Benchmarking the efficiency of distribution warehouses using a four-phase integrated PCA-DEA-improved fuzzy SWARA-CoCoSo model for sustainable distribution

2.1 Problem description

Measuring efficiency in logistics is a subject that has received considerable attention in the literature. Understanding and measuring warehouse efficiency is essential to optimizing logistics operations. There are various models and approaches for measuring logistics process efficiency in particular systems. However, the analysis of warehouse efficiency in trade SCs has not been adequately explored in the literature [1]. In this sense, certain gaps have been identified. The first gap refers to the definition of key indicators that provide the most accurate information about the warehouse’s and distribution center’s operations. In the literature, a small number of available indicators are often used, which do not describe how the observed system is working in the best way.

The second gap is related to the lack of adequate models for measuring warehouse efficiency. In fact, there are no models in the literature dealing with measuring warehouse efficiency in retail SCs. The third gap that is present in the literature regarding efficiency measurement in logistics is the lack of specific case studies and testing of theoretical models on real examples. Many models proposed in the literature (e.g., network DEA models that are more suitable for simplified networks and do not perform well when considering complex networks) cannot be applied to real logistics systems due to numerous limitations. All previously mentioned gaps are the research subject in this article. A new PCA-DEA-IMF SWARA-CoCoSo model has been proposed for measuring warehouse efficiency in retail SCs. Special emphasis is given to the indicators that describe observed warehouses in the best way. The approach was proposed and tested on a real system (company) and overcomes all limitations of existing models in the literature. A limitation observed in all existing research is the absence of models that comprehensively address the presented problem.

2.2 Literature review

Liu and Li [4] proposed a two-dimensional linguistic similarity-degree-based clustering analysis method, the two-dimensional linguistic partitioned Maclaurin symmetric mean operator, and the two-dimensional linguistic weighted partitioned Maclaurin symmetric mean operator for comprehensive logistics DC location selection. Similarly, a model for location selection for a fruit DC in the southern and eastern regions of Serbia based on an AHP and weighted aggregated sum product assessment methods has been proposed [5]. In order to evaluate potential retail locations for the apparel stores, Burnaz and Topcu [6] developed an approach based on the analytic network process (ANP). For this purpose and in order to obtain the results, the authors observed 23 criteria and 2 alternatives. Kuo [7] implemented a hybrid methodology, integrating fuzzy decision-making trial and evaluation laboratory and AHP-ANP methods, for solving the intricate challenges of international distribution center (IDC) location selection in the context of complex decision-making and uncertain conditions. Ou and Chou [10] addressed a similar problem where the selection of an IDC from a foreign market perspective was resolved through the application of a weighted fuzzy factor rating system. Liao et al. [11] proposed the Pythagorean fuzzy CoCoSo method for selecting a distribution center in a cold chain. In addition to DC selection, a review of existing literature revealed the presence of articles addressing DC location selection. Nong [12] proposed a hybrid model based on ANP and a technique for order preference by similarity to the ideal solution (TOPSIS) for distribution center location selection. The ANP method was used to determine the criteria weights, while the TOPSIS method was used to rank alternatives. Similarly, Hu et al. [13] proposed an algorithm for logistics DC location selection for supply and demand network enterprises. The authors proposed an improved firefly algorithm in order to improve the optimization effectiveness of the traditional methods used in solving the location selection problem. He et al. [14] proposed a new hybrid fuzzy model for the location selection of joint distribution centers, taking into account sustainability. In order to obtain the results, fuzzy AHP (for determining criteria weights) and improved fuzzy TOPSIS (for ranking the alternatives) were used. Özmen and Aydoğan [15] presented a three-stage methodology for logistics center location selection within the framework of Kayseri’s logistics development plan. In the first stage, criteria were determined through a literature review and expert interviews. The second stage involved the weighting of identified criteria using the linear Best–Worst method. In the third stage, locations were ranked using the evaluation based on distance from average solution (EDAS) method with various distance measures. Wan et al. [16] developed a model for DC location selection in case of large-scale emergencies based on a bi-objective trapezoidal fuzzy mixed integer linear program. Besides DC location selection, another problem that has been solved in the literature is warehouse location selection. Bairagi [17] proposed a model for warehouse location selection in SCM based on MCDM methods. Ulutaş et al. [18] proposed a new model for warehouse location selection based on an integrated grey MCDM model, encompassing grey preference selection index and grey proximity indexed value, to determine the most suitable warehouse location for a supermarket. Khaengkhan et al. [19] compared three methods, simple additive weighting, AHP, and TOPSIS in order to select the most suitable location for an agricultural products warehouse in Thailand. Amin et al. [20] aimed to efficiently select a warehouse and addressed the warehouse selection problem by applying AHP and TOPSIS methods, preceded by a survey on warehouse selection problems.

