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Scientific Journal of Maritime Research 30 (2016) 141-150 © Faculty of Maritime Studies , 2016

Multidisciplinary Multidisciplinarni SCIENTIFIC JOURNAL OF znanstveni časopis MARITIME RESEARCH POMORSTVO

1 1 Decision making background2 for the location of inland terminals Tomislav1 Rožić , Dario Ogrizović , Marinela Galić 2 University of , Faculty of Transport and Traffic Sciences, Vukelićeva 4, 10000 Zagreb, , e-mail: [email protected] University of Rijeka, Faculty of Maritime Studies Rijeka, Studentska ulica 2, 51000 Rijeka, Croatia

ABSTRACT ARTICLE INFO

Inland terminals are becoming important objects (knots) in today’s supply chain. This implies new Original scientific paper methods to determine the location of inland terminal. Appropriate inland terminal location (ITL) Received 20 September 2016 decision depends on analyzing demand, employee’s availability, investment capabilities and other KeyAccepted words: 25 October 2016 factors. In this paper we present gravity center method and median method as quantitative ones and Analytic Hierarchical Process (AHP), ELECTRE and PROMETHEE as complex decision methods to determine inland terminal location. Given methods are implemented on the example of inland Inland terminals terminal location determination in Republic of Croatia. AHP method Gravity center method Median method ELECTRE method PROMETHEE method

1 Introduction

which is referred to herein as the alternatives and five cri- teria which are evaluated. Inland terminals represent objects that enable port In classical gravitation method the optimal inland ter- capacities disburdening and the expansion of the port minal location (ITL) is determinedN as a point on the map gravitational areas. This makes them vital part in today’s where[11 the] total transport costs that are induced by trans- supply chain management. One of the most important porting goods to and from different customers are mini- Ri , Vi di i – trends in the inland terminal system are methods to de- mal . Because the costs depend on unit transport costs termine location of inland terminals by satisfying different demand volume and the shortest distance from requirements. th customer to the optimal location as the center of gravity: m Choosing the location of inland terminals has to be conducted with care, because it can cause irreversible con- ∙ (1) sequences in urban planning and can create bottlenecks that lead to increase of the price of logistics services [1]. In median method the ITL is obtained by – the – calcu- According to Sorensen et al. [2] the best approach to de- Xi Yi i N X Y lation of the cumulative weight. Cartesian coordinates termine the location of inland terminal is the application [ ] 0 0 of network models and the use of multi-criteria analysis. ( , ), = 1, ..., are used for customers, and ( , ) are coordinates for ITL 6 . In the minimization of objective In this paper we used the gravity center method Vi Ri wi and median method as quantitative ones and Analytic function, we use the Manhattan or taxi – cab metric pon- dered by weights � = . Hierarchical Process (AHP), ELECTRE and PROMETHEE as | | + | | complex decision methods to determine inland terminal location. The analysis contains five across Croatia: ∙ (2) , , , and Split, T. Rožić et al.

