An Integrated Hybrid Model for Evaluating Performance and Allocating Incentives to Order Pickers in E-Commerce Fulfillment

Abstract

E-commerce has been a rapidly growing sales channel in recent years, with a strong trend toward further expansion. However, logistics companies face significant challenges in the preparation and sorting of orders when delivering shipments purchased through e-commerce platforms. In this process, order pickers play a pivotal role, as their efficiency directly impacts both the operational performance of logistics companies and the quality of service provided to customers. During peak periods of high order volumes, it is common for order pickers to exceed the prescribed work norm, making them eligible for performance-based bonuses. This study aims to develop a model for evaluating order picker efficiency, ranking them, and determining the optimal allocation of bonuses. It addresses a critical gap in the existing literature, as only a handful of studies have explored this issue in depth. To assess the efficiency of 56 order pickers, the DEA method was applied, incorporating three input and five output variables. The analysis identified 18 order pickers as fully efficient. These individuals were then ranked using the IMF SWARA and COPRAS methods, where IMF SWARA was employed to determine the weights of nine evaluation criteria, while COPRAS was used for the final ranking process. Based on the ranking results, a structured bonus allocation model was developed, encompassing four distinct scenarios. Furthermore, a sensitivity analysis and model validation were conducted to ensure the robustness and reliability of the proposed approach.

1. Introduction

The rapid expansion of e-commerce, intensified competition, and increasingly demanding consumers are imposing ever-stricter requirements on all participants in the supply chain. According to recent studies, global e-commerce sales continue to grow at a significant pace, with projections indicating a steady increase in market share. In 2021, the European e-commerce market reached EUR 718 billion, reflecting an annual growth rate of 13% compared to EUR 633 billion in 2020. Forecasts for 2022 suggested that this growth trend would continue, with the growth rate stabilizing at an estimated 11%. The projected e-commerce turnover for 2022 was EUR 797 billion. These figures highlight the significant role of e-commerce in the European economy and its increasing importance for consumers [1,2]. Additionally, the Global E-Commerce Market—Industry Trends, Share, Size, Growth, Opportunities, and Forecasts—2022–2027 report by Research and Markets states that the Global E-Commerce Market was valued at USD 13 trillion in 2021. The market is expected to grow to USD 55.6 trillion by 2027, with a projected compound annual growth rate (CAGR) of 27.4% during the 2022–2027 forecast period [2,3]. China is the fastest growing e-commerce market in the world. In 2019, it was the largest e-commerce market globally, with over $1.935 billion in sales. The United States ranked second, with $586.9 billion in e-commerce sales. By 2021, China was expected to become the first country where more than half of all retail sales would occur online. Additionally, China was projected to account for 56.8% of global e-commerce sales, exceeding $2.8 trillion [4,5].

The literature offers various classifications of e-commerce processes. Among the most critical process groups, the following stand out: payment, warehouse operations, distribution (delivery), customer support and returns, marketing, and analytics. It is evident that a substantial portion of these activities falls under logistics operations. While the majority of existing research focuses on product distribution and delivery, significantly fewer studies address warehouse processes [6,7,8]. This gap serves as a key motivation for the present study. In the context of warehouse operations, prior research has primarily explored storage technologies, automation, and inventory management strategies. However, there is a distinct lack of studies dedicated to measuring and monitoring order picker performance in e-commerce logistics. This research gap represents the core issue this study aims to address.

Order pickers play a crucial operational role in e-commerce, directly influencing the accuracy, speed, and efficiency of order fulfillment. These factors are critical in determining service quality and overall company profitability. The order-picking process in e-commerce differs significantly from traditional order-picking methods. In conventional logistics systems, order picking is predominantly focused on assembling bulk quantities of products for retail stores or business customers (B2B model). In contrast, e-commerce follows a B2C model, where orders consist of smaller quantities and a wide assortment of products. This significantly increases the complexity of order picking, demanding greater flexibility, accuracy, and efficiency. In traditional supply chain operations, order picking is synchronized with scheduled deliveries to retail stores or production lines, where minor deviations from planned timelines are relatively inconsequential. However, in e-commerce, end consumers expect rapid and precise deliveries, often within the same day or within 24 h. This necessitates more rigorous operational organization and heightened accuracy in order fulfillment. Even minor errors in product selection can lead to customer dissatisfaction and increased return costs, adversely affecting operational efficiency.

Moreover, there are notable differences in technology utilization and automation levels between conventional and e-commerce warehouses. Warehouse operating costs also vary significantly, primarily due to the adoption of advanced technologies, increased labor requirements, pronounced seasonality, and other operational challenges. A key aspect of this study is the standardization and performance measurement of order pickers, an area that has received limited attention in prior research. The factors outlined above directly influence workforce standardization and the design of incentive programs. Given that e-commerce success is heavily reliant on rapid and accurate order processing to maintain customer satisfaction and competitive advantage, defining and implementing performance standards for order pickers is of paramount importance.

This study proposes a hybrid approach that combines quantitative performance indicators with qualitative assessments to ensure a fair and objective distribution of bonuses. In the first phase, the Data Envelopment Analysis (DEA) method was applied to distinguish efficient order pickers from inefficient ones, ensuring that only the efficient ones were analyzed and ranked in the later phases of the model. This approach aimed to establish a structured framework for bonus allocation. Meanwhile, in the second phase, the Improved Fuzzy Step-Wise Weight Assessment Ratio Analysis (IMF SWARA) method which was chosen because it simplifies the evaluation of alternatives using fuzzy scales. One key advantage of the IMF SWARA method is its use of the triangular fuzzy numbers (TFN) scale, which enables more precise and higher-quality assessment of criteria significance. Additionally, compared to other methods such as the Analytic Hierarchy Process (AHP), Pivot Pairwise Relative Criteria Importance Assessment (PIPRECIA), and PIPRECIA-S, IMF SWARA requires fewer pairwise comparisons and is easier to use—an important factor when developing a model for managers or decision-makers who may not be well-versed in these methodologies [9]. The advantage of using the complex proportional assessment (COPRAS) method is reflected in the fact that it is adaptable and effective in tackling a wide range of issues. Its ability to handle both quantitative and qualitative criteria allows for a comprehensive analysis, making it a valuable tool for various stakeholders. The adaptation of this method highlights its robustness and its capacity to support decision-making in industries seeking to integrate multidimensional criteria into their evaluation processes [10]. For these reasons, the COPRAS method was applied in this paper for ranking the alternatives.

The paper is organized as follows. After the introduction, Section 2 presents a review of the relevant literature. Section 3 outlines the research methodology, while Section 4 provides a detailed description of the analyzed case study and the results of the proposed model implementation. This section also defines the bonus allocation model for order pickers. Section 5 discusses the results of the sensitivity analysis, model validation, and theoretical and managerial implications. Finally, Section 6 presents the concluding remarks, study limitations, and directions for future research.

2. Literature Review

Performance evaluation in warehouse systems must be understood as a multidimensional and behavior-sensitive construct rather than as a purely technical measurement exercise. According to established performance measurement theory, organizational performance systems are designed not only to quantify outputs, but also to align operational activities with strategic objectives. In labor-intensive logistics environments such as order picking, performance therefore encompasses productivity, quality, reliability, and behavioral compliance dimensions simultaneously. From the perspective of Agency theory, warehouse management acts as the principal, while order pickers operate as agents whose effort levels, accuracy, and work discipline cannot be perfectly observed. This information asymmetry generates classical principal–agent problems, where employees may optimize their own utility rather than organizational performance if monitoring and incentive systems are poorly structured. Performance indicators thus serve a dual role; they are both measurement instruments and governance mechanisms intended to reduce opportunistic behavior and moral hazard. Furthermore, insights from Incentive theory suggest that the structure of performance metrics directly influences effort allocation. When productivity indicators (e.g., number of picked items) dominate the evaluation system, employees may increase speed at the expense of accuracy, thereby raising internally and externally detected errors. In addition, Behavioral economics provides further explanation of how evaluation systems shape behavior. Empirical evidence indicates that workers respond not only to financial incentives but also to fairness perceptions, monitoring intensity, and reputational considerations. Overly rigid monitoring systems may reduce intrinsic motivation, while balanced score structures can enhance long-term engagement and loyalty [11,12,13].

