Plane Thermoelastic Waves in Infinite Half-Space Caused Decision Making: Applications in Management and Engineering Vol. 2, Issue 1, 2019, pp. 49-65 ISSN: 2560-6018 eISSN: 2620-0104 DOI: https://doi.org/10.31181/dmame1901065f * Corresponding author. E-mail addresses: hamed.hero@gmail.com (H. Fazlollahtabar), aldina12345aldina@gmail.com (A. Smailbašić) zeljkostevic88@yahoo.com and zeljko.stevic@sf.ues.rs.ba (Ž. Stević) FUCOM METHOD IN GROUP DECISION-MAKING: SELECTION OF FORKLIFT IN A WAREHOUSE Hamed Fazlollahtabar1, Aldina Smailbašić2 and Željko Stević2* 1 Department of Industrial Engineering, School of Engineering, Damghan University, Damghan, Iran 2 University of East Sarajevo, Faculty of Transport and Traffic Engineering, Doboj, Bosnia and Herzegovina Received: 29 September 2018; Accepted: 13 February 2019; Available online: 19 February 2019. Original scientific paper Abstract. A warehouse system as a time transformation of the flows of goods plays an essential role in a complete logistics chain. The efficiency of a complete warehouse system largely depends on the efficiency of carrying out transport and handling operations. Therefore, it is essential to have adequate means of internal transport that will influence the efficiency of the warehouse system by its performance. In this paper, the evaluation and selection of side- loading forklift using the FUCOM-WASPAS model, which has been used for the first time in the literature in this paper, is performed. The FUCOM method was used to obtain the weight values of the criteria, while WASPAS was applied for the evaluation and ranking of forklifts. A possibility to apply the FUCOM method in group decision-making was presented. A comparative analysis, in which other methods of multi-criteria decision-making were applied, was carried out. The analysis showed the stability of the results obtained. Key words: FUCOM method, Forklift, WASPAS method, Warehouse, group decision-making 1. Introduction In the day-to-day performance of various activities and processes, logistics as an integral and indispensable part of each business system plays a very important role (Stević et al., 2017a). There is a need to rationalize activities and processes that may significantly affect a company's competitive position (Stević et al., 2017b). A warehouse as a special logistics subsystem and transport represent the major cause of logistics costs and there is a constant search for potential places of savings in these subsystems. In the very beginning, a warehouse was just a place used to separate Fazlollahtabar et al./Decis. Mak. Appl. Manag. Eng. 2 (1) (2018) 49-65 50 surplus products, while today its function is completely different (Stojčić et al., 2018). Compared to the former static function, today's warehouses represent dynamic systems in which the movement of goods is dominant. Taking into account the above considerations, it is necessary to perform transport and handling operations as rationally as possible. From this aspect, forklifts within internal transport and warehousing operations play an important role. Internal transport is the basis of every production process, both in functional and organizational terms. Accordingly, rationalizing the movement of the means of transport and selecting the most convenient means of transport would lead to more efficient exploitation and reduction of costs. Forklifts are the most widely used, most useful and most practical means of internal transport. Forklifts are transport work machines for unloading, transport, warehousing and loading of various freight. There are a number of forklifts of different characteristics on the market. The side-loading forklift is intended for handling all types of freight. In this paper, seven criteria that could be taken into account when selecting a side- loading forklift were chosen. The aim of the paper is to obtain the best solution, i.e. an appropriate side-loading forklift that will meet the requirements of the Euro-Roal company where the research was carried out using multi-criteria decision-making. The choice of a specific side-loading forklift is conditioned by the optimality of the criteria that refer to the purchase price, age, working hours, maximum load capacity, maximum lift height, ecological factor and the supply of spare parts. In the paper, the FUCOM (Full