Applying Multi-Criteria Analysis of Electrically Powered Vehicles Implementation in Urban Freight Transport

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23rd International Conference on Knowledge-Based and Intelligent Information & Engineering 23rd International Conference on Knowledge-Based Systems and Intelligent Information & Engineering Systems

Applying Multi-Criteria Analysis of Electrically Powered Vehicles Applying Multi-Criteria Analysis of Electrically Powered Vehicles Implementation in Urban Freight Transport Implementation in Urban Freight Transport Kinga Kijewskaaa, Stanislaw Iwanaa, Krzysztof Małeckibb* Kinga Kijewska , Stanislaw Iwan , Krzysztof Małecki *

Maritime University of Szczecin, Faculty of Economics and Engineering of Transport, Szczecin, Poland b WestUniversity Pomeranian University of Technology, Faculty Computer Science, Szczecin, Poland Maritime of Szczecin, Faculty of Economics andofEngineering of Transport, Szczecin, Poland b West Pomeranian University of Technology, Faculty of Computer Science, Szczecin, Poland

a a

Abstract Abstract One of the most important problems in the cities is atmospheric emission of anthropogenic origin. This problem is the key challenge One of themostly most for important city municipalities problems inbut thealso cities for is business atmospheric stakeholders, emission which of anthropogenic are involved inorigin. freightThis transport problem at urban is theareas. key challenge for city municipalities also for stakeholders, whichisare involved in freight transport at urban areas. One of themostly most important and efficient but solutions to business reduce this negative impact implementation of electric vehicles. In recent One ofmany the most important and efficient in solutions reduce thisdone. negative implementation of electric vehicles. Inanalysis recent years activities and developments this areatohave been This impact paper isisfocused on utilization of multi-criteria years many vehicles activitiesselection and developments in this area usability have beenfor done. This paper is focused on utilization for electric in the context of their deliveries realization in cities. Moreover,ofitmulti-criteria also presentsanalysis general for electric vehicles in the context of motor their usability deliveries realization in vehicles. cities. Moreover, it also issues regarding the selection use of alternative fuels in vehicles,for with emphasis on electric It discusses thepresents extent togeneral which issues regarding of It alternative in motor vehicles, emphasisthe on usability electric vehicles. It discusses theurban extentdeliveries. to which electric vehicles the are use used. describesfuels the key parameters forwith determining of electric vehicles in electricon vehicles are used. Itassumptions, describes thea key parametersmodel for determining thetousability electric out vehicles in defined urban deliveries. Based the formulated multi-criteria is proposed enable of selecting, of the vehicles Based on solutions the formulated a multi-criteria is proposed to enable out isoftothe defined vehicles catalogue, that areassumptions, optimal in terms of potential model effectiveness. The general aimselecting, of the paper support the logistics catalogue, solutions are optimal in terms of potential effectiveness. general the paper to support city the logistics companies’ decision that makers in the improvement of the freight vehicles The fleets, takingaim intoofaccount theissustainable companies’ decision makers in the improvement of the freight vehicles fleets, taking into account the sustainable city logistics expectations. expectations. © 2019 The Author(s). Published by Elsevier B.V. © 2019 2019 The Authors. bybyElsevier B.V. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © The Author(s). Published Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review This is an open under access responsibility article under of the KESCC International. BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of KES International. Peer-review under responsibility of KES International.

Keywords: multi-criteria decision making; multi-criteria model; city logistics; urban freight transport; Electric Freight Vehicles (EFVs); sustainable transport; environmental friendly transport model; city logistics; urban freight transport; Electric Freight Vehicles (EFVs); Keywords: multi-criteria decision making; multi-criteria sustainable transport; environmental friendly transport

* Corresponding author. E-mail address: [email protected] * Corresponding author. E-mail address: [email protected] 1877-0509 © 2019 The Author(s). Published by Elsevier B.V. This is an open access underPublished the CC BY-NC-ND 1877-0509 © 2019 The article Author(s). by Elsevier license B.V. (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of KES International. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of KES International. 1877-0509 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of KES International. 10.1016/j.procs.2019.09.326