142 / Scientific Journal of Maritime Research 30 (2016) 141-150 = 0 and = 0 Complex decision by AHP method is to rank criteria [8] (7) and alternatives in purpose to obtain optimal solution. Qualitative criteria are compared in pairs . Preference TC After finding the derivative of the transport cost func- is used in the process of finding optimal choice, i in ji our tion , it is possible to express the unknown coordinates jcase the location of inland terminal.j It is usual to mark the explicitly: weak preferencei relation by symbol �. In our case � � = = represents that the location has weak preference over aij ∑ ∑ location . i j (8) We calculateA each coefficient which represent the – – ∑ X Y ∑ value preference of criterion ahead of criterion and con- X Y V R struct matrix shown in (3). These coefficientsa presenta i i 0 i 0 i ji ij Initial average coordinates , are the mean values ranking preference from the same over weak, strong, dem- … of , respectively, pondered by � according to the fol- onstrated and absolute preference. In that case, = 1/ . … lowing= formula: = … ∑ ∑ (9) ∑ ∑ ⋮ ⋮ ⋮ (3) The unknown – values– are found by iterative method w X Y Xi Criteria are obtained as the components of eigenvec- Ythroughi theN following steps: αmax A i tor and then can be ranked. In the procedure we also get 1. The initial– – ( , ) is the arithmetic mean of given ( , X Y di maximal eigenvalue of the matrix using the power ), = 1, ..., TC – – method. a b aSb aPb a 2. With ( , X), theY distance can be calculated by (6) In Elimination Et Choice Translating Reality (ELECTRE) – – b a b 3. Calculate the TC by (1) X Y method alternatives and are ranked by or if is 4. The new ( , ) is now obtained by (8) at least good as or if is much better[4 than] . Alternatives 5. Calculate the by (1) with new ( , ) are ranked according the criteria, by counting criteria that 6. Repeat steps 2.-5. till the costs become the same un- support one of given alternative pair . der some tolerance X Y Preference Ranking Organization METHod for i i S [ ] Problem described in (2) is solved using median meth- Enrichment Evaluation (PROMETHEE), for complex deci- [ ] Max f a f a od by findingX a mean coordinate within and separately, sion in a set1 of alternativesk , represent a problem 3 : i considering their weights 6 . After aligning the coordi- f a j ( ( ), ..., ( )) i (4) nates increasingly, we calculate the cumulative values for related sequence of weights. If – th cumulative value where criterion functions ( ) are defined discretely by Xj X amounts a half or a more than a half of the last cumulative sequences of arbitrary ordinal numbers assigned to each – j alternative.F S S Preference function value, then = . Formally, this method is written in fol- lowing inequality< conditionsand for – th coordinate: : × � �0,1� F a,b (5) a b F a,b a b ∑ ∑ ∑ Y ≥ ∑Y (10) is defined such thatF a,b( ) =P 0f meansa f weakb preferenceP d Pofx k k – over and ( ) = 1 means strong preference of over . Analogue solution method for = is written in fol- If we assumed thatf a ( f )b = ( ( ) – ( )) = ( ), then ( ) lowing inequality conditions for – th coordinate: is some non-decreasing function which takes value zero < and 2 2 for negative = ( ) – ( ). Problem could be defined vice versa, but the preference function must be defined first. In ≥ –(11)– our paper we defined criterion functions first. X Y 2 Solution methods Xj Yk Finally, optimal location is obtained as a pair ( , ) = λmax ( , ). w A R V i i In AHP[ method,] the maximal eigenvalue and its ei- Given values[ 11in] the classic gravitation problem (1) are genvector for the matrix from (3) satisfies following , and Cartesian coordinates for each customer in kil- A w λ w relation 10max: ometer’s units . If we use the shortest, Euclidian, dis- tance, then (1) is transforming into � = � (12) ( ) + ( ) A Each eigenvector’s component is obtained, in the first K ∙ (6) witeration, by summing related row of matrix . Vector in i the first iterationA A is hardly close to the wanted eigenvector where is strong unit weight value in coordinate system. A . InA theA. second iteration, elements in rows are summing Unknown ITL coordinates are obtained from necessary for matrix � . In the third iteration summing is done for conditions for extrema: � � Process stops when difference between compo- T. Rožić et al.

/ Scientific Journal of Maritime Research 30 (2016) 141-150 143 = nents of two successivew vectors are less then (small) value given in advance. The vector obtained in the last iteration (19) is wanted eigenvector from (12).[ ] Solving the complex decision problem by ELECTRE … 6. Calculate domination in concordance matrix by the method presumes given matrix 13 … formula: = ℎ ℎ … ℎ ℎ ℎ … ℎ (13) (20) ⋮ ⋮ ⋮ E e kl ℎ ℎhij f g ℎ kl kl 7. Format Total DominanceF Matrixf = � � withG eleg - where elements are numbers from an arbitrary or- kl kl hij ments obtained by multiplying related elements � fkl ckl c gkl dinary scalei such that every column describesj order from the obtained matrix = � � and matrix = � �. gkl dkl d of given alternatives. So every is a ranking estima- Elements are given by condition that if � then = gkl tion for – th alternative according to the – th criteri- 1. Elements are given by condition that if � then on. Furthermore, the vector for ranking criteria is also B b b b = 1. Otherwise, both elements equal zero. necessary:1 n 8. The order of alternatives is defined by counting val- = � 2 ... � (14) ues 1 in related row for every alternative. Absolutely dom- A B inated alternative has the highest number of values 1 in its where components are elements of arbitrary ordinary correspondence row. f scale. Considering and are given, one must R proceedr i ij PROMETHEE methodπ giveni by (4)k is based on assump- through the next steps. a i ij tion that decision maker defined criterion[ ]functions and 1. Calculate the normalized decision matrix = ( ) its importance factors , = 1, ..., . For example, prefer- = with elements 2calculated by from (12): ence (function) can( be) defined( ) by formula( ) = 3 : ℎ ∑ ℎ (15) (21)

