and safety as well as the quality and efficiency
2 of carrying out transportation activities in the Serbian Armed Forces
(SAF).
Methods: This paper thus proposes the BWM (Best Worst Method) and the COPRAS (Compressed Proportional Assessment) models forthe ° selection of the optimal off-road vehicle for the needs of the SAF. The
g relative weight of the criteria used to assess potential off-road vehicles
> was established using the BWM method. In addition to the COPRAS
method which is a component of the basic decision-making model, in this paper, the MABAC (MiltiAttributive Border Approximation Area Comparison) and MAIRCA (MultiAttributive Ideal-Real Comparative Analysis) methods were also applied through result validation. Results: By testing the BWM-COPRAS model on the example of optimal off-road vehicle selection in the SAF, a high rank correlation was achieved. The results were validated through the statistical processing of the results obtained through the implementation of various multi-criteria techniques by applying the Spearman's rank correlation coefficient. Conclusion: The results display stability of the results of the proposed model in ranking alternatives and prove the feasibility of the proposed approach to handle multi-criteria decision making problems.
Key words: BWM, COPRAS, MABAC, MAIRCA, vehicle selection, multi-criteria decision making.
Introduction ?
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When observing the efficiency of units in off-road conditions in both peace and war, it is impossible to miss its high dependence on adequate vehicle selection for carrying out a mission, for it is precisely this process that represents an important factor which directly influences the lowering ^ of risk and time involved in performing this activity. Proper assessment £ and selection of the right vehicle provides proper conditions for efficient g performance of tasks set before the units of the Serbian Armed Forces (SAF). Taking into consideration the aforementioned, the optimal off-road si vehicle selection process is of great importance for successful and safe transport of units. Identifying actions that have the biggest impact on the efficiency of vehicles during task performance enables the users (units) to modify the operation accordingly and reduce the time needed to perform these activities. This research paper presents the multi-criteria BWM-COPRAS model for evaluation and optimal off-road vehicle selection for the units of the Serbian Armed Forces. The hybrid BWM-COPRAS model is carried out in three phases. The first phase of the model includes calculating the optimal values of weight coefficients by applying the non-linear model in BWM. The second phase is where the ^ COPRAS model is applied. The values put into the COPRAS model represent the values of the BWM weight coefficients, and the elements of the basic Decision matrix. The third phase includes the validation of the obtained results through: (1) the comparison of the results with other multi-criteria (MCDM) models, (2) the analysis of the result stability in a dynamic environment, and (3) the analysis of the result stability when the weight coefficients of the criteria are changed.
Through research and development of the models, several goals have been set in this paper. The first goal pertains to the advancement and enhancement of the optimal vehicle selection methodology in the area of multi-criteria decision making through development and j= introduction of a new FUCOM-COPRAS approach. The second goal of this paper is to bridge the gap that currently exists in the evaluation and adequate vehicle selection methodology within the military as a whole. The third goal of the paper is a possibility of enhancing the efficiency and lowering the risks of performing SAF assignments by defining models for adequate vehicle selection. And the fourth goal of this paper is the popularization and affirmation of the idea of multi-criteria decision making in reaching complex decisions in the SAF through a presentation of the BWM-COPRAS model. am
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The authors of this paper have opted for the use of the hybrid BWM-COPRAS model due to its following advantages. (1) Use of the BWM and COPRAS models enables a successful simulation of the decision-making processes, starting from defining the goal, criteria and alternatives, to comparison of the criteria, i.e. establishing the priority of each of the alternatives over the set goal. (2) Application of the BWM-COPRAS model breaks down the concrete decision making process by taking apart the problem into a hierarchy of its elements. A hierarchical examination of the decision making process allows for easier control over the consistency of estimates while paying attention to the entirety of the problem and functional interactions between criteria and alternatives. (3) Using the BWM-COPRAS model enables the integration of the qualitative and quantitative factors into decision making, because most real problems most often occur as a combination of qualitative and quantitative elements. (4) The BWM-COPRAS model successfully identifies and points to the inconsistency of the decision-maker by tracking the inconsistencies of estimates during the entire process, and calculating the index and ratio of consistency. (5) Redundancy of pair comparison makes the BWM-COPRAS model less sensitive to estimation errors. (6) The implementation of the BWM-COPRAS model in group decision making significantly improves communication between group members. In case of a discussion, a group must agree on every joint estimate that is to be entered into the matrix. This helps in structuring the discussion and reaching a consensus.
The BWM-COPRAS model also has certain limitations which the users might encounter while using it, such as: (1) insufficiently large scale (Saaty scale of relative importance) for comparison of elements in pairs, related to some decision making problems; (2) the number of necessary pair comparisons which is not negligible in most problems; (3) frequent difficulty in achieving an acceptable consistency ratio; and (4) the complexity of the mathematical algorithm which can be a limiting factor for widespread use of the model.
This paper contains a total of six sections, the first of which refers to introducing the problem of adequate vehicle selection for the SAF. The second, containing the literature review, takes a closer look at the already existing research on similar topics in which multi-criteria decision making models were applied. The third section briefly introduces the previously used models and lays out the algorithm of the hybrid BWM-COPRAS model. The fourth section displays a study of the case in which vehicle evaluation was performed by using the BWM-COPRAS model. The fifth section is a discussion of the results which includes a result
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stability check through the change of the weight coefficients of the criteria in the BWM, and the validation of the obtained results through comparison with other MCDM models. The sixth section shows the key contributions of the developed model and the performed research, as well as suggestions for future research. e
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Literature review £
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Based on research from the most important indexes of international science journals (SCOPUS and Web of Science), a literature analysis has been performed which demonstrates the implementation of MCDM models in transport and logistics optimization. It analyzes the period | between 2008 and 2018. During this period, only two papers on the topic g. of vehicle selection in the military were published (Pamucar, et al, 2013); (Starcevic, et al, 2019). Starcevic et al (2019) have presented the selection of military vehicles for use in multinational operations by using the hybrid AHP-DEA (Analytic Hierarchy Process - Data Envelopment Analysis) models, while Pamucar et al (2013) have shown the application of the neuro-fuzzy system for the selection of military motor vehicles used for performing transportation assignments in the SAF. Due to scarcity of papers on the topic of application of the MCDM models for military off-road vehicle selection, this paper analyzes papers from the domain of transport and logistics which deal with similar topics. For example, Jeon et al (2010) showed the application of the MCDM methods in the sustainable transport plan selection based on the sustainability index. In the research, the authors used the Weighted Sum o Model. Cadena & Magro (2015) presented a new methodology for | assigning the weight coefficients of the sustainability criteria in transport projects. In order to solve the problem of imprecision and subjectivity, the authors applied the MCDM models in fuzzy environment.
