FACTA UNIVERSITATIS
Series: Mechanical Engineering Vol. 19, No 3, Special Issue, 2021, pp. 537 - 553

https://doi.org/10.22190/FUME210416052M

Original scientific paper

AN INTEGRATED DECISION-MAKING MODEL FOR

EFFICIENCY ANALYSIS OF THE FORKLIFTS IN

WAREHOUSING SYSTEMS

Eldina Mahmutagić1, Željko Stević1, Zdravko Nunić1,

Prasenjit Chatterjee2, Ilija Tanackov3

1University of East Sarajevo, Faculty of Transport and Traffic Engineering,

Bosnia and Herzegovina
2Department of Mechanical Engineering, MCKV Institute of Engineering, India

3University of Novi Sad, Faculty of Technical Sciences, Serbia

Abstract. In the logistics world, special attention should be given to warehousing

systems, cost rationalization, and improvement of all the factors that affect efficiency

and contribute to smooth functioning of logistics subsystems. In real time industrial

practice, the issue of evaluating and selecting the most appropriate forklift involves a

complex decision-making problem that should be formulated through an efficient

analytical model. The forklifts efficiency plays a very important role in the company.

The forklifts are being used on a daily basis and no logistical processes could be done

without them. Therefore, it has been decided to determine their efficiency, which will

contribute to the optimization of the process in this logistics subsystem. This study puts

forward an integrated forklift selection model using Data Envelopment Analysis (DEA),

Full Consistency Method (FUCOM) and Measurement Alternatives and Ranking

According to the Compromise Solution (MARCOS) methods. Five input parameters

(regular servicing costs, fuel costs, exceptional servicing costs, total number of all

minor accidents and damage caused by forklifts) and one output parameter (number of

operating hours) were first identified to assess efficiency of eight forklifts in a

warehousing system of the Natron-Hayat company using the DEA model. This step

allows sorting of efficient forklifts which are subsequently evaluated and ranked using

FUCOM and MARCOS methods. A sensitivity analysis is also performed in order to

check reliability and accuracy of the results. The findings of this research clearly show

that the proposed decision-making model can significantly contribute to all spheres of

business applications.

Key Words: DEA, FUCOM, MARCOS, Warehouse, Forklifts

Received April 16, 2021 / Accepted June 28, 2021

Corresponding author: Eldina Mahmutagić

University of East Sarajevo, Faculty of Transport and Traffic Engineering, Vojvode Mišića 52, 74000 Doboj,
Bosnia and Herzegovina

E-mail: mahmutagiceldina24@gmail.com

538 E. MAHMUTAGIĆ, Ž. STEVIĆ, Z. NUNIĆ, P. CHATTERJEE, I. TANACKOV

1. INTRODUCTION

The warehouse, in addition to being one of the basic subsystems of logistics, is an

important part in every organization for which it deserves special attention in terms of

monitoring and analyzing its associated processes and activities. When planning, building

and using any warehouse, the greatest attention is paid to size of the warehouse, layout,

and training of employees who manage the warehousing system. On the other hand, enough

attention is generally not given to selecting the most appropriate forklift which is one of the

most important items that can greatly affect the entire warehousing system, optimization of

vehicles’ waiting for loading and unloading, efficiency and overall effectiveness of the entire

organization. Considering that the Natron-Hayat company is one of the leading ones in the

region of Bosnia and Herzegovina, optimization of parameters in the warehousing system

can bring superior results which finally lead to business success. There are currently eight

forklifts in the warehouse of the considered company and it is necessary to analyze efficiency

of these forklifts in order to justify those procurement investments that will contribute to the

business success of the company. Data Envelopment Analysis (DEA), which is a linear

programming-based method, is here adopted in order to analyze efficiency of forklifts which

are currently operating at the considered warehouse. DEA is primarily used to determine

relative efficiencies of decision-making units (DMUs) or alternatives. Major reasons for a

rapid increase in the use of the DEA method lie in the fact that this model is interdisciplinary

in applications; it is also suitable in the cases where other approaches do not provide

satisfactory results due to their complex or unknown nature of the links between multiple

inputs and outputs [1]. The main benefit of this method is its competence to quarter a variety

of input-output combinations. Another advantage of the DEA method is that there is no

requirement of clearly stipulating mathematical form for the considered functions which

enables it to be used for any input-output measurement. Based on the collected data for all

the forklifts that serve in the warehousing system of the case company, the DEA method

has identified the forklifts which are not efficient enough, and they are excluded from

further considerations. Based on the DEA-based results, two popular multi-criteria decision-

making (MCDM) methods, called Full Consistency Method (FUCOM) and Measurement

Alternatives and Ranking According to the Compromise Solution (MARCOS) are further

applied to derivation of a complete ranking of the efficient forklifts in order to identify

the most efficient forklift alternative. The FUCOM method is used here to obtain criteria

weights, whereas the rankings of forklift alternatives are derived using the MARCOS

method. The contribution of this paper is reflected in the fact that based on the DEA-