In addition to the problems related to the selection of DC, as well as the location for DCs and warehouses, based on a literature review it was concluded that there are articles dealing with the analysis and improvement of warehouse efficiency. Karim et al. [21] revised the warehouse productivity measurement indicators by conducting a literature review and semi-structured survey. As a result, the authors highlighted the warehouse resources related to the respective activities in the warehouse. Freitas et al. [22] analyzed a bus manufacturing organization in order to improve efficiency in a hybrid warehouse. Warehouse safety and operational efficiency were also addressed by Halawa et al. [23], where authors examined how real-time location system technology can be used to enhance warehouse safety and efficiency. In order to obtain the results, the authors implemented a novel three-phase framework. In order to precisely measure overall warehouse performance, Islam et al. [24] proposed a novel particle swarm optimization-based grey model to predict the warehouse’s key performance indicators with less forecasting error. Fuzzy AHP was used by Abdul Rahman et al. [25] to analyze the most important warehouse productivity indicators in order to improve warehouse operation efficiency. The obtained results showed that space stood out as the top-ranked criterion, followed by information systems, labor, and equipment. Pajić et al. [26] in their article proposed an approach based on the DEA-full consistency method (FUCOM)-CoCoSo methodology for supplier selection, where the DEA method was used to separate efficient suppliers from the inefficient. Based on the results of this phase, in the second phase, FUCOM was applied to determine criteria weights. Finally, a CoCoSo method was applied for the final ranking of the alternatives. In order to measure the efficiency of the retail SC, four main groups of models were identified [1]. The main goal of the article was to test different approaches (standard DEA models, efficiency decomposition models, network models, and game-theory-based models) using real data from a company operating in Serbia. Andrejić et al. [3] developed a model for distribution centers’ efficiency measuring based on the DEA method in order to facilitate the decision-making process and improve efficiency. Operational, quality, energy, utilization, and equipment warehouse and transport indicators were integrated into the proposed model. Another model based on the DEA method was proposed by Andrejić et al. [27] for measuring distribution centers’ efficiency change in time. For this purpose, the Malmquist productivity index was used in order to determine the impact of input and output variable selection on the resulting efficiency in the context of measuring the change in efficiency over time. Istiqomah et al. [28] in their article analyzed how implementation of barcode can affect warehouse efficiency. Namely, by using the qualitative method, the authors determined that barcode should be implemented in order to improve efficiency, minimize human errors, and provide accurate data in a real-time. IMF SWARA was proposed by Vrtagić et al. [8], where authors used it for determining criteria weights in order to rank the road sections. Puška et al. [29] used IMF SWARA in combination with fuzzy Compromise Ranking of Alternatives from Distance to Ideal Solution in order to select DC locations. Conversely, a combination of IMF SWARA and EDAS methods was used by Stević et al. [30] to evaluate the safety of road sections. IMF SWARA was used for determining criteria weights while the EDAS method was used for ranking the road sections. Besides IMF SWARA, there are other methods for determining criteria weights present as well. For instance, Đalić et al. [31] implemented fuzzy PIPRECIA for analyzing the competitiveness to improve logistics performances. In other words, Stanujkic et al. [32] proposed a simplified version of the PIPRECIA method (PIPRECIA-S) for determining criteria weights. IMF SWARA was combined with the fuzzy Bonferroni operator by Moslem et al. [33] in order to improve the service quality of the public transport system in Turkey. Conversely, a parsimonious spherical fuzzy AHP was proposed by Moslem [34] to evaluate sustainable urban transport solutions. The interval valued Fermatean fuzzy SWARA was used by Aytekin and Korucuk [35] in order to determine criteria weights when concerning SC integration. A combination of AHP and MABAC (multi-attributive border approximation area comparison) methods was applied by Đoković and Doljanica [36] to select investment projects.