Consistency Method) and WASPAS (Weighted Aggregated Sum Product Assessment) method were used to enable the evaluation and selection of a used side- loading forklift at the Euro-Roal company. Using the FUCOM method, the determination of relative weights was performed, while using the WASPAS method, the ranking was completed. The remainder of the paper is organized as follows. In the second section of the paper, the methods used in the work, the FUCOM and WASPAS methods, are presented. FUCOM provides a possibility to determine accurately the weight coefficients of all the elements that are mutually compared. WASPAS represents a relatively new method of multi-criteria decision-making (MCDM) that is derived from two methods: Weighted Sum Model (WSM) and Weighted Product Model (WPM). The third section of the paper demonstrates the applicability of FUCOM method in group decision-making. Based on the expert assessment of three decision-makers, the weight values of criteria are obtained. The fourth section is the evaluation and selection of forklifts using the WASPAS method, while in the fifth section, a comparative analysis is carried out using other methods. The paper ends with conclusions and directions for future research. 2. Methods By applying multi-criteria decision-making methods, it is possible to select adequate strategies, rationalize certain logistics and other processes, and make appropriate decisions that affect the company's business or their subsystems, as evidenced by the following research (Tzeng and Huang, 2012; Prakash and Barua, 2016; Żak and Węgliński, 2014; Hanaoka and Kunadhamraks, 2009; Zavadskas et al., 2018; Stojić et al., 2018; Radović et al., 2018; Sremac et al., 2018) 2.1. FUCOM (Full COnsistency Method) FUCOM (Pamučar et al., 2018) is a new MCDM method for determination of criteria weights. The problems of multi-criteria decision-making are characterized by the FUCOM method in group decision-making: selection of forklift in a warehouse 51 choice of the most acceptable alternative out of a set of the alternatives presented on the basis of the defined criteria. A model of multi-criteria decision-making can be presented by a mathematical equation      1 2max , ,..., , n 2nf x f x f x    , with the condition that  1 2, ,..., mx A a a a  ; where n represents the number of the criteria, m is the number of the alternatives, fj represents the criteria ( 1, 2,...,ј n ) and A represents the set of the alternatives ai ( 1, 2,...,i m ). The values ijf of each considered criterion j f for each considered alternative i a are known, namely    , , ; 1, 2,..., ; 1, 2,...,ij j if f a i j i m j n    . The relation shows that each value of the attribute depends on the jth criterion and the ith alternative. Real problems do not usually have the criteria of the same degree of significance. It is therefore necessary that the significance factors of particular criteria should be defined by using appropriate weight coefficients for the criteria, so that their sum is one. Determining the relative weights of criteria in multi-criteria decision-making models is always a specific problem inevitably accompanied by subjectivity. This process is very important and has a significant impact on the final decision-making result, since weight coefficients in some methods crucially influence the solution. Therefore, particular attention in this paper is paid to the problem of determining the weights of criteria, and the new FUCOM model for determining the weight coefficients of criteria is proposed. This method enables the precise determination of the values of the weight coefficients of all of the elements mutually compared at a certain level of hierarchy, simultaneously satisfying the conditions of comparison consistency. In real life, pairwise comparison values / ij i j a w w (where aij shows the relative preference of criterion i to criterion j) are not based on accurate measurements, but rather on subjective estimates. There is also a deviation of the values ija from the ideal ratios /i jw w (where iw and jw represents criteria weights of criterion i and criterion j). If, for example, it is determined that A is of much greater significance than B, B of greater importance than C, and C of greater importance than A, there is inconsistency in problem solving and the reliability of the results