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1. Introduction A major problem of the present and future cities is an atmospheric emission of anthropogenic origin, where the urban transport is a major source of pollution emissions [1,2]. A particularly discrete ecological footprint in urban environment is made by urban freight transport [3,4]. The problem of urban logistics operations in the context of its impact on the environment has become the key challenge for all stakeholder groups involved in freight transport in urban areas [5–7]. Resulting from that, over the recent years there has been a growing interest in increasing the efficiency of transport telematics systems [8–12] and using alternative fuel vehicles in urban logistics, including those equipped with electric drive systems [13]. Alternative propulsion systems for motor vehicles include mainly: gas-powered drives, biofuels, hydrogen drives, hybrid drives and electric drives. Gas-powered drives (LPG I CNG), which compared to traditional fuels produce 18% less greenhouse gases and generate ca. 3 dB less noise. Their major drawbacks include greater fuel consumption and limited possibilities of filling up the tank [14]. Biofuels engines are modified in such a way so that instead of petrol or diesel they use ethanol being the result of biomass fermentation [1]. Hydrogen drives, where the fuel is hydrogen, are based on two major solutions [15]: hydrogen combustion taking place in a typical piston engine combustion chamber and using fuel cells that produce energy as a result of oxidising the fuel constantly supplied from outside. All introduced engines are interesting alternatives for traditional gasoline engines. However, nowadays they are not efficient enough. Comparing to the above mentioned systems, electric drives using battery powered electric engines only, theoretically seem to be the best of the existing drives. One of the vital arguments for electro-mobility development is not only less environmental impact, but also economic considerations. The electric power needed to charge traction batteries costs 6 times less than fuel combusted by IC engine vehicles, assuming similar distances covered by both types of vehicles. Besides, the insurance and servicing costs are also lower. Moreover, electric engine is also simpler and less susceptible to technical failures compared to IC engines. Due to that, despite the higher price of electric vehicles, the maintenance costs of large company fleets based on electric drives may be substantially lower compared to conventional cars. It’s been more than 100 years since an electric vehicle first exceeded the speed of 100 km/h [16]. Nevertheless, the fundamental difficulty still to be overcome is the problem of storing large amounts of energy in batteries with relatively small weight as well as the problem of how to charge them rapidly [17]. Due to that, the prerequisite for introducing e-mobility is a well-developed and well-managed EV charging infrastructure. The energy storage and time of charging are the most important barriers in utilization of EV on long distances. Nevertheless, this is not a problem for shorter travels with smaller speeds, which are realized at the area of the cities. Due to that, EV seem to be a very good alternative for local transport and city logistics [18,19]. One of the first research projects regarding the utilization of EV in city logistics was the ELCIDIS project – Electric Vehicle City Distribution. In recent years many other initiatives of this kind have been realized [20–23]. Nowadays, a number of city logistic solutions involve modifying freight vehicles including alternative fuels such as electric vehicles that can be implemented [24]. More and more effective measures have started to be implemented in cities in recent years [25–27]. However, the costs of purchasing electric vehicles are still perceived to be a substantial barrier to their wide-spread use [28]. Additionally, a substantial difficulty lies in selecting vehicles with operation parameters that fulfil the needs of the logistic processes they are to serve. Therefore, the key challenge is optimisation of the transport fleet while taking into account a multi-criteria evaluation of benefits. This paper presents multi-criteria analysis of selected electric vehicles in the context of their application for the purposes of deliveries in cities. Multi-criteria decision making is one of the most important approaches in the analysis of green logistics systems [13,29]. In addition, generalised guidelines to facilitate effective selection of such solutions in urban logistics are provided. It describes the key parameters for determining the usability of electric vehicles in urban deliveries. Finally, based on the formulated assumptions, a multi-criteria model is proposed to enable selecting, out of the defined vehicles catalogue, solutions that are optimal in terms of potential effectiveness. The use of multi-criteria methods is the subject of many publications [30-33].

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2. The methodological background Promethee methods are used in determining a synthetic ranking of options. Depending on implementation, they operate on the basis of real or pseudo-criteria [34]. It may be said that methods of this type combine most of Electre methods in terms of determining preference coefficients (compliance or reliability). Moreover, they enrich their methodology at the stage of determining the ranking of objects [35]. In the Promethee II method a decision-maker may choose from six preference functions applying: simple criterion, quasi-criterion, criterion with preference level, criterion with linear preference, criterion with linear preference and indifference area, Gaussian criterion. In this article, the Promethee II method was applied. Apart from the above presented functionalities, it is also important that the Promethee II method enables a complete order of the resulting ranking of alternatives to be obtained, while in the case of the earlier version of this method the resulting ranking was rather partial [35]. Subsequently, upon determining the compliance coefficients for each pair of options, dominance flows are determined for each of the options [36]: • output dominance flow describing how much option a i outranks the other options bj (1): n

 + (a i ) =   (a i , b j )