A review of the literature has shown that there are studies addressing the role of warehouses in e-commerce, as well as specific aspects such as order-picking methods, warehouse layout, product allocation, and others. For example, Yang et al. [14] examined the differences between batch picking systems and flow picking systems, where, in the latter, the order picking list is updated in real time. The authors first developed analytical models to estimate key performance indicators of a flow picking system, such as picking density and order turnover time. Then, using these models and real warehouse data, they conducted a simulation to compare the performance of batch picking and flow picking systems. The findings indicate that, in most scenarios, particularly those with a high order arrival rate, a flow picking system requires fewer order pickers and involves shorter walking distances than a batch picking system while maintaining the same service level. Zhong et al. [15] examined the advantages of integrating order picking and packing planning in e-commerce warehouses. Based on the results, it was concluded that this integration can enhance performance across various aspects, depending on factors such as objective configurations, order volumes, order categories, and workforce allocation. On the other hand, Schiffer et al. [16] were examining optimal picking policies in e-commerce warehouses. The paper focused on optimizing picker routing in mixed-shelves warehouses. The authors proposed a versatile exact algorithmic framework that accommodates various picking policies, regardless of the picking zone layout, and is suitable for real-time applications. Results showed that the optimal combination of drop-off points, dynamic batching, picking carts, and picking zone layout can significantly enhance picking performance. Notably, some policy combinations achieve efficiency gains of over 30% compared to standard practices currently in use. Hu and Chuang [17] focused on optimizing the layout of e-commerce warehouses using a genetic algorithm (GA). After re-layout, the authors observed that it is possible to reduce the material handling cost and improve the picking efficiency. Wan et al. [18] proposed a multi-objective model for optimizing storage locations in manual picking zones, based on the principles of high delivery frequency priority, correlation, and large-capacity priority which is based on the intelligent genetic algorithm and particle swarm optimization (IGPSO) algorithm. Klumpp and Loske [19] used the non-parametric DEA to assess the efficiency of 23 order pickers handling 6109 batches containing 865,410 stock keeping units (SKUs). The inputs considered by the authors were distance per location, picks per location, and volume per SKU, while the output was picks per hour. Li et al. [20] examined order picking efficiency in e-commerce warehouses through a literature review. Similarly, Boysen et al. [6] conducted a survey regarding warehousing in the e-commerce era. Van der Gaast and Weidinger [21] proposed a framework leveraging recent advancements in deep neural networks that offers an efficient approach for selecting not only the optimal order picking system for a given order structure but also the most suitable design parameters. This allows warehouse companies to objectively compare a wide range of systems and identify the most promising ones. In order to test the proposed framework, the authors conducted a comprehensive comparison of three different fixed-path order picking systems to determine the best fit for a specific order structure. On the other hand, van Gils et al. [22] analyzed how integration of storage, batching, zone picking, and routing policy decisions affect order picking efficiency. Similarly, Rahman and Kirby [7] investigated how Lean Six Sigma tools used for transformation of e-commerce warehouse operations influence efficiency and sustainability. By applying methods such as Value Stream Mapping (VSM) the authors concluded it is possible to achieve a 23% reduction in total lead time, to double the value-added time, and bring significant improvements in inspection, picking, packing, and automation. This resulted in reduced delays, lower costs, and enhanced workflow efficiency. Liu and Poh [23] in their paper proposed an efficient scattered storage assignment algorithm with bulky locations.

On the other hand, when examining studies focused on bonus allocation, a significant gap can be observed as there are very few such studies, especially those related to order pickers. This was one of the main motivations for writing this paper. Novković et al. [24] proposed a performance appraisal and bonus calculation framework for warehouse employees. Similarly, Mendis [25] examined the impact of a reward system on employee turnover intentions in Sri Lanka. Andrejić [26] proposed different approaches for performance appraisal and bonus calculation for truck drivers. Wu et al. [27] proposed a framework for multi-stage bonus allocation in meal delivery platform. Song et al. [28] examined a cross-border product stochastic inventory management problem, where capital-constrained retailers can secure additional working capital through bonded warehouse financing and entrusted loan financing. The study identified an optimal inventory policy that allows retailers to purchase cross-border products with financing and sell them in markets with uncertain demand. The results indicate that entrusted loan financing enables capital-constrained retailers to increase their inventory procurement. On the other hand, Zhao et al. [29] examined warehouse layout optimization for fishbone robotic mobile fulfillment systems. A Pythagorean fuzzy SWARA in combination with the COPRAS method was used by Pandey and Khurana [30] to prioritize the solutions for mitigating Industry 4.0 risks. Stević et al. [31] used IMF SWARA in combination with the MARCOS method for assessment of human resources performance. While previous studies on bonus allocation for order pickers exist, they are limited in scope and often lack systematic empirical evidence, particularly in modern warehouse and e-commerce contexts, which underscores the relevance of the present study in providing a structured and quantitative evaluation framework.

3. Methodology

The methodology of the model proposed in this study consists of five phases. The first phase involves a literature review and the definition of inputs/outputs, criteria, and Decision-Making Units (DMUs). In the second phase, the DEA method is applied to assess the efficiency of order pickers. The third phase utilizes the IMF SWARA method to determine the criteria weights, which are then used in the fourth phase during the application of the COPRAS method. Finally, in the fifth phase, based on the results of all previous phases, a bonus allocation model for order pickers is defined. The described methodology is illustrated in Figure 1.

3.1. DEA Method

In order to determine efficient order pickers an output-oriented CCR model was used [32].

$$Min h_o=\sum _{i=1}^m{v}_i{x}_{io}$$

s.t.

$$\begin{gathered} \sum _{i=1}^m{v}_i{x}_{ij}-\sum _{r=1}^s{u}_r{y}_{rj}\ge 0\hspace{0.5em}j=1,2,\dots ,n \\ \sum _{\mathrm{r}=1}^s{u}_r{y}_{ro}=1 \\ {v}_i{u}_r\ge 0\hspace{0.5em}i=1, 2,\dots ,m;r=1, 2, \dots ,s \end{gathered}$$

(1)

where there are n DMUs (j = 1, 2, …, n) that produce s outputs (y_rj) and consume m inputs (x_ij) u_r represents output weights, while v_i input weights.

3.2. Improved Fuzzy SWARA Method

The IMF SWARA was applied in this paper in order to obtain criteria weights by conducting the following steps [9,33].

Step 1. A set of decision criteria {c₁, c₂, …, c_n} is determined. Then, it is necessary to arrange them in descending order. In this way, the first criterion represents the most important one, while the last represents the least important.

Step 2. In this step, the relatively smaller significance of the criterion C_j is determined in relation to the previous one (C_j−1). By doing so, a comparative significance of the average value is obtained ($\overline{s_j}$). In order to compare the criteria, the scale containing linguistic meanings as well as triangular fuzzy numbers must be used (

Table 1. Scale used in IMF SWARA method scale [33].

Linguistic Scale	Abbreviation	TFN Scale
Absolutely less significant	ALS	(1, 1, 1)
Dominantly less significant	DLS	(1/2, 2/3, 1)
Much less significant	MLS	(2/5, 1/2, 2/3)
Really less significant	RLS	(1/3, 2/5, 1/2)
Less significant	LS	(2/7, 1/3, 2/5)
Moderately less significant	MDLS	(1/4, 2/7, 1/3)
Weakly less significant	WLS	(2/9, 1/4, 2/7)
Equally significant	ES	(0, 0, 0)

).

