**A New Integrated Fuzzy Approach to Selecting the Best Solution for Business Balance of Passenger Rail Operator: Fuzzy PIPRECIA-Fuzzy EDAS Model**

**Slavko Veskovi´c <sup>1</sup> , Željko Stevi´c 2,\* , Darjan Karabaševi´c <sup>3</sup> , Snježana Rajili´c <sup>4</sup> , Sanjin Milinkovi´c <sup>1</sup> and Gordan Stoji´c <sup>5</sup>**


Received: 21 March 2020; Accepted: 12 April 2020; Published: 5 May 2020

**Abstract:** The analysis of operations of the passenger traffic operator in the Republic of Srpska (RS) showed that the volume of passenger transport has, for the last fifteen years, been in constant decline. It is of particular importance that the operator has, year after year, recorded a negative balance of business. The way out of the current unfavorable situation in the sector of passenger traffic is based on the application of Public Service Obligation (PSO) based on the Regulation 1370/2007. In order to solve the problems, seven realistically possible variants have been identified. This paper defines the criteria for selecting the best variant, as well as a new integrated fuzzy model for the selection of the best variant that will enable the operator to make a profit. To define the weights of criteria in this paper, we have used the fuzzy PIvot Pairwise RElative Criteria Importance Assessment (F-PIPRECIA) method, while for ranking and selection of the best variant, we have used the Fuzzy Evaluation based on Distance from Average Solution (F-EDAS) method. Results show that the seventh variant: "Increase in revenue from ticket sales and PSO services and reduction in costs" is the best solution in current conditions. Validation tests are performed with different scenarios and approaches and show that the model is stable. A validity test was created consisting of variations in the significance of model input parameters, testing of reverse rank, applying the fuzzy Measurement Alternatives and Ranking according to the COmpromise Solution (F-MARCOS), fuzzy Simple Additive Weighing (F-SAW) method, and fuzzy Technique for Order of Preference by Similarity to Ideal Solution (F-TOPSIS). As a part of the validation tests, Spearman's coefficient of correlation (SCC) in some scenarios is performed and weights of the criteria have been obtained using the Fuzzy Analytic Hierarchy Process (F-AHP) and Full Consistency Method (FUCOM).

**Keywords:** fuzzy PIPRECIA; fuzzy EDAS; railway; multi-criteria decision-making; transport policy

### **1. Introduction**

One of the most important factors for the functioning and development of cities and regions according to Stoji´c et al. [1] is the public transport of passengers. The transport policy developed by the European Union (EU) has one of the main goals of overcoming the undesirable "modal split," in which road transport has a dominant position, strengthening the role of the railway, thus establishing the possibility of developing a transport system in the spirit of sustainable development. In fact, the Public Service Obligation (PSO) system represents a model for financing unprofitable transport services of a common interest of the country, the region, or the city and local community. Since the end of the 1960s, the EU has tried to improve and develop the concept of PSO in a number of sub-legal acts and regulations in all modes of transport, especially in rail and road public passenger transport (PPT). The basic idea of this concept was that the competent authority (state or local) should provide PPT on lines where the operator (transport company) cannot profitably operate practically, the public authority (ordering party) "buys" (negotiates) the transport service on the "open" market publicly and without discrimination. The volume and service quality, the number of lines and transportation units, the model of determining the amount of compensation for the execution of the service, as well as other mutual rights and obligations, are regulated by the contract. The operator is awarded a Public Service Compensation (PSC) for public transport. According to Regulation (EC) No 1370/2007 [2], the fee for covering the costs arising from the performance of the PSO should, therefore, be determined to prevent over-compensation, and it must be determined so that it does not exceed the amount corresponding to the net financial effect of an equal amount of effects, either positive or negative. The two basic terms that are contained in the new PPT system are: Public Service Obligation (PSO) and Public Service Compensation (PSC). For definition and details of these terms, see (Regulation (EC) No 1370/2007 [2]. By optimizing the PSO system in the PPT process, it is possible to achieve a number of effects, the most significant of which are: Increasing the volume of passenger transport (especially regional and suburban) and, in the worst case, a stoppage in the volume of transport, higher and more stable quality of transport services, reduction in travel costs, better and more efficient cost control, achieve the preconditions for the stabilization and reliability of the operation of railway companies that carry out the transport of passengers (operators). There is no universal and generally accepted model for defining the PSO and the PSC. For example, socio-economic and transport data for PPT services in European cities [3] show the ratio between subventions and operating costs, as well as the ratio of total revenue from the sale of tickets and total operating costs of PPT services in selected cities. According to the mentioned study, the revenues from the sale of tickets cover an average of 44% of the total operating costs of public transport companies. The second indicator shows the percentage of subventions in total operating costs of transport. On average, 48% of the total operating costs of transport are covered by subventions. This means that one-half of the total operating costs of transport is covered by sales revenues, while the other half comes from different subventions from the local, municipal, or national level.