MCDM model applied to the warehousing system and handling equipment; it can

significantly improve the decision-making process, reduce costs and increase work

efficiency. Based on the recommendations of the proposed model, procurement of

handling and transportation equipment can be planned efficiently. The contribution of

this research in scientific terms can be observed through the original integration of DEA

and two MCDM methods for handling efficiency estimation problems when solo

application of the DEA method is unable to provide for a complete ranking order of

alternatives in multi-criteria environment. There are different places and ways of

determining efficiency in the company. However, due to many parameters, the DEA

method proved to be a good method, whose results will show efficient as well as less

efficient forklifts. The results of the DEA method can help managers with the selection

and purchasing of forklifts in the future. However, after the DEA method, it has been

An Integrated Decision-Making Model for Efficiency Analysis of Forklifts in Warehousing Systems 539

decided to use multi-criteria methods to obtain the best and most realistic results. The

main reason for the combination and development of the DEA-FUCOM-MARCOS

model is that any company that faces decision-making challenges can get comprehensive

and as realistic results as possible through this model.

In addition to introductory considerations, the paper is structured through other five

sections. Section 2 presents an overview of the literature used throughout the research.

Section 3 presents the methods used to select the most efficient forklift in the warehousing

system, namely DEA, FUCOM and MARCOS methods. Section 4 presents application of

DEA method, while Section 5 provides selection of the most efficient forklift using

FUCOM and MARCOS methods. Section 6 refers to sensitivity analysis of the obtained

results and Section 7 concludes the paper.

2. LITERATURE REVIEW

A large number of modern studies in which they are used prove the application of DEA

and MCDM methods in logistics and transport. The Charnes, Cooper and Rhodes (CCR)

model is considered as the most primary and vastly applied DEA model. The CCR model

was first conceptualized and formulated by Charnes, Cooper and Rhodes in 1978 [2]. The

basic theme of this model actually originated from earlier work on the basic theory of

productivity measurement using single output and single input ratio concept. Applications of

the DEA method are now found in many areas, and DEA has become a central technique in

productivity and efficiency analyses for comparing organizations, enterprises, regions and

countries. The DEA method has also made its contribution to logistics [3, 4, 5], warehousing

[6] and transportation [7] as its subsystems and supply chains [8, 9].

The paper [4] presents an overview of DEA models for measuring the efficiency of

supply chains. The process of measuring efficiency in production companies differs greatly

from the process of measuring efficiency in service companies. It was concluded that in order

to successfully measure efficiency in logistics, it is necessary to consider a large number of

inputs and outputs that are heterogeneous (financial, technical, environmental, energy, social,

etc.) and are expressed in different units of measurement. In this sense, it is possible to

measure energy, environmental, cost and other types of efficiency in logistics. In the paper

[10], the DEA model was applied in order to analyze the efficiency of the bus subsystem

of public passenger transport in Belgrade, on a sample of five small, three medium, and

two large companies. The subject of the research in [11] is the analysis of the efficiency

of airlines in the European Union in 2012, where the application of the DEA model

assessed the individual efficiency of each airline; besides, it also identified inefficient

elements of business that could be improved. The paper [12] deals with the analysis of

the efficiency of intermodal terminals with the aim of identifying terminals that would

serve as models for the improvement of existing and development of new terminals. The

DEA method was used to determine the efficiency of the terminals, and the research was

conducted on a sample of 35 real land trimodal terminals in Europe. The results of the

research showed that for the defined sample, the parameters storage capacity and length

of railway tracks had the greatest influence on achieving the efficiency of the terminal.

In addition to assessing efficiency, this method is also used to define degree of safety,

i.e. to evaluate risk in transportation and traffic systems [13, 14]. The DEA method has

also found application in military organization [15, 16, 17]. This is shown in Ref. [15]

540 E. MAHMUTAGIĆ, Ž. STEVIĆ, Z. NUNIĆ, P. CHATTERJEE, I. TANACKOV

presenting the application of the DEA and SFA methods for evaluating the efficiency of

the work of the selected ten military transport units and 173 military motor vehicles used

in cargo transportation tasks for the needs of supply and special needs of the army,

individually and within six defined classes. We also see the application of the DEA

method and the determination of the efficiency of the Liaoning port logistics [16]. This

paper used DEA to analyze the logistics efficiency of four major ports in the Liaoning

Province. Then based on the results of DEA analysis, the relationship between logistics

efficiency and its influencing factors is studied. The results show that the overall pure

technical efficiency of port logistics in the Liaoning Province has been maintained at a

high level and the state is stable. Also, there is an increasing number of papers related to

solving logistics problems using MCDM methods. This research [17] created the hybrid

BWM-COPRAS model for the assessment of off-road vehicles.