Step 3. Determining the fuzzy coefficient $\overline{k_j}$ by applying Equation (2):

$$\overline{k_j}=\{\begin{array}{c}\overline{1} j=1\\ \overline{s_j} j>1\end{array}$$

(2)

Step 4. Obtaining the calculated weights $\overline{q_j}$ by applying Equation (3):

$$\overline{q_j}=\{\begin{array}{c}\overline{1} j=1\\ \overline{{\displaystyle \frac{q_{j-1}}{\overline{k_j}}}} j>1\end{array}$$

(3)

Step 5. Obtaining the fuzzy weight coefficients by applying Equation (4).

$$\overline{w_j}={\displaystyle \frac{\overline{q_j}}{\sum _{j=1}^m\overline{q_j}}}$$

(4)

Step 6. Defuzzification to obtain crisp values. The final step includes defuzzification using Equation (5). The graded mean integration representation (GMIR) method was used to obtain crisp values [34].

$$w_j={\displaystyle \frac{w_j^l+4w_j^m+w_j^u}{6}},j=1,2,\dots ,n$$

(5)

3.3. COPRAS Method

In order to implement the COPRAS method, the following steps should be conducted [10].

Step 1. Determining initial decision-making matrix with m alternatives and n criteria and where r_ij represents the value of ith alternative in respect to the jth criteria.

Step 2. Normalization of initial decision-making matrix by applying Equation (6).

$$r_{ij}^{*}={\displaystyle \frac{r_{ij}}{\sum _{i=1}^m{r}_{ij}}},\hspace{1em}j=1,\dots ,n$$

(6)

Step 3. Determining the weighted normalized decision-making matrix using Equation (7).

$$r_{ij}^{^}=r_{ij}^{*}\ast w_j,\hspace{1em}i=1,\dots ,m,\hspace{1em}j=1,\dots ,n$$

(7)

Step 4. Calculating the maximizing (S_+i) and minimizing (S_−i) indexes for each criterion based on their type (positive or negative) using Equations (8) and (9).

$$S_{+i}=\sum _{j=1}^g{r}_{ij}^{^},\hspace{1em}i=1,\dots ,m$$

(8)

$$S_{-i}=\sum _{j=g+1}^n{r}_{ij}^{^},\hspace{1em}i=1,\dots ,m$$

(9)

where g represents the number of positive criteria while remaining (n-g) represents the number of negative criteria.

Step 5. Calculating the relative significance value by applying either Equation (10) or (11).

$$Q_i=S_{+i}+{\displaystyle \frac{\underset{i}{\min }{S}_{-i}\sum _{i=1}^m{S}_{-i}}{S_{-i}\sum _{i=1}^m\frac{\underset{i}{\min }{S}_{-i}}{S_{-i}}}}$$

(10)

$$Q_i=S_{+i}+{\displaystyle \frac{\sum _{i=1}^m{S}_{-i}}{S_{-i}\sum _{i=1}^m\frac{1}{S_{-i}}}}$$

(11)

Step 6. Final ranking of the alternatives based on the relative significance values, where the alternative with the highest value represents the best-ranked one.

4. Case Study Description and Results

4.1. Case Study Description

The developed model was tested on a case study of an e-commerce company. This domestic company primarily sources its products from China and sells them exclusively through online channels. The warehouse, where goods are stored, prepared for delivery, and shipped, employs 56 order pickers. As previously mentioned, the focus was on developing a new employee incentive system. The existing system only considered the number of items picked beyond the average quota, which was unsatisfactory for both employees and management. In the first phase of model implementation, the DEA method was applied using the following inputs and outputs to assess efficiency. The efficiency evaluation of 56 order pickers was conducted based on seven variables, three inputs and five outputs (Table 2):

• Number of working days (Input 1—I1)—Total number of working days per month for an order picker;
• Total picking time (Input 2—I2)—Total picking time expressed in hours;
• Overtime hours (Input 3—I3)—Number of hours worked beyond the standard 8 h workday;
• Number of picked items (Output 1—O1)—Total number of items picked by the order picker;
• Number of internal errors (Output 2—O2)—Number of incorrectly picked items (for this indicator, the inverse value was used, as this approach aligns with the principles of the DEA method);
• Number of external errors (Output 3—O3)—Number of externally detected errors (for this indicator, the inverse value was used, as this approach aligns with the principles of the DEA method);
• Average number of items (Output 4—O4)—Average number of items picked per month;
• Number of items picked above the norm (Output 5—O5)—Number of items picked beyond the defined norm within the observed period. The average predefined norm is determined by company management and may vary depending on the time of year, warehouse zone, working conditions, etc.

Table 2. Input data for the DEA method.

DMU	I1	I2	I3	O1	O2	O3	O4	O5
DMU1	8	48	1	2506	1	0.08	183	217
DMU2	21	126	1	4654	1	0.04	126	274
DMU3	12	108	12	2232	1	0.25	153	247
DMU4	25	125	1	3367	0.07	0.08	48	352
DMU5	1	4	1	549	1	0.25	149	251
DMU6	19	114	1	3147	1	0.05	77	323
DMU7	5	20	1	320	1	0.33	0	152
DMU8	27	216	1	5247	0.07	0.07	108	400
DMU9	24	96	1	7030	1	0.01	63	337
DMU10	19	95	1	2272	0.17	0.07	35	365
DMU11	26	130	1	4973	0.08	0.02	19	381
DMU12	27	108	1	6308	0.09	0.06	151	249
DMU13	26	130	1	6507	0.05	0.06	133	267
DMU14	13	130	26	924	0.08	0.08	77	477
DMU15	26	260	52	3423	0.05	0.05	6	395
DMU16	27	135	1	11,122	0.2	0.02	270	130
DMU17	11	77	1	1138	1	0.33	74	326
DMU18	23	207	23	13,402	1	0.2	562	162
DMU19	19	133	1	4311	1	0.08	172	228
DMU20	24	192	1	5684	1	0.01	234	167
DMU21	23	161	1	4859	0.5	0.13	176	224
DMU22	12	72	1	1106	1	0.17	46	355
DMU23	20	160	1	1070	0.11	0.5	10	391
DMU24	24	240	48	7876	0.03	0.06	145	255
DMU25	26	156	1	1670	1	0.5	55	345
DMU26	24	192	1	7492	0.03	0.25	202	198
DMU27	13	52	1	3330	0.04	0.01	115	285
DMU28	24	120	1	2549	0.5	0.01	100	300
DMU29	26	104	1	7182	0.02	0.25	107	293
DMU30	25	200	1	6828	0.03	0.2	136	264
DMU31	24	120	1	4361	0.02	0.2	18	418
DMU32	24	240	48	4138	1	0.17	149	251
DMU33	16	128	1	4614	1	0.09	228	172
DMU34	23	115	1	4927	1	0.01	211	189
DMU35	25	175	1	4934	1	0.01	194	206
DMU36	23	138	1	6643	1	0.01	285	115
DMU37	24	120	1	5703	0.5	0.01	231	169
DMU38	20	160	1	3702	0.33	1	169	231
DMU39	18	72	1	4580	1	0.01	250	150
DMU40	23	161	1	4467	0.11	0.01	163	237
DMU41	18	180	36	3543	0.5	0.01	188	212
DMU42	21	210	42	2490	1	0.2	96	304
DMU43	27	270	54	8587	0.04	0.33	238	162
DMU44	21	105	1	4633	0.03	0.25	87	313
DMU45	13	130	26	2786	0.06	0.25	85	315
DMU46	27	162	1	6380	0.03	0.25	133	267
DMU47	19	152	1	4032	1	0.01	208	192
DMU48	23	138	1	4434	1	0.01	189	211
DMU49	19	152	1	3472	1	0.01	179	221
DMU50	21	105	1	4043	1	0.01	189	211
DMU51	24	168	1	5324	1	0.01	219	182
DMU52	23	92	1	5428	1	0.01	233	167
DMU53	23	115	1	4732	1	0.01	202	198
DMU54	20	160	1	4163	1	0.01	204	196
DMU55	19	76	1	3629	1	0.01	187	213
DMU56	22	154	1	4218	1	0.01	188	212

Table 2. Input data for the DEA method.