The first aim of the paper refers to the development of a new integrated fuzzy PIvot Pairwise RElative Criteria Importance Assessment (F-PIPRECIA)—Fuzzy Evaluation based on Distance from Average Solution (F-EDAS)—model for solving the business balance of a passenger rail operator, which is harmonized with the EU transport policy. The second aim of the paper is the possibility to overcome the gap between different variants of solving concrete problems in, often, very different demographic, infrastructural, economic, and level-of-service quality levels. The design of the new integrated fuzzy model for the solution business balance of the passenger rail operator allows, within a reasonable time, the non-operational balance sheet of the passenger operator and even the possibility of achieving a rational profit. In order to solve the problem, seven realistic variants based on the combination of procedures, which, in different ways, lead to a defined goal, have been identified. In addition, the criteria for selecting the most favorable variant are defined, and the integrated model for selecting the most favorable variant should provide a positive balance.

This paper is structured as follows. Section 2 shows some brief backgrounds, while Section 3 shows the material and methods, the basic characteristics of railway transport in the Republic of Srpska (RS), its organization, and its current and future role. In addition, in this section, the proposed methodology is explained in detail. Section 4 shows the obtained results, applying a new developed fuzzy model, while Section 5 shows the extent of the validation tests. Section 6 presents the discussion and conclusions.

### **2. Brief Background**

In the paper about public suburban transport in Germany, Beck [4] analyzes the state of the so-called commercial and non-commercial transport. In doing so, he notes that, after a decade of stagnation due to non-commercial transport, in the performance of the PSO, there is a positive change and the intensification of competition. The methodology for assessment of the future transport needs in PPT by Rojo et al. [5] is upgraded by the inclusion of the subjective value of time and readiness users pay for the improvement of services in order to determine the optimal concept of PSO. The system is optimized in two ways: With and without considering the economic business of the company in the function of the goal. Veskovi´c et al. [6] used fuzzy logic for the assessment of the liberalization of rail passenger traffic on the example of Serbia, and one of the criteria in the model for assessment is PSO. Nash et al. [7] used quantitative and qualitative methods to investigate the impact on the cost of the vertical separation of railways in cases of a radical approach to restructuring. They are suspicious that reforming the railways through vertical and horizontal separation leads to cost savings. They state that precisely determining the methods and control of the distribution "of state money," subventions (PSO, maintenance and infrastructure development) have primarily led to cost reductions. In order to achieve the aims defined by the overall transport policy according to Ibarra-Rojas and Rios-Solis [8], cities and municipalities choose to subsidize PPT. These aims are different and range from providing transport options to all social categories to increase mobility for all residents. As a special advantage of these systems, Tirachini and Hensher [9] and Kim and Schonfeld [10] point out that the implementation of such a transport policy reduces the need for the use of personal vehicles. This, in turn, offers the opportunity to better manage urban space and transform the environment for the sustainable development of urban communities. In his paper, Van Reeven [11] developed a model aiming to demonstrate that the costs on the principle of consumer spending time do not provide justification for public transport subventions. PPT subventions are common in developing countries and are often justified by the availability of traffic accessibility, but not efficiency. In view of this justification, it is of interest to know how to use and distribute transport subventions.