3.1 PCA-DEA methods

The combination of PCA-DEA methods was used in this article to determine efficient DWs that will be analyzed in the second and in the third phase of the article. The formulation of the PCA-DEA model used in this article is as follows, equation (1) [3,38]:

s.t.

where V PC and U PC represent vectors of weights assigned to inputs and outputs PCs, v a is scalar, X PC a and Y PC a are input and output column vectors for certain principal components for DMU a .

3.2 IMF SWARA method

In order to obtain criteria weights, the IMF SWARA was applied using the following steps [8]:

Step 1 – First, a set of decision criteria {c ₁, c ₂, …, c _n } must be determined. After that, it is necessary to arrange them in descending order, where the first criterion is the most significant, while the last one is the least significant.

Step 2 – Comparing the criteria. Namely, the relatively smaller significance of the criterion (criterion C _j ) was determined in relation to the previous one (C _j−1), and this was repeated for each subsequent criterion. In this way, a comparative significance of the average value is obtained ( s j ¯ ). The comparison was made using the following scale (Table 1).

Step 3 – Calculating the fuzzy coefficient k j ¯ using equation (2):

Step 4 – Determining the calculated weights q j ¯ using equation (3):

Step 5 – Calculating the fuzzy weight coefficients using equation (4).

3.3 CoCoSo method

The implementation of the CoCoSo method can be divided into five steps [26,39,40].

Step 1 – Determine the initial decision-making matrix with alternatives and criteria.

Step 2 – The criteria normalization is performed using equations (5) and (6) in accordance with the type of criteria:

Step 3 – In this step, the total of the weighted comparability sequence and the whole of the power weight of comparability sequences for each alternative sum of the weighted comparability sequence and also an amount of the power weight of comparability sequences for each alternative (S _i and P _i ), respectively, are determined using equations (7) and (8):

Step 4 – Determining the relative weights of the alternatives by calculating the aggregation strategies using equations (9)–(11):

In equation (11), λ is chosen by decision-makers and can take a value between 0 and 1.

Step 5 – In the last step, the alternatives are ranked based on the value of k _i (the higher value represents better rank) [equation (12)]:

4.1 Case description

This article presents a case study of a Serbian retail company. The company operates 18 warehouses where perishable goods are procured from suppliers and stored for a designated period, depending on their type. Subsequently, the goods are distributed to various retail stores. Notably, the company follows a distinctive approach by providing its own retail stores with products from nine warehouses (referred to as RW), while also servicing retail stores not owned by the company from the remaining nine warehouses (referred to as WW). It is worth noting that these additional nine warehouses function as wholesale facilities catering to the owners of smaller shops, as indicated in Figure 2.

Figure 2

Case study company.

In the observed system, a greater number of performance indicators are monitored. Most of the indicators are financial, which fully corresponds to the real system. Namely, a company whose main activity is not logistics but trade observes logistics as the cost of placing goods on the market. In addition, the company also monitors certain indicators that are operational-related. So, for example, the number of boxes that the warehouse prepares (after order-picking) and delivers is of particular importance in performance measurement, in addition to turnover. Also, the number of order-picking transactions realized by one warehouse is monitored as a very significant indicator. In order to obtain a pragmatic and reliable scenario of warehouse operations, 21 performance indicators were taken into account in this article, of which 18 are inputs and 3 are outputs. These performance indicators were meticulously chosen through an extensive literature review and subsequent interviews with industry experts possessing substantial experience. All experts involved in the assessment are in a higher position (two warehouse managers, one logistics manager, one SC manager, and one reverse logistics manager) in the company and are competent for the observed issue. Their expertise and authority in addressing the observed issue affirm the relevance of the selected indicators, focusing on key financial, operational, and quality aspects [3]. The data used in this case study were collected for the period of 1 year (12 months). The values presented in Table 2 represent average monthly values for the observed period.

Description of the variables (indicators) used in this article are as follows.