DMU	I1	I2	I3	O1	O2	O3	O4	O5
DMU1	8	48	1	2506	1	0.08	183	217
DMU2	21	126	1	4654	1	0.04	126	274
DMU3	12	108	12	2232	1	0.25	153	247
DMU4	25	125	1	3367	0.07	0.08	48	352
DMU5	1	4	1	549	1	0.25	149	251
DMU6	19	114	1	3147	1	0.05	77	323
DMU7	5	20	1	320	1	0.33	0	152
DMU8	27	216	1	5247	0.07	0.07	108	400
DMU9	24	96	1	7030	1	0.01	63	337
DMU10	19	95	1	2272	0.17	0.07	35	365
DMU11	26	130	1	4973	0.08	0.02	19	381
DMU12	27	108	1	6308	0.09	0.06	151	249
DMU13	26	130	1	6507	0.05	0.06	133	267
DMU14	13	130	26	924	0.08	0.08	77	477
DMU15	26	260	52	3423	0.05	0.05	6	395
DMU16	27	135	1	11,122	0.2	0.02	270	130
DMU17	11	77	1	1138	1	0.33	74	326
DMU18	23	207	23	13,402	1	0.2	562	162
DMU19	19	133	1	4311	1	0.08	172	228
DMU20	24	192	1	5684	1	0.01	234	167
DMU21	23	161	1	4859	0.5	0.13	176	224
DMU22	12	72	1	1106	1	0.17	46	355
DMU23	20	160	1	1070	0.11	0.5	10	391
DMU24	24	240	48	7876	0.03	0.06	145	255
DMU25	26	156	1	1670	1	0.5	55	345
DMU26	24	192	1	7492	0.03	0.25	202	198
DMU27	13	52	1	3330	0.04	0.01	115	285
DMU28	24	120	1	2549	0.5	0.01	100	300
DMU29	26	104	1	7182	0.02	0.25	107	293
DMU30	25	200	1	6828	0.03	0.2	136	264
DMU31	24	120	1	4361	0.02	0.2	18	418
DMU32	24	240	48	4138	1	0.17	149	251
DMU33	16	128	1	4614	1	0.09	228	172
DMU34	23	115	1	4927	1	0.01	211	189
DMU35	25	175	1	4934	1	0.01	194	206
DMU36	23	138	1	6643	1	0.01	285	115
DMU37	24	120	1	5703	0.5	0.01	231	169
DMU38	20	160	1	3702	0.33	1	169	231
DMU39	18	72	1	4580	1	0.01	250	150
DMU40	23	161	1	4467	0.11	0.01	163	237
DMU41	18	180	36	3543	0.5	0.01	188	212
DMU42	21	210	42	2490	1	0.2	96	304
DMU43	27	270	54	8587	0.04	0.33	238	162
DMU44	21	105	1	4633	0.03	0.25	87	313
DMU45	13	130	26	2786	0.06	0.25	85	315
DMU46	27	162	1	6380	0.03	0.25	133	267
DMU47	19	152	1	4032	1	0.01	208	192
DMU48	23	138	1	4434	1	0.01	189	211
DMU49	19	152	1	3472	1	0.01	179	221
DMU50	21	105	1	4043	1	0.01	189	211
DMU51	24	168	1	5324	1	0.01	219	182
DMU52	23	92	1	5428	1	0.01	233	167
DMU53	23	115	1	4732	1	0.01	202	198
DMU54	20	160	1	4163	1	0.01	204	196
DMU55	19	76	1	3629	1	0.01	187	213
DMU56	22	154	1	4218	1	0.01	188	212

4.2. Results

4.2.1. DEA Results

Thus, as stated in the Section 3, the DEA method was applied in this study to distinguish efficient order pickers from inefficient ones. After defining the inputs and outputs, the DEA method was implemented. The results obtained from the analysis are presented in

Table 3. DEA results.

DMU	Objective Value	Efficient
DMU1	1	Yes
DMU2	1
DMU3	0.323544956
DMU4	0.896224334
DMU5	1	Yes
DMU6	1
DMU7	1	Yes
DMU8	1	Yes
DMU9	1	Yes
DMU10	0.95003597
DMU11	0.963946082
DMU12	0.956579537
DMU13	0.931456486
DMU14	0.146184493
DMU15	0.229157868
DMU16	1	Yes
DMU17	1	Yes
DMU18	1	Yes
DMU19	1
DMU20	1	Yes
DMU21	0.903217364
DMU22	1	Yes
DMU23	1	Yes
DMU24	0.564762709
DMU25	1	Yes
DMU26	0.955559713
DMU27	0.985153419
DMU28	0.887143247
DMU29	1	Yes
DMU30	0.951214383
DMU31	1	Yes
DMU32	0.297876595
DMU33	1
DMU34	1
DMU35	1
DMU36	1	Yes
DMU37	0.960162684
DMU38	1	Yes
DMU39	1	Yes
DMU40	0.882146935
DMU41	0.34002194
DMU42	0.206574281
DMU43	0.547590884
DMU44	0.952130749
DMU45	0.372907705
DMU46	0.933267699
DMU47	1
DMU48	1
DMU49	1
DMU50	1
DMU51	1	Yes
DMU52	1
DMU53	1
DMU54	1
DMU55	1
DMU56	1

.

As seen from the results presented in Table 3, only 18 out of 56 order pickers were identified as efficient. The remaining order pickers had efficiency scores either below 1 or close to 1. For this reason, their values were rounded to 1 in the table; however, these DMUs were not truly efficient and were therefore excluded from consideration in the subsequent phases of model implementation. The average efficiency of all order pickers is 0.877. Consequently, only 32.14% of the order pickers were classified as efficient. The results of the DEA method also indicate significant potential for improving the quality and efficiency of order pickers’ performance, as well as for defining preventive and corrective measures to enhance overall operational effectiveness.

4.2.2. IMF SWARA Results

To evaluate the efficiency of order pickers and rank them accordingly, based on a review of the literature and data obtained from the company, nine key criteria used in the subsequent phases of the model were defined. Some of the criteria applied in the DEA method were also utilized here, with additional criteria incorporated. Ultimately, the following nine criteria were considered: the number of picked items (C1), internally detected errors (reliability) (C2), externally detected errors (C3), the average number of items picked per day (C4), the number of items picked daily above the norm (C5), total picking time (C6), order fulfillment rate (C7), loyalty (C8), and adherence to work obligations (C9). Since explanations for some of these criteria were already provided in the beginning of this section, they will not be repeated here. Internally detected errors (reliability) refer to the number of mistakes made by the order picker that were identified during internal quality control before shipment. These errors are internal and are significantly less costly to correct. Externally detected errors represent the number of mistakes made by the order picker that were identified by customers. These errors require product returns and cause significantly greater damage to the company compared to internally detected errors, as they necessitate additional deliveries, lead to customer dissatisfaction, and incur higher operational costs. The order fulfillment rate measures the effectiveness of an order picker in terms of both quantity and accuracy, whether the correct number of requested items was picked. Loyalty is defined in this study as the number of years an order picker has been employed by the analyzed company. Lastly, adherence to work obligations is assessed on a scale from 1 to 10, based on warehouse managers’ evaluations of individual order pickers. To assess these criteria, the IMF SWARA method was applied, as it allowed experts to express the importance of each criterion more effectively through linguistic terms. The evaluation of criteria significance involved five experts from the observed company (

Table 4. Expert’s description.