Given that the traffic system is the life force of every country and one of the bases for its economic development, Baric et al (2016) suggest that the AHP method be applied when choosing the best project in the realization of city traffic projects. The model has been tested on a real system and has yielded reliable results. Baric et al (2016) have also pointed out the main drawback of applying the AHP model which is a large number of inputs making the validation of the obtained results more difficult. In order to solve this problem, Inti & Tandon (2017) presented a o modified AHP method characterized by additive transitivity of fuzzy relations. The model was tested in choosing a contractor for the
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In order to improve sustainability in transport, one of the solutions is to use various alternative fuels and vehicle propulsion systems. In this way, with the help of the sustainability index, Mitropoulos & Prevedouros, (2016) make estimates of vehicle characteristics. The identified indicators were grouped into five categories of sustainability: Environment, Technology, Energy, Economy and Users, and then they were aggregated using the WSM method. Also, Safaei Mohamadabadi et al (2009) have selected the types of propulsion fuel for vehicles based on three basic sustainability aspects. For ranking the alternatives based on the five criteria, the PROMETHEE method was used. Intermodal transportation can greatly improve the sustainability of a transportation system. It is necessary to choose the optimal location of terminals based on different requirements of different partakers in a transportation process. With that aim, Zecevic et al (2017) have suggested a new hybrid MCDM model for selecting locations. Sustainable transport systems have today become a necessity, especially in large cities because of various harmful effects on the environment. An approach for choosing the best alternative of transport systems based on 24 criteria grouped in three categories was defined in (Awasthi et al, 2011). The abovementioned approach contains three steps, and the tOpSIS method is applied in a combination with fuzzy theory with the aim to assess the criteria and choose an alternative. Castillo & Pitfield (2010) suggest the Evaluative and Logical Approach to Sustainable Transport Indicator Compilation (ELASTIC) framework for choosing a sustainable transport system indicator with the help of AHP and SAW methods. Although the improvements of transport planning methods over the past few years are visible, according to López & Monzón (2010), in order to improve the sustainability level in transport, it is necessary to apply a multidiciplinary approach based on GIS. In addition to that, it is necessary to integrate methods of multi-critearia decision making within the suggested approach.
An estimate of transport system sustainability in individual European countries based on selected economic, ecological and social indicators was presented in Bojkovic et al (2010). The ELECTRE (ELimination and Choice Expressing Reality) method was used together with its modification based on the Absolute Significance Treshold (AST). The framework for selecting sustainable transport projects in urban areas of developing countries was proposed in Jones et al (2013). The choice of alternatives is performed based on the Localized Sustainability Score index whereby the AHP method is used. In addition to the AHP method, assessing the sustainability of different transport solutions such as mode
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sharing, multimodal transport, intelligent transportation systems, Awasthi & Chauhan (2011) use the Dempster-Shafer theory in the proposed hybrid approach. While the AHP method is primarily used for ranking criteria based on their weight, the Dempster-Shafer theory enables a synthesis of multiple information sources. Dimic et al (2016) have e developed a model for strategic transport steering based on the SWOT analysis, fuzzy Delphi and DEMATEL - ANP method. □:
There are a certain number of studies which contemplate the 8 application of different theories of uncertainty in multi-criteria models for solving numerous logistical and transportation problems. For example, ^ Sremac et al (2018) have shown the ranking of logistical providers by using the Rough SWARA (Step-Wise Weight Assessment Ratio Analysis) and Rough WASPAS (Weighted Aggregated Sum Product Assessment) models, while Badi et al (2018) demonstrated the use of the CODAS model. Later, Badi & Ballem (2018) and Stevic et al (2017) demonstrated the application of rough numbers in multi-criteria models for vehicle rationalization within the inner transport of logistical | companies. The paper puts forward a new approach based on the combination of the Simple Additive Weighing (SAW) method and the rough BWM. Radovic et al (2018) showed the use of rough numbers for 2 valuating performance indicators which was applied in three different countries: Bosnia and Herzegovina, Libya and Serbia. The multi-criteria model includes the use of the rough ARAS (Additive Ratio Assessment) approach for performance indicator valuation in nine transportation § companies from the three countries. Pamucar et al (2019) have shown £
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the possibilities of applying the multi-criteria models based on Linguistic Neutrosophic Numbers (LNN) in managing human resources in the process of transporting hazardous substances. The application of the LNN-WASPAS model for the evaluation of security advisors when
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transporting hazardous substances on Serbian soil was demonstrated. Pamucar et al (2016) showed a green p-median problem combined with <o a fuzzy multi-criteria model which processes environmental parameters, sociological parameters and the expenses of logistical distributors and applies their influence on the planning of the city logistical terminal location in a discrete traffic network.
Sustainability is a very important concept in logistics, and reverse ro" logistics as one of its sub-branches can greatly improve the efficiency and the ecological aspect of doing business. Wang et al (2018) have presented a method for choosing returnable product collectors. The hybrid approach based on the AHP and Entropy Weight (AHP-EW) | methods is used in order to estimate the weight of certain criteria, while P
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the Multi-Attributive Border Approximation area Comparison (MABAC) method is used for ranking the alternatives. Different initiatives for city logistics (e.g. proper location of distribution centers) can significantly contribute to improving the degree of sustainability in a city. This is precisely the research topic in (Awasthi & Chauhan, 2012). Out of the MCDM methods, the aforementioned paper uses the AHP and Fuzzy TOPSIS. With the help of the Fuzzy Step-wise Weight Assessment Ratio Analysis (SWARA) and Fuzzy MOORA, Mavi et al, (2017) perform a selection of a third-person provider of reverse logistics services in the plastic industry. Later, Badi and Ballem, (2018) showed the possibilities of applying the BWM and MAIRCA models for selecting a third-person provider for reverse logistics services in the pharmaceutical industry. Pamucar & Cirovic, (2015) demonstrated the application of the hybrid DEMATEL-MABAC model in the process of making investment decisions about the acquisition of manipulative vehicles in logistics centers. The DEMATEL method was used for obtaining the weight coefficient of criteria, while the valuation and selection of forklifts was done by using the MABAC model. The following table (Table 1) shows an overview of fields which most frequently employ the MCDM models.
