Engine Selection Based on Utility Theory

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College of Civil Aviation, Nanjing University of Aeronautics and Astronautics,Nanjing 210016, P. R. China



Engine Selection Based on Utility Theory

DingSongbin*,WangXiaoli,WangHongyu

College of Civil Aviation, Nanjing University of Aeronautics and Astronautics,Nanjing 210016, P. R. China

(Received 18 March 2016; revised 20 July 2016; accepted 5 August 2016)

Since an engine is seen as the ″heart″ of an airplane, the objective and scientific evaluation of it is significant to ensure normal operation of airlines. Aiming at the limitations of current studies on selecting engines, a quantitative comprehensive evaluation system of engine options was established and an optimization model based on the utility theory and analytic hierarchy process (AHP) was proposed. Considering the judgement of different customers on the balance between income and risk, the utility of each evaluation index was determined by utilizing the piecewise utility function. The AHP was used to analyze individual demands of customers. Finally, the optimal scheme was selected through calculating the weighted utility value. According to the actual needs of a domestic airline, the utility of three engine options was calculated. The results showed that the value of risk factor can be set to determine the selection scheme based on the degree of preferences (conservative type, neutral type or adventurous type).

air transportation; engine selection; utility theory; civil aircraft; personalized demands

0 Introduction

When airlines are planning to purchase aircraft to meet the operational requirements of expanding routes, they have to determine the type of aircraft. Engine selection directly affects performance, economy, maintainability, adaptability of routes and environmental protection level indicators of a whole aircraft. Therefore, with the increasing demand of consumers, evaluations of comprehensive performances of different engines are becoming crucial, as the national regulations are getting stringent.

In recent years, considerable scholars and airlines conducted a series of studies on engine selection, which mainly focused on the reliability, maintainability, operation cost, economy and other aspects. Each of them only analyzed a single engine index, such as engine economical index analysis based on cash operating cost (COC) and engine reliability analysis[1], the economic analysis of engine based on developing production cost[2], the engine evaluation and selection method based on performance[3-4], the reliability and life cycle evaluation analysis of engines[5-6]and so on. Besides, the results of some studies were based on qualitative evaluation, instead of quantitative methods. The final evaluation results are thus not intuitionistic. Therefore, the utility theory together with the analytic hierarchy process (AHP) method is proposed in this paper to establish the engine selection effectiveness evaluation system and to conduct the quantitative evaluation.

Utility, using probability to reflect the uncertainty of the research problem, refers to the satisfaction degree of customer for particular services or resources and their function under the action of market orientation[7]. At present, utility theory has been widely used risk evaluation[8-9], consumption theory[10], resource scheduling[11], investment portfolio[12]and target selection[13], etc. When selecting engines, using the quantitative evaluation method based on utility function can help to obtain the orders of the alternative engines. At the same time, the results may reflect the preferences and goals of airlines on engine selection, and the differences among the demands of users. Therefore, a method of selecting a suitable engine model is provided, according to the requirements and application characteristics of a specific user. In addition, the utility function is combined with AHP to investigate the reliability, sustainable development, economical efficiency, competitiveness, the level of environmental protection and some other factors of engines. The impact of the development orientation of airlines is considered, which may help to provide quantitative evaluation results more scientifically and intuitively.

1 Engine Evaluation Index System

The scientific and quantitative selection of engines is crucial to normal operation of aircraft. The seletion should meet the requirements of reliability, economical efficiency, competitiveness, environmental protection level, sustainablty, ect. Accordingly, the first-level indicators and the secondary evaluation index system is constructed, as shown in Fig.1.

Fig.1 The evaluation index system of civil aircraft engines

1.1 Reliability index

Reliability is one of the important indexes to measure the quality of aviation engines. It is also an important parameter to represent aircraft comprehensive efficiency. Engine reliability evaluation focuses on engine operating reliability and will indirectly affect the capacity and efficiency of the airlines. If it cannot meet the minimum requirements, it will become a negative factor. At present, according to Air Transport Association(ATA)[14], the most common maintainability and reliability parameters of civil aviation engines are: In-flight shut-down rate (IFSDR), indicating the number of engine parking in the air per one million hours of flight; Punctuality rate (PR), indicating the number of punctual opened flights per 100 flights, which equal to one minus the number of flight delay or cancellation due to engine reasons, repair rate (RR), indicating the number of engines sent back to factory for repair in every 1 000 h of flight, and so on. In addition, the service life of the aviation engine is one of the important characteristics of its competitiveness and durability, which inturn greatly affects the reliability and safety of the engine.