Expert	Position	Years of Experience
Expert 1	Warehouse manager	16
Expert 2	Sales manager	12
Expert 3	Logistics manager	15
Expert 4	Logistics director	30
Expert 5	Procurement and distribution manager	18

).

The experts were presented with the criteria, after which they ranked them according to the first step of the IMF SWARA method. Since multiple experts were involved, a single assessment was determined by selecting the most frequently occurring response as the expert consensus. This approach was applied during the second step of the IMF SWARA method, where the criteria were compared against each other (

Table 5. Expert assessment of criteria significance.

Criteria	Expert 1	Expert 2	Expert 3	Expert 4	Expert 5	Linguistic Score (Final)
Number of picked items (C1)	-	-	-	-	-	-
Internally detected errors (reliability) (C2)	ES	ES	ES	ES	ES	ES
Externally detected errors (C3)	WLS	WLS	WLS	MDLS	WLS	WLS
Average number of items picked per day (C4)	MDLS	MDLS	LS	MDLS	MDLS	MDLS
Number of items picked daily above the norm (C5)	LS	LS	LS	MDLS	LS	LS
Total picking time (C6)	MDLS	MDLS	MDLS	LS	MDLS	MDLS
Order fulfillment rate (C7)	LS	LS	LS	LS	MDLS	LS
Loyalty (C8)	RLS	RLS	RLS	WLS	RLS	RLS
Adherence to work obligations (C9)	LS	LS	MDLS	LS	LS	LS

).

Based on this table, the remaining steps of the IMF SWARA method were applied to determine the criteria weights, which were then used in the next phase of the model, specifically during the application of the COPRAS method (

Table 6. IMF SWARA results.

Criteria	sj			kj			qj			wj			w (crisp)
C1	-	-	-	1.000	1.000	1.000	1.000	1.000	1.000	0.195	0.206	0.219	0.206
C2	0	0	0	1.000	1.000	1.000	1.000	1.000	1.000	0.195	0.206	0.219	0.206
C3	0.222	0.250	0.286	1.222	1.250	1.286	0.778	0.800	0.818	0.152	0.164	0.179	0.165
C4	0.250	0.286	0.333	1.250	1.286	1.333	0.583	0.622	0.655	0.114	0.128	0.143	0.128
C5	0.286	0.333	0.400	1.286	1.333	1.400	0.417	0.467	0.509	0.081	0.096	0.111	0.096
C6	0.250	0.286	0.333	1.250	1.286	1.333	0.313	0.363	0.407	0.061	0.075	0.089	0.075
C7	0.286	0.333	0.400	1.286	1.333	1.400	0.223	0.272	0.317	0.044	0.056	0.069	0.056
C8	0.333	0.400	0.500	1.333	1.400	1.500	0.149	0.194	0.238	0.029	0.040	0.052	0.040
C9	0.286	0.333	0.400	1.286	1.333	1.400	0.106	0.146	0.185	0.021	0.030	0.040	0.030
						SUM	4.569	4.864	5.128

).

Based on these results, it can be concluded that the most significant criteria identified were C1 and C2, while the least significant criterion was C9. The criteria weights obtained in this manner were used in the subsequent phase during the application of the COPRAS method.

4.2.3. COPRAS Results

To apply the COPRAS method, the initial decision matrix was defined. In this step, only the order pickers who were identified as efficient through the DEA method were considered and evaluated, i.e., the 18 efficient order pickers. The evaluation was carried out based on the criteria that had been previously observed and defined. This process resulted in the creation of the initial decision matrix (

Table 7. Initial decision-making matrix.

Alternatives/Criteria	C1	C2	C3	C4	C5	C6	C7	C8	C9
A1	2506	1	12	183	217	48	97	10	2
A2	549	1	4	149	251	4	96	4	4
A3	320	1	3	1	152	20	94	15	3
A4	5247	14	15	108	400	216	99	11	4
A5	7030	1	68	63	337	96	99	10	2
A6	11122	5	43	270	130	135	99	5	9
A7	1138	1	3	74	326	77	97	14	4
A8	13402	1	5	562	162	207	100	1	8
A9	5684	1	1	234	167	192	96	3	9
A10	1106	1	6	46	355	72	94	6	5
A11	1070	9	2	10	391	160	96	9	7
A12	1670	1	2	55	345	156	94	20	10
A13	7182	51	4	107	293	104	99	14	2
A14	4361	55	5	18	418	120	92	13	2
A15	6643	1	1	285	115	138	99	4	9
A16	3702	3	1	169	231	160	97	11	2
A17	4580	1	1	250	150	72	98	7	5
A18	5324	1	1	219	182	168	99	12	5

).

In the next step, normalization was performed using Equation (6). This resulted in the normalized decision matrix (

Table 8. Normalized decision-making matrix.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
A1	0.0303	0.0067	0.0678	0.0653	0.0469	0.0224	0.0556	0.0592	0.0217
A2	0.0066	0.0067	0.0226	0.0532	0.0543	0.0019	0.0550	0.0237	0.0435
A3	0.0039	0.0067	0.0169	0.0004	0.0329	0.0093	0.0539	0.0888	0.0326
A4	0.0635	0.0940	0.0847	0.0385	0.0865	0.1007	0.0567	0.0651	0.0435
A5	0.0851	0.0067	0.3842	0.0225	0.0729	0.0448	0.0567	0.0592	0.0217
A6	0.1346	0.0336	0.2429	0.0963	0.0281	0.0629	0.0567	0.0296	0.0978
A7	0.0138	0.0067	0.0169	0.0264	0.0705	0.0359	0.0556	0.0828	0.0435
A8	0.1622	0.0067	0.0282	0.2005	0.0350	0.0965	0.0573	0.0059	0.0870
A9	0.0688	0.0067	0.0056	0.0835	0.0361	0.0895	0.0550	0.0178	0.0978
A10	0.0134	0.0067	0.0339	0.0164	0.0768	0.0336	0.0539	0.0355	0.0543
A11	0.0129	0.0604	0.0113	0.0036	0.0846	0.0746	0.0550	0.0533	0.0761
A12	0.0202	0.0067	0.0113	0.0196	0.0746	0.0727	0.0539	0.1183	0.1087
A13	0.0869	0.3423	0.0226	0.0382	0.0634	0.0485	0.0567	0.0828	0.0217
A14	0.0528	0.3691	0.0282	0.0064	0.0904	0.0559	0.0527	0.0769	0.0217
A15	0.0804	0.0067	0.0056	0.1017	0.0249	0.0643	0.0567	0.0237	0.0978
A16	0.0448	0.0201	0.0056	0.0603	0.0500	0.0746	0.0556	0.0651	0.0217
A17	0.0554	0.0067	0.0056	0.0892	0.0325	0.0336	0.0562	0.0414	0.0543
A18	0.0644	0.0067	0.0056	0.0781	0.0394	0.0783	0.0567	0.0710	0.0543

).