3. METHOD

In this section, Fig. 1 presents the methodology which includes application of the

DEA method for assessing relative efficiencies of the alternative of forklifts and the

FUCOM and MARCOS methods application to identifying the most efficient forklift.

Fig. 1 Research methodology

The research methodology in this paper consists of four phases. The first phase refers

to the analysis and collection of necessary data on the operation of forklifts in the

warehousing system. In the second phase, the DEA method is applied which is presented

through three steps, namely: defining input and output parameters, applying CCR model

and results of DEA method. After obtaining results of the DEA CCR model, the third

An Integrated Decision-Making Model for Efficiency Analysis of Forklifts in Warehousing Systems 541

phase starts in which the FUCOM and MARCOS methods are applied to selecting the

most efficient forklift. The last step of the third phase is a sensitivity analysis of the

obtained results. Finally, at the end of the paper, the results of all the applied steps aim at

determining the most efficient forklift.

3.1. DEA method

This section presents two DEA CCR models [2] that have been applied to obtaining

the values of alternatives, i.e. DMUs according to an input-oriented model (min) and an

output-oriented model (max). The DEA CCR input oriented model (min) is as follows:

𝐷𝐸𝐴𝑖𝑛𝑝𝑢𝑡 = min ∑ 𝑤𝑖
𝑚
𝑖=1 𝑥𝑖−𝑖𝑛𝑝𝑢𝑡

𝑠𝑡:
∑ 𝑤𝑖

𝑚
𝑖=1 𝑥𝑖𝑗 − ∑ 𝑤𝑖

𝑚+𝑠
𝑖=𝑚+1 𝑦𝑖𝑗 ≥ 0, 𝑗 = 1, … , 𝑛

∑ 𝑤𝑖
𝑚+𝑠
𝑖=𝑚+1 𝑦𝑖−𝑜𝑢𝑡𝑝𝑢𝑡 = 1

𝑤𝑖 ≥ 0, 𝑖 = 1, . . . , 𝑚 + 𝑠

(1)

DMUs consist of m input parameters for each alternative xij, while s represents the

output parameters for each alternative yij, taking into account weights of the parameters

denoted by wi,n represents total number of DMUs. The DEA CCR output oriented model

(max) is as follows:

𝐷𝐸𝐴𝑜𝑢𝑡𝑝𝑢𝑡 = max ∑ 𝑤𝑖
𝑚+𝑠
𝑖=𝑚+1 𝑦𝑖−𝑜𝑢𝑡𝑝𝑢𝑡

𝑠𝑡:
−(∑ 𝑤𝑖

𝑚
𝑖=1 𝑥𝑖𝑗 ) + ∑ 𝑤𝑖

𝑚+𝑠
𝑖=𝑚+1 𝑦𝑖𝑗 ≤ 0, 𝑗 = 1, . . . , 𝑛

∑ 𝑤𝑖
𝑚
𝑖=1 𝑥𝑖−𝑖𝑛𝑝𝑢𝑡 = 1

𝑤𝑖 ≥ 0, 𝑖 = 1, . . . , 𝑚 + 𝑠

(2)

3.2. FUCOM method

FUCOM method was developed by Pamučar, Stević and Sremac [18] to determine the

criteria weights in mutually conflicting MCDM environment. FUCOM provides the

possibility to perform model validation by calculating error size for the obtained weight

vectors by determining degree of consistency [18-21]. Fig. 2 presents FUCOM algorithm

including steps of this method.

3.3. MARCOS method

The MARCOS method (Fig. 3) is based on defining relations between an alternative

and reference values (ideal and anti-ideal alternatives). Based on these defined relations,

utility functions of the alternatives are determined and a compromise ranking is made in

relation to ideal and anti-ideal solutions. Decision preferences are defined based on utility

functions. Utility functions represent position of an alternative in relation to an ideal and

anti-ideal solution. The best alternative is the one which is closest to an ideal as well as

furthest from an anti-ideal reference point. The MARCOS method is implemented through

the following simple steps [22-24] presented in Fig. 3.

542 E. MAHMUTAGIĆ, Ž. STEVIĆ, Z. NUNIĆ, P. CHATTERJEE, I. TANACKOV

Fig. 2 Overview of FUCOM method and its steps

Fig. 3 Algorithm of the MARCOS method

Algorithm: FUCOM
Input: Expert pairwise comparison of criteria
Output: Optimal values of the weight coefficients of criteria/sub-criteria

Step 1: Expert ranking of criteria/sub-criteria.