Vij bi 2. Calculate the0 normalized… weighted decision matrix… 0 Final result is obtained from the preference function by values from (13):… … 0 0 values matrix with rows defined by every possible pair of … k k … alternatives, and columns defined by criteria. Every row as 0 0 – dimensional vector in dot product with – dimensional ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ 0 … 0 … vector of scalar weights gives decision intensities for each alternative pair. 0 … 0 … (16) i … … – Scalars obtainedj – above are elements in matrix withi – al- ternatives in rowsj – and in the columns. Elements in the 0 0 + ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ th row and th columnT represents the flow fromT th C D alternative to th alternative. Then it is possible to calcu- kl kl – late average input flow T and+ T average output flow for j Ckl j hkj hlj 3. Determinate concordance ( ) and discordance ( ) every alternative. j – sets consisted of criteria indices by definition = � , � �. The bigger difference – is, the better alternative Elements of nonconformity Cset consist of values that Ddo preference is. 3 Solution methods applications Cnot belong tom the m relevant conformity set. 4. Format concordance ( ) and discordanceC matrix ( ). matrix is × dimensional and it does not take value on diagonal. The elements of matrix are calculated by In this chapter, the methods explained above are com- the following= formula. pared to each other. Every method takes the same alterna- tives given as the possible location for an ITL. There are (17) Slavonski Brod, Karlovac, Koprivnica, Osijek and Split. D For solving the ITL problem by classical gravity meth- od, according to (9), the initial ITL coordinates are ob- The elements of discordance matrix ( ) are calculated tained in the Table 1. – – by the formulamax below: X Y = According to (8) further iterative performance is pro- max ceeded from initial point ( 0, 0) = (140, 173). In the Table (18) 2, the first step is shown. The next step is obtained by re- placing the coordinates of previous step with the coordi-

nates of the next step. 5. Calculate domination in concordance matrix by the In this problem, the second step is immediately the fi- formula: nal one as shown in Table 3. 144 T. Rožić et al.

Table 1 / Scientific Journal of Maritime Research 30 (2016) 141-150

No. GivenAlternative values and initial ITLAbscissa coordinates calculatedOrdinate Demand Unit costs Unit weight Pondered Coordinates

a Xi Yi Vi Ri Vi · Ri Xi · Vi · Ri Yi · Vi · Ri 1

Slavonski Brod 190 152 60 0.15 9.00 1710 1368 2 Karlovac 43 190 72 0.15 10.80 464.4 2052 4 3 Koprivnica 112 239 24 0.15 3.60 403.2 860.4 Osijek 232 199 60 0.15 9.00 2088 1791 Total/Average values: 5 Split 101 20 20 0.15 3.00 303 60 35.40 140 173 Table 2

The step procedure from initial to the first step No. Xi Yi Vi · Ri Xi · Vi · Ri /di Yi · Vi · Ri /di d i Vi · Ri· di Vi · Ri /di km km kn kn kn km kn kn/km 1

190 152 9.00 47.48 37.98 54 324.15 0.25 2 43 190 10.80 2.38 10.53 124 2103.89 0.06 4 3 112 239 3.60 1.53 3.26 264 950.19 0.01 232 199 9.00 6.83 5.86 306 2750.90 0.03 Total/Average value 5 101 20 3.00 2.94 0.58 103 308.88 0.03 previous step 61.00 58.00 851 6438.01 0.38 the next step 140 173 162 154 Table 3