In the next step, to obtain the weighted decision matrix, Equation (7) was applied along with the weights determined using the IMF SWARA method. This process resulted in the weighted decision matrix (

Table 9. Weighted decision-making matrix.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
A1	0.0062	0.0014	0.0111	0.0084	0.0045	0.0017	0.0031	0.0024	0.0007
A2	0.0014	0.0014	0.0037	0.0068	0.0052	0.0001	0.0030	0.0009	0.0013
A3	0.0008	0.0014	0.0028	0.0000	0.0032	0.0007	0.0030	0.0036	0.0010
A4	0.0131	0.0194	0.0139	0.0049	0.0083	0.0075	0.0031	0.0026	0.0013
A5	0.0175	0.0014	0.0630	0.0029	0.0070	0.0033	0.0031	0.0024	0.0007
A6	0.0277	0.0069	0.0398	0.0123	0.0027	0.0047	0.0031	0.0012	0.0029
A7	0.0028	0.0014	0.0028	0.0034	0.0068	0.0027	0.0031	0.0033	0.0013
A8	0.0334	0.0014	0.0046	0.0257	0.0034	0.0072	0.0032	0.0002	0.0026
A9	0.0142	0.0014	0.0009	0.0107	0.0035	0.0067	0.0030	0.0007	0.0029
A10	0.0028	0.0014	0.0056	0.0021	0.0074	0.0025	0.0030	0.0014	0.0016
A11	0.0027	0.0124	0.0019	0.0005	0.0081	0.0056	0.0030	0.0021	0.0023
A12	0.0042	0.0014	0.0019	0.0025	0.0072	0.0054	0.0030	0.0047	0.0033
A13	0.0179	0.0705	0.0037	0.0049	0.0061	0.0036	0.0031	0.0033	0.0007
A14	0.0109	0.0760	0.0046	0.0008	0.0087	0.0042	0.0029	0.0031	0.0007
A15	0.0166	0.0014	0.0009	0.0130	0.0024	0.0048	0.0031	0.0009	0.0029
A16	0.0092	0.0041	0.0009	0.0077	0.0048	0.0056	0.0031	0.0026	0.0007
A17	0.0114	0.0014	0.0009	0.0114	0.0031	0.0025	0.0031	0.0017	0.0016
A18	0.0133	0.0014	0.0009	0.0100	0.0038	0.0059	0.0031	0.0028	0.0016

).

In the next step, by applying Equations (8) and (9), the sums of weighted normalized values were obtained (

Table 10. Sums of weighted normalized values.

Alternatives	S+	S−
A1	0.0252	0.0142
A2	0.0187	0.0052
A3	0.0115	0.0049
A4	0.0334	0.0408
A5	0.0336	0.0677
A6	0.0500	0.0515
A7	0.0207	0.0068
A8	0.0685	0.0132
A9	0.0350	0.0090
A10	0.0183	0.0094
A11	0.0187	0.0199
A12	0.0248	0.0087
A13	0.0360	0.0778
A14	0.0270	0.0849
A15	0.0390	0.0071
A16	0.0281	0.0106
A17	0.0323	0.0048
A18	0.0347	0.0082

).

Finally, the values for the relative significances of the alternatives (Q), and quantitative utility (U) were obtained, based on which the order pickers were ranked (

Table 11. Relative significances of the alternatives, quantitative utility and ranking.

Alternatives	Q	U	Ranking
A1	0.0434	49.3663	13
A2	0.0681	77.4159	4
A3	0.0647	73.5448	6
A4	0.0397	45.1192	14
A5	0.0374	42.4674	16
A6	0.0550	62.5414	9
A7	0.0585	66.4285	8
A8	0.0880	100.0000	1
A9	0.0638	72.4447	7
A10	0.0456	51.8395	12
A11	0.0317	36.0393	17
A12	0.0547	62.1029	10
A13	0.0393	44.6580	15
A14	0.0301	34.1659	18
A15	0.0753	85.5900	3
A16	0.0524	59.4944	11
A17	0.0860	97.7461	2
A18	0.0663	75.3931	5

).

Based on Table 11, it can be concluded that the best-ranked order picker is A8, followed by A17, A15, A2, etc., while the lowest-ranked order pickers were A5, A11, and A14. In the next phase of the model, a methodology for determining bonuses for the best-ranked order pickers was proposed. This was identified as a significant gap during the literature review, as there are no studies addressing this topic and problem.

4.3. Model for Bonus Allocation

The fifth phase of this approach deals with the bonus distribution itself. The most common scenario is that the company defines a total amount to be distributed among order pickers based on their performance in the previous period. In such cases, different strategies can be used, such as rewarding a smaller number of order pickers with a larger amount or rewarding a larger number with a smaller amount.

In the observed case, the company defined a total reward of 10,000 monetary units (m.u.) for 56 order pickers. The order pickers eligible for the bonus distribution are those who scored one in the second phase (efficiency assessment). In this case, this includes 18 order pickers. Their ranking was performed in the third and fourth phases using the aforementioned methods, which also forms the basis for bonus payment.

The essence of any bonus distribution from the total amount is the weighted coefficient (w_i) for each order picker, depending on their rank. If each order picker had the same weight to receive the same amount regardless of their rank, their weight coefficient would be:

w₁ = w₂ =…= w₁₈ = 1/18 = 0.0556

However, since this approach does not make sense in the context of this study based on insights from the literature, the author’s experience, and information obtained from the management of the company, several scenarios were defined.

Scenario 1 (10%)—This scenario involves distributing the order pickers into three groups based on their rank: Group I (ranks 1 to 6), Group II (ranks 7 to 12), and Group III (ranks 13 to 18). The reason for such grouping lies in the assumption that all groups should be similar in terms of the number of order pickers, as well as in the need to divide them into more than two groups. The first group receives a 10% increase in the weight coefficient, the second group remains at the average coefficient, and the third group receives a 10% decrease in the average coefficient.

Scenario 2 (30%)—This scenario is similar to Scenario 1, but the percentage increase/decrease is now 30%.

Scenario 3 (50%)—This scenario is similar to the previous two, but the percentage increase/decrease is now 50%.

Scenario 4 (Continuous)—This scenario does not divide the order pickers into groups. Instead, they are rewarded based on their rank on the list. In this case, the challenge is to define the weight coefficients for the 18 order pickers, ensuring that each order picker has the same decrease in weight coefficient compared to the previous one. An additional condition is that the last order picker must have a weight coefficient different from zero. Also, the sum of all coefficients must equal one.

$$w_1,w_2,\dots w_{18}-\mathrm{I}\mathrm{t} \mathrm{r}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{a}\mathrm{n} \mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c} \mathrm{s}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t} \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{s} \mathrm{b}\mathrm{y} \mathrm{a} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t} d$$

$$w_k=w_1-\left(k-1\right)\ast d,\hspace{1em}\mathrm{f}\mathrm{o}\mathrm{r} k=1,2,3,\dots ,18$$

Since $w_{18}>0$ the following condition appears:

$$w_{18}=w_1-17d>0$$

$$w_1>17d$$

The sum of the arithmetic sequence of 18 order pickers is:

$$S={\displaystyle \frac{18}{2}}\ast \left(w_1+w_{18}\right)=1$$

$$9\ast \left(w_1+w_1-17d\right)=1$$

$$18\ast w_1-153d=1$$

$$w_1={\displaystyle \frac{1+153d}{18}}$$

When $w_1$ is substituted into the previously obtained inequality $w_1>17d$, the following expression is obtained:

${\displaystyle \frac{1+153d}{18}}>17d$, from which we derive that

$$d<{\displaystyle \frac{1}{153}}$$

The selection of the parameter d (the decrement step) depends on the decision-makers and provides the flexibility to adjust the distribution to a specific situation and its requirements. In this case, it was decided that

$$d={\displaystyle \frac{1}{306}}$$

The results of all scenarios are presented in

Table 12. Bonus allocation in different scenarios.