decreases. This is especially true when there are a large number of the pairwise comparisons of criteria. FUCOM reduces the possibility of errors in a comparison to the least possible extent due to: (1) a small number of comparisons (n-1) and (2) the constraints defined when calculating the optimal values of criteria. FUCOM provides the ability to validate the model by calculating the error value for the obtained weight vectors by determining deviation from full consistency (DFC). On the other hand, in other models for determining the weights of criteria (the BWM, the AHP models), the redundancy of the pairwise comparison appears, which makes them less vulnerable to errors in judgment, while the FUCOM methodological procedure eliminates this problem. In the following section, the procedure for obtaining the weight coefficients of criteria by using FUCOM is presented. Step 1. In the first step, the criteria from the predefined set of the evaluation criteria  1 2, ,..., nC C C C are ranked. The ranking is performed according to the significance of the criteria, i.e. starting from the criterion which is expected to have the highest weight coefficient to the criterion of the least significance. Thus, the criteria ranked according to the expected values of the weight coefficients are obtained: Fazlollahtabar et al./Decis. Mak. Appl. Manag. Eng. 2 (1) (2018) 49-65 52 (1) (2) ( ) ... j j j k C C C   (1) where k represents the rank of the observed criterion. If there is a judgment of the existence of two or more criteria with the same significance, the sign of equality is placed instead of “>” between these criteria in the expression (1) Step 2. In the second step, a comparison of the ranked criteria is carried out and the comparative priority ( / ( 1)k k   , 1, 2,...,k n , where k represents the rank of the criteria) of the evaluation criteria is determined. The comparative priority of the evaluation criteria ( / ( 1)k k   ) is an advantage of the criterion of the ( )j k C rank compared to the criterion of the ( 1)j k C  rank. Thus, the vectors of the comparative priorities of the evaluation criteria are obtained, as in the expression (2):  1/ 2 2 / 3 / ( 1), ,..., k k     (2) where / ( 1)k k   represents the significance (priority) that the criterion of the ( )j k C rank has compared to the criterion of the ( )j k C rank. The comparative priority of the criteria is defined in one of the two ways defined in the following part: a) Pursuant to their preferences, decision-makers define the comparative priority / ( 1)k k   among the observed criteria. Thus, for example, if two stones A and B, which, respectively, have the weights of 300Aw  grams and 255Bw  grams are observed, the comparative priority ( /A B ) of Stone A in relation to Stone B is / 300 / 255 1.18 A B    . Additionally, if the weights A and B cannot be determined precisely, but a predefined scale is used, e.g. from 1 to 9, then it can be said that stones A and B have weights 8 A w  and 7 B w  . respectively. Then the comparative priority ( /A B  ) of Stone A in relation to Stone B can be determined as / 8 / 7 1.14 A B    . This means that stone A in relation to stone B has a greater priority (weight) by 1.18 (in the case of precise measurements), i.e. by 1.14 (in the case of application of measuring scale). In the same manner, decision-makers define the comparative priority among the observed criteria / ( 1)k k   . When solving real problems, decision-makers compare the ranked criteria based on internal knowledge, so they determine the comparative priority / ( 1)k k   based on subjective preferences. If the decision-maker thinks that the criterion of the ( )j k C rank has the same significance as the criterion of the ( 1)j k C  rank, then the comparative priority is / ( 1) 1 k k    . b) Based on a predefined scale for the comparison of criteria, decision-makers compare the criteria and thus determine the significance of each individual criterion in the expression (1). The comparison is made with respect to the first-ranked (the most significant) criterion. Thus, the significance of the criteria ( ( )j kC  ) for all of the criteria ranked in Step 1 is obtained. Since the first-ranked criterion is compared with itself (its significance is (1) 1 jC   ), a conclusion can be drawn that the n-1 comparison of the criteria