The end of iteration– process Iteration X TC weights have to be assigned to related coordinates and then the conditions (10) and (11) are taken to get both 1 0 140 173 6599.70 median coordinate value. These median coordinates rep- – – 162 154 6438.01 resent solution of ITL problem.X YData is given in Table 4. 2 162 154 6438.01 Abscissa and ordinate of ITL solution by median meth- od are bolded in Table 4, so ( , ) = (190, 190). According to the Table 3, the best alternative for set- AHP method, according to (3) and (12) solves the ting the ITL is Slavonski Brod because the distance be- problem by finding the eigenvector through the following tween (162, 154) and (190,152) is the smallest among all procedure. Criteria definition and their relationships are alternatives.X Y given in Table 5. Median method requires increase ranking, separately Values from Table 5 are shown in the following matrix done by and coordinates of alternatives. After that, for the procedure. Table 4

Alternative Weighted median coordinateAbscissa valueUnit calculation weight Cumulative weight Alternative Ordinate Unit weight Cumulative weight

a Xi Vi · Ri a Yi Vi · Ri

Σ Σ Karlovac 43 10.80 10.80 Osijek 20 3.00 3.00 Split 190 10.80 22.80 Split 101 3.00 13.80 Karlovac 152 9.00 12.00 Slavonski Brod 190 9.00 26.40 Koprivnica 112 3.60 17.40 Slavonski Brod 199 9.00 31.80 Osijek 232 9.00 35.40 Koprivnica 239 3.60 35.40 Table 5

CriteriaCriteria definition with preferenceGoods flow relation Infrastructure Labour market Port influence logistics

Goods flow 1.00 3.00 5.00 4.00 0.33 Infrastructure 0.33 1.00 2.00 0.33 3.00 Labour market 0.20 0.50 1.00 2.00 2.00 Port influence 0.25 3.00 0.50 1.00 0.33 City logistics 3.00 0.33 0.50 3.00 1.00 ∑ 4.78 7.83 9.00 10.33 6.67 T. Rožić et al.

/ Scientific Journal of Maritime Research 30 (2016) 141-150 145 1,00 3,00 5,00 4,00 0,33 ALM 0,33 1,00 2,00 0,33 3,00 0,20 0,50 1,00 2,00 2,00 Calculating from (28) we obtain the normalized ei- 0,25 3,00 0,50 1,00 0,33 genvector which indicate that the fifth criteria is the most 0,13 3,00 0,33 0,50 3,00 1,00 (22) important one.0,07 = 0,05

A, A A, A A 0,27 0,48 (29) A Requested eigenvector’s components are obtained by summingA each row values from matrices � � � 6 … till the components reiterate themselves. Calculating from (22) we obtain the normalized eigenvector which 1,00 3,00 5,00 4,00 0,33 0,31 For the port impact there is a matrix indicates that the first criteria is the most important one: 0,33 1,00 2,00 0,33 3,00 0,19 = 0,20 0,50 1,00 2,00 2,00 = 0,14 0,25 3,00 0,50 1,00 0,33 0,13 3,00 0,33 0,50 3,00 1,00 (30) 0,23 (23) A PI

Calculating from (30) we obtain the normalized ei- Now we have to compare the alternatives consider- genvector which indicate that the third criteria is the most ing the criteria given in Table 5. For goods flow there is a 0,25 1,00 3,00 5,00 4,00 0,33 important one. matrix 0,10 0,33 1,00 2,00 0,33 3,00 = 0,42 = 0,20 0,50 1,00 2,00 2,00 0,19 0,25 3,00 0,50 1,00 0,33 0,04 (31) 3,00 0,33 0,50 3,00 1,00 (24)