To understand the idea behind public transport subsidies, Vuchic [12] and Hanson and Giuliano [13] emphasize that cities and municipalities do not subsidize operators, but the actual public transport service offered to citizens. In the absence of a subsidy, carriers are forced to charge the full cost of transportation for passengers through the price of tickets, which would lead to a significant reduction in transport demand and thus a decrease in traffic supply. Such a transport strategy implies, on the one hand, reduced mobility and, on the other, increased citizen dissatisfaction.

### **3. Materials and Methods**

### *3.1. Proposed Methodology*

The multi-criteria decision-making (MCDM) methods are widely used for the facilitation of the decision-making process in various fields [14–16]. The original developed MCDM methodology shown in Figure 1 was applied for selection of the best solution for the business balance of the passenger rail operator.

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**Figure 1.** Proposed methodology. **Figure 1.** Proposed methodology.

As part of the first phase of the research, data were collected. After that, an adequate database on transport policy was created in order to obtain and to analyze their effects on the business operators. Based on the collected data and created base, the forming of the MCDM model represents the second phase of the proposed methodology. Five most important criteria, explained in detail in the further text, were considered, while seven different variants were identified. Based on such parameters, an initial fuzzy decision matrix was formed. The third part of the methodology represents the most important part of the research and consists of two steps that are causally linked both to each other and to the elements of the following phase. These steps represent the development of an original integrated fuzzy MCDM model. First, the significance of the criteria was determined using the F-PIPRECIA method [17] according to the assessment of three decision-makers. Evaluation of various variants for selecting the best solution for the business balance of the passenger rail operator was performed using the F-EDAS method [18]. The fourth phase of the methodology involves the validation and sensitivity analysis of the proposed model. It is implemented throughout a few steps, where the first step relates to variations in the significance of the criteria. All individual approaches are individually included in the calculation of the F-EDAS method and a comparative analysis is given with respect to the proposed model. Testing the influence of dynamic factors—of the reverse rank and calculation of the criteria weights using the Fuzzy Analytic Hierarchy Process (F-AHP) [19] and Full Consistency Method (FUCOM) [20] methods—is also a part of the validity test. The next step includes the comparison of the developed model with three other fuzzy MCDM methods: fuzzy Measurement Alternatives and Ranking according to the COmpromise Solution (F-As part of the first phase of the research, data were collected. After that, an adequate database on transport policy was created in order to obtain and to analyze their effects on the business operators. Based on the collected data and created base, the forming of the MCDM model represents the second phase of the proposed methodology. Five most important criteria, explained in detail in the further text, were considered, while seven different variants were identified. Based on such parameters, an initial fuzzy decision matrix was formed. The third part of the methodology represents the most important part of the research and consists of two steps that are causally linked both to each other and to the elements of the following phase. These steps represent the development of an original integrated fuzzy MCDM model. First, the significance of the criteria was determined using the F-PIPRECIA method [17] according to the assessment of three decision-makers. Evaluation of various variants for selecting the best solution for the business balance of the passenger rail operator was performed using the F-EDAS method [18]. The fourth phase of the methodology involves the validation and sensitivity analysis of the proposed model. It is implemented throughout a few steps, where the first step relates to variations in the significance of the criteria. All individual approaches are individually included in the calculation of the F-EDAS method and a comparative analysis is given with respect to the proposed model. Testing the influence of dynamic factors—of the reverse rank and calculation of the criteria weights using the Fuzzy Analytic Hierarchy Process (F-AHP) [19] and Full Consistency Method (FUCOM) [20] methods—is also a part of the validity test. The next step includes the comparison of the developed model with three other fuzzy MCDM methods: fuzzy Measurement Alternatives and Ranking according to the COmpromise Solution (F-MARCOS) [21], fuzzy Simple

Preference by Similarity to Ideal Solution (F-TOPSIS) [23].