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Table 1 - MCDM methods in the transport and logistics subfield Таблица 1 - MCDM методы в области транспорта и логистики Табела 1 - ВКО методе у области транспорта и логистике
Field of application for the MCDM method MCDM method Literature
Determining the impacts of ecological transport measures on city sustainability AHP; AHP-EW; MABAC; FUCOM (Awasthi et al, 2011); (Zecevic et al, 2017); (Fazlollahtabar et al, 2019); (Stankovic et al, 2019); (Nunic, 2018)
Logistical provider assessment with acknowledging the risks and sustainability Fuzzy SWARA, Fuzzy MOORA (Mavi et al, 2017)
Identification of interactions between manufacturing and logistical industries Grey DANP (Jiang et al, 2018)
Transport management WSM; REMBRANDT; Delphi; Fuzzy TOPSIS; AHP; SAW; PROMETHEE; (Jeon et al, 2010); (Cadena & Magro, 2015); (Awasthi & Chauhan, 2011); (Castillo & Pitfield,
Field of application for the MCDM method MCDM method Literature
ELECTRE I; Modified ELECTRE I; Fuzzy Delphi; DEMATEL-ANP 2010); (Simongati, 2010); (Bojkovic et al, 2010); (Dimic et al, 2016); (Awasthi & Chauhan, 2012)
Vehicle evaluation WSM; PROMETHEE; (Mitropoulos & Prevedouros, 2016); (Safaei Mohamadabadi et al, 2009)
Location Evaluation Problem for Logistical Center Construction Fuzzy Delphi; Fuzzy Delphi ANP; Fuzzy Delphi VIKOR; Fuzzy MAGDM; Fuzzy ARAS; AHP; DEMATEL-MAIRCA (Zecevic et al, 2017); (Rao et al, 2015); (Turskis & Zavadskas, 2010); (Pamucar et al, 2018a); (Noureddine & Ristic, 2019); (Puska et al, 2018); (Fazlollahtabar, 2018)
Assessment and construction of transport infrastructure AHP; FAHP; REMBRANDT; WASPAS (Baric et al, 2016); (Inti & Tandon, 2017); (Lopez & Monzon, 2010); (Jones et al, 2013); (Stanujkic & Karabasevic, 2018); (Pamucar et al, 2018b)
Selection and ranking of military vehicles AHP-DEA; neuro-fuzzy sistem (Starcevic et al, 2019); (Pamucar et al, 2013)
Based on the presented literature analysis, we can conclude that the most frequently used method for solving problems in the field of transport and logistics in the past ten years was the AHP method. However, the AHP method requires the use of n (n -1) /2 comparison of criteria pairs.
A large number of comparisons makes the application of the model more complicated, especially in cases with a larger number of criteria. For this reason, the use of this method is not advised in cases with a larger number of criteria. The model which eliminates the abovementioned drawback of the AHP method is the BWM method. But even with this
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fact, and the numerous advantages of the BWM over the AHP method we can see that the BWM has not been used in the field in question. Therefore, a logical need arises for the development of MCDM models which imply the implementation of all BWM advantages. In addition to the BWM method, by analyzing the literature, we can see that the COPRAS (COmpressed PRoportional Assessment) method has not been used either, even though it falls into models which yield stable results. Considering that in the presented literature there are no examples of either BWM or COPRAS models for off-road vehicle assessment in either civilian or military organizations, the need for their application is imposed. The application of the BWM-COPRAS model fills the gap that exists in the literature which deals with this field.
BWM-COPRAS multi-criteria model
As previously emphasized, the BWM-COPRAS implies the use of two methods, the BWM method for determining the weight coefficients of criteria, and the COPRAS method for assessing, i.e. ranking alternatives (Figure 1)
Determining criteria and sub-critera
Expert opinions
Forming the matrix of average expert responses
Determining the optimal values of weight coefficients
Ranking the criteria and sub-critria
Calculating values of consistency coefficients
^ Determining the alternatives
Forming and normalization of the basic matrix
Forming a weight normalized matrix
Determining the total values of max and min criteria
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Comparison with other multi-criteria models
Effect of dynamic matrices on MCDM models
Effect of the shift of weight coefficients on results of MCDM models
Phase I: BWM
Phase II: the COPRAS model
Phase III: Validation of results
Figure 1 - BWM-COPRAS multi-criteria model Рис. 1 - BWM-COPRAS многокритериальная модель Слика 1 - BWM-COPRAS вишекритериумски модел
The model contains three phases. Phase one calculates the optimal values of the weight coefficients of criteria through the application of the BWM. The end results of the BWM method are the values of the weight coefficients of criteria. The output results of the BWM, the weight
coefficients, are further processed through the COPRAS method algorithm. In phase two, the COPRAS method is used to rank the alternatives. Phase three is the validation of the results. The next section shows the algorithms of the BWM and COPRAS methods.
Best-Worst method
The following section contains the algorithm of the BWM method for determining the weight coefficients of evaluation criteria (Rezaei, 2015), (Stevic et al, 2018).
Algorithm: BWM_
Input: Expert pairwise comparison of criteria
Output: Optimal values of the weight coefficients of criteria/sub-criteria
Step 1: The identification of the selected criteria as a set of the criteria related to the
topic. The set of the criteria can be evaluated as C1} C2, C3, C4......Cn.
Step 2: Finding the best and the worst criteria. As mentioned above, it should be done
Step 3: The creation of a matrix of the preference of the best criterion over all the other criteria (BO vector) by applying numbers between 1 and 9:
Ab = (aiB , a2B , a3B ,'"anB )
Step 4: The creation of a matrix of the preference of the worst criterion over all the other criteria (OW vector) by applying numbers between 1 and 9.
Ab = ( aiW , a2W , a3W ,"-anW )
Step 5: Generating the relative importance of the criteria through calculating the final and optimal weights for the criteria. The weights will show the same as: min % s.t.
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Step 6: The same as with the AHP, there is a consistency index shown in Table 2. The consistency ratio should be calculated as follows:
Consistency =
Consistency index
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For different values aBW e{1,2,...,9} we get the maximum values £(max£). Table 2 contains the maximum values of £ for different values
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Table 2 - Consistency Index values (CI) Таблица 2 - Значения степени надежности (CI) Табела 2 - Вредности степена конзистентности (CI)
aBW 1 2 . . 7 8 9
CI ( max£ ) 0.00 0.44 . . 3.73 4.47 5.23
Based on CI, we get the consistency ratio (CR) which takes the values of interval [0, 1], where the values closer to zero indicate a high consistency, and the CR values closer to one indicate a low consistency.
COPRAS Method
Within the decision-making theory, there is a large number of multi-criteria decision making methods (MCDM) which support us in solving different problems. The COPRAS method (Zavadskas & Kaklauskas, 1996) is one of newer methods which is increasingly used in literature (Chatterjee et al, 2018), (Pamucar et al, 2018a), (Mukhametzyanov & Pamucar, 2018). Each MCDM method is characterized by a specific mathematical apparatus. The COPRAS method is partly characterized by a more complicated procedure of criteria function value aggregation, and the simplified procedure of data normalization (the nature of the criteria is irrelevant - min/max). The following section succinctly displays the mathematical apparatus of the COPRAS method.