should be performed. For example: a problem with three criteria ranked as C2>C1>C3 is being subjected to consideration. Suppose that the scale   ( ) 1, 9 j kC   is used to determine the priorities of the criteria and that, based on the decision-maker’s preferences, the FUCOM method in group decision-making: selection of forklift in a warehouse 53 following priorities of the criteria 2 1 C   , 1 3.5 C   and 3 6 C   are obtained. On the basis of the obtained priorities of the criteria and condition / ( 1) 1 k k k k w w     we obtain following calculations 2 1 3.5 1 w w  i.e. 2 1 3.5w w  , 1 3 6 3.5 w w  i.e. 1 3 1.714w w  . In that way, the following comparative priorities are calculated: 2 1/ 3.5 / 1 3.5 C C    and 1 3/ 6 / 3.5 1.714 C C    (expression (2)). As we can see from the example shown in Step 2b, the FUCOM model allows the pairwise comparison of the criteria by means of using integer, decimal values or the values from the predefined scale for the pairwise comparison of the criteria. Step 3. In the third step, the final values of the weight coefficients of the evaluation criteria  1 2, ,..., T n w w w are calculated. The final values of the weight coefficients should satisfy the two conditions: (1) that the ratio of the weight coefficients is equal to the comparative priority among the observed criteria ( / ( 1)k k   ) defined in Step 2, i.e. that the following condition is met: / ( 1) 1 k k k k w w     (3) (2) In addition to the condition (3), the final values of the weight coefficients should satisfy the condition of mathematical transitivity, i.e. that / ( 1) ( 1) / ( 2) / ( 2) k k k k k k          . Since / ( 1) 1 k k k k w w     and 1 ( 1) / ( 2) 2 k k k k w w       , that 1 1 2 2 k k k k k k w w w w w w       is obtained. Thus, yet another condition that the final values of the weight coefficients of the evaluation criteria need to meet is obtained, namely: / ( 1) ( 1) / ( 2) 2 k k k k k k w w         (4) Full consistency, i.e. minimum DFC (  ) is satisfied only if transitivity is fully respected, i.e. when the conditions of / ( 1) 1 k k k k w w     and / ( 1) ( 1) / ( 2) 2 k k k k k k w w         are met. In that way, the requirement for maximum consistency is fulfilled, i.e. DFC is 0  for the obtained values of the weight coefficients. In order for the conditions to be met, it is necessary that the values of the weight coefficients  1 2, ,..., T n w w w meet the condition of / ( 1) 1 k k k k w w       and / ( 1) ( 1) / ( 2) 2 k k k k k k w w           , with the minimization of the value  . In that manner, the requirement for maximum consistency is satisfied. Based on the defined settings, the final model for determining the final values of the weight coefficients of the evaluation criteria can be defined. Fazlollahtabar et al./Decis. Mak. Appl. Manag. Eng. 2 (1) (2018) 49-65 54 ( ) / ( 1) ( 1) ( ) / ( 1) ( 1) / ( 2 ) ( 2 ) 1 min . . , , 1, 0, j k k k j k j k k k k k j k n j j j s t w j w w j w w j w j                          (5) By solving model (5), the final values of the evaluation criteria  1 2, ,..., T n w w w and the degree of DFC (  ) are generated. 2.2. WASPAS method The weighted aggregated sum product assessment (WASPAS) method (Zavadskas et al., 2012) represents a relatively new MCDM method that is derived from two methods: Weighted Sum Model (WSM) and Weighted Product Model (WPM). The WASPAS method consists of the following steps: Step 1. Forming the initial decision-making matrix ( X ). The first step is to evaluate m alternatives according to n criteria. The alternatives are shown by vectors  1 2, ,...,i i i inA x x x where ijx is the value of ith alternative according to jth criterion ( 1, 2,..., ; 1, 2,...,i m j n  ). 1 2 1 11 12 1 2 21 22 2 1 2 ... ... ... ... ... ... ... ... n n n m m m mn C C C A x x x A x x x X A x x x             (6) where m denotes the number of the alternative, and n denotes the total number of criteria. Step 2. In this step, normalization of the initial matrix is required by applying the following equations: 1 2 , ,..., max ij ij n ij i x n for C C C B x   (7) 1 2 min , ,..., ij i ij n ij x n for C C C C x   (8) Step 3. Weighting the normalized matrix, so that the previously obtained matrix needs to be multiplied by the weight values of criteria: FUCOM method in group decision-making: selection of forklift in a warehouse 55 n ij m n V v      (9) , 1, 2,..., , ij j ij V w n i m j   (10) Step 4. Summing all the values of the alternatives obtained (summing by rows): 1 i ij m Q q      (11) 1 n ij ij j q v    (12) Step 5: Determining a weighted product model by applying the following equation: 1 i ij m P p      (13)   1 j n w ij ij j p v   (14) Step 6. Determining the relative values of alternatives Ai: 1 i ij m A a      (15)  1i i iA Q P      (16) The coefficient λ ranges from 0, 0.1, 0.2,….1.0 Step 7. Ranking the alternatives. The highest value of alternatives implies the best- ranked one, while the smallest value refers to the worst alternative. 