Order Picker	Rank	Group for Scenario 1, 2 and 3	Scenario 1 (10%)		Scenario 2 (30%)		Scenario 3 (50%)		Continuous
			Weight	Amount (m.u.)	Weight	Amount (m.u.)	Weight	Amount (m.u.)	Weight	Amount (m.u.)
A8	1	I	0.0611	611.1111	0.0722	722.2222	0.0833	833.3333	0.0833	833.3333
A17	2	I	0.0611	611.1111	0.0722	722.2222	0.0833	833.3333	0.0801	800.6536
A15	3	I	0.0611	611.1111	0.0722	722.2222	0.0833	833.3333	0.0768	767.9739
A2	4	I	0.0611	611.1111	0.0722	722.2222	0.0833	833.3333	0.0735	735.2941
A18	5	I	0.0611	611.1111	0.0722	722.2222	0.0833	833.3333	0.0703	702.6144
A3	6	I	0.0611	611.1111	0.0722	722.2222	0.0833	833.3333	0.0670	669.9346
A9	7	II	0.0556	555.5556	0.0556	555.5556	0.0556	555.5556	0.0637	637.2549
A7	8	II	0.0556	555.5556	0.0556	555.5556	0.0556	555.5556	0.0605	604.5752
A6	9	II	0.0556	555.5556	0.0556	555.5556	0.0556	555.5556	0.0572	571.8954
A12	10	II	0.0556	555.5556	0.0556	555.5556	0.0556	555.5556	0.0539	539.2157
A16	11	II	0.0556	555.5556	0.0556	555.5556	0.0556	555.5556	0.0507	506.5359
A10	12	II	0.0556	555.5556	0.0556	555.5556	0.0556	555.5556	0.0474	473.8562
A1	13	III	0.0500	500.0000	0.0389	388.8889	0.0278	277.7778	0.0441	441.1765
A4	14	III	0.0500	500.0000	0.0389	388.8889	0.0278	277.7778	0.0408	408.4967
A13	15	III	0.0500	500.0000	0.0389	388.8889	0.0278	277.7778	0.0376	375.8170
A5	16	III	0.0500	500.0000	0.0389	388.8889	0.0278	277.7778	0.0343	343.1373
A11	17	III	0.0500	500.0000	0.0389	388.8889	0.0278	277.7778	0.0310	310.4575
A14	18	III	0.0500	500.0000	0.0389	388.8889	0.0278	277.7778	0.0278	277.7778

.

Based on the previous table, several key observations can be made. The first scenario does not create a significant enough difference in rewards, as the best and worst-ranked order pickers differ by only 111 m.u. In the second scenario, the difference is much larger: 722 and 388 m.u. In the third scenario, the difference is more than twice as large: 833 and 277 m.u. However, a major drawback in scenarios 2 and 3 is the large gap between group transitions. For example, the order pickers in sixth and seventh place will see a much larger difference in compensation (e.g., 833 and 555 m.u.) than the first and sixth place pickers, who will receive the same amount. The main disadvantage of these approaches is this grouping, which creates a problem. This causes dissatisfaction among employees and warehouse managers, leading to additional issues. The main objective was to overcome this problem, which is precisely what the fourth scenario achieves. This scenario distributes the funds in the most objective way, without grouping the order pickers. It adopts a consistent step that ensures a fair difference in compensation, which reflects the performance parameters of the order pickers during the observed period. Interestingly, under this approach, the first and last order pickers receive a significant difference in compensation, with a continuous and proportional decrease depending on their rank. This model has been verified and approved by all employees in the observed system because it is objective, transparent, clear, and fair.

5. Discussion

5.1. Sensitivity Analysis

To determine whether changes in the weights of the criteria would lead to a change in the ranking of alternatives, a sensitivity analysis was conducted. The analysis was carried out by defining four scenarios in which different weights were assigned to the criteria (

Table 13. Criteria weights in different scenarios.

Scenario	C1	C2	C3	C4	C5	C6	C7	C8	C9
Scenario 1	0.206	0.0747	0.0551	0.206	0.128	0.096	0.164	0.0401	0.0301
Scenario 2	0.0747	0.206	0.206	0.128	0.164	0.0551	0.096	0.0401	0.0301
Scenario 3	0.1111	0.1111	0.1111	0.1111	0.1111	0.1111	0.1111	0.1111	0.1111
Scenario 4	0.164	0.128	0.096	0.0747	0.0551	0.0401	0.0301	0.206	0.206

). In the first scenario, called performance-based, higher weights were given to the criteria related to the performance of the order pickers, i.e., criteria C1 and C4. In the second scenario, called error-free, higher weights were assigned to the criteria related to errors, namely C2 and C3. In the third scenario, all criteria were considered to have equal importance, and thus, equal weights were assigned to them. In the final, fourth scenario, called devotion, the highest weights were assigned to the criteria C8 and C9, which pertain to the order pickers’ loyalty to the company. The weights used in the different scenarios are shown in Table 13.

After defining the scenarios, the COPRAS method was applied to rank the alternatives. The ranking results by scenario are shown in

Table 14. Sensitivity analysis ranking.

Scenario	Scenario 1			Scenario 2
Alternatives	Q	U	Ranking	Q	U	Ranking
A1	0.0509	51.5383	9	0.0426	47.5378	12
A2	0.0739	74.8210	2	0.0667	74.4647	5
A3	0.0543	54.9564	8	0.0644	71.9016	8
A4	0.0492	49.8125	12	0.0395	44.0316	14
A5	0.0470	47.5931	14	0.0328	36.6441	17
A6	0.0684	69.2222	3	0.0409	45.6797	13
A7	0.0482	48.7384	13	0.0645	71.9350	7
A8	0.0988	100.0000	1	0.0730	81.4157	3
A9	0.0576	58.2348	7	0.0660	73.6279	6
A10	0.0428	43.3135	16	0.0498	55.5333	11
A11	0.0345	34.8822	18	0.0390	43.4995	15
A12	0.0449	45.4512	15	0.0637	71.0288	9
A13	0.0498	50.4064	10	0.0346	38.5912	16
A14	0.0386	39.0335	17	0.0315	35.1492	18
A15	0.0658	66.6230	5	0.0758	84.5540	2
A16	0.0497	50.3240	11	0.0559	62.3510	10
A17	0.0672	67.9549	4	0.0896	100.0000	1
A18	0.0582	58.9125	6	0.0697	77.7401	4
Scenario	Scenario 3			Scenario 4
Alternatives	Q	U	Ranking	Q	U	Ranking
A1	0.0476	61.1824	13	0.0414	54.3832	16
A2	0.0778	100.0000	1	0.0520	68.1726	10
A3	0.0723	92.9489	3	0.0599	78.6334	8
A4	0.0451	57.9444	14	0.0458	60.0621	12
A5	0.0390	50.1842	17	0.0403	52.8164	17
A6	0.0540	69.3971	10	0.0617	80.9529	7
A7	0.0595	76.4780	7	0.0583	76.4625	9
A8	0.0731	93.9829	2	0.0762	100.0000	1
A9	0.0557	71.5575	9	0.0626	82.1914	6
A10	0.0495	63.6029	11	0.0439	57.6489	14
A11	0.0427	54.8983	16	0.0428	56.1834	15
A12	0.0616	79.2439	6	0.0754	98.9688	2
A13	0.0428	54.9663	15	0.0457	59.9474	13
A14	0.0370	47.5583	18	0.0377	49.4892	18
A15	0.0637	81.9528	5	0.0710	93.2045	4
A16	0.0491	63.0733	12	0.0486	63.7616	11
A17	0.0715	91.9674	4	0.0711	93.2318	3
A18	0.0582	74.7779	8	0.0655	85.9646	5

.

Based on the results of the sensitivity analysis, it can be concluded that in scenarios 1 and 4, the best-ranked alternative remained unchanged, i.e., it is still A8. On the other hand, there was a change in the rank of the other alternatives. When considering scenarios 2 and 3, it can be concluded that the best-ranked alternative changed in these scenarios, with A17 becoming the best in scenario 2 and A2 in scenario 3. However, when looking at the worst-ranked alternatives, it can be said that there were minimal differences across the different scenarios. Based on these results, it can be concluded that changes in the weights of the criteria do have some impact on the solution, but only in terms of the best-ranked alternatives, while the worst-ranked alternatives remain unaffected.

5.2. Model Validation

Along with the sensitivity analysis, a model validation was also carried out to evaluate the proposed model. The validation process involved the application of a combination of several methods, including techniques for determining the criteria weights and methods for ranking alternatives (Figure 2).