The problem is formally presented by choosing one of the m options (alternatives), Ai,i = 1,2,...,m which are assessed and compared among each other based on the n criterion (Xj, j = 1,2,...,n) whose values are familiar. The alternatives are presented as vectors xj where xj is the
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Step 1. Normalization of the basic matrix. The first step of the COPRAS method includes the normalization of the elements of the basic decision-making matrix (X).
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The main goal of criteria value normalization is the transformation of different values of criteria ("benefit" or "cost") into values which allow mutual comparison. The normalization values are shown in the matrix D.
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The elements of the normalized matrix (x.) are obtained by applying additive normalization:
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where x. represents the elements of the basic decision-making matrix
(X), x. represents the normalized values of the elements from the basic
decision-making matrix, and m represents the total number of alternatives.
Step 2. Forming of the weighted normalized matrix. In the second step, a weighted normalized matrix (Z), obtained by multiplying the elements of the normalized matrix (D) with the weight coefficients of the criteria (w.), is constructed.
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where n is the total number of criteria, and m is the total number of alternatives.
Step 3. In the following, third step, the values of the Z matrix are summed up in columns. The values are summed up depending on which
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criteria group they belong to ("benefit" ^max or "cost" ^ min). The values of the benefit criterion (higher criterion value is desirable) are obtained by applying formula (5) or formula (6):
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where p is the total number of the cost criteria.
Step 4. Aggregation of the criteria function values. In step four, by 55 applying formula (9), we determine the significance (influence) of each of the given alternatives from the set of the compared alternatives:
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Step 5. Ranking of alternatives. In the final, fifth step, the ranking of alternatives is performed based on the values of the criterion function which is assigned to each alternative. The end-values of the criteria functions of alternatives are gained by applying formula (10):
N. -100% (10)
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Application of the BWM-COPRAS model to off-road vehicle selection in the SAF
Military cargo motor vehicles for passenger transport are only one of the vehicles categories used in the SAF. Since this paper deals only with this vehicle category, the following section will briefly introduce the
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classification of vehicles in the SAF and the types of vehicles used in the SAF as well as in other militaries across the world.
Classification of vehicles
Mark Vehicle description
1.04 T- CM CO ^ 0000 Off-road vehicle for passenger transport, up to 5 seats; Off-road vehicle for passenger transport, 6 to 8 seats; Off-road vehicle for passenger transport, more than 8 seats; Off-road vehicle for passenger transport, with protection.
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The classification of motor vehicles and other means of £ transportation that use liquid fuels in the MoD and the SAF (except <| waterborne vessels, aircraft, stationary aggregates and boiler rooms), ^ aims to group the encompassed vehicles according to the criterion of purpose or according to similar technical characteristics.
The classification includes the division of vehicles into classes, types, groups and the assignment of numbers for marking them: I -classes of vehicles are marked with numbers 1-9; II -types of vehicles within classes are marked with numbers 01-99 and III -groups of vehicles within types are marked with numbers 01-99. This paper deals with vehicles that belong to the first group of the aforementioned gen classification as shown in Table 3.
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Table 3 - Classification of off-road vehicles for passenger transport in the SAF Таблица 3 - Классификация внедорожных транспортных средств для перевозки
пассажиров в ВСРС ^
Табела 3 - Класификаци^а теренских возила за транспорт путника у ВС
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The supply of this vehicle category from the SAF fleet is low and amounts to approximately 43%, while the total number (of vehicles from the prescript fleet) is 92%. The structure of vehicles from this category in § the SAF is also inhomogeneous, i.e. they are of different brands and -s types, mostly obtained more than 30 years ago. The most prominent brands of manufacturers are: PUCH (around 33%), PINZGAUER (around 27%), LADA (around 14%) and LANDROVER (around 10%). The inhomogeneity of the fleet vehicles complicates the maintenance process of these vehicles. The average functionality of off-road vehicles for passenger transport in the SAF is approximately 66%. The average age ci of off-road vehicles for passenger transport in SAF units is 26.9 years. It is especially important to stress that approximately 80% of this category is older than 12 years, which is also the designed lifespan of these o. vehicles. In addition to the abovementioned statistical data, it is
E
necessary to point out that an average off-road vehicle for passenger transport in SAF has crossed approximately 141,000 kilometers, where the vehicles older than 12 years have on average crossed 162,728 km, and vehicles less than 12 years old 56,000 km.
Defining the criteria for off-road vehicle selection and characteristics of alternatives
Given than in the publicly available literature there are not a large number of papers dealing with the topic of military off-road vehicle selection, the criteria have been defined based on the available literature, internal regulations and requirements of the SAF. The chosen criteria are shown in Figure 2. In addition to the abovementioned criteria, criteria such as equipment with the AC, GPS, traction-control system, etc. were excluded.
Alternatives
Selection of off-road motor vehicle for passenger transport
Warranty- provisions
Figure 2 - Hierarchical modei for vehicle selection Рис. 2 - Иерархическая модель для выбора транспортного средства Слика 2 - Хи]ерархи]ски модел за избор возила
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The first level represents a goal which is a choice between the given vehicle types, while the second level includes 7 criteria for vehicle selection: obstacle clearing capability (C1), equipped soldier transportation capacity (C2), characteristics of the motor (C3), price (C4), maintenance (C5), safety (C6), and warranty provisions (C7). The third e level consists of seven sub-criteria that are sorted within the group of the main criteria, while the potential vehicle types are shown on the fourth level.
By comparing the characteristics of the vehicles used by the SAF ^ and modern vehicles used for the same purpose, a conclusion is drawn that a modernization of SAF's fleet vehicles is needed. Modern vehicles f have significantly improved characteristics when looking at maneuverability, tank capacity and horsepower. Since there is no consensus among manufacturers concerning the evaluation of the g abovementioned vehicle types, as well as because of data confidentiality policies, this paper will not talk about specific types of vehicles - instead, | the vehicles will be marked as vehicle 1 - vehicle 4.
up
o
Vehicle 1 (A1) has the following technical characteristics: its ability to 2 clear obstacles is higher than that of vehicle 2 and lower than that of vehicle 4; the vehicle can simultaneously carry four persons; the level of :p passenger and cargo security is higher compared to other given types of vehicles; it has 190 HP, and fuel consumption is 23.75 l/km; the price of §
the vehicle is 15,785,100 RSD with the possibility of payment in 18 £
o
installments without interest; the shipment deadline is 6 months and it m has a 24 month guarantee; and the availability of the service network and E spare parts is poorer than for other given vehicle types.
o
Vehicle 2 (A2) has the following technical characteristics: the ability o to clear obstacles is the lowest with this vehicle; the vehicle can <o simultaneously carry 6 persons, and the security of the passengers and cargo is on a high level; the engine has 122 HP, and consumes fuel at the rate of 10.1 l/km; the price of the vehicle is 13,702,500 RSD with the possibility of payment in 18 installments without interest; the shipment deadline is 4 months and it has a 24-month guarantee; the widespread availability of the service network and the availability of spare parts is better than for vehicle 1, but worse than for other given types of vehicles.