INPUT indicators

• Rent (IP1) – the cost of renting the warehouse facilities expressed in monetary units (m.u.).

• Amortization (IP2) – the cost of depreciation of buildings and equipment expressed in m.u.

• Electricity (IP3) – the cost of electricity expressed in m.u. Electricity consumption is a consequence of the need for cooling buildings, lighting the building, as well as charging batteries for electric forklifts.

• Other energy (IP4) – consumption of other energy sources such as gas and similar expressed in m.u.

• Forklifts (rental fee – IP5) – the cost of renting a forklift expressed in m.u. In the observed warehouses, a certain number of forklifts are leased, while the other is owned.

• Forklifts (maintenance – IP6) – the maintenance cost of forklifts regardless of ownership expressed in m.u.

• Salaries (IP7) – fixed and variable earnings, expressed in m.u.

• Shrinkage (IP8) – write-offs, breaks, damaged goods, expired dates, expressed in m.u.

• Consumables (IP9) – the cost of materials used for packing shipments, e.g., foils, cardboard, paper, styrofoam, as well as other consumables, expressed in m.u.

• Other costs (IP10) – tax costs, labor protection costs, cleaning costs, etc., expressed in m.u.

• Total costs (IP11) – represents the sum of all arising costs, expressed in m.u.

• Operating costs (including lease – IP12) – represents the sum of all operating costs including a lease, expressed in m.u.

• Costs of operations (without depreciation and lease – IP13) – costs of operations without depreciation and lease, expressed in m.u.

• % cost in the turnover (IP14) – shows the ratio/participation of costs in the output.

• Cost of item without lease and amortization (IP15) – a partial indicator of the cost of an item without lease and amortization, expressed in m.u.

• Cost of the box without lease and amortization (IP16) – a partial indicator of the cost of the box without lease and amortization, expressed in m.u.

• Cost of an item with lease (IP17) – a partial indicator of the cost of the item with lease and amortization, expressed in m.u.

• Cost of a box with lease (IP18) – a partial indicator of the cost of a box with lease and amortization, expressed in m.u.

OUTPUT indicators

• Transaction (OP1) – total number of transactions, i.e., items on all orders for order picking.

• Box (OP2) – total number of boxes that leave the warehouse.

• Turnover (OP3) – total turnover, expressed in m.u.

In addition to the presented indicators used in the first phase of the proposed methodology, in the second and the third phase a set of evaluation criteria had to be defined. Based on the company data, as well as the literature review, a set of nine criteria was defined. Six criteria have been established based on data from the observed company, including fixed costs (C1), variable costs (C2), and turnover (C3), expressed in m.u., as well as the number of boxes shipped (C4), number of order-picking lines (C5), and shrinkage (C6), which is also expressed in m.u. In this study, fixed costs encompass the aggregate of rent, amortization, and rental fees for the forklifts. Variable costs, in contrast, encompass the total of electricity, other energy, salaries (considering potential variations due to bonuses), consumables, maintenance costs for the forklifts, and miscellaneous expenses. Conversely, the remaining three criteria used in this case study were defined based on the literature review, such as closeness to the market (C7), available space (C8), and expansion possibility (C9). The values for these three criteria were determined based on the evaluation of the five experts from the observed company (average or simple mean value was taken into account). In the context of this research, the terms “inputs,” “outputs,” and “criteria” are central to the proposed integrated model for assessing the efficiency of retail DWs using PCA-DEA-IMF SWARA-CoCoSo method. Inputs are the factors or resources that are consumed or utilized in the process being assessed. In the context of retail DWs, inputs generally include variables such as rental costs, consumables, maintenance costs, electricity and energy consumption, etc. In the PCA-DEA phase (II phase), these inputs are analyzed to reduce the number of variables and identify the most efficient warehouses. The goal is to find a set of inputs that maximizes the efficiency of the warehouse. In a retail DW, outputs are the results or outcomes generated by the process and include variables like the number of boxes shipped, turnover, or any other measurable outcome. PCA-DEA is used to identify the most efficient warehouses based on their ability to produce the desired outputs with the given inputs. In the third phase, IMF SWARA is applied to determine the weights of the criteria. Criteria refer to the factors that are considered in the decision-making process. In this context, criteria could include elements such as fixed costs, variable costs, or any other relevant factors that contribute to the efficiency assessment. The importance or weight of each criterion is determined using the IMF SWARA method.