1.2 Economic index

At present, there are only a few international civil aviation engine manufacturers in the world. Through the long-term operation of the civil aviation aircraft, the reliability of their engines has been fully testified. In contrast, the economic performance of engine accounts for a large proportion of the entire aircraft cost, which is an important impact on the operating cost control of airlines. The economic assessment of engine includes acquisition cost (10 000 RMB), maintenance cost used in the process (10 000 RMB), engine residual value (10 000 RMB) and fuel consumption per flight hour.

1.3 Competitive index

There is a competitive relationship between different engine suppliers in the engine selection of a certain aircraft. Various factors, including market shares, applications to other similar models, sale strategies of suppliers, and differentiations of cost, cannot be ignored in the assessment of engine selection, because they are to bring revenue or cost to competition of suppliers.

1.4 Environmental protection level index

Aircraft are playing an increasingly important role in people′s daily life. However, the adverse effects caused by the aircraft to the environment have become serious. The impact of tail gas on the environment is considerable. In addition, as the environmental standards are getting stringent， the aircraft take-off and landing engine noise also can not be negleted. DB can be used as the index parameters to measure noise pollution (the distance is 1—1.5 m from the sound source).

1.5 Sustainable development index

The average life cycle of an aircraft is almost 25 to 30 years. Thus, when purchasing aircraft, airlines need not only to consider short-term goal, but also to predict future demand. For example, the choice of the engine should route adaptive capacity to adapt to the development of new routes in the future, and forcast the seriation development to ensure the chosen engine to be stable and healthy, etc. Obviously, in case being eliminated in the future competition, the sustainable development of engine is also essential for engine selection.

2 Engine Selection Model Based On Utility Theory

Engine selection should be based on the specific needs of users. Therefore, the utility function is introduced to describe the heterogeneity of the needs of different users, and reflect preferences and goals of different airlines when purchasing an aircraft.

2.1 Utility theory

The utility theory provides the conditions for the consistency of the value of the decision makers and the utility function, which is the rational axiom[15]. As the cardinal utility is unique under the positive linear transformation[16], the total effect can be expressed as

(1)

whereμmeans the overall evaluation of the utility;ω1,ω2,…,ωnare the corresponding weights of evaluation indexes;U(f1),U(f2),…,U(fn) the evaluation indexes of the corresponding utility.

AHPisusedtodeterminetheweightsofeachutilityevaluationindex[17].TheindexhierarchyisshowninFig.1.

2.2 Establishment of utility function

(1) Construction of utility matrix

(2)

The indexes are distinguished as deterministic indexes and uncertainty indexes. The deterministic index are represented as practical values, and the uncertainty indexes are represented as a five grade classification method in fuzzy mathematics, namely excellent, good, medium, poor and worse, which corresponds to 0.9, 0.7, 0.5, 0.3 and 0.1 in the utility function respectively.

(2) Pretreatment of evaluation indexes

Before using the utility function, the evaluation indexes need not only to be quantified, but also to be standardized (namely non-dimensional treatment). Quantitative indexes can be generally divided into four types: Cost (the smaller, the better), benefit (the bigger, the better), fixed (up to a fixed value for optimal) and interval (stable within a certain interval for optimal). In this paper, the engine evaluation index system can be divided into two types: Cost type and benefit type. Using the range transforming method for standardization, the expression is shown as

① Cost type

(3)

② Benefit type

(4)

(3) Determination of the utility value of all level evaluation indexes

Utility represents the relationship between the studied objects and the preferred values of users. So the first step is to establish the utility function to determine the utility value. As mentioned above, the utility function contains the value judgment of users. There are some differences among users with different needs and desires of product. Some of them are risk-preferred， while others are risk-averse. Therefore, the piecewise utility function model is chosen to calculate the utility value the different indexe

① Cost type

(5)

② Benefit type

(6)

Fig.2 Cost-type utility function curves

Fig.3 Efficiency-type utility function curves

3 Application

3.1 Engine options

A domestic airline intends to introduce the A330-300 airplane. Airbus Company gives the selection manual which provides three engine options. The selection model based on utility theory is established as mentioned above to determine which option is most suitable for this airline. These three engines are: Pratt & Whitney PW4000 series, General Electric CF6-80 series and Rolls Royce Trent of 700 series. According to the investigation, the specific parameters of the three engines are obtained and shown in Table 1.