Vehicle 3 (A3) has the following technical characteristics: this
vehicle's ability to clear obstacles is the same as with vehicle 1; the
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vehicle can simultaneously carry 4 persons, the security of passengers and cargo is lower compared to vehicle 1 and vehicle 2; the engine has 177 HP, and consumes fuel at the rate of 10.4 l/km; the price of the vehicle is 14,210,000 RSD with the possibility of payment in 12 installments without interest; the shipment deadline is 4 months, and it has a 12-month guarantee; the widespread availability of the service network and the availability of spare parts is better than with all other given vehicles.
Vehicle 4 (A4) has the following characteristics: the ability to clear obstacles is on a higher level than with other vehicles; the vehicle can simultaneously carry 6 persons; the level of passenger and cargo security is the lowest compared to all other vehicle types; the engine has 268 HP and consumes power at the rate of 9.5 l/km; the price of the vehicle is 10,380,000 RSD with the possibility of payment in 24 installments without interest; the shipment deadline is 6 months, and it has a 60-month guarantee; the widespread availability of the service network and the availability of spare parts is better than with vehicle 1 and vehicle 2, but worse than with vehicle 3.
Vehicle assessment through the application of the BWM-COPRAS model
This research includes three groups of experts. Within every criteria/sub-criteria group experts have defined the best (B) and worst (W) criterion/sub-criterion. Based on this, the BO and OW vectors were defined for B and W criteria/sub-criteria. The criteria/sub-criteria assessment was performed through the application of [1,9] scale: 1 -very low influence; 2 - low influence;...; 8 - high influence; 9 - very high influence. The values of BO and OW vectors within the groups of criteria/sub-criteria are shown in Table 4.
The optimal values of the weight coefficients of the criteria/sub-criteria vectors are calculated based on the defined ratios from Table 5. This is how the four non-linear models for calculating the optimal values of the criteria/sub-criteria weight coefficients were formed.
Table 4 - BO and OWvectors Таблица 4 - BO и OW векторы Табела 4 - BO и OW вектори
Criteria
The best: C4 (Price) Expert evaluation The worst: C3 (Characteristics of the motor) Expert evaluation
C1 (Obstacle clearing capability) 5; 6; 6 C1 (Obstacle clearing capability) 4; 4; 4
C2 (Equipped soldier transportation capacity) 7; 7; 8 C2 (Equipped soldier transportation capacity) 3; 2; 2
C3 (Characteristics of the motor) 9; 9; 9 C4 (Price) 9; 9; 9
C5 (Maintenance) 2; 2; 2 C5 (Maintenance) 7; 7; 7
C6 (Safety) 3; 5; 2 C6 (Safety) 5; 5; 7
C7 (Warranty provisions) 3; 4; 4 C7 (Warranty provisions) 5; 6; 6
C3 (Characteristics of the motor)
The best: C31 (Fuel consumption) Expert evaluation The best: C32 (horsepower) Expert evaluation
C32 (horsepower) 4; 3; 2 C31 (Fuel consumption) 2; 4; 3
C4 (price)
The best: C41 (Price) Expert evaluation The best: C42 (shipment time) Expert evaluation
C42 (shipment time) 6; 5; 5 C41 (price) 6; 5; 7
C43 (payment conditions) 3; 3; 2 C43 (payment conditions) 4; 2; 6
C5 (maintenance)
The best:C51 The best: C52 (availability of spare parts)
(widespread availability of the service network) Expert evaluation Expert evaluation
C52 (availability of spare parts) 2; 3; 3 C51 (widespread availability of the service network) 2; 3; 5
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Medium values of expert evaluations are shown in Table 5.
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Table 5 - Medium values of the BO and OW vectors Таблица 5 - Средние значения BO и OW векторов Табела 5 - Средне вредности BO и OWвектора
Criteria
The worst: C3
The best : C4 (Price) Medium value (Characteristics of the Medium value
motor)
C1 (Obstacle clearing capability) 5.7 C1 (Obstacle clearing capability) 4
C2 (Equipped soldier transportation capacity) 7.33 C2 (Equipped soldier transportation capacity) 2.33
C3 (Characteristics of the motor) 9 C4 (Price) 9
C5 (Maintenance) 2 C5 (Maintenance) 7
C6 (Safety) 3.33 C6 (Safety) 5.67
C7 (Warranty provisions) 3.67 C7 (Warranty provisions) 5.67
C3 (Characteristics of the motor)
The best: C31 (fuel consumption) Medium value The worst: C32 (horsepower) Medium value
C32 (horsepower) 3 C31(fuel consumption) 3
C4 (price)
The best: C41 (price) Medium value The worst: C42 (shipment time) Medium value
C42 (shipment time) 5.33 C41 (price) 6
C43 (payment conditions) 6.67 C43 (payment conditions) 4
C5 (maintenance)
The best: C51 (widespread availability of the service network)
Medium value
The worst: C52 (availability of spare parts)
Medium value
C52 (availability of spare parts)
2.67
C51 (widespread availability of the service network)
3.33
Model 1 (Criteria)
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W - 5.67
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Model 3 (Price)
min^
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W41 — 5.33 W41 — 6
W42 W42
W41 - 6.67 IA ; W43 - 4
W43 W42
S3 W, = 1
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Model 2 (Characteristics of the motor)
min^
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Model 4 (Maintenance)
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The optimal values of the weight coefficients were obtained based on the aforementioned models, Table 6.
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Table 6 - Optimal values of the sub-criteria Таблица 6 - Оптимальные значения субкритериев Табела 6 - Оптималне вредности поткритериума
Criteria/Sub-criteria Local weights Global weights Ra
C1 0.077 0.077 5
C2 0.059 0.059 6
C3 0.033 - -
C31 0.750 0.025 10
C32 0.250 0.008 11
C4 0.365 - -
C41 0.754 0.276 1
C42 0.097 0.035 9
C43 0.149 0.054 7
C5 0.217 - -
C51 0.750 0.163 2
C52 0.250 0.054 8
C6 0.130 0.130 3
C7 0.118 0.118 4
Table 6 shows the global and local values of the criteria/sub-criteria weight coefficients. The global values were obtained through multiplication of the weight criteria coefficients and the weight sub-criteria coefficients. The global weight values are further used to assess the alternatives in the multi-criteria model.
By solving the non-linear models the values £= 0.06868,
ïKapa~opa = 0, ^ = 0.238385 and £0dpxm = 0.33 are obtained. The r values are used for defining the consistency coefficients. Using the
obtained values of , the values of the consistency index and the consistency ratio were defined, Table 7.
Table 7 - Values of the Consistency index and the Consistency ratio Таблица 7 - Значения степени надежности и индекса надежности Табела 7 - Вредности степена и индекса конзистентности
Sub-criteria level Ccriteria Ccharacteristics of the motor Cprice Cmaintenance
aBW 9 3 6.67 3.33
Cl 5.23 1.00 3.335 1.11
CR 0.013 0.000 0.071 0.297
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After obtaining the weight coefficient values, the COPRAS method is used for choosing the best alternative. The first step is to form the basic matrix (X)
A1
X = A2 A3 A4
C1 C 2 C3 C 4 C5 C 6 C 7 C8 C 9 C10 Cll
6 4 23.75 190 15785100 6 18 2 2 8 24
4 6 10.1 122 13702500 4 18 4 4 6 24
6 4 10.4 177 14210000 4 12 8 8 4 12
8 6 9.5 268 10380000 6 24 6 6 2 60
In the first phase, by applying formula (3), the normalization of the basic decision-making matrix (X) is performed. This is how we get the normalized matrix (D).
C1 C 2 C 3 C 4 C5 C 6 C 7 C8 C 9 C10 C11
A1 0.250 0.200 0.442 0.008 0.292 0.300 0.25 0.1 0.1 0.4 0.2
D = A2 0.167 0.300 0.188 0.005 0.253 0.200 0.25 0.2 0.2 0.3 0.2
A3 0.250 0.200 0.193 0.005 0.263 0.200 0.167 0.4 0.4 0.2 0.1
A4 0.333 0.300 0.177 0.008 0.192 0.300 0.333 0.3 0.3 0.1 0.5
In the second phase, we perform the multiplication of the value of the matrix (D) with the weight coefficients by applying formula (4) and form the weight-normalized matrix (Z).
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C1 C 2 C3 C 4 C5 C 6 C7 C8 C9 C10 C11
0.019 0.012 0.011 0.000 0.081 0.011 0.014 0.016 0.005 0.052 0.024
0.013 0.018 0.005 0.000 0.070 0.007 0.014 0.033 0.011 0.039 0.024
0.019 0.012 0.005 0.000 0.073 0.007 0.009 0.065 0.022 0.026 0.012
0.026 0.018 0.004 0.000 0.053 0.011 0.018 0.049 0.016 0.013 0.059
In the third phase, we sum up the values of the Z matrix by columns. The values are summed up based on which criterion group they belong to (max or min). The total values of the max and min criteria are shown in the following matrix.
Si + Si -
A1 0.2037 0.0403
A2 0.1786 0.0531
A3 0.1679 0.0812
A4 0.1890 0.0774
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In the fourth phase, we apply formula (9) to define the significance of each of the considered alternatives from the set of alternatives being compared. In the end, the ranking of the alternatives is performed based on the value of the criterion function that is assigned to every alternative. The final values of the COPRAS method and the alternative ranks are shown in the Q matrix.
~ Qi Pi Pane
A1 0.294504 100.00 1
A2 0.247505 84.04 2
A3 0.212909 72.29 4
A4 0.236293 80.23 3
Based on the criteria function values, the final rank of the alternatives is defined: A1 > A2 > A4 > A3.
Validation of the results
Before making a decision, it is necessary to perform a validation of the obtained results. In this paper, the validation of the results is
performed in three phases. In phase one, the initial rank of the alternatives gained by applying the BWM-COPRAS model is compared to the ranks obtained through the MIRCA (Chaterjee et al, 2018) and MABAC (Pamucar & Cirovic, 2015) methods (Figure 3).
A2 A3
MABAC ■ COPRAS ■ MAIRCA
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Рис. 3 - Ранг альтернатив
Слика 3 - Ранг алтернатива ~
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Compared to other methods, the rank of the alternatives A1 and A2 remained unchanged. The tesults obtained through the COPRAS method differ from those obtained through the MABAC and MAIRCA methods 2 only in the position of the A3 and A4 alternatives. In order to determine o the statistical significance between the ranks obtained through the BWM- | COPRAS model and though other approaches, the Spearman's rank correlation coefficient was used (SRCC). The SRCC is the coefficient of the basic linear correlation between ranks. The Spearman's rank 1
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correlation coefficient is a non-parametrical method for ascertaining the e strength of the correlation applied when (Pamucar et al, 2018b): (1) the data for at least one of the variables is displayed as ordinal data or in ranks, (2) at least one of the variables does not have a normal distribution, and (3) the ratio among variables is not linear. The value of the rank correlation coefficients is obtained through formula (11):
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where D represents the variance in the ranks and n the number of the units of the analysis. The results of the rank comparison though the application of the SRCC are shown in Table 8.
MCDM method COPRAS MAIRCA MABAC
SRCC 0.800 1.000 1.000
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о Table 8 - Rank correlation of the tested methods
>v Таблица 8 - Ранговая корреляция тестируемых методов
см Табела 8 - Корелацц'а рангова тестираних метода
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° From Table 8, we see that the results of the MABAC and MAIRCA
methods are in complete correlation, while the results of the COPRAS method have also shown a high level of correlation when compared to о other methods. Since the lowest level of correlation is 0.8 and the middle
Ш
value is 0.9, we can conclude that the suggested rank is confirmed and oc credible.
^ The second phase of the result validation is a performance analysis
of the proposed model in the dynamic basic matrix environment. In the dynamic basic matrix, for every scenario, a change in the number of alternatives was performed and the obtained ranks were analyzed. The < matrices are formed by removing the lowest-ranking alternative, and then о by ranking the remaining ones based on the newly-obtained basic * decision-making matrix. By applying the BWM-COPRAS model, the solution A1>A2>A4>A3 was obtained. Given that the A3 alternative is the ш worst in the modified matrix, A3 is eliminated from the set of alternatives. о The new decision-making matrix is solved again and we get a new rank A1>A2>A4. After this, the worst alternative (A4) is once again eliminated, > and with the application of the BWM-COPRAS model the final rank A1>A2 is obtained.
Based on the obtained results, we can conclude that, by eliminating the worst method, the rank of the remaining alternatives stays the same through all three scenarios. Alternative A1 has stayed the best ranked through all scenarios which has confirmed the robustness of the ranks obtained in a dynamic environment.
The third phase of result validation is performed by changing the weight criteria. The goal of this phase of the result validation is to estimate the influence of the most influential criterion on the performances of ranking the proposed model. After determining the weight coefficients of the criteria by applying the BWM-COPRAS method for the purposes of sensitivity analysis, the "most important criterion" is
identified. By applying formula (12), the weight proportionality is defined during the sensitivity analysis.
= (1 - w )x(w° /Wcc) = w°-Axac (12)
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where wc is the shift in the weight criteria within the sensitivity analysis,
ai
ws represents the weight of the most important criterion, w°c represents cl the original values of the weight criteria and Wcc represents the sum of g the original weight criteria values that are changing. The ac parameter is ¡5 defined as the weight coefficient of elasticity that expresses a relative compensation of other weight coefficient values compared to the given changes in the weight of the most important criterion. The ac value is obtained through formula (13) (Kahraman, 2002). « = wC / W; (13)
The assumptions during the performance of sensitivity analysis are as follows: (1) the value of the weight coefficient of elasticity for the most significant criterion is defined as one; (2) the ratio of the variable weights stays constant during the entirety of the sensitivity analysis (Kirkwood, =6
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1997). The Ax parameter (formula (12)) represents the amount of change applied to the set of weight coefficients depending on their weight coefficients of elasticity. The change of weights of the most important criteria should be limited. Otherwise, the weights can take on negative values which would lead to a disturbance in limiting the weight proportionality. The Ax parameter can be (1) positive, which is indicated by the increase of the relative significance or (2) negative, as indicated by the decrease of the relative significance. The limits of Ax are defined ° as the greatest change in weight of the most important criterion in the
e
negative and positive direction. The boundary values of Ax are defined E by applying formula (14). J
-wc < Ax < min {w° / ac} (14)
After defining the boundary values of Ax , new criteria weights are calculated according to the previously established parameters for the sensitivity analysis. The set of these new weight coefficient values is calculated using formulas (15) and (16).
ws = wC +as Ax (15)
wc = wCAx (16) E
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where w°s is the initial weight of the criteria subjected to the sensitivity analysis, w°c je the original value of the variable weights. This new set of criteria always satisfies the universal state of weigh coefficient proportionality that ^ ws + ^ wc = 1. Based on the newly-obtained criteria
values, new ranks of alternatives for the given scenario are calculated.
In this research, the C5 criterion is identified as the most influential one because it has the highest weight coefficient value w2 = 0.276. In the next step, the coefficient of weight elasticity of the most important criterion is determined (as) (Table 9) and the boundary values for the weight coefficient change of the most important criterion (Ax) are defined.
Table 9 - Elasticity coefficient for changing weights Таблица 9 - Коэффициент гибкости главных критериев Табела 9 - Коефици^ент еластичности на]знача]ни]ег критериума
Criteria labels as
C1 0.1070
C2 0.0820
C3 0.0350
C4 0.0110
C5 1.0000
C6 0.0480
C7 0.0747
C8 0.2254
C9 0.0747
C10 0.1798
C11 0.1632
That is how the boundary values of the C5 criterion were obtained and they are -0.2760< Ax <0.723. Based on the defined boundaries of the weight coefficient change for the most important criterion, the scenarios for the sensitivity analysis were determined. The -0.2760<Ax <0.723 interval was divided into a total of 21 scenarios. After defining the boundary values of the most influential criterion, new weight coefficient values were defined for the 21 scenarios, Table 10.
The influence of the new weight coefficient values on the change of the ranks of alternatives is shown in Figure 4.
Figure 4 - Sensitivity analysis of alternative ranks through 21 scenarios Рис. 4 - Анализ чувствительности альтернативных рангов по 21 сценарию Слика 4 - Анализа остеъивости рангова алтернатива кроз 21 сценарио
The final step is the review of the SRCC for all scenarios (Figure 5) by using formula (21).
S13
S12
Sll
S10
Figure 5 - Correlation coefficient for each scenario Рис. 5 - Коэффициент корреляции по каждому сценарию Слика 5 - Коефици^ент корелаци^е за сценари^е
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Table 10 - Weights of the new criteria Таблица 10 - Коэффициент важности (весов) новых критериев Табела 10 - Тежински коефици^енти новог скупа критериума
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Scenario C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11
S1 0.107 0.082 0.035 0.011 0.000 0.048 0.075 0.225 0.075 0.180 0.163
S2 0.101 0.078 0.033 0.011 0.050 0.046 0.071 0.214 0.071 0.171 0.155
S3 0.096 0.073 0.031 0.010 0.100 0.044 0.067 0.203 0.067 0.162 0.147
S4 0.091 0.069 0.029 0.009 0.150 0.041 0.063 0.192 0.063 0.153 0.139
S5 0.085 0.065 0.028 0.009 0.200 0.039 0.060 0.180 0.060 0.144 0.131
S6 0.080 0.061 0.026 0.008 0.250 0.036 0.056 0.169 0.056 0.135 0.122
S7 0.075 0.057 0.024 0.008 0.300 0.034 0.052 0.158 0.052 0.126 0.114
S8 0.069 0.053 0.022 0.007 0.350 0.031 0.049 0.147 0.049 0.117 0.106
S9 0.064 0.049 0.021 0.007 0.400 0.029 0.045 0.135 0.045 0.108 0.098
S10 0.059 0.045 0.019 0.006 0.450 0.027 0.041 0.124 0.041 0.099 0.090
S11 0.053 0.041 0.017 0.006 0.500 0.024 0.037 0.113 0.037 0.090 0.082
S12 0.048 0.037 0.016 0.005 0.550 0.022 0.034 0.101 0.034 0.081 0.073
S13 0.043 0.033 0.014 0.004 0.600 0.019 0.030 0.090 0.030 0.072 0.065
S14 0.037 0.029 0.012 0.004 0.650 0.017 0.026 0.079 0.026 0.063 0.057
S15 0.032 0.024 0.010 0.003 0.700 0.015 0.022 0.068 0.022 0.054 0.049
S16 0.027 0.020 0.009 0.003 0.750 0.012 0.019 0.056 0.019 0.045 0.041
S17 0.021 0.016 0.007 0.002 0.800 0.010 0.015 0.045 0.015 0.036 0.033
S18 0.01 6 0.012 0.005 0.002 0.850 0.007 0.011 0.034 0.011 0.027 0.024
S19 0.01 1 0.008 0.003 0.001 0.900 0.005 0.007 0.023 0.007 0.018 0.016
S20 0.005 0.004 0.002 0.001 0.950 0.002 0.004 0.011 0.004 0.009 0.008
S21 0.000 0.000 0.000 0.000 0.999 0.000 0.000 0.000 0.000 0.000 0.000
The medium value of the correlation coefficient for all scenarios is 0.752 - with this we conclude that the scenarios show a high degree of correlation. Given that A1 remained the highest ranked through all three phases of the result validation of alternatives, we can conclude that the proposed rank is confirmed and credible.
Conclusion
This research created the hybrid BWM-COPRAS model for the assessment of off-road vehicles for the units of the SAF. For the evaluation of alternatives, seven criteria used in the first hierarchical level were broken down into seven additional sub-criteria on the second hierarchical level. The key contribution of this paper is the new BWM-
References
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COPRAS model for the assessment of vehicles in the SAF, as well as the original BWM-MABAC and BWM-MAIRCA models which were created for the needs of result verification. The presented model enables the inclusion of subjectivities which arise in the process of group decision making through linguistic validation of evaluation criteria. In addition to e this, though the model presented in this paper, new methodological bases for SAF vehicle evaluation were introduced, which simultaneously □: contributes to the betterment of the theoretical bases of multi-criteria g decision making as a whole. The developed approach enables the bridging of the gap that currently exists within the methodology for off- ^ road vehicle assessment for the units of the SAF. By choosing the optimal off-road vehicle, the risk of performing tasks for the SAF units is significantly lowered and their efficiency is greatly enhanced.
The hybrid BWM-COPRAS model has been applied for the assessment of the four vehicles considered for use in the SAF units. The £ obtained results were checked though the discussion of the results for different scenarios in which a dynamic environment was simulated | through the application of weight criteria values. The stability of the model was verified through the statistical coefficient of correlation which showed a high correlation of the ranks in all scenarios. The research presented in this paper can serve as a methodology for decision making when choosing the optimal off-road vehicle. Also, the results can be used in the analysis of the certain criteria influence on the selection of the military vehicle, which can serve as a systematical approach to path defining in a model of the authority's decision making in the process of £
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см МНОГОКРИТЕРИАЛЬНАЯ МОДЕЛЬ ВЫБОРА ОПТИМАЛЬНОГО
oR ВНЕДОРОЖНОГО ТРАНСПОРТНОГО СРЕДСТВА ДЛЯ
^ ОСУЩЕСТВЛЕНИЯ ПЕРЕВОЗКИ ПАССАЖИРОВ: BWM-COPRAS
g МОДЕЛЬ
и Драган С. Памучар, корреспондент, Лазар M. Савин
< Университет обороны в г. Белград, Военная академия,
Департамент логистики, г. Белград, Республика Сербия
о РУБРИКА ГРНТИ: 28.17.31 Моделирование процессов управления
^ ВИД СТАТЬИ: оригинальная научная статья
>- ЯЗЫК СТАТЬИ: английский
ос
¡5 Резюме:
Введение/цель: Соответствующее развитие и выбор внедорожных транспортных средств с целью выполнения различных видов задач являются весьма важными факторами, Q которые влияют на мобильность пользователей, качество
^ передвижения и безопасность при выполнении транспортной
2 деятельности в рамках Вооруженных сил Республики Сербия
у (ВСРС), а также на эффективность ее осуществления.
Методы: В данной работе представлена модель для выбора оптимального внедорожного транспортного средства для нужд О ВСРС, с применением BWM (Best Worst Method) и COPRAS
g (Compressed Proportional Assessment) моделей. Определение
> относительной сложности критериев на основании, которых
производится оценка потенциальных внедорожных транспортных средств выполнено с помощью BWM метода. Наряду с COPRAS методом, который является неотъемлемой частью основной модели принятия решений, в данной работе в части валидации результатов применялись и MABAC (MultiAttributive Border Approximation area Comparison) и MAIRCA (MultiAtributive Ideal-Real Comparative Analysis) методы.
Результаты: Испытание BWM-COPRAS модели проведено на примере выбора оптимального внедорожного транспортного средства в ВСС в результате чего был получен высокий коэффициент корреляции рангов. Валидация результатов выполнена с помощью статистической обработки данных, полученных благодаря применению различных
Сажетак:
многокритериальных методов, в том числе ^ коэффициента корреляций рангов Спирмена. Выводы: Полученные результаты показывают устойчивость результатов предлагаемой модели при ранжировании <и альтернатив и доказывают ее применимость для решений ° многокритериальных задач.
Ключевые слова: BWM, COPRAS, MABAC, MAIRCA, выбор £ автомобиля, принятие многокритериальных решений. о
ВИШЕКРИТЕРШУМСКИ BWM-COPRAS МОДЕЛ ЗА ИЗБОР ОПТИМАЛНОГ ТЕРЕНСКОГ ВОЗИЛА ЗА ПРЕВОЗ ПУТНИКА й
Драган С. Памучар, аутор за преписку, Лазар M. Савин
Универзитет одбране у Београду, BojHa академи]а, °
Катедра логистике, Београд, Република Срби]а
ОБЛАСТ: математика, саобрапа], логистика ю
ВРСТА ЧЛАНКА: оригинални научни рад JЕЗИК ЧЛАНКА: енглески
го
Увод/цил>: Адекватна евалуац^а и избор теренског возила за о извршеъе различитих врста задатака веома je важан фактор щи ^ утиче на мобилност корисника, ъихову безбедност, као и на
квалитет и ефикасност извршаваъа транспортних активности у Воjсци Срб^е (ВС). "I
тз го о
Методе: Стога je за избор оптималног теренског возила за потребе ВС, у овом раду предложен BWM (Best Worst Method) и COPRAS (Compressed Proportional Assessment) модел . Одре^иваше о релативних тежина критери]ума, на основу щих се врши вредноваше потенци]алних теренских возила, извршено jе Ц. применом BWM методе. Поред COPRAS методе, ща ¡е саставни део основног модела за доношеше одлуке, у овом раду су, кроз i ф валидаци]у резултата, примешене и методе MABAC (MultiAttributive о Border Approximation area Comparison) и MAIRCA (MultiAtributive Ideal- э Real Comparative Analysis). Резултати: Тестирашем BWM-COPRAS модела на примеру избора V оптималног теренског возила у ВС доби}ена jе висока корелаци]а рангова. Валидаци}а резултата извршена jе статистичком обрадом резултата доби}ених различитим вишекритери]умским техникама, применом Спирмановог коефици]ента корелацще. Закъучак: Резултати показу}у стабилност резултата q предложеног модела у рангирашу алтeрнативa и доказу}у шегову примешивост за решаваше вишекритери]умских проблема. ^
Къучне речи: BWM, COPRAS, MABAC, MAIRCA, избор возила, cl доношеше вишекритери]умских одлука.
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Paper received on / Дата получения работы / Датум приема чланка: 23.08.2019. Manuscript corrections submitted on / Дата получения исправленной версии работы / Датум достав^а^а исправки рукописа: 14.12.2019.
Paper accepted for publishing on / Дата окончательного согласования работы / Датум коначног прихвата^а чланка за об]ав^ива^е: 16.12.2019.
© 2020 The Authors. Published by Vojnotehnicki glasnik / Military Technical Courier (www.vtg.mod.gov.rs, втг.мо.упр.срб). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/rs/).
© 2020 Авторы. Опубликовано в «Военно-технический вестник / Vojnotehnicki glasnik / Military Technical Courier» (www.vtg.mod.gov.rs, втг.мо.упр.срб). Данная статья в открытом доступе и распространяется в соответствии с лицензией «Creative Commons» (http://creativecommons.org/licenses/by/3.0/rs/).
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