Step 2: Determining the vectors of the comparative significance of evaluation criteria.
Step 3: Defining the restrictions of a non-linear optimization model.

Restriction 1: The ratio of the weight coefficients of criteria is equal to the comparative

significance among the observed criteria, i.e.
1 / ( 1)k k k k

w w 
+ +
= .

Restriction 2: The values of weight coefficients should satisfy the condition of
mathematical transitivity, i.e.

/ ( 1) ( 1) / ( 2) / ( 2)

k k k k k k
  

+ + + +
 = .

Step 4: Defining a model for determining the final values of the weight coefficients of evaluation

criteria:

( )

/ ( 1)

( 1)

( )

/ ( 1) ( 1) / ( 2)

( 2)

min

. .

j k

k k

j k

k k k k

j k

s t

w
j

w j



 

  

+ + +

−  

−   

 



Step 5: Calculating the final values of evaluation criteria/sub-criteria ( )1 2, ,...,
T

n
w w w .

Steps of MARCOS model

II - Creating of an extended initial matrix

I - Creating an initial decision-making matrix

IV - Computation of the weighted matrix

VI - Calculation of the utility degree of alternatives

III - Creating a normalized matrix

V - Calculation of matrix

VII - Calculation of matrix Ti

VIII - . Determination of utility functions in relation

to the ideal and anti-ideal

IX - Determination of the utility function of alternatives

X - Ranking the alternatives

An Integrated Decision-Making Model for Efficiency Analysis of Forklifts in Warehousing Systems 543

4. APPLICATION OF THE DEA METHOD FOR EVALUATION OF FORKLIFT EFFICIENCY

Natron-Hayat Ltd. is a highly recognized and reputable European company in the

field of manufacturing paper and paper packaging applications. In this company, the

method of storage is decentralized, and includes four warehouses for storage of finished

products (warehouse of Paper machine PM4, warehouse of Paper machines PM3-PM1,

warehouse of production plant Paper Products and customs warehouse). It is clear that the

main handling equipment in the warehouses is a forklift, so it is the reason for conducting

this research in order to determine how efficiency of a forklift affects the entire

warehousing process. The collected data from the analysis of forklift efficiency and

application of the integrated DEA-MCDM model cover one calendar year (2019). Most

of the data were recorded in previous years; however, special attention was paid to some

parameters for getting precise and comprehensive data for the considered case study.

The data that form the basis for the DEA method in this paper are presented in Fig. 4.

Fig. 4 Input and output parameters required to determine efficiency of forklifts

In order to determine efficiencies of the considered forklifts, data were collected for all

forklifts, currently in operation. Table 1 shows input and output parameters for all eight

forklifts. Input parameters for each of the eight forklifts are difficult to be determined, but

the most important input parameters on the basis of which the efficiency can be determined

using the DEA method are: regular servicing costs, fuel costs, exceptional servicing costs,

and the total number of minor accidents and damage caused by the forklift. Output

parameter, i.e. the result of forklift operation is the number of operating hours for each

forklift individually.

544 E. MAHMUTAGIĆ, Ž. STEVIĆ, Z. NUNIĆ, P. CHATTERJEE, I. TANACKOV

Table 1 Input and output parameters for all forklifts

Parameters

Regular

servicing

costs (BAM)

Fuel costs

(BAM)

Exceptional

servicing costs

(BAM)

The total number of all

minor accidents and

damage caused by the

forklift

The number

of operating

hours (h)

Forklift 1 870 483 562.5 12 864

Forklift 2 1820 5622 562.5 36 4320

Forklift 3 2534 14806 2,222.11 36 5184

Forklift 4 3503 13706 5,094.27 36 5184

Forklift 5 1500 6097 1,363.85 36 2400

Forklift 6 1890 7593 2,887.89 60 3240

Forklift 7 1800 4046 562.5 60 2640

Forklift 8 2700 8856 562.5 36 3840

Table 1 shows all input as well as output parameters for forklifts currently in operation.

Each of these forklifts caused certain costs as stated, and also a certain number of minor

accidents and damage. The number of operating hours is an output parameter that is very

important for determining efficiency, and from this table, we can see that forklifts 3 and 4

have the highest number of operating hours, which does not mean that they are the most

efficient as there are other forklifts as well with lower costs, fewer accidents and less damage.

The input and output DEA models are given below by Eqs. (1) and (2).

By solving the DEA models for all the considered forklifts, the obtained values are

shown in Table 2. This table also presents the final DEA values, obtained by comparing

the two input and output oriented DEA models. The DEA final values are being derived

from: DEA-finaln = DEA-outputn / DEA-inputn.