MARCOS) [21], fuzzy Simple Additive Weighing (F-SAW) [22], and fuzzy Technique for Order of

Additive Weighing (F-SAW) [22], and fuzzy Technique for Order of Preference by Similarity to Ideal Solution (F-TOPSIS) [23].

Finally, the Spearman's correlation coefficient (SCC) was calculated to determine the correlation of all obtained ranks across previously formed scenarios. As the F-PIPRECIA [17,24–26], F-EDAS [18,27–29], FUCOM [30,31], F-MARCOS [21], F-SAW [22,32], and F-AHP [23,33,34] methods have been exploited in the literature, their detailed algorithms are not presented.

### *3.2. The Position of Public Transport Services (PTS) for Passengers by Rail in the Transportation System of the Republic of Srspka*

The Railways of the Republic of Srpska (RRS) have been established as a public transport company, and it is important to emphasize that by "under the railway traffic of interest for the Republic of Srpska," we mean "railway public passenger transport." Irrespective of commercial interest, RRS must have at their disposal adequate capacity (material and human) and organizational conditions for the provision of public transport services (PTS) for passengers. Therefore, the authorities of the Republic of Srpska exert significant impact on the results of operations and the balance sheet of the company. RRS, and the segment of the company that deals with passenger transport (passenger transport operations) in particular, must establish an original system of determining results (revenues, expenses, profit-loss) on the grounds of the public transport of passengers. The opening of the railways to competition in the market of transport services brought about a separation of management and accounts (balance sheet) of infrastructure and transport. Consistent realization of this process means that "RRS shall—through a special type of bookkeeping—present to its founder the state and the railway infrastructure costs compared to the costs of operators." Separate reporting of costs is aimed at expressing the impact of business segments upon the operating results, which are determined by the balance sheet. Therefore, it is necessary to separately determine the balance of infrastructure and the balance of transport (assets, debts, obligations, liabilities, equity, revenues, expenses, results), as well as the consolidated balance of the corporation. In its efforts to provide for the traffic of interest for the Republic of Srpska, the government participates through partial financing. This means that RRS provide funding for a part of the public transport system that is of interest for the Republic of Srpska. According to Gangwar and Raghuram [35], one of the options is structuring public private partnerships. The volume of passenger transport is in a constant downward trend, and the largest volume of transport was recorded in 1996, amounting to 1,648,000 of transported passengers, while in 2009, the RRS transported no more than 368,289 passengers. The negative trend has continued in the years to come, so in the last two years, the annual number was at the level of about 150,000 passengers. Financial results regarding passenger traffic have been made according to the planning documents: Annual report of RRS for 2014, and business plan for the period 2012 to 2014.

The revenue and expenditure plan in passenger traffic is projected at the level of the financial loss of over −19,000,000 KM for each considered year, which is why the plan of inflows and outflows of funds remains at the level of loss of −26,869,280 KM in 2012 to −38,616,384 KM in 2014. The increase in expenditure in 2012 was by 67% higher compared to 2011, amounting to 10,371,589 KM, and the revenues were lower by about 30%, i.e., by 2,559,281 KM. The increase in expenditure in the said amount was the result of an increase in the following: Cost of fees for access and use of railway infrastructure in the amount of KM + 5,458,404 (+52%); cost of wages, salaries, and other employee benefits in the amount of KM +2,996,647 (+29%), cost of materials for the work in the amount of KM + 1,020,676 (+10%), and costs of production services in the amount of + 966,014 (9%) (Figure 2).

The problem with the above, i.e., the problem with the operations in the reported period with a huge financial loss, lies in reduced business competitiveness of RRS as the operator at a future liberalized market of transport services, and, therefore, its uncertain business future. In this sense, the "experts" of the Railways of the Republic of Srpska have reduced passenger traffic for the 2008/2009 timetable by eliminating 22 passenger trains that were, by internal calculations, within the area of unprofitable business.