3. FUCOM method in group decision-making processes The optimal choice of overhaul mechanization, in this case a forklift, depends solely on the precise determination and selection of appropriate criteria and their evaluation. The weights of the selected criteria were determined on the basis of their importance and needs of "Euro-Roal", Doboj Jug,, which were presented by experts and employees responsible for overhaul mechanization. Table 1 gives the name, label and description of the criteria used for the selection of a forklift. Table 1. Criteria for forklift selection Name and label of criteria Criterion description Purchase price (C1) Forklift prices on the market are different and depend on manufacturers. When making an investment decision, the purchase price should not be decisive to the buyer, but it has a significant impact on the final decision. In an unsystematic approach, once the basic conditions are met, the purchase price is often a decisive factor. Fazlollahtabar et al./Decis. Mak. Appl. Manag. Eng. 2 (1) (2018) 49-65 56 Age (C2) The age or year of production characterizes the production period of a forklift. Forklifts manufactured recently have better specifications and options for adjustment to the requirements. Working hours (C3) Forklift utilization time is one of the most important criteria when selecting a forklift. The less the hours of the forklift utilization are, the lesser possibility of its breakdown is. Maximum load capacity (C4) Maximum load capacity is a criterion that represents the load capacity that a forklift can lift and it is expressed in kilograms. Maximum lift height (C5) Maximum lift height is a criterion that represents the height that a forklift can reach when lifting. Ecological factors (C6) Impact of forklift operation on the environment. Supply of spare parts (C7) In experience, some representatives working in the market of the Republic of Serbia do not have in stock all necessary spare parts that are subject to frequent replacements, and their delivery is being waited for weeks, so the repairs of the means are long lasting. This criterion is in a group of qualitative criteria and is expressed by a fuzzified Likert scale. Table 2 shows seven criteria that were evaluated by three decision-makers. The decision-makers evaluated the criteria according to their importance to the company. Table 2. Comparison of criteria DM1 DM2 DM3 C1 5 5 5 C2 4 2 2 C3 1 1 1 C4 2 3 3 C5 3 4 4 C6 7 7 7 C7 6 6 6 Determining the significance of criteria according to Petrović et al. (2017) is one of the most important stages in a decision-making process. 3.1. Determining the weight values of criteria for DM1 Step 1. In the first step, the decision-makers rank the criteria: C3>C4>C5>C2>C1>C7>C6. Step 2. In the second step (step 2b), the decision-maker performs a parwise comparison of ranked criteria from step 1. The comparison is made with respect to the first-ranked criterion C1. The comparison is based on the scale  1, 9 . Thus, we obtain the significance of the criteria ( ( )j kC  ) for all the criteria ranked in step 1 (Table 3). FUCOM method in group decision-making: selection of forklift in a warehouse 57 Table 3. The significance of criteria Criteria C3 C4 C5 C2 C1 C7 C6 ( )j kC  1 2.2 3,8 4.5 5 6,5 7 Based on the obtained significance of the criteria, the comparative significance of the criteria is calculated: 3 4/ 2.20 / 1.0 2.20 c c    ; 4 5/ 3.8 / 2.20 1.73 c c    ; 5 2/ 4.50 / 3.8 1.18 c c    ; 2 1/ 5.00 / 4.50 1.11 c c    ; 1 7/ 6.50 / 5.00 1.30 c c    ; 7 3/ 7.00 / 6.50 1.08 c c    Step 3. The final values of weight coefficients should meet two conditions: (1) The final values of weight coefficient should meet the condition (3), i.e. that: 3 4 4 5 5 2 2 1 1 7 7 6 / 2.20; / 1.73; / 1.18; / 1.11; / 1.30; / 1.08 w w w w w w w w w w w w       (2) In addition to the condition (3), the final values of weight coefficients should meet the condition of mathematical transitivity, i.e. that: 3 54 5 2 1 2 1 7 6 2.20 1.73 3.81; 1.73 1.18 2.04; 1.18 1.11 1.31; 1.11 1.30 1.44; 1.30 1.08 1.40 w ww w w w w w w w                Using the expression (5), we can define the final model for determining weight coefficients: 8 5 74 2 1 4 5 2 1 7 6 8 54 2 1 5 2 1 7 6 7 1 min . . 