Table 2 Results of DEA method

DEA-input DEA-output DEA-final

Forklift 1 1.000 1.000 1.000

Forklift 2 1.000 1.000 1.000

Forklift 3 1.000 1.000 1.000

Forklift 4 1.000 1.000 1.000

Forklift 5 1.483 0.674 0.454

Forklift 6 1.384 0.722 0.521

Forklift 7 1.234 0.809 0.655

Forklift 8 1.125 0.888 0.789

From Table 2, it is clear that forklifts 5, 6, 7 and 8 have values less than 1. They are

not considered further into the model since they are neither efficient enough nor do they

contribute to the Natron-Hayat company like other forklifts. After obtaining the results of

the DEA method, it is observed that the first four forklifts have efficiency values of 1,

indicating them as efficient alternatives; the most efficient of these four forklifts will now

be selected in the next phase using FUCOM-MARCOS methods.

An Integrated Decision-Making Model for Efficiency Analysis of Forklifts in Warehousing Systems 545

5. RANKING EFFICIENT FORKLIFTS BY APPLYING THE FUCOM AND MARCOS METHODS

The DEA model results indicate that the first four forklifts are efficient alternatives,

fulfilling their tasks satisfactorily. This section of the paper presents results of MCDM

methods as applied for these four forklifts. Criteria weights are determined by the

FUCOM method, while the MARCOS method is used to determine the most efficient

forklift, i.e. ranking of these four forklifts is derived according to their efficiency.

Calculation of criteria weights by the FUCOM method is performed as follows.

The first step is an activity in which the criteria are ranked as follows:

C2>C5>C1>C4>C3

After ranking the criteria, they are compared, so the values of comparative priorities

are defined according to the second step, which can be seen in Table 3.

Table 3 Overview of comparative priorities for comparing criteria

Criterion name (in accordance with ranking) C2 C5 C1 C4 C3

Comparison of criteria 1 1.15 1.3 1.6 2.1

It is then necessary to apply the third, fourth and fifth steps of the FUCOM method in

order to obtain final values of criteria weights. The final results of the FUCOM method,

i.e. significance of the criteria on the basis of which final evaluation of the forklift

efficiency is performed, are shown in Fig. 5.

Fig. 5 Criteria weights as given by FUCOM method

According to the results of the FUCOM method, as shown in Fig. 5, we can see that out

of five criteria, the criterion related to fuel costs is the most significant (C2). It is then

subsequently followed by criterion C5 (number of operating hours) and C1 (regular servicing

costs). The last two and the least significant criteria are those relating to the total number of all

minor accidents and damage caused by the forklift (C4) and exceptional servicing costs (C3).

546 E. MAHMUTAGIĆ, Ž. STEVIĆ, Z. NUNIĆ, P. CHATTERJEE, I. TANACKOV

After determining the criteria weights, the MARCOS method is applied in order to

derive a complete ranking order of the four forklifts. Table 4 presents an extended initial

matrix formed according to the second step of the MARCOS method. Essence of forming

this matrix is to consider the initial decision matrix while taking into account orientation

of the criteria themselves, i.e. the need to minimize or maximize the criteria. It should be

emphasized that the first four criteria: regular servicing costs, fuel costs, exceptional

servicing costs and the total number of all minor accidents and damage caused by the

forklift are minimized, and the total number of operating hours needs to be maximized.

Accordingly, for the first four criteria, the ideal solution that enters the extended initial

decision matrix is the minimum value, while for the fifth criterion, the highest value is

the ideal solution. When forming an anti-ideal solution, which is also an integral part of

the aforementioned matrix, opposite values are taken.

Table 4 Extended initial matrix

C1 C2 C3 C4 C5

AII 3503 14806 5094.3 36.0 864

A1 870 483 562.5 12 864

A2 1820 5622 562.5 36 4320

A3 2534 14806 2222.11 36 5184

A4 3503 13706 5094.27 36 5184

AI 870 483 562.50 12.00 5184

max/min min min min min max

Normalization of the extended initial matrix is performed according to step 3, and

values of the normalized matrix can be seen in Table 5:

𝑛𝑖𝑗 =
𝑥𝑎𝑖
𝑥𝑖𝑗

; 𝑥21 =
870

1820
= 0.478

𝑛𝑖𝑗 =
𝑥𝑖𝑗

𝑥𝑎𝑖
; 𝑛15 =

864

5184
= 0.167

Table 5 Normalized matrix

C1 C2 C3 C4 C5

AII 0.248 0.033 0.110 0.333 0.167

A1 1.000 1.000 1.000 1.000 0.167

A2 0.478 0.086 1.000 0.333 0.833

A3 0.343 0.033 0.253 0.333 1.000

A4 0.248 0.035 0.110 0.333 1.000

AI 1.000 1.000 1.000 1.000 1.000

Weighted normalized matrix is then obtained according to the fourth step of the

MARCOS method by multiplying the values from the normalized matrix by weight

coefficients of the criteria, which were previously obtained using the FUCOM method, as

shown in Table 6.