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**Figure 2.** Increase in expenditures of Railways of the Republic of Srpska (RRS) for 2011−2012 years. **Figure 2.** Increase in expenditures of Railways of the Republic of Srpska (RRS) for 2011−2012 years. **Figure 2.** Increase in expenditures of Railways of the Republic of Srpska (RRS) for 2011−2012 years.

Reactions of passengers to this move were completely understandable, so the reduction in the number of trains by 25% (from 76 to 54 trains a day) led to a reduction in the number of passengers for close to 50%, or to be more exact, by 45% in that same (first) year when they implemented the reduction in the number of trains (from 635,000 annually to 368,000). This trend of reducing the number of passengers due to an unsatisfactory timetable and reduced frequency of trains was carried out on almost all routes. The authorities of the Republic of Srpska noted that by this move, they achieved a reduction in operating costs of about 2,000,000 KM but failed to note the loss and reduction in income due to a drastic reduction in the number of passengers. Reactions of passengers to this move were completely understandable, so the reduction in the number of trains by 25% (from 76 to 54 trains a day) led to a reduction in the number of passengers for close to 50%, or to be more exact, by 45% in that same (first) year when they implemented the reduction in the number of trains (from 635,000 annually to 368,000). This trend of reducing the number of passengers due to an unsatisfactory timetable and reduced frequency of trains was carried out on almost all routes. The authorities of the Republic of Srpska noted that by this move, they achieved a reduction in operating costs of about 2,000,000 KM but failed to note the loss and reduction in income due to a drastic reduction in the number of passengers. Reactions of passengers to this move were completely understandable, so the reduction in the number of trains by 25% (from 76 to 54 trains a day) led to a reduction in the number of passengers for close to 50%, or to be more exact, by 45% in that same (first) year when they implemented the reduction in the number of trains (from 635,000 annually to 368,000). This trend of reducing the number of passengers due to an unsatisfactory timetable and reduced frequency of trains was carried out on almost all routes. The authorities of the Republic of Srpska noted that by this move, they achieved a reduction in operating costs of about 2,000,000 KM but failed to note the loss and reduction in income due to a drastic reduction in the number of passengers.

The downward trend in train numbers has led to an increase in the company's financial losses. It is true that the cost of doing business has been somewhat reduced (Figure 2), but revenue has fallen significantly, leading to greater financial losses (Figure 3). The financial loss of the company in 2011 amounted to 6,969,205 KM. In 2012, expenditures of KM 10,441,741 were still high, although they were somewhat reduced, but revenues were significantly lower and decreased by over KM 2.5 million so that the company's negative balance in fiscal 2012 increased to 19,970,227 million KM. The downward trend in train numbers has led to an increase in the company's financial losses. It is true that the cost of doing business has been somewhat reduced (Figure 2), but revenue has fallen significantly, leading to greater financial losses (Figure 3). The financial loss of the company in 2011 amounted to 6,969,205 KM. In 2012, expenditures of KM 10,441,741 were still high, although they were somewhat reduced, but revenues were significantly lower and decreased by over KM 2.5 million so that the company's negative balance in fiscal 2012 increased to 19,970,227 million KM. The downward trend in train numbers has led to an increase in the company's financial losses. It is true that the cost of doing business has been somewhat reduced (Figure 2), but revenue has fallen significantly, leading to greater financial losses (Figure 3). The financial loss of the company in 2011 amounted to 6,969,205 KM. In 2012, expenditures of KM 10,441,741 were still high, although they were somewhat reduced, but revenues were significantly lower and decreased by over KM 2.5 million so that the company's negative balance in fiscal 2012 increased to 19,970,227 million KM.

**Figure 3.** Financial loss of RRS 2011−2012. **Figure 3. Figure 3.**  Financial loss of RRS 2011 Financial loss of RRS 2011−−2012. 2012.

### *3.3. Problem Identification and Solving Methodology* until today, the number of passengers has been in constant decline, the number of passenger trains has decreased in domestic traffic by 28 trains, in inter-entity transport by 18 trains, and by 8 trains in

The analysis of the passenger traffic subsystem showed the following characteristics: From 1996 until today, the number of passengers has been in constant decline, the number of passenger trains has decreased in domestic traffic by 28 trains, in inter-entity transport by 18 trains, and by 8 trains in international transport. The railway fee for the infrastructure in domestic services amounts to 4,176,295 KM, in inter-entity transport amounts to 601,836 KM, and in international transport amounts to 1,603,022 KM. The other elements of the RRS business operations are shown in [36]. The problem-solving methodology is based on: *Symmetry* **2020**, *12*, x FOR PEER REVIEW 7 of 20 *3.3. Problem Identification and Solving Methodology*  The analysis of the passenger traffic subsystem showed the following characteristics: From 1996 until today, the number of passengers has been in constant decline, the number of passenger trains has decreased in domestic traffic by 28 trains, in inter-entity transport by 18 trains, and by 8 trains in international transport. The railway fee for the infrastructure in domestic services amounts to 4,176,295 KM, in inter-entity transport amounts to 601,836 KM, and in international transport international transport. The railway fee for the infrastructure in domestic services amounts to 4,176,295 KM, in inter-entity transport amounts to 601,836 KM, and in international transport amounts to 1,603,022 KM. The other elements of the RRS business operations are shown in [36]. The problem-solving methodology is based on: 1. increase in revenue from direct ticket sales and increase in revenue from agreements on PSO, 2. reduction in expensing, i.e., operating costs. The expected result of the mentioned activities according to the given methodology should be

*Symmetry* **2020**, *12*, x FOR PEER REVIEW 7 of 20

The analysis of the passenger traffic subsystem showed the following characteristics: From 1996


The expected result of the mentioned activities according to the given methodology should be sustainable business operations. Figure 4 shows the cost realization plan for the next fiscal year, as well as the perception of cost coverage by government revenues and government subsidies (PSOs), and a model of the long-term business stabilization goal (Figure 5). 2. reduction in expensing, i.e., operating costs. The expected result of the mentioned activities according to the given methodology should be sustainable business operations. Figure 4 shows the cost realization plan for the next fiscal year, as well as the perception of cost coverage by government revenues and government subsidies (PSOs), and a model of the long-term business stabilization goal (Figure 5).

**Figure 4.** Business plan for the period of 2013 year (costs and revenue). **Figure 4.** Business plan for the period of 2013 year (costs and revenue). liberalized transport market. In [6], details about the model for liberalization in Serbia can be found.

**Figure 5.** Problem-solving methodology.

The aim of the problem solving is to bring RRS as the operator in passenger traffic into the domain of positive operations, thus providing the necessary conditions for successful operation at a liberalized transport market. In [6], details about the model for liberalization in Serbia can be found.

In this paper, a new integrated F-PIPRECIA-F-EDAS model is created for solving problems. Multi-criteria methods for decision-making are used to resolve a large number of problems in all spheres of business, and they represent an area that is developing rapidly, primarily due to a large number of methods that have been developed, particularly within the last decade. The combination of these methods with fuzzy logic gives excellent results because classical methods cannot, with such precision, perform the required quantification, and this is where fuzzy logic shows all its advantages [37,38]. *Symmetry* **2020**, *12*, x FOR PEER REVIEW 8 of 20 In this paper, a new integrated F-PIPRECIA-F-EDAS model is created for solving problems. Multi-criteria methods for decision-making are used to resolve a large number of problems in all spheres of business, and they represent an area that is developing rapidly, primarily due to a large

number of methods that have been developed, particularly within the last decade. The combination

### *3.4. Forming a MCDM Model* of these methods with fuzzy logic gives excellent results because classical methods cannot, with such

### 3.4.1. Possible Solutions precision, perform the required quantification, and this is where fuzzy logic shows all its advantages [37,38].

In order to resolve the problem, seven realistically possible variants (V) have been identified. All variants are described in [36]: *3.4. Forming a MCDM Model* 

In order to resolve the problem, seven realistically possible variants (V) have been identified. All