(1)

j =1

• input dominance flow informing how much option a i is dominated by the other options bj (2): n

 − ( a i ) =   (b j , a i )

(2) One by one, a decision-maker may establish the complete ranking of options. In the Promethee II method, in order to establish a complete ranking of options, it is necessary to compute the net dominance flow according to formula (3): j =1

 (ai ) =  + (ai ) −  − (ai )

In this method, equivalence and preference relations are distinguished in a broad sense [34]:

(3)

• option a i outranks option b j(a i L bj), when ϕ(a i) > ϕ(bj) • option a i is equivalent to option b j(a i I bj), when ϕ(a i) = ϕ(bj). 3. The evaluation model and recommendations with regard to selecting electric freight vehicles The study considered 36 decision options in view of 9 criteria. The criteria pertained to the vehicle performance in its broad sense, motor, batteries, and price. The structure of criteria broken down into groups is presented in Fig. 1.

Fig. 1. The structure of criteria broken down into groups.

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Unfortunately, with regard to many of the considered options it was not possible to obtain all information on the criteria, therefore there were numerous data gaps and consequently the decision problem was considered under uncertainty. The structure of the decision problem (table of criteria efficiencies for options) is presented in Table 1. Table 1. Table of criteria efficiencies for options with data gaps. Criteria Engine

Performance Code

A1 A2 A3 A4 A5

Name

Berlingo Electric Boulder Delivery Truck Boulder DV-500 Ecomile Electric Delivery Van 1000

A6

EVI MD

A7

EVI Walk-In Van

A8 A9 A10 A11 A12 A13 A14 A15 A16

A17 A18 A19 A20 A21 A22

e-NV200+ e-Wolf Omega 0.7 Jolly 2000 Kangoo Maxi Z.E. MegaVan Vito ECell Sprinter E-CELL MinicabMiEV MinicabMiEV (10,5 kWh) MinicabMiEV (16kWh) Modec MT-EV WIV Navistar eStar e-NT400 Concept Vivaro econcept

Carrying capacity

Max velocity

Travel range

Engine power

Engine torque

Battery charging time 100%

[kg]

[km/h]

[km]

[kW]

[Nm]

[h]

695

110

170

49

200

2700

104

160

80

1400

120

160

935

80

120

28

830

40

118

14

3000

96

145

200

610

10

2000

100

145

200

610

705

120

170

80

e-Wolf

613

140

180

140

l'Moving

1820

80

110

40

Renault

650

130

170

44

226

Manufacturer

Citroën Boulder Electric Vehicle Boulder Electric Vehicle l'Moving Spijkstaal Electro B.V. Electric Vehicles Int. Electric Veh. Int./ Freightliner Custom Chassis Corp. Nissan

Battery Battery charging time 80%

Price Battery capacity

Price

[min]

[kWh]

[thous. USD]

7,5

30

22,5

8

30*

80

8

30*

8

30*

100 70

14,4

51,5

30*

99

120

10

30*

99

4

30

24

25

8

30*

24,2

50

6

30*

38,4

74

8

30*

22

22

120

400

Mega

600

60

150

6

30*

Mercedes

900

89

130

60

280

6

30*

36

14,1

Mercedes

1200

80

135

100

220

2

30*

35,2

Mitsubishi Motors Corp.

350

100

110

30

196

4,5

15

10,5

12,9

Mitsubishi Motors Corp.

350

100

100

30

196

4,5

15

10,5

15,5

Mitsubishi Motors Corp.

350

100

150

30

196

7

35

16

18,7

Modec Freightliner Custom Chassis Corp./ Morgan Olson Navistar Int. Corp./ Modec Nissan Motor Co.

2000

80

160

70

300

8

30*

2000

104

160

120

650

7

30*

55,5

2000

80

160

70

300

8

30*

80

1830

90

140

80

320

9

60

50

Opel

750

110

400

8

30*

32,3

150

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Criteria Engine

Performance Code

A23 A24 A25 A26 A27 A28 A29 A30 A31 A32 A33 A34 A35 A36

Name

Partner Panel Van Peugeot eBipper Peugeot eBoxer Peugeot eExpert Motorcars SUV Porter electricpower Ranger EV Maxity Electric Smile SEV Edison (Chassis Cab) SEV Newton Toyota EV Truck Transit Connect BEV ZeroTruck

Carrying capacity

Max velocity

Travel range

Engine power

Engine torque

Battery charging time 100%

[kg]

[km/h]

[km]

[kW]