An Integrated Decision-Making Model for Efficiency Analysis of Forklifts in Warehousing Systems 547

𝑣𝑖𝑗 = 𝑛𝑖𝑗 × 𝑤𝑗 ; 𝑣11 = 1.000 × 0.206 = 0.206

Table 6 Weighted normalized matrix

C1 C2 C3 C4 C5

AII 0.051 0.009 0.014 0.056 0.039

A1 0.206 0.267 0.127 0.167 0.039

A2 0.098 0.023 0.127 0.056 0.194

A3 0.071 0.009 0.032 0.056 0.233

A4 0.051 0.009 0.014 0.056 0.233

AI 0.206 0.267 0.127 0.167 0.233

Calculation of utility degree of Ki alternative: according to step 5, utility degrees of

the alternatives in relation to an anti-ideal and ideal solution are calculated as follows.

𝐾𝐼
− =

𝑆𝑖
𝑆𝑎𝑎𝑖

=
0.806

0.168
= 4.790, 𝐾𝐼

+ =
𝑆𝑖
𝑆𝑎𝑖

=
0.806

1
= 0.806

where expression Si(i=1,2,…,m) represents the sum of the weighted matrix elements.

𝑆𝑖 = ∑ 𝑣𝑖𝑗

𝑛

𝑖=1

= 𝑆1 = 0.206 + 0.267 + 0.127 + 0.167 + 0.039 = 0.806

Also, we have that

𝑆𝑎𝑎𝑖 = 0.051 + 0.009 + 0.014 + 0.056 + 0.039 = 0.168

Determining utility function of alternative f(Ki). The utility function represents a

compromise of the observed alternative in relation to an ideal and anti-ideal solution.

Utility functions of alternatives are defined according to the sixth step:

𝑓(𝐾𝑖 ) =
𝐾𝑖

+ + 𝐾𝑖
−

1 +
1−𝑓(𝐾𝑖

𝑓(𝐾𝑖
+)

+
1−𝑓(𝐾𝑖

−)

𝑓(𝐾𝐼
−)

=
0.806 + 4.790

1 +
1−0.856

0.856
+

1−0.144

0.144

= 0.787

where f (Ki
-) represents a utility function in relation to an anti-ideal solution, while f (Ki

represents a utility function in relation to an ideal solution.

The utility functions in relation to an ideal and anti-ideal solution are determined by

applying step 8 as follows

𝑓(𝐾𝐼
−) =

𝐾𝑖
+

𝐾𝑖
+ + 𝐾𝑖

− =
0.806

0.806 + 4.790
= 0.144

𝑓(𝐾𝐼
+) =

𝐾𝑖
−

𝐾𝑖
+ + 𝐾𝑖

− =
4.790

0.806 + 4.790
= 0.856

The ninth and tenth steps represent ranking of alternatives on the basis of utility

functions. It is always preferable when an alternative has the highest possible value of

utility function.

548 E. MAHMUTAGIĆ, Ž. STEVIĆ, Z. NUNIĆ, P. CHATTERJEE, I. TANACKOV

Table 7 Results of MARCOS method

Si Ki- Ki+ fK- fK+ Ki Rank

A1 0.806 4.790 0.806 0.144 0.856 0.787 1

A2 0.498 2.959 0.498 0.144 0.856 0.486 2

A3 0.400 2.375 0.400 0.144 0.856 0.390 3

A4 0.363 2.155 0.363 0.144 0.856 0.354 4

Results of the MARCOS method of Table 7 show that the most efficient forklift is

A1, i.e. alternative 1. From Table 7, it is observed that utility function of forklift A1 is

significantly higher than the obtained values of other forklifts. Forklift A2 is less efficient

as compared to the forklift A1, and the next position in terms of efficiency is occupied by

forklift A3. The least efficient among these four forklifts is forklift A4, i.e. alternative 4

due to its lowest utility function value.

6. SENSITIVITY ANALYSIS

In order to test accuracy of the obtained results, a sensitivity analysis has been

performed. In this paper, the sensitivity analysis has been done in two parts. The first part

involves changing criteria weights to determine how the criteria weights affect the

results. The second part is a comparison of the obtained results with those of seven other

well established MCDM methods.

6.1. Changes in weight values of criteria

In this part of the sensitivity analysis, impact of changes in criteria weights is

analyzed. Criteria weights are changed in a range of 15-90%, starting from the most

significant criterion C2, followed by criteria C5, C1, C4 to criterion C3. By applying Eq.

(3), a total of 30 scenarios are formed.