Table 1 The specific parameters of the three kinds of engines for A330-300

3.2 Evaluation index system

As the evaluation index system given in Fig.1 is too complicated to be used in practice, the indexes are not always considered together. Therefore, in order to simplify the model, according to Table 1, it can be found that these three engines are almost the same in routes adaptability, seriation, development level of maintenance industry and benefits from competition; the purchase cost and use cost of engine are proportionally related with each other; per flight hour exhaust emissions and per flight hour fuel consumption are positively correlated. In this case, the model will not consider the following six indexes:f21,f33,f42,f51,f52, andf53.

3.3 Weight vector of index system

According to the demand of a certain airline, the subjective and objective methods are combined to determine the weight of indexes. The comparison tables exhibiting the relative importance of the selected indexes are shown in Tables 2—6.

Table 2 Primary index importance comparison given by a certain airline

Indexf1f2f3f4f5f11131/31/5f251821f31/31/811/51/8f431/2511/2f551821

Table 3 The secondary index importance comparison under reliability index

Indexf11f12f13f14f1111/312f123133f1311/313f141/21/31/31

Table 4 The secondary index importance comparison under economic index

Indexf21f22f23f24f2111/531/2f225173f231/31/711/3f2421/331

Table 5 The secondary index importance comparison under competitive index

Indexf31f32f33f34f3111/31/21f323123f3321/213f3411/31/31

Table 6 The secondary index importance comparison under environmental protection level index

Indexf41f42f4111f4211

According to the method of AHP, the weight vector of the first level indexes is given as:ω1=[0.102 3, 0.339 1, 0.035 7, 0.183 8, 0.339 1]. The weight vector under reliability index of the secondary level indexes is given as:ω2=[0.193 5, 0.488 3, 0.214 2, 0.104 0]. The weight vector under economic index of the secondary level indexes is given as:ω3=[0.134 9, 0.583 6, 0.064 7, 0.216 8]. The weight vector under competition index of the secondary level indexes is given as:ω4=[0.139 1, 0.448 5, 0.286 6, 0.125 7]. The weight vector under environmental protection level index of the secondary level indexes is given as:ω5=[0.5, 0.5].

Through the weighted multiplication of the weight of the first level indexes and secondary indexes above, the weight of the evaluation factors of civil aviation engines are calculated, so the index weight vector of A330-300 airplane′s engine evaluation of this airline isω=[0.019 8, 0.050 0, 0.021 9, 0.010 6, 0.197 9, 0.021 9, 0.073 5, 0.005 0,0.016 0, 0.004 5, 0.091 9].

3.4 Modeling based on the utility theory

Considering the effectiveness of the three engines of A330-300 with the 11 indexesf11,f12,f13,f14,f22,f23,f24,f31,f32,f34,f41, the utility matrixAof the original data according to the Table 1 is constructed, and then the utility value matrix of the original data is obtained. Among them,f12,f14,f23,f31,f32are benefit indexes, andf11,f13,f22,f24,f34,f41are cost indexes.

(1) Evaluation index pretreatment

According to Eqs.(3),(4), the parameters of the three engines of A330-300 are standardized. The results are shown in Table 7.

(2) Determination of the utility value of evaluation indicators at all levels

As the provided solutions of engines by aircraft manufactures are few in actual engine selections, this paper gives the acceptable interval of the index parameters (i.e., the user can accept all the parameters of the bottom line and the engine itself can achieve the optimal situation) to facilitate the application of the utility function, as shown in Table 8.