A GF 1,00 3,00 5,00 4,00 0,33 For the city logistics there is a matrix Calculating from (24) we obtain the normalized ei- 0,33 1,00 2,00 0,33 3,00 genvector which indicate that the first criteria is the most = 0,20 0,50 1,00 2,00 2,00 0,44 0,25 3,00 0,50 1,00 0,33 important one. 0,07 3,00 0,33 0,50 3,00 1,00 (32) = 0,18 0,28 A CL 0,03 (25) Calculating from (32) we obtain the normalized ei- genvector which indicate that the fifth criteria is the most 0,13 1,00 3,00 5,00 4,00 0,33 important one. For the infrastructure there is a matrix 0,06 0,33 1,00 2,00 0,33 3,00 = 0,04 = 0,20 0,50 1,00 2,00 2,00 0,24 0,25 3,00 0,50 1,00 0,33 0,53 (33) 3,00 0,33 0,50 3,00 1,00 (26)

A IN Final result is obtained by multiplying the matrix, con- w wGF wIN wLM wPI wCL Calculating from (26) we obtain the normalized ei- sisted of alternative eigenvectors as columns, with criteria genvector which indicate that the fifth criteria is the most 0 0,05 eigenvector : � : : : : �. In practice, the 0,13 important 0,1one.0 result is:0,44 0,05 0,13 0,25 0,31 0,15 = 0,16 0,07 0,10 0,07 0,10 0,06 0,19 0,06 0,22 0,18 0,16 0,05 0,42 0,04 0,14 = 0,12 0,47 (27) 0,28 0, 22 0,27 0,19 0,24 0,13 0,20 0,03 0,47 0,48 0,04 0,53 ∙ 0,23 0,29

0,44 0,05 0,13 0,25 0,13 0,31 0,15 1,00 3,00 5,00 4,00 0,33 For the labour market there0,07 is0,1 a matrix0 0,0 7 0,10 0,06 0,19 0,06 (34) 0,33 1,00 2,00,10 80,30,13 63,000,05 0,42 0,04 0,14 = 0,12 2,00 = 0,20 0,50 1,00,0282,000, 22 0,27 0,19 0,24 0,13 0,20 0,25 3,00 0,50,00 31,00,40 70,303,48 0,04 0,53 ∙ 0,23 0,29 3,00 0,33 0,50 3,00 1,00 (28)

Table 6 shows final results obtained by AHP method where alternatives are ranked by preferences. T. Rožić et al.

Table146 6 / Scientific Journal of Maritime Research 30 (2016) 141-150

RankingNo. alternatives according to preferences Alternative Preference 1

Split 0.29 2 Osijek 0.20 4 3 Slavonski Brod 0.15 Koprivnica 0.12 5 Karlovac 0.06 Table 7

AlternativesAlternative comparisonGoods according flow to criteriaInfrastructure Labour market Port influence City logistics 8

Slavonski Brod 7 6 7 7 8 Karlovac 6 5 6 6 7 8 Koprivnica 7 6 5 5 8 4 Osijek 5 6 7 6 Split 7 7 9 Table 8

Criteria Weights coefficients Goodsfor each flow criteria Infrastructure Labour market Port influence City logistics 8

Weights 9 7 5 6

H B 379 Input values necessary for constructing the matrix In =fifth and six =step,18 ,according95 to (19) and (20): from (13) and vector from (14) in ELECTRE method are 5(5 1) given by Table 7 and Table 8 respectively. (39) − Steps mentioned in chapter 1 are now processed. 0,5357 0,5013 0,4140 0,4937 0,4276 15,7309 In the first step the matrix = = 0,7865 0,5013 0,3581 0,4140 0,4232 0,4276 5( 1) 0,4140 0,4297 0,3450 0,5643 0,3054 (40) 0,4937 0,4297 0,4830 0,4232 0,4887 5 − c d 0,4276 0,5013 0,5521 0,2821 0,5498 (35) F ConsideringG the values and in (39) and (40) we can obtain dominance matrices of concordance and of dis- 1 1 1 1 The second step is processed by formula (16) and pro- cordance by step seven. 4,8213 3,5091 2,0700 2,9622 3,4208 0 0 0 0 vide the following matrix: 4,5117 2,5067 2,0700 2,5392 3,4208 −0 1 1 0 3,7260 3,0079 1,7241 3,3858 2,4432 0 −0 0 0 4,4430 3,0079 2,4150 2,5392 3,9096 1 1 −1 1 (41) 3,8484 3,5091 2,7605 1,6926 4,3984 (36) − − 0 0 1 1 1 1 1 1 C C −1 1 1 1 Third step is D left for the reader. For example, 43 0 0− 0 0 = �2,3,5�. In step four, concordance matrix ( ) and dis- 1 1 −1 0 (42) cordance matrix ( ) are obtained by formula (17) and − 35 29 (18) respectively. 22 22 − 13 13 15 15 E F G −6 22 22 15 0 0 1 1 13 −12 12 6 Finally,0 we get0 matrix0 0 = � : 20 29 −29 29 (37) −0 1 1 0 − 1 −0 0 0 − 0,0000 0,2174 1 ,0000 1,0000 1 1 −1 0 (43) 1,0000 1,0000 1,0000 1,0000 − 1,000− 0 0,8914 1,0000 1,0000 −