𝑊𝑛𝛽 = (1 − 𝑊𝑛𝛼 )
𝑊𝛽

(1−𝑊𝑛)
(3)

In scenarios S1-S6, weight of the most significant criterion C2 was changed, while in

scenarios S7-S12, weight of criterion C5 was changed, followed by subsequent weight

changes in criterion C1 for scenarios S13-S18, criterion C4 for scenarios S19-S24 and

criterion C3 for scenarios S25-S30, respectively.Wnβ represents a new value of criteria C1,

C3, C4, C5,Wnα represents a reduced value of criterion C2, Wβ is an original value of the

observed criterion and Wn represents an original value of the criterion whose value is

reduced – C2 (for the first group of scenarios,S1-S6). Wnβ represents a new value of criteria

C1, C2, C3, C4, Wnα represents a reduced value of criterion C5, Wβ is an original value of

the observed criterion and Wn represents an original value of the criterion whose value is

reduced –C5 (for the second group of scenarios,S7-S12).Wnβ represents a new value of

criteria C2, C3, C4, C5, Wnα represents a reduced value of criterion C1, Wβ is an original

value of the observed criterion and Wn represents an original value of the criterion whose

value is reduced –C1 (for the third group of scenarios,S13-S18). Wnβ represents a new value

of criteriaC1, C2, C3, C5, Wnα represents a reduced value of criterion C4, Wβ is an original

value of the observed criterion and Wn represents an original value of the criterion whose

An Integrated Decision-Making Model for Efficiency Analysis of Forklifts in Warehousing Systems 549

value is reduced - C4 (for the fourth group of scenarios, S19-S24). Wnβ represents a new

value of criteria C1, C2, C4, C5, Wnα represents a reduced value of criterion C3, Wβ is an

original value of the observed criterion and Wn represents an original value of the

criterion whose value is reduced - C3 (for the fifth group of scenarios, S25-S30).

All simulated values of the criteria through the newly formed 30 scenarios are

presented in Table 8.

Table 8 Simulated values of criteria through newly formed 30 scenarios

W1 W2 W3 W4 W5 W1 W2 W3 W4 W5

S1 0.217 0.227 0.134 0.176 0.245 S16 0.082 0.309 0.147 0.193 0.269

S2 0.228 0.187 0.141 0.185 0.258 S17 0.051 0.319 0.152 0.200 0.278

S3 0.239 0.147 0.148 0.195 0.271 S18 0.021 0.330 0.157 0.206 0.287

S4 0.251 0.107 0.155 0.204 0.283 S19 0.212 0.275 0.131 0.142 0.240

S5 0.262 0.067 0.162 0.213 0.296 S20 0.218 0.283 0.135 0.117 0.247

S6 0.273 0.027 0.169 0.222 0.309 S21 0.224 0.292 0.139 0.092 0.253

S7 0.215 0.280 0.133 0.175 0.198 S22 0.230 0.300 0.143 0.067 0.260

S8 0.224 0.292 0.139 0.182 0.163 S23 0.237 0.308 0.146 0.042 0.267

S9 0.234 0.304 0.145 0.190 0.128 S24 0.243 0.316 0.150 0.017 0.274

S10 0.243 0.316 0.150 0.197 0.093 S25 0.210 0.273 0.108 0.171 0.238

S11 0.252 0.328 0.156 0.205 0.058 S26 0.215 0.279 0.089 0.174 0.243

S12 0.262 0.340 0.162 0.213 0.023 S27 0.219 0.285 0.070 0.178 0.248

S13 0.175 0.278 0.132 0.174 0.242 S28 0.224 0.291 0.051 0.182 0.253

S14 0.144 0.288 0.137 0.180 0.251 S29 0.228 0.297 0.032 0.185 0.258

S15 0.113 0.299 0.142 0.187 0.260 S30 0.233 0.302 0.013 0.189 0.263

Fig. 6 Results of the sensitivity analysis for new criterion values

Fig. 6 clearly shows that the initially obtained results do not change with changes in

criteria weights which is a clear indicator of invariability of the obtained results. Forklift

A1 remains the most efficient alternative, followed by forklifts A2, A3 and A4.

550 E. MAHMUTAGIĆ, Ž. STEVIĆ, Z. NUNIĆ, P. CHATTERJEE, I. TANACKOV

6.2. Comparative analysis

In this section, a comparative analysis is performed with seven other MCDM methods,

namely ARAS - additive ratio assessment [25], MABAC - Multi-Attributive Border

Approximation area Comparison [26, 27], SAW - Simple Additive Weighting method [28],

WASPAS - weighted aggregated sum product assessment [29], EDAS - evaluation based

on distance from average solution [30], CoCoSo - Combined Compromise Solution [31]

and TOPSIS - Technique for Order of Preference by Similarity to Ideal Solution [32].