4.2 Results

The case study analyzed in this article was conducted as follows. After defining the input and output indicators for all warehouses, an initial analysis was performed using the standard DEA approach. In the literature, initial evaluation with basic models is recommended [3,41]. However, the results obtained using this model showed an extremely low discrimination power (third column of Table 3) where the average efficiency was 0.927, where as many as 13 DMUs were efficient. The consequence of such results is a large number of variables (21) and a relatively small number of observed storage units (DMU), 18 of them.

After that, the evaluation using the PCA-DEA approach was conducted with a 95% of degree information retention. A high retention rate is very important when it comes to measuring the effectiveness of real systems. Conversely, the model has a very high discrimination power, which is confirmed by the average efficiency of 0.674 (fourth column Table 3). In the combined set of all 18 DMUs (9 retail and 9 wholesale warehouses), it was established that there are large mutual differences in efficiency. Thus, it was established that the average efficiency of the first group (DMU1–DMU9) is 0.793, while the efficiency of the second group (DMU10–DMU18) is 0.556. This directly indicates that the observed set has certain inhomogeneities (heterogeneity), which can be explained by certain differences in the functioning and realization of logistic processes and activities.

It is precisely for this reason that an independent assessment of PCA-DEA efficiency (95%) was performed for nine retail and nine wholesale warehouses. The reason is to obtain more authoritative results. The last column of Table 3 shows that the average efficiency of retail warehouses is 0.814, where five warehouses are efficient, while in the group of wholesale warehouses, the average efficiency is 0.719 where only two DMUs had an efficiency of 1.

Efficient DMUs were selected as the best representatives and analyzed in the next phase, with the aim of determining the authoritative benchmark for the entire set. Inefficient warehouses in terms of operational business need to emulate exactly that warehouse.

After determining the efficient warehouses, the second phase which included obtaining criteria weights was conducted. A set of nine criteria was defined after which the criteria were sorted in descending order (from the most to the least significant). Fixed costs (C1) were taken as the most significant criterion, while expansion possibility (C9) was taken as the least significant. Since IMF SWARA was used, the results based on the experts’ assessment were obtained (Table 4).

Crisp criteria weights were then obtained by applying equations (2)–(4), as given in Table 5.

As already mentioned, nine evaluation criteria and seven alternatives were considered. The initial decision-making matrix (Table 6) was derived from the real data of the company, along with the expert’s assessment. Since two types of warehouses were taken into account in this article, it is worth mentioning that the first five alternatives (A1–A5) represent warehouses for retail stores owned by the company, while the remaining two alternatives (A6 and A7) represent warehouses for wholesale.

After developing the initial decision-making matrix, the second step in implementing the CoCoSo method involved normalization through the application of equations (5) and (6), respectively, for benefit and cost criteria, as shown in Table 7. Additionally, this step presented the weights of the criteria obtained using the IMF SWARA method.

S _i and P _i values for each alternative were determined in the next step by applying equations (7) and (8), as presented in Table 8.

Finally, in the last step, the values of k _ia , k _ib , k _ic , and k _i were determined (Table 9) by applying equations (9)–(12) in order to obtain the final ranking of the alternatives (warehouses).

Based on the obtained results, it can be concluded that alternative 4 (A4) is the best-ranked alternative followed by A2, A3, A5, A7, A1, and A6. The final ranking can also be shown as A4 > A2 > A3 > A5 > A7 > A1 > A6. Besides ranking, the results showed that warehouses for retail stores owned by the company are better ranked (hence more efficient) than warehouses for wholesale. This is an expected result since the company has greater control over its own operations and can manage them better when compared with external management when it comes to wholesale warehouses.

5.1 Theoretical and managerial implications

In accordance with the established gaps, this article has unequivocal practical and theoretical contributions.