2.20 , 1.73 , 1.18 , 1.11 , 1.30 , 1.08 , 3.81 , 2.04 , 1.31 , 1.44 , 1.40 , 1, 0, j j j s t w w ww w w w w w w w w w ww w w w w w w w w w j                                        By solving this model, we obtain the final values of weight coefficients for: purchase price, age, working hours, maximum load capacity, maximum lift height, ecological factor, supply of spare parts (0.082, 0.091, 0.410, 0.186, 0.108, 0.059, 0.068)τ and the deviation from a complete consistency, a result 𝑥 = 0.001. After calculating, it can be concluded that the most important criterion is working hours. For this element, the final value of the weight coefficient is 0.410. 3.2. Determining the weight values of criteria for DM2 Step 1. In the first step, the decision-makers ranked the criteria: C3>C2>C4=C5>C1>C7>C6. Step 2. In the second step (step 2b), the decision-maker performs a pairwise comparison of ranked criteria from step 1. The comparison is made with respect to the Fazlollahtabar et al./Decis. Mak. Appl. Manag. Eng. 2 (1) (2018) 49-65 58 first-ranked criterion C1. The comparison is based on the scale  1, 9 . Thus, we obtain the significance of the criteria ( ( )j kC  ) for all the criteria ranked in step 1 (Table 4). Table 4. The significance of criteria Criteria C3 C2 C4 C5 C1 C7 C6 ( )j kC  1 2.8 3.5 3.5 4.2 5.5 6.5 Based on the obtained significance of the criteria, the comparative significance of the criteria is calculated: 3 2/ 2.80 / 1.0 2.80 c c    ; 2 4/ 3.5 / 2.80 1.25 c c    ; 4 5/ 3.50 / 3.50 1.00 c c    ; 5 1/ 4.20 / 3.50 1.20 c c    ; 1 7/ 5.50 / 4.20 1.30 c c    ; 7 6/ 6.50 / 5.50 1.18 c c    Step 3. The final values of weight coefficients should meet two conditions: (1) The final values of weight coefficient should meet the condition (3), i.e. that: 3 2 2 4 4 5 5 1 1 7 7 6 / 2.80; / 1.25; / 1.00; / 1.20; / 1.30; / 1.18 w w w w w w w w w w w w       (2) In addition to the condition (3), the final values of weight coefficients should meet the condition of mathematical transitivity, i.e. that: 3 2 4 4 5 1 5 1 7 6 2.80 1.25 3.50; 1.25 1.00 1.25; 1.00 1.20 1.20; 1.20 1.30 1.56; 1.30 1.18 1.53 w w w w w w w w w w                Using the expression (5), we can define the final model for determining weight coefficients. 3 5 72 4 1 2 4 5 1 7 6 3 52 4 1 4 5 1 7 6 7 1 min . . 2.80 , 1.25 , 1.00 , 1.20 , 1.30 , 1.18 , 3.50 , 1.25 , 1.20 , 1.56 , 1.53 , 1, 0, j j j s t w w ww w w w w w w w w w ww w w w w w w w w w j                                        By solving this model, we obtain the final values of weight coefficients: purchase price, age, working hours, maximum load capacity, maximum lift height, ecological factor, supply of spare parts (0.094, 0.140, 0.398, 0.115, 0.116, 0.064, 0.077)τ and the deviation from a complete consistency, a result 𝑥 = 0.004. After calculating, it can be concluded that the most important criterion is working hours. For this element, the final value of the weight coefficient is 0.398. 3.3. Determining the weight values of criteria for DM3 Step 1. In the first step, the decision-makers ranked the criteria: C3>C2>C4=C5>C1>C7>C6. FUCOM method in group decision-making: selection of forklift in a warehouse 59 Step 2. In the second step (step 2b), the decision-maker performs a pairwise comparison of ranked criteria from step 1. The comparison is made with respect to the first-ranked criterion C1. The comparison is based on the scale  1, 9 . Thus, we obtain the significance of criteria ( ( )j kC  ) for all the criteria ranked in step 1 (Table 5). Table 5. The significance of criteria Criteria C3 C2 C4 C5 C1 C7 C6 ( )j kC  1 2.8 3.5 3.5 4.5 6 7 Based on the obtained significance of the criteria, the comparative significance of the criteria is calculated: 3 2/ 2.80 / 1.0 2.80 c c    ; 2 4/ 3.5 / 2.80 1.25 c c    ; 4 5/ 3.50 / 3.50 