[Nm]

[h]

Peugeot

635

110

170

49

200

Allied Electric

350

100

100

Allied Electric

800

100

Allied Electric

660

Phoenix Motorcars

Battery Battery charging time 80%

5

Price Battery capacity

Price

[min]

[kWh]

[thous. USD]

8

35

22,5

31,5

30

3

30*

20

60

155

60

10,5

30*

56

85,5

105

155

60

8,5

30*

43

75

340

150

160

110

6

10

35

45

Piaggio Porter

750

57

110

10,5

8

120

Ford

520

110

100

45

8

30*

30

1895

70

100

47

8

30*

42

365

45

110

9

2500

80

150

90

3200

80

160

134

1000

60

100

70

700

121

129

50

2800

90

160

100

Manufacturer

Renault Trucks/PVI l'Moving Smith Electric Vehicles Smith Electric Vehicles US Toyota Motor corp./ Hino Motors Ford/ Smith Electric Vehicles Electrorides

500

270

24,4

30*

21

7

180

81

650

7

30*

117,9

280

8

45

28

7

30*

21

12

30*

550

* Average charging time for CHAdeMO charging mode.

The data gaps in the structured decision problem have been filled in three ways: with mean, minimum and maximum values, based on known criteria values transferred from the other options. As a result, criteria values to fill the data gaps were obtained and presented in Table 2. Table 2. The values applied in filling the data gaps. Criterion

Engine power

Engine torque

Mean Min Max

70.6 9 200

357.7 196 650

Battery charging time 100% 7.3 2 12

Battery charging time 80% 57.9 10 180

Battery capacity

Price

39 10.5 99

56.4 12.9 150

4. Results After the data gaps had been filled, the preferences were modelled. At that stage, weights of individual criteria were defined along with their preference direction, preference functions and thresholds values. In this study, equal criteria weights were assumed so that none of them had a greater impact on the decision problem solution. For criteria such as “profit”, the preference direction was “maximum”, whereas in the case of “cost” – “minimum”. The applied preference function was V-shape, so even small differences between the criteria efficiencies of options

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affected the determination of outranking relation between them. Concurrently, application of the preference threshold made it possible to change the outranking value fluently. The threshold was established as the two-fold value of the standard deviation for the option efficiency in relation to a given criterion. The full preference model is presented in Table 3. Table 3. Preference model. Preference threshold Mean Min Max 1687.74 1687.74 1687.74 48.53 48.53 48.53 98.67 98.67 98.67 89.6 95.85 114.65 247.1 294.76 381.37

Criterion

Direction

Weight

Carrying capacity Max velocity Travel range Engine power Engine torque Battery charging time 100% Battery charging time 80% Battery capacity Price

Max Max Max Max Max

1 1 1 1 1

Preference function V-shape V-shape V-shape V-shape V-shape

Min

1

V-shape

3.92

Min

1

V-shape

Max Min

1 1

V-shape V-shape

4.61

4.47

59.04

74.34

129.36

42.47 60.93

49.56 80.82

68.48 108.61

The solution obtained for the situation where data gaps were filled with mean values is presented in Table 4. Appendixes 1 and 2, in turn, show the solutions obtained when the data gaps were filled with minimum and maximum values respectively. Table 4. The ranking and options efficiencies obtained when the data gaps were filled with mean values. Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Option A27 A19 A7 A6 A8 A33 A9 A2 A36 A22 A3 A18 A14 A12 A21 A11 A20 A23

Phi net 0.3056 0.3009 0.2996 0.2356 0.2184 0.171 0.1474 0.1391 0.1059 0.1003 0.0445 0.0406 0.0358 0.0067 0.0062 -0.0143 -0.0154 -0.0324

Phi + 0.4223 0.3914 0.439 0.451 0.3396 0.3647 0.3032 0.3108 0.3075 0.2548 0.2046 0.207 0.2395 0.2056 0.1981 0.2013 0.2394 0.1876

Phi 0.1167 0.0905 0.1395 0.2154 0.1212 0.1937 0.1558 0.1717 0.2015 0.1545 0.1601 0.1664 0.2036 0.1989 0.1918 0.2156 0.2548 0.22

Rank 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Option A15 A16 A35 A1 A13 A10 A26 A32 A17 A24 A25 A29 A30 A34 A31 A4 A28 A5

Phi net -0.0324 -0.0477 -0.0486 -0.0491 -0.0602 -0.0608 -0.0625 -0.0629 -0.0843 -0.0883 -0.0981 -0.1249 -0.1283 -0.1861 -0.1887 -0.1915 -0.2712 -0.3099