Fig. 7 Results of comparative analysis with seven other MCDM methods

Based on the results of comparative analysis with seven other MCDM methods, we can

conclude that no changes are observed in terms of forklift ranking. Fig. 7 clearly shows that

in all the considered MCDM methods, forklift A1 retains its first position, i.e. it is the most

efficient forklift; with respect to efficiency, it is followed by forklifts A2, A3 and A4. Based

on the performed comparative analysis and the applied integrated DEA-FUCOM-MARCOS

model, it can be concluded that the proposed methodology is quite reliable, and any

changes in parameters do not affect stability of alternative rankings.

6.3. Changing the number of inputs and the creation of the PCA-DEA model

In this part of the sensitivity analysis, the number of inputs was changed, forming four

scenarios (S) in which one input was eliminated, starting from the first. Subsequently, the

Principal Component Analysis PCA-DEA [33] was applied with 85% of the information

retained. The results of this part of the sensitivity analysis are shown in Fig. 8.

The results shown in Fig. 8 show that if we eliminate the first input (regular servicing

costs) or third input (exceptional servicing costs), the results do not change, i. e. V1-V4

forklifts are efficient, while the others are not. In the second scenario, when we eliminate

the second input (fuel costs), the efficiency of forklifts V2-V4 does not change (1.000). In

contrast, the efficiency of the first forklift V1 changes drastically because it gets inefficient

and the lowest value. This means that the efficiency of the first forklift is strictly related to

the second input. In the fourth scenario, when the total number of all minor accidents and

An Integrated Decision-Making Model for Efficiency Analysis of Forklifts in Warehousing Systems 551

damage caused by the forklift is eliminated, the V1 and V2 forklifts are efficient, which is

the final rank by applying the integrated DEA-FUCOM-MARCOS model. Finally, by

applying the PCA-DEA model, the results tend to the second scenario.

Fig. 8 Results of the sensitivity analysis with PCA-DEA and a reduced number of inputs

7. CONCLUSIONS

This paper presents the way of dealing with determining the efficiency of handling

and transportation equipment in each company. Based on the efficiency analysis (DEA),

it has been determined which forklifts currently operating in this warehousing system are

efficient and which of them do not contribute to work to the extent they should. Based on

the data (regular servicing costs, fuel costs, exceptional servicing costs, total number of all

minor accidents and damage caused by the forklift, number of operating hours) for all eight

forklifts operating in the warehousing system of the Natron-Hayat company, it has been

determined that four out of eight forklifts are not efficient enough and do not contribute to

work in this company (A5-A8) like other forklifts. After that, using multi-criteria decision-

making methods, the ranking and selection of the most efficient forklift out of the remaining

four ones are carried out. After determining the weight coefficients of the criteria using the

FUCOM method, the MARCOS method is presented, step by step, and its final results.

Based on the results of the applied MARCOS method, it has been determined that

forklift A1 is currently the most efficient forklift serving in this system. Also, a sensitivity

analysis has been performed in order to determine the stability of the final results. After

changing the weight values of the criteria, it has been determined that these changes do not

affect the final result. Then a comparative analysis is carried out, i.e. testing the stability of the

results with seven other MCDM methods. After applying all these methods, we have come to

the conclusion that there are no changes in terms of determining the efficiency of forklifts,

forklift A1 is still the most efficient forklift, followed by forklifts A2, A3 and A4.

The contribution of this paper is evident in forming an original integrated model for

determining efficiency, which can be applied to other fields as well. Specifically in this

552 E. MAHMUTAGIĆ, Ž. STEVIĆ, Z. NUNIĆ, P. CHATTERJEE, I. TANACKOV

paper, the significance of the applied model is that the warehousing system managers are

provided with a quantified analysis based on which they can make further decisions in

order to increase the overall efficiency of warehousing systems of the company that is the

object of the research. By applying this model, it is possible to easily determine the efficiency

of both forklifts and other equipment, and pay more attention to identifying and monitoring

input and output parameters. Regarding the obtained results, it is necessary that the managers

in warehousing systems perform adequate monitoring of all activities done by forklifts, and to

rationalize all unnecessary movements and pointless operation of forklifts. The issues with

previous works in determining the efficiency are that only one of the above methods was

used, but their combination was not applied.

From all said above, we can conclude that the decentralized warehousing system of

the company is very complex, that there are great opportunities for savings and possibilities to

improve all activities and processes in it. This paper has shown that the DEA analysis can be

applied in this segment and that in combination with multi-criteria decision-making methods it

can provide significant results just as it can direct companies‘ business operations in the right

direction in terms of future plans. Future research could focus on ensuring that inefficient

forklifts are no longer in use, and that additional funds are invested in the forklifts which

contribute to a successful business. Also, this model can be applied to determine the

efficiency of other means of transport handling.

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