1.00 c c    ; 5 1/ 4.50 / 3.50 1.29 c c    ; 1 7/ 6.00 / 4.50 1.34 c c    ; 7 6/ 7.00 / 6.00 1.17 c c    Step 3. The final values of weight coefficients should meet two conditions: 1) The final values of weight coefficients should meet the condition (3), i.e. that: 3 2 2 4 4 5 5 1 1 7 7 6 / 2.80; / 1.25; / 1.00; / 1.29; / 1.34; / 1.17 w w w w w w w w w w w w       (2) In addition to the condition (3), the final values of weight coefficients should meet the condition of mathematical transitivity, i.e. that: 3 2 4 4 5 1 5 1 7 6 2.80 1.25 3.50; 1.25 1.00 1.25; 1.00 1.29 1.29; 1.29 1.34 1.73; 1.73 1.17 2.02 w w w w w w w w w w                Using the expression (5), we can define the final model for determining weight coefficients: 3 5 72 4 1 2 4 5 1 7 6 3 52 4 1 4 5 1 7 6 7 1 min . . 2.80 , 1.25 , 1.00 , 1.29 , 1.34 , 1.17 , 3.50 , 1.25 , 1.29 , 1.73 , 2.02 , 1, 0, j j j s t w w ww w w w w w w w w w ww w w w w w w w w w j                                        By solving this model, we obtain the final values of weight coefficients: purchase price, age, working hours, maximum load capacity, maximum lift height, ecological factor, supply of spare parts (0.095, 0.170, 0.418, 0.110, 0.112, 0.050, 0.065)τ and the deviation from a complete consistency, a result 𝑥 = 0.001. After calculating, it can be concluded that the most important criterion (Table 6) is working hours. For this element, the final value of the weight coefficient is 0.418. Fazlollahtabar et al./Decis. Mak. Appl. Manag. Eng. 2 (1) (2018) 49-65 60 Table 6. The criterion values for each decision-maker and values obtained by applying a geometric mean DM1 DM2 DM3 The values obtained by applying a geometric mean 0.082 0.094 0.095 0.090 0.091 0.140 0.170 0.129 0.410 0.398 0.418 0.409 0.186 0.115 0.110 0.133 0.108 0.116 0.112 0.112 0.059 0.064 0.050 0.057 0.068 0.077 0.065 0.070 The final values of weight coefficients were obtained by LINGO software. From the table of results, it is clear that in this case working hours (C3) and maximum load capacity (C4) are the most important criteria. 4. The selection of forklift in a warehouse using the WASPAS method The Euro-Roal company owns several forklifts over 20 years of age and, in order to improve and refine their fleet, 10 alternatives (Figure 1) (side-loading forklifts) will be evaluated. One of them, which would be suitable for the Euro-Roal, will be selected. Figure 1. The alternatives in a multi-criteria model Table 7 shows a formed multi-criteria model consisting of ten alternatives and seven criteria. FUCOM method in group decision-making: selection of forklift in a warehouse 61 Table 7. Initial decision-making matrix Alternatives CRITERIA C1 C2 C3 C4 C5 C6 C7 Forklift 1 7.950 10 5012 4000 5400 5 7.67 Forklift 2 12.900 10 7140 3000 3500 7 7.67 Forklift 3 17.800 9 6500 5000 4500 7 5 Forklift 4 19.300 19 4312 3000 6000 3 3.67 Forklift 5 10.870 18 12000 3000 4000 5 3 Forklift 6 30.400 7 4800 4000 4000 7.67 9 Forklift 7 8.093 25 12000 4000 5900 3 5 Forklift 8 29.800 11 3720 3000 5100 9 9 Forklift 9 13.750 17 15350 4500 4800 3 5 Forklift 10 18.297 13 6122 3000 4000 5 7 min min min max max max max 7.950 7 3720 5000 6000 5 7 The criteria that prefer minimal values are normalized by applying the following procedure: 11 21 31 41 51 10 1 7950 7950 7950 7950 1; 0.616; 0.446; 0.411; 7950 12900 17800 19300 7950 7950 0.731 . . . 0.434; 10870 18297 x x x x x x              The criteria that prefer maximum values are normalized by applying the following procedure: 14 24 34 44 54 10 4 4000 3000 5000 3000 0.80; 0.60; 1.00; 0.60; 5000 5000 5000 5000 3000 3000 0.60; . . . 0.60; 5000 5000 x x x x x x              Table 8. Normalized matrix Alternatives CRITERIA C1 C2 C3 C4 C5 C6 C7 Forklift 1 1.000 0.700 0.742 0.800 0.900 0.556 0.852 Forklift 2 0.616 0.700 0.521 0.600 0.583 0.778 0.852 Forklift 3 0.447 0.778 0.572 1.000 0.750 0.778 0.556 Forklift 4 0.412 0.368 0.863 0.600 1.000 0.333 0.408 Forklift 5 0.731 0.389 0.310 0.600 0.667 0.556 0.333 Forklift 6 0.262 1.000 0.775 0.800 0.667 0.852 1.000 Forklift 7 0.982 0.280 0.310 0.800 0.983 0.333 0.556 Forklift 8 0.267 0.636 1.000 0.600 0.850 1.000 1.000 Forklift 9 0.578 0.412 0.242 0.900 0.800 0.333 0.556 Forklift 10 0.434 0.538 0.608 0.600 0.667 0.556 0.778 W 0.090 0.129 0.409 0.133 0.112 0.057 0.070 Weighting the normalized matrix, so that the previously obtained matrix needs to be multiplied by the weight values of criteria: Fazlollahtabar et al./Decis. Mak. Appl. Manag. Eng. 2 (1) (2018) 49-65 62 11 21 10 1 0.090 1.000 0.090; 0.090 0.616 0.055 . . . 