0,7360 − 0, 3009 0,5373 0,6428 1,0000 0,9862 −0,9123 0,5065 (38) By the ELECTRE Emethod the best alternative to solve − ITL problem is the one with the highest number of value 1 − in the row of matrix (43). T. Rožić et al.

/ Scientific Journal of Maritime Research 30 (2016)Table 141-150 9 147

Number of values 1 for each alternative From Table 9 it is clear that Split is the best alternative. Alternative Totality of value 1 in the row of E Given data for using the PROMETHEE method are in the next two tables. As in the all methods above, here the five Slavonski Brod 2 alternatives and five criteria are observed. Table 10 displays Karlovac 0 criteria functions and Table 11 displays criteria estimations. Koprivnica 2 The last alternative (Split) is obviously dominate and Osijek 0 there for it is excluded from further observations. Split 3 Table 10

Alternatives Criteria functionsAlternative mark Goods flow Infrastructure Labour market Port influence City logistics 4 4 4 Slavonski Brod A 3 34,212 2.18 2 C Karlovac B 33,632 1.89 2 D 4 Koprivnica 2 2 36,011 2.42 3 E 4 Osijek 3 3 84,765 1.39 Split 5 158,226 0.62 5 Table 11

Criteria Criteria estimation estimations Goods flow Infrastructure Labour market Port influence City logistics

q Importance factor 0.5 0.3 0 0.2 0.2 p Indifference threshold 0 0 580 0.24 0 Preference threshold 0 0 0 0.5 0

Each of five preference functions is defined by (21). The According to Table 11, the preference function given following tables display preference functions for each possi- by (21) is modified for labor market criterion into formula ble pear of alternatives according to every criteria functions. (44): Table 12 ( ) Alternative Preference pair function for Goods flowd criterion P (d) (44)

1 (A, B) 4 – 4 = 0 0 Table 14 1 (A, C) 4 – 2 = 2 Alternative Preference pair function for Labour dmarket criterion P (d) (A, D) 4 – 3 = 1 1 (B, A) 4 – 4 = 0 0 1 (B, C) 4 – 2 = 2 (A, B) 580 0 (B, D) 4 – 3 = 1 (A, C) -1,799 0 (C, A) 2 – 4 = -2 0 (A, D) -50,553 0 (C, B) 2 – 4 = -2 0 (B, A) -580 0 (C, D) 2 – 3 = -1 0 (B, C) -2,379 0 1 (D, A) 3 – 4 = -1 0 (B, D) -51,133 0 Table 13 1 (C, A) 1,799 Alternative Preference pair function for Infrastructured criterion P (d) (C, B) 2,379 1 (C, D) -48,754 0 1 1 (D, A) 50,553 (A, B) 3 – 4 = -1 0 1 (D, B) 51,133 (A, C) 3 – 2 = 1 1 (D, C) 48,754 (A, D) 3 – 3 = 0 0 1 (B, A) 4 – 3 = 1 1 (B, C) 4 – 2 = 2 According to Table 11, the preference function given (B, D) 4 – 3 = 1 by (21) is modified for Port impact criterion into formula (C, A) 2 – 3 = -1 0 (45): (C, B) 2- 4 = -2 0 ( ) = (C, D) 2- 3 = -1 0 0,5 0,24 (D, A) 3- 3 = 0 0 1 (45) (D, B) 3- 4 = -1 0 − (D, C) 3- 2 = 1