Phi + 0.2526 0.2472 0.155 0.1754 0.1456 0.1699 0.1464 0.2179 0.1768 0.175 0.1629 0.1154 0.1354 0.1066 0.1286 0.09 0.115 0.0915

Phi 0.285 0.2949 0.2036 0.2245 0.2058 0.2307 0.2089 0.2808 0.2611 0.2633 0.261 0.2403 0.2637 0.2926 0.3173 0.2815 0.3862 0.4014

To determine whether the filling of the data gaps yields correct results, 5 options with complete data were analysed separately. These options were: A15, A16, A17, A23, A27. The ranking of these options, obtained for the preference model shown in Table 3, is presented in Table 5. It should be noted that in this case the preference threshold values were changed, as due to changing the set of options other values of standard deviations were obtained. Table 5. Efficiencies and ranking of a subset of options: A15, A16, A17, A23, A27. Rank 1 2 3 4 5

Wariant A27 A23 A15 A16 A17

Phi net 0.4318 -0.0493 -0.0842 -0.102 -0.1963

Phi + 0.5915 0.2859 0.1764 0.1714 0.1233

Phi 0.1597 0.3352 0.2606 0.2734 0.3196

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Fig. 2. GAIA analysis, broken down into criteria.

The sequence of options in the presented ranking corresponds to the orders of options in the rankings, where data gaps were filled with mean, minimum and maximum values. Thus, it may be assumed that the obtained rankings are reliable, whereas in terms of methodology the most correct ranking is the one where data gaps have been replaced with mean values. A mean value provides more information, as computation of a mean value aggregates the values of multiple options, whereas minimum and maximum values are assumed on the basis of just one option. For that reason, the further study considered a ranking in which data gaps were replaced with mean values. Another step was the GAIA analysis. Due to the need to keep it clear, it included only 10 top options. Fig. 2 shows the GAIA analysis, broken down into the individual criteria. As a result of projecting the decision problem solution onto the GAIA plane, 29% of the information was lost, therefore it does not fully reflect all the interdependencies between the criteria or between the alternatives.

Fig. 3. GAIA analysis, broken down into criteria groups.

As a result of the GAIA analysis it may be asserted that the Travel Range criterion is in conflict with the Engine Power and Engine Torque criteria. This means that the greater the Travel Range, the smaller the Engine Power and Engine Torque. Moreover, Carrying Capacity is in conflict with Max. Velocity, Price, and also Battery Charging

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Time. The alternatives that these four criteria support the most are A8, A9 and A27. Carrying Capacity, in turn, supports options A36, A33 and A2. Engine Power, Engine Torque and Battery Capacity have a positive effect on the ranking position of options A7, A19 and partially A6. A compromise solution is located between the option pairs A19, A7 and A9, A27. An analogous analysis was carried out for criteria groups; it is presented in Fig. 3. In this case, as a result of projecting the solution onto the plane, only 10% of the information was lost. This analysis of indicates that the Battery criteria group is in conflict with the Engine group, and Price is in conflict with Performance. Moreover, the strongest effect on the obtained solution was exerted by the Engine and Price criteria groups, and it is the Performance and predominantly Battery criteria groups that diversify the decision options to the least extent. In the case of the Battery group, this may be due to the fact that it is the criteria group that contains the most of the averaged data. The Engine criteria group supports mainly options A7 and A19, whereas the Price group has a positive effect on the ranking position of options A9, A27 and A36. 5. Summary Utilization of EV in city logistics is more and more attractive proposal for both business stakeholders and municipalities. The lack of local pollutions is the most important added value for the cities from the quality of life point of view. For the business entities, the smaller costs of utilization of the vehicles fleet seem to be an advantage. However, the most important challenge is the choice of the most efficient vehicles, taking into account the specificity of the urban deliveries process. The model introduced in the paper could help to solve this problem. Data analysis has shown that many manufacturers of EFVs do not provide some data about their vehicles. This causes difficulties in comparing available models and selecting the most advantageous offer. The authors proposed a method of supplementing data and on this basis, selecting the best offer in terms of technical parameters. The choice of EV is the challenging issue for decisions makers. It should be based on the analysis of set of criterions related to few major parameters, like distance, battery capacity, charging time etc. Utilization of multicriteria analysis is very helpful in this case. The PROMETHEE method is one of the possibilities. The Authors introduced the example of utilization of this method on the basis of selected electric freight vehicles. It should be mentioned that is the early stage of the research. From practical perspective it is important to develop the tools, which will be easy to use and will not expect the knowledge related to the multi-criteria analysis. This kind of tools will be developed under EUFAL project. The major objective of this project is to establish the web-based platform for decision makers, which will help them to implement and develop EFV in city logistics. The choice of the appropriate vehicles will be one of the tools. Acknowledgements The project EUFAL (Electric urban freight and logistics) is co-funded by the ERA-NET Cofund Electric Mobility Europe (EMEurope) and national funding organizations. EMEurope is co-funded by the European Commission within the research and innovation framework programme Horizon 2020 (Project No. 723977). Appendix A. The ranking and options efficiencies obtained when the data gaps were replaced with minimum values 1 2 3 4 5 6

