FUCOM METHOD IN GROUP DECISION-MAKING: SELECTION OF FORKLIFT IN A WAREHOUSE

. 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.


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 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 value of the attribute depends on the j th criterion and the i th 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 (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 ij a from the ideal ratios / ij ww (where i w and j w 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 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: (1) (2) ( ) ...
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 ( 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  .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 When solving real problems, decision-makers compare the ranked criteria based on internal knowledge, so they determine the comparative priority kk   based on subjective preferences.If the decision-maker thinks that the criterion of the  jk C  rank, then the comparative priority is 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 ( ) for all of the criteria ranked in Step 1 is obtained.Since the first-ranked criterion is compared with itself (its significance is 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) that the ratio of the weight coefficients is equal to the comparative priority among the observed criteria ( Step 2, i.e. that the following condition is met: (2) In addition to the condition (3), the final values of the weight coefficients should satisfy the condition of mathematical transitivity, i.e. that is obtained.Thus, yet another condition that the final values of the weight coefficients of the evaluation criteria need to meet is obtained, namely: Full consistency, i.e. minimum DFC (  ) is satisfied only if transitivity is fully respected, i.e. when the conditions of 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   12 , ,..., , 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.

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 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: Step 3. Weighting the normalized matrix, so that the previously obtained matrix needs to be multiplied by the weight values of criteria: Step 4. Summing all the values of the alternatives obtained (summing by rows): Step 5: Determining a weighted product model by applying the following equation: Step 6. Determining the relative values of alternatives Ai: The coefficient λ ranges from 0, 0.1, 0.2,….1.0 Step 7. Ranking the alternatives.The highest value of alternatives implies the bestranked one, while the smallest value refers to the worst alternative.

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.

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.

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.2017) is one of the most important stages in a decision-making process.
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 ( ) for all the criteria ranked in step 1 (Table 3).
Using the expression (5), we can define the final model for determining weight coefficients: 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  = 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.
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 the criteria ( ) for all the criteria ranked in step 1 (Table 4).
Using the expression (5), we can define the final model for determining weight coefficients.
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  = 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.
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 ( ) for all the criteria ranked in step 1 (Table 5).
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  = 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.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.

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.
In Table 9, after obtaining the values v ij , the matrix is weighted, so that obtained values are multiplied by the values of weight coefficients.
Determining a weighted product model using the following equation: 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.

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.Obtaining the final weight values of the criteria was achieved using a geometric mean.The research has been conducted in a company whose primary task is to trade and distribute aluminum profiles.The applied model allows for an objective consideration of input parameters that have an impact on making a final decision.Comparative analysis, which implies the application of two additional MCDM methods, presents the stability of originally obtained results if the model is generally observed throughout all possible variants.If individual positions are taken into account then the model shows the sensitivity to certain changes.Future research regarding this paper relates to the formation of a model for determining the efficiency of using the selected side-loading forklift.
the same significance as the criterion of the 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 determine the priorities of the criteria and that, based on the decision-maker's preferences, the following priorities of the criteria . The final values of the weight coefficients should satisfy the two conditions: of DFC (  ) are generated.

Figure 1 .
Figure 1.The alternatives in a multi-criteria model Table7shows a formed multi-criteria model consisting of ten alternatives and seven criteria.

Table 2 .
Comparison of criteria

Table 3 .
The significance of criteria

Table 4 .
The significance of criteria

Table 5 .
The significance of criteria 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: In addition to the condition (3), the final values of weight coefficients should meet the condition of mathematical transitivity, i.e. that:

Table 6 .
The criterion values for each decision-maker and values obtained by applying a geometric mean

Table 7 .
Initial decision-making matrix

Table 10 .
Results and ranking the forkliftsDetermining 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