148 T. Rožić et al.

Table 15 / Scientific Journal of Maritime Research 30 (2016) 141-150

Preference functionAlternative for Port pairimpact criterion d P (d) 1

(A, B) 0.29 1 (A, C) -0.24 0 (A, D) 0.79 (B, A) -0.29 0 1 (B, C) -0.53 0 (B, D) 0.5 1 (C, A) 0.24 0 1 (C, B) 0.53 (C, D) 1.03 (D, A) -0.79 0 (D, B) -0.5 0 (D, C) -1.03 0

Preference function for City logistics criterion, accord- ing to Table 11 is calculated by (21). Table 16

Preference functionAlternative for City pairlogistics criterion d P (d)

(A, B) 2 – 2 = 0 0 (A, C) 2 – 3 = -1 0 (A, D) 2 – 4 = -2 0 (B, A) 2 – 2 = 0 0 (B, C) 2 – 3 = -1 0 1 (B, D) 2 – 4 = 0 0 1 (C, A) 3 – 2 = 1 (C, B) 3 – 2 = 1 1 (C, D) 3 – 4 = -1 0 1 (D, A) 4 – 2 = 2 1 (D, B) 4 – 2 = 2 (D, C) 4 – 3 = 1

Final results table is filed with preference function val- ues as follows. Table 17

Final results of preferenceGoods flow functions Infrastructure Labour market Port influence City logistics 1

1 1 (A, B) 0 0 0 0 1 1 (A, C) 0 0 0 1 (A, D) 0 0 0 1 1 (B, A) 0 0 0 0 1 1 1 (B, C) 0 0 0 1 1 (B, D) 0 0 1 1 1 (C, A) 0 0 0 1 (C, B) 0 0 1 1 (C, D) 0 0 0 0 1 1 1 (D, A) 0 0 0 1 1 1 1 (D, B) 0 0 (D, C) 0 T. Rožić et al.

/ Scientific Journal of Maritime Research 30 (2016) 141-150 149

For every alternative pear, according to importance factor from Table 11, preference indices for each pair are calculated as a dot product. Dot products described in chapter 2 give the values displayed in Table 18. Table 18

Pair notation Final results Alternative pair Final result

(A, B) Slavonski Brod, Karlovac 0.1 (A, C) Slavonski Brod, Koprivnica 0.6 (A, D) Slavonski Brod, Osijek 0.5 (B, A) Karlovac, Slavonski Brod 0.2 (B, C) Karlovac, Koprivnica 0.6 (B, D) Karlovac, Osijek 0.7 (C, A) Koprivnica. Slavonski Brod 0.3 (C, B) Koprivnica, Karlovac 0.4 (C, D) Koprivnica, Osijek 0.1 (D, A) Osijek, Slavonski Brod 0.3 (D, B) Osijek, Karlovac 0.7 (D, C) Osijek, Koprivnica 0.9 T+ Final resultT from Table 18. is clearly presented in Table 19, together with average output flow ( ) and average in- – put flow ( ). Table 19

Average output and input flowSlavonski for each Brod alternative Karlovac Koprivnica Osijek T+ Slavonski Brod

Karlovac - 0.1 0.6 0.5 0.4 Koprivnica 0.2 - 0.6 0.7 0.5 Osijek _ 0.3 0.4 - 0.1 0.27 T 0.3 0.7 0.9 - 0.63 0.27 0.4 0.7 0.43

Final alternative ranking is done according to the ab- solute difference between average input and output flows. Table 20 _ _ Alternative Final alternative ranking T+ T |T| T+ – T Rank

= Osijek 0.63 0.43 0.20 1. Slavonski Brod 0.40 0.27 0.13 2. Karlovac 0.50 0.40 0.10 3. Koprivnica 0.27 0.70 -0.43 4.

Finally, the best alternative for ITL problem is Split. From Table 20, the other alternatives are ranked, so Osijek is second best, then Slavonski Brod is following and at the end are Karlovac and Koprivnica. T. Rožić et al.

150 / Scientific Journal of Maritime Research 30 (2016) 141-150 4 Conclusion

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