From the perspective of practical application, this model was developed and proposed for the needs of a real company. In this sense, it overcomes all the shortcomings of theoretically developed approaches. An integrated model based on four methods overcomes the shortcomings of other approaches and uses all their individual advantages. The evaluation is based on real variables (inputs/outputs and criteria) that provide a real picture of the functioning of a retailer’s warehouse. Most of the indicators are financial, which corresponds to the real system and type of company. Since it is a retailing company, and not a logistics one, from the perspective of the company’s management, greater emphasis is placed on financial indicators. However, apart from financial ones, operational indicators were also taken into account. Operational indicators in logistics are of crucial importance for measuring the efficiency of the process [3]. The usefulness and reliability of the approach was additionally increased by the inclusion of experts from the observed company during the evaluation of alternatives in accordance with the observed criteria (mainly C7, C8, and C9) and during the ranking of efficient warehouses in the last phase. The proposed approach is easily applicable and easily adaptable, so it can be applied to different logistics systems regardless of primary business activity, size, market, etc. For decision-makers, this model represents an excellent decision support system (DSS) tool with the help of which they can make quick and reliable decisions.

As it was emphasized in Section 2, there are no articles dealing with measuring the efficiency of warehouses in retail chains. But with this research, that gap has been partially filled and an excellent foundation has been laid for further research. The parameters (variables) identified in this article can be useful for the calculation of other warehouse performance indicators of retail chains. The integration of these four approaches into one integrated model has not been used in the literature so far and is very different from all efficiency measurement approaches in the literature. Since there are no articles that deal with the same problem as in this article, obtained results could not be compared with the results of other research. Therefore, the results of this article were compared with the results obtained in [3]. It was concluded that certain inputs/outputs were taken into account in both articles, while the results obtained in [3] confirmed that there is a difference in efficiency scores of large and small DCs. These results are similar to the results presented in the previous section since in this article a difference in efficiency between warehouses for retail stores owned by the company and wholesale warehouses was determined. Another similarity between these two articles is reflected in the fact that the number of efficient warehouses is greater when implementing only the DEA method when compared to PCA-DEA application. In the literature, efficiency is most often evaluated using DEA and Stochastic frontier analysis, while the PCA-DEA approach is used significantly less. By including IMF SWARA and CoCoSo approaches, a completely new model was obtained that has a significantly higher discriminating power than the previously mentioned approaches. The problem of developing theoretical models without the possibility of practical application on real systems was successfully solved with this new model. This is also confirmed by subsequent consultations with experts from the observed company. Namely, the results were presented to the company’s experts and they confirmed that the obtained results are in accordance with the actual situation in the company (in terms of warehouse efficiency and a final ranking of the warehouses).

5.2 Sensitivity analysis

In order to conduct a sensitivity analysis and to determine whether the ranking of the alternatives will be different, four scenarios were created. Namely, in the first scenario, experts from the observed company gave their opinion about the significance and criteria weights. Since five experts evaluated each criterion average value of all assessments was taken into account. Those criteria weights were then implemented in the CoCoSo method to rank the alternatives. Based on the results, it can be seen that there is a small change in the final ranking of the alternatives (A2 switched places with A3, and A1 switched places with A7). So, based on the first scenario, ranking can be shown as A4 > A3 > A2 > A5 > A1 > A7 > A6. In the second scenario, it was assessed that all criteria are of the same importance (hence, have equal weights). The ranking in this scenario can be shown as A4 > A3 > A2 > A5 > A1 > A7 > A6. Based on the results, it can be concluded that the results are the same as in scenario 1. In the third scenario, it was assessed that the operational indicators (criteria) should be more important. Hence, the number of orders picking lines, the number of boxes shipped and available space were given the highest values (Table 10). After conducting analysis, it was concluded that the order of the alternatives has changed and is now as follows: A3 > A4 > A1 > A5 > A2 > A6 > A7 (Table 11). Finally, in the last scenario, financial indicators (criteria) were considered as the most important, hence, fixed costs, variable costs, turnover, and shrinkage had the highest values. Alternatives changed places in this scenario as well. The final ranking according to this scenario is as follows: A4 > A3 > A5 > A2 > A1 > A7 > A6.

Based on the results of the sensitivity analysis, it can be concluded that the solution is pretty stable (since minor changes in the ranking occurred in different scenarios) and that the criteria weights can affect the results (Figure 3).

Figure 3

Sensitivity analysis for different scenarios.