0.090 0.434 0.039x x x           In Table 9, after obtaining the values vij, the matrix is weighted, so that obtained values are multiplied by the values of weight coefficients. Table 9. Weighted normalized matrix 1 0.090 0.090 0.304 0.106 0.101 0.032 0.060 0.783Q         Determining a weighted product model using the following equation:               0.090 0.129 0.409 0.133 0.112 0.557 1 0.070 1.000 0.700 0.742 0.800 0.900 0.556 0.852 0.776 p         Determining the relative values of alternatives Ai :  1 0.5 0.783 1 0.5 0.782 0.779A       Ranking the alternatives. The highest value of alternatives shows the best-ranked one, while the smallest value refers to the worst alternative. Table 10 presents the results of ranking of forklifts based on the previous calculation. Table 10. Results and ranking the forklifts P A Rank Forklift 1 0.776 0.779 2 Forklift 2 0.600 0.604 6 Forklift 3 0.656 0.666 4 Forklift 4 0.630 0.653 5 Forklift 5 0.426 0.439 10 Forklift 6 0.734 0.752 3 Forklift 7 0.458 0.492 8 Forklift 8 0.768 0.793 1 Forklift 9 0.412 0.442 9 Forklift 10 0.593 0.595 7 Determining the relative weights of criteria was performed by the FUCOM method, while the ranking was performed using the WASPAS method. Based on the results of Alternatives CRITERIA C1 C2 C3 C4 C5 C6 C7 Forklift 1 0.090 0.090 0.304 0.106 0.101 0.032 0.060 Forklift 2 0.055 0.090 0.213 0.080 0.065 0.044 0.060 Forklift 3 0.040 0.100 0.234 0.133 0.084 0.044 0.039 Forklift 4 0.037 0.048 0.353 0.080 0.112 0.019 0.029 Forklift 5 0.066 0.050 0.127 0.080 0.075 0.032 0.023 Forklift 6 0.024 0.129 0.317 0.106 0.075 0.049 0.070 Forklift 7 0.088 0.036 0.127 0.106 0.110 0.019 0.039 Forklift 8 0.024 0.082 0.409 0.080 0.095 0.057 0.070 Forklift 9 0.052 0.053 0.099 0.120 0.090 0.019 0.039 Forklift 10 0.039 0.069 0.249 0.080 0.075 0.032 0.054 FUCOM method in group decision-making: selection of forklift in a warehouse 63 the applied model, a solution that meets the current needs of the Euro-Roal company has been found, which is Alternative 8, i.e. the BAUMANN EHX 30/14/51 forklift 5. Sensitivity analysis and discussion A logical sequence in most processes of multi-criteria decision-making is sensitivity analysis. For the sensitivity analysis of this model, the results of the SAW method (MacCrimon, 1968), the WASPAS method and the ARAS method (Zavadskas and Turskis, 2010) were compared. Table 11 and Figure 2 show the results and ranking the forklifts according to SAW, WASPAS and ARAS methods. Table 11. The results of sensitivity analysis according to SAW, WASPAS and ARAS methods SAW WASPAS ARAS A1 0.782 2 0.779 2 0.779 2 A2 0.608 6 0.604 6 0.607 6 A3 0.675 5 0.666 4 0.666 5 A4 0.677 4 0.653 5 0.671 4 A5 0.452 10 0.439 10 0.445 10 A6 0.769 3 0.752 3 0.768 3 A7 0.526 8 0.492 8 0.508 8 A8 0.817 1 0.793 1 0.817 1 A9 0.471 9 0.442 9 0.453 9 A10 0.598 7 0.595 7 0.594 7 Alternative 1 according to SAW, WASPAS and ARAS has the same rank (2). Alternative 2 according to SAW, WASPAS and ARAS has the same rank (6). Alternative 3 according to the SAW and ARAS methods is ranked fifth, whereas according to the WASPAS method, it is positioned fourth. Alternative 4 according to the SAW and ARAS methods is ranked fourth, whereas according to the WASPAS method, the fifth position is taken. Alternative 5 according to SAW, WASPAS and ARAS has the same rank (10). Alternative 6 according to SAW, WASPAS and ARAS has the same rank (3). Alternative 7 according to SAW, WASPAS and ARAS has the same rank (8). Alternative 8 is the best solution according to all methods. Alternative 9 according to SAW, WASPAS and ARAS has the same rank (9). Alternative 10 according to SAW, WASPAS and ARAS has the same rank (7). Fazlollahtabar et al./Decis. Mak. Appl. Manag. Eng. 2 (1) (2018) 49-65 64 Figure 2. Sensitivity analysis 6. Conclusion In this paper, a selection of transport and handling means was carried out in a warehouse system applying a combined FUCOM-WASPAS model. FUCOM was implemented throughout a group decision-making process where an expert team was formed to evaluate the significance of the criteria. 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