Substituting the numerical indexes in the matrix andamin,amaxin each known index into Eqs.(5), (6), the utility value of each index is obtained, and the utility matrixUcan be constituted:U=[U(f11),U(f12),U(f13),U(f14),U(f22),U(f23),U(f24),U(f31),U(f32),U(f34),U(f41)]T.

3.5 Scheme weighted utility value

When the values ofkare different, the preference orders of the three schemes are also different. The results in differentkvalues are shown in Table 9.

3.6 Analysis of results

(1) Analysis of evaluation index weight

According to the airlines evaluation index weight vector of A330-300, we can see that this company pays special attention on the maintenance cost of the engines, followed by the noise pollution problems of the engines, the fuel con sumption of engine and the airline operations flight punctuality rate.

Table 7 Standardized parameters

Table 8 The acceptable range of each index parameters

Table 9 The optimization results in different k values

(2) Analysis of scheme utility value

As shown in Table 9, the differences among the utility values of the three engines are not significant, but there are still advantages and disadvantages. Whenk<1，k=1 (conservative and neutral type), GE CF6-80E1 has the maximum utility value. Whenk>1 (adventure type), RR Trent 700 has the maximum utility value.

In the airline′s four most important indicators, the maintenance cost minimum utility value of RR Trent 700 is the highest, but the utility value of punctuality rate and fuel consumption per flight hour are both the lowest. So when the airline is adventuring and searching for lower input cost, RR Trent 700 is the best choice.

GE CF6-80E1 has the worst maintenance cost index utility but the best utility value of punctuality rate and noise index. In addition, the in-flight shutdown rate and repair rate of GE CF6-80E1 are also the lowest, so when airlines are in conservative and neutral type, considering company operation and social benefit, GE CF6-80E1 is the best choice.

(3) Analysis ofkvalue selection

At present, the development of manufacturer or the use of airline aspects of the Rolls Royce RR Trent 700, GE′s CF6-80E1 and Pratt & Whitney PW4000-100 both have been in a mature and stable stage. The airlines tend to care more about its operational efficiency. In addition, China has clearly defined the civil aviation industry as an important strategic industry in the national economic and social development, and the competition among airlines is becoming more and more fierce. So the good corporation image and social benefits are becoming more and more important. To sum up, thekvalue should be in conservative and neutral type (k<1 ork=1). As shown in Table 9, GE CF6-80E1 is the best scheme.

4 Conclusions

Engine selection is essential to the airline in purchasing aircraft. It can directly affect the airline's future operation and social benefits. However, at present, the research on the engine are qualitative or one-sided. The airlines still lack a quantitative comprehensive and feasible method in the actual purchasing process.

In this paper, we use the utility theory to construct the evaluation model, and use the real data to improve the validity of the model selection results. On the basis of the previous results, a relatively comprehensive civil aviation engine evaluation index system is established, considering the engine reliability, economic efficiency, competitiveness, environmental protection level and the capacity for sustainable development.

In addition, we also combined the qualitative and quantitative methods. The subjective attitudes of different subjects are displayed in the final selection, that is the selection ofk-the peo-ple′s attitudes are quantified and integrated into the structure of the utility function. Combined with the AHP method for quantitative analysis of the weight of each index, the needs for different airlines to select engines is personalized when purchasing aircraft is realized.

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Prof. Ding Songbin is currently a professor in College of Civil Aviation at Nanjing University of Aeronautics and Astronautics. His research interests include aircraft performances and aeroplane safety system.

Ms. Wang Xiaoli is currently an M.E. candidate of Civil Aviation at Nanjing University of Aeronautics and Astronautics. Her research interest include safety of civil aviation.

Mr. Wang Hongyu is currently an M.E. candidate of College of Civil Aviation at Nanjing University of Aeronautics and Astronautics. His research interests include transportation planning and management of civil aviation.

(Executive Editor： Zhang Bei )

U8 Document code:A Article ID:1005-1120(2016)06-0639-08

*Corresponding author, E-mail address: dingzhili@nuaa.edu.cn. How to cite this article: Ding Songbin, Wang Xiaoli, Wang Hongyu. Engine selection based on utility theory[J]. Trans. Nanjing Univ. Aero. Astro., 2016,33(6):639-646. http://dx.doi.org/10.16356/j.1005-1120.2016.06.639