As can be seen from the figure, the methods used to determine the weights of the criteria are Criteria Impact Loss (CILOS) [35], Criteria Importance Through Inter-criteria Correlation (CRITIC) [36], Integrated Determination of Objective Criteria Weights (IDOCRIW) [37], and Method based on the Removal Effects of Criteria (MEREC) [38]. The weights obtained by applying these methods are presented in

Table 15. Criteria weights using different methods.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
CILOS	0.031	0.219	0.029	0.031	0.109	0.024	0.481	0.026	0.049
CRITIC	0.084	0.124	0.100	0.092	0.148	0.092	0.099	0.121	0.140
IDOCRIW	0.028	0.784	0.082	0.034	0.026	0.012	0.000	0.012	0.022
MEREC	0.131	0.182	0.165	0.265	0.042	0.050	0.003	0.120	0.042

.

Subsequently, the obtained criteria weights were combined using various MCDM methods, such as Additive Ratio Assessment (ARAS) [39], Combined Compromised Solution (CoCoSo) [40], Combinative Distance-based Assessment (CODAS) [41], Multi-attributive border approximation area comparison (MABAC) [42,43], Multi-Attributive Ideal–Real Comparative Analysis (MAIRCA) [39], Measurement Alternatives and Ranking according to Compromise Solution (MARCOS) [44], Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) [45], and VIseKriterijumska Optimizacija i Kompromisno Resenje (VIKOR) [46], to generate the ranking of alternatives. The ranking based on different method combinations is presented in

Table 16. Alternatives ranking when combining different methods.

Methods	A1	A2	A3	A4	A5	A6	A7	A8	A9	A10	A11	A12	A13	A14	A15	A16	A17	A18
ARAS-IDOCRIW	0.734	0.79	0.74	0.128	0.733	0.241	0.756	0.83	0.855	0.734	0.181	0.793	0.112	0.092	0.863	0.39	0.847	0.85
Rank	10	7	9	16	12	14	8	5	2	10	15	6	17	18	1	13	4	3
ARAS-CRITIC	0.326	0.562	0.344	0.314	0.343	0.36	0.375	0.487	0.454	0.33	0.326	0.483	0.314	0.29	0.469	0.359	0.433	0.456
Rank	14	1	11	16	12	9	8	2	6	13	14	3	16	18	4	10	7	5
ARAS-CILOS	0.647	0.748	0.627	0.526	0.683	0.54	0.684	0.748	0.709	0.664	0.527	0.729	0.498	0.482	0.717	0.554	0.695	0.712
Rank	11	1	12	16	9	14	8	1	6	10	15	3	17	18	4	13	7	5
ARAS-MEREC	0.326	0.413	0.269	0.228	0.293	0.363	0.31	0.642	0.493	0.237	0.192	0.372	0.272	0.185	0.536	0.389	0.502	0.512
Rank	10	6	14	16	12	9	11	1	5	15	17	8	13	18	2	7	4	3
COCOSO-IDOCRIW	3.801	3.965	3.652	3.239	3.485	3.721	3.99	3.962	4.021	3.972	3.626	4.05	1.536	1.313	3.9	3.744	4.007	4.009
Rank	10	7	13	16	15	12	5	8	2	6	14	1	17	18	9	11	4	3
COCOSO-CRITIC	1.686	1.792	1.469	1.746	1.538	1.851	1.908	1.833	1.815	1.814	1.856	2.013	1.645	1.273	1.792	1.661	1.856	1.886
Rank	13	10	17	12	16	6	2	7	8	9	4	1	15	18	10	14	4	3
COCOSO-CILOS	2.552	2.577	1.898	2.861	2.739	2.944	2.806	3.059	2.57	2.362	2.626	2.465	2.416	1.26	2.876	2.534	2.832	3.001
Rank	12	10	17	5	8	3	7	1	11	16	9	14	15	18	4	13	6	2
COCOSO-MEREC	1.823	1.888	1.668	1.746	1.488	1.984	1.947	2.172	2.008	1.844	1.793	2.019	1.638	1.234	1.942	1.835	2.062	2.074
Rank	12	9	15	14	17	6	7	1	5	10	13	4	16	18	8	11	3	2
CODAS-IDOCRIW	7.915	8.048	7.966	−18.48	7.938	−14.698	8.068	8.292	8.548	7.965	−16.742	8.271	−19.328	−19.539	8.565	−9.806	8.495	8.521
Rank	12	8	9	16	11	14	7	5	2	10	15	6	17	18	1	13	4	3
CODAS-CRITIC	−1.411	0.432	−0.767	−2.014	−0.291	−1.769	0.494	2.162	2.13	−0.41	−1.381	4.031	−2.58	−2.207	2.294	−1.483	0.919	1.851
Rank	13	8	11	16	9	15	7	3	4	10	12	1	18	17	2	14	6	5
CODAS-CILOS	1.672	1.866	1.484	−3.612	2.057	−3.98	2.02	2.182	1.982	1.916	−3.627	2.29	−4.598	−4.321	2.056	−3.323	1.898	2.038
Rank	11	10	12	14	3	16	6	2	7	8	15	1	18	17	4	13	9	5
CODAS-MEREC	−0.424	−0.405	−0.891	−5.176	−0.744	−1.854	−0.302	6.86	4.133	−1.604	−5.233	1.864	−3.989	−5.749	4.847	−0.145	4.227	4.585
Rank	10	9	12	16	11	14	8	1	5	13	17	6	15	18	2	7	4	3
MABAC-IDOCRIW	0.124	0.135	0.121	−0.055	0.066	0.056	0.141	0.176	0.15	0.136	0.028	0.16	−0.581	−0.642	0.154	0.106	0.145	0.146
Rank	10	9	11	16	13	14	7	1	4	8	15	2	17	18	3	12	6	5
MABAC-CRITIC	−0.004	0.01	−0.042	0.049	−0.016	0.045	0.084	0.127	0.019	0.02	0.06	0.166	−0.027	−0.109	0.076	−0.023	0.039	0.057
Rank	13	12	17	7	14	8	3	2	11	10	5	1	16	18	4	15	9	6
MABAC-CILOS	0.033	−0.009	−0.166	0.162	0.171	0.144	0.082	0.25	−0.013	−0.096	0.011	−0.055	−0.012	−0.42	0.161	0.026	0.094	0.162
Rank	9	12	17	3	2	6	8	1	14	16	11	15	13	18	5	10	7	3
MABAC-MEREC	0.036	0.007	−0.017	−0.02	−0.107	0.047	0.037	0.272	0.07	−0.025	−0.045	0.088	−0.079	−0.16	0.117	0.043	0.098	0.104
Rank	10	11	12	13	17	7	9	1	6	14	15	5	16	18	2	8	4	3
MAIRCA-IDOCRIW	0.006	0.005	0.006	0.016	0.009	0.01	0.005	0.003	0.005	0.005	0.011	0.004	0.045	0.049	0.004	0.007	0.005	0.005
Rank	8	10	8	3	6	5	10	18	10	10	4	16	2	1	16	7	10	10
MAIRCA-CRITIC	0.028	0.027	0.03	0.025	0.029	0.025	0.023	0.021	0.027	0.027	0.025	0.019	0.029	0.034	0.024	0.029	0.026	0.025
Rank	6	7	2	11	3	11	16	17	7	7	11	18	3	1	15	3	10	11
MAIRCA-CILOS	0.021	0.023	0.032	0.013	0.013	0.015	0.018	0.009	0.023	0.028	0.022	0.026	0.023	0.046	0.014	0.021	0.017	0.014
Rank	9	5	2	16	16	13	11	18	5	3	8	4	5	1	14	9	12	14
MAIRCA-MEREC	0.026	0.027	0.028	0.029	0.033	0.025	0.025	0.012	0.024	0.029	0.03	0.023	0.032	0.036	0.021	0.025	0.022	0.022
Rank	9	8	7	5	2	10	10	18	13	5	4	14	3	1	17	10	15	15
MARCOS-IDOCRIW	0.734	