Rank

Option A19 A7 A33 A6 A27 A9

Phi net 0.3646 0.3615 0.2722 0.2606 0.2299 0.1716

Phi + 0.4252 0.4629 0.3833 0.4554 0.371 0.3291

Phi 0.0606 0.1014 0.111 0.1947 0.1411 0.1575

Rank 19 20 21 22 23 24

Option A30 A29 A23 A15 A26 A10

Phi net -0.0184 -0.072 -0.0723 -0.076 -0.0792 -0.0852

Phi + 0.1907 0.1364 0.1431 0.1504 0.1492 0.1655

Phi 0.2091 0.2084 0.2154 0.2263 0.2284 0.2508

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A36 A14 A2 A8 A18 A21 A13 A20 A22 A11 A35 A1

0.1425 0.1412 0.1185 0.0945 0.0477 0.0441 0.0422 0.0365 0.0231 0.0176 0.0027 -0.0096

0.3272 0.2781 0.2988 0.2524 0.2074 0.2509 0.1966 0.265 0.2218 0.1902 0.1692 0.1671

0.1847 0.1368 0.1803 0.1579 0.1596 0.2068 0.1543 0.2285 0.1986 0.1726 0.1665 0.1767

25 26 27 28 29 30 31 32 33 34 35 36

A16 A3 A25 A17 A24 A34 A12 A32 A31 A4 A5 A28

-0.0872 -0.1018 -0.105 -0.1051 -0.1127 -0.1466 -0.1491 -0.1649 -0.1839 -0.209 -0.2397 -0.3535

9 0.1488 0.1484 0.1636 0.1227 0.1559 0.1357 0.115 0.1769 0.1413 0.0724 0.1486 0.0574

0.236 0.2503 0.2686 0.2279 0.2686 0.2823 0.2641 0.3418 0.3252 0.2814 0.3883 0.4109

Appendix B. Appendix B. The ranking and options efficiencies obtained when the data gaps were replaced with maximum values 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Rank

Option A8 A3 A27 A22 A33 A12 A6 A32 A2 A7 A19 A9 A18 A36 A23 A28 A10 A26

Phi net 0.2744 0.2702 0.2385 0.2229 0.2006 0.1777 0.1744 0.1666 0.1582 0.118 0.1015 0.0768 0.0576 0.0186 0.0067 -0.021 -0.0243 -0.0274

Phi + 0.3971 0.3709 0.3937 0.378 0.3441 0.3415 0.3481 0.3073 0.2967 0.308 0.2679 0.2869 0.257 0.2663 0.2474 0.2356 0.203 0.1763

Phi 0.1227 0.1008 0.1552 0.155 0.1434 0.1639 0.1736 0.1407 0.1385 0.19 0.1664 0.2101 0.1995 0.2478 0.2408 0.2566 0.2273 0.2038

Rank 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Option A15 A24 A16 A17 A21 A11 A25 A20 A1 A35 A14 A4 A29 A31 A13 A5 A34 A30

Phi net -0.0329 -0.0447 -0.0458 -0.0466 -0.0523 -0.0624 -0.0643 -0.0826 -0.0914 -0.0994 -0.1152 -0.1348 -0.1823 -0.19 -0.2099 -0.2281 -0.2367 -0.2705

Phi + 0.2615 0.2151 0.2583 0.2268 0.2187 0.2 0.1711 0.1816 0.1962 0.1544 0.1914 0.1376 0.1141 0.1784 0.1071 0.1611 0.1405 0.0984

Phi 0.2944 0.2597 0.3041 0.2734 0.271 0.2624 0.2354 0.2641 0.2876 0.2538 0.3066 0.2724 0.2964 0.3684 0.317 0.3892 0.3771 0.369

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