Badania nad właściwościami operacyjnymi metody AHP

An ability to generate consistent results is the most critical operational feature of every method. The objective of the present paper was to demonstrate the results of the study conducted within the Ministry of Science and Higher Education Grant NN111345138 (Methodology of multicriteria comparative analysis of elements), regarding the relationship between the level of inconsistency of the AHP results, measured by Consistency Ratio (CR), and number of the compared criteria. Experiment involved analysis of 3-8 characteristics of selected objects (laptop, printer, public transport, mobile phone, flat and food store). The results showed that the analysis of as few as 3 characteristics resulted in a very high fraction of inconsistent opinions (more than 50%). In case of 6,7 and 8 characteristics this fraction exceeded 80%

Evaluating Different Multi-Criteria Decision Methods for the Comparison and Investigation of Public Transport Projects

There is a need for affordable, reliable, and safe public transport in South Africa. In Cape Town, the most popular modes of public transport are rail, bus, Bus Rapid Transit (BRT) and minibus taxis. At this stage, the various modes are not integrated and, in some instances, are running in parallel. Many research papers have focused on comparing the capital costs and benefits of public transport investments and the results often exclude the effects of criteria that are not easily monetised. In South Africa, the Cost-Benefit Analysis (CBA) is often used to evaluate public transport projects, whereas, in this research, Multi-Criteria Decision Analysis (MCDA) methods were investigated and used. The objective of this research was to evaluate the MCDA methods available and establish it as an alternative or supplementary method, or tool, that public transport planners could use when evaluating public transport projects. In order to test the MCDA methods, Cape Town's existing public transport was used as a case study with each mode assumed to be operating exclusively. Therefore, the five scenarios analysed are: Rail (MetroRail); Bus (Golden Arrow); BRT (MyCiTi) Minibus Taxis, and Integrated Public Transport System (theoretical). These modes were evaluated against a number of criteria including economic, social, and environmental impacts. Qualitative methods were focused on, incorporating quantitative methods, in order to gain indepth insight into public transport management and operations, as well as the costs and benefits involved, both direct and indirect. Research on public transport practices, locally, nationally, and internationally was performed. From this, alternatives for the case study, as well as the assessment criteria, were established. The research also included investigating multi-criteria analysis methods, ultimately leading to the methods chosen for the analysis. In order to perform the analyses using the alternatives and assessment criteria, the criteria needed to be weighted. The scenarios were analysed using an UNWEIGHTED viewpoint, where each criterion was equally weighted; WEIGHTEDs viewpoint, where each criterion was weighted by key players (specialists) in the public transport discipline; WEIGHTEDp viewpoint, where each criterion was weighted by the general public who have used public transport in Cape Town. As this may lead to differing results, aggregation methods were also included in the research. As mentioned, the integration of this investigation involves optimising the method in which public transport projects are being evaluated by establishing a multi-criteria analyses method which is reliable, simple, and capable of including a variety of criteria, both monetary, qualitative, and quantitative. A variety of comparative evaluation methods exist. Within this, as mentioned, the popular methods for public transport appraisal are Cost-Benefit Analysis and a variety of Multi-Criteria Decision Analysis methods. Cost-Benefit Analysis (CBA) is the most used evaluation method for assessing infrastructural investments. In the transport field, it is the basic tool in most countries (Beria et al., 2012). The CBA is based on the monetisation and inter-temporal discount. Money is the measure unit used as common numeracy to translate all costs and benefits associated to an investment or a policy. Once all relevant effects of an investment are quantified, the concept of inter-temporal discount is used to translate future costs and benefits to present day by means of a social discount rate. In this way, the future can be compared with the present (Beria et al., 2012). CBA weighs the pros and cons of a project in a rational and systematic process. It inherently requires the creation and evaluation of at least two options, “do it or not”, plus it requires an evaluation at several different scales (nothing, minimum and all, as the least requirements) (OECD, 2006; EC, 2008; Ninan, 2008 as cited in Jones et al., 2014). Costs generally associated with a cost-benefit analysis include those related to construction and future maintenance, such as capital, major rehabilitation and annual maintenance costs over the life-cycle of the project. Other considerations include discounting of future costs and benefits, dealing with opportunity costs, inflation, avoidance of double counting, avoidance of sunk costs, dealing with joint costs and dealing with the sensitivity analysis (Kentucky Transportation Center, 2016). The limitations often associated with CBA includes omitting costs or key benefits, as well as measuring factors like travel time savings and safety improvements, which are not easily monetised (Kentucky Transportation Center, 2016). In an attempt to mitigate the weaknesses of the CBA, Multi-Criteria Decision Analysis (MCDA) methods were investigated. Generally speaking, a multiple criteria decision problem is a scenario in which having defined a set of actions/solutions (Do nothing / Upgrade Rail / Additional buses etc.) and a consistent family of criteria (Cost / Accessibility / Safety etc.), the Decision Maker (DM) tends to determine the best subset of actions and solutions according to the criteria (choice problem), divide the solutions into subsets representing specific classes of solutions according to the concrete classification rules (sorting problem) or rank the actions and solutions from best to worst, according to the criteria (ranking problem) (Zak, 2010). As previously mentioned, there are many MCDA methods available, Macharis & Bernardini (2015) performed an investigation to establish the most commonly used methods used for transport project analysis. The top three most popular methods are AHP/ANP (Analytic Hierarchy/Network Process) – often used in combination with another method, such as the Evaluation of Mixed Data method (EVAMIX), TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) and Fuzzy Set – often used as a part another method, such as the Simple Additive Weighting Method (SAW, also known as Weighted Sum). The SAW method appeals to the school of thought of unified scores across alternatives, applying weighting and sums the result per alternative. The EVAMIX method appeals to the second school of thought and takes it one step further. After the unification of scores, the alternatives are compared pairwise (Vanderschuren & Frieslaar, 2008). In order to compare the outcomes of different methods without the use of specialised software, to make the method accessible, the SAW method and EVAMIX method was used in conjunction with the AHP method, therefore, appealing to both schools of thought. The AHP method, as developed by Saaty (1980) is a helpful tool for managing qualitative and quantitative criteria involved in decision-making. As stated in the name, it is based on a hierarchical structure (Taherdoost, 2017). The AHP method also develops a linear additive model, but in its standard format, uses procedures for deriving weights and the scores achieved by alternatives which are based, respectively, on pair-wise comparisons between criteria and / or options (Department of Communities and Local Government, 2009). The fundamental input to the AHP method is the decision makers' answers to a series of questions in the general form, ‘How important is criterion A relative to criterion B?' These pair-wise comparisons can be used to establish the weights for criteria and the performance scores for the options on the different criteria (Department of Communities and Local Government, 2009). The SAW method, also known as weighted linear combination, weighted summation or scoring methods is a simple and often used multi attribute decision technique. The method is based on the weighted average. An evaluation score is calculated for each alternative by multiplying the scaled value given to the alternative of that attribute with the weights of relative importance directly assigned by the decision maker, followed by summing of the products for all criteria. The advantage of the method is that it is a proportional linear transformation of the raw data which means the relative order of magnitude of the standardised scores remains equal (Afshari et al., 2010) The EVAMIX method was first introduced by Voogd (1982, 1983) and developed by Nijkamp et al. (1990), and Martel and Matarazzo (2005) as cited in Tuş Işık & Aytaç Adalı, (2016). A key component of the method is that it includes and combines both ordinal and cardinal, beneficial and non-beneficial data within the same evaluation matrix, hence the name. The EVAMIX method makes different computations to the data in the evaluation matrix depending on whether it is ordinal or cardinal (Hajkowicz & Higgins, 2008, as cited in Tuş Işık & Aytaç Adalı, 2016). The EVAMIX is a simple decision support tool, it requires pairwise comparison of alternatives, for each pair of alternatives, a dominance score for the ordinal and cardinal criteria are calculated. Then these dominance scores are combined into an overall dominance score of each alternative (Hinloopen et al., 2004, as cited in Tuş Işık & Aytaç Adalı, 2016). Finally, the alternatives are ranked based on the appraisal scores (Chatterjee & Chakraborty, 2013, as cited in Tuş Işık & Aytaç Adalı, 2016). The two chosen MCDA methods rank the alternatives, however the results of these rankings may not be the same, because of the different assumptions made in each method as well as the difference in criteria weights between the weighted and unweighted analyses. In this case, the aggregation of the methods may be needed. In this paper, it is proposed that the Borda and Copeland methods are used, as well as the Average Ranking Procedure. The Average Ranking Procedure ranks the alternatives by their mean values as opposed to the Borda and Copeland Method which rank alternatives by voting (Cheng & Saskatchewen, 2000). As mentioned, there are many ways that public transport projects are evaluated and part of the reason that a structured methodology is not used, is due to the complex nature of public transport. The potential impacts are directly related to the range (e.g., economic, financial, environmental, social, direct/indirect) and affected groups (users, non-users, as well as government and private operators) (Ferreira & Lake, 2002). For the sake of this thesis, a multiactor multi-criteria analysis was adopted and the three views were analysed (specialist, academic and transport users). Using the existing public transport in Cape Town as a case study, the following scenarios were analysed: Existing rail (MetroRail); Existing bus service (Golden Arrow); Existing BRT service (MyCiTi); Existing minibus taxi service and Theoretical integrated public transport system. It should be noted that for the theoretical integrated transport system, it was assumed that the existing rail, BRT and bus service continued operating and the minibus taxis would operate as feeders to the rest of the system. The services would not operate in parallel. In addition to this, it was also assumed that the BRT system would not expand and instead the funds available would be used to upgrade the existing public transportation along the proposed routes. The above scenarios were evaluated against a set of criteria. To establish the criteria, the most important criteria were identified by evaluating official statements and government documents to establish what the focus is regarding public transport in South Africa. The criteria were as follows: Cost, Land-Use, Affordability for Users, Accessibility, Estimated Speed, Convenience & Reliability, Environmental Effects, and Safety & Security. Two methods of MCDA were used with three alternate weightings as previously described, specialist, general public and academic (unbiased). The AHP method used to establish weightings was simple to use for both the planners/engineers and the general public, as the consistency ratio was under 10% it can, therefore, be concluded that the general public were consistent in their answers thereby understanding the questions and the survey method. The general public rated ‘Accessibility' as the top criteria, whereas the specialists in the private sector and public sector agreed that ‘Safety & Security' is the top criteria, which is the second most important criteria to the general public. Tied with ‘Safety & Security' for the second most important criteria, the general public also voted for ‘Affordability', the private sector specialists agreed, whereas the public sector rated ‘Accessibility' as the second most important criteria. In third place, the general public, as well as the specialists in the public sector agreed that ‘Cost' is important, whereas the private sector rated ‘Accessibility' as the third most important criteria. While the three perspectives differed in ranking, it can be seen that the top four criteria across the board, in no particular order were ‘Accessibility', ‘Affordability', ‘Safety & Security' and ‘Cost'. On the other end of the scale, the lowest weighted criteria were seen to be ‘Speed' for the general public and ‘Environmental' for engineers in both the public and private sector. The engineers in both the public and private sector agree that ‘Speed' is the second least important criteria and conversely, the general public has ‘Environmental' listed as the second least important criteria. All three perspectives agree that ‘Convenience & Reliability' was the third least important criteria. Therefore, it can be seen that the bottom three criteria, in no particular order were ‘Speed', ‘Environmental' and ‘Convenience & Reliability'. The SAW method using the specialist weighting (public and private combined) and the general public weighting, resulted in the same conclusion. The theoretical integrated transport system was the best choice, and the BRT system was considered the least favourable. The academic perspective resulted in minibus taxis being the best choice and the worst choice coincided with the specialist and general public perspective, i.e. BRT. The EVAMIX method results differ slightly between the three perspectives, however, all three agreed that the theoretical integrated transport system was the best alternative. The specialist perspective resulted in the trains being the worst option and the general public and academic perspective resulted in the BRT being the least favourable option. The results were aggregated using three aggregation methods. These methods resulted in the same three rankings with the theoretical integrated system being the best option for investment and the BRT being least desirable option. It should be noted that this evaluation was based on a theoretical approach to the integrated transport system and once the system is designed, further evaluation using accurate data, should be performed. This may change the outcome. In conclusion, both methods of MCDA were implemented with feasible results and, therefore, both methods of MCDA are easily applicable to the evaluation of public transport projects. It is recommended that, as far as possible, primary data be collected when implementing public transport evaluations. It is also recommended to evaluate public transport projects over the lifecycle of the chosen project. Generally, public transport projects are evaluated by or by the order of the City of Cape Town or Western Cape Government and should this be the case, access to more accurate data should be achievable. It is further recommended that should an integrated transport system be considered, the analysis is re-evaluated with the detailed design of the integrated transport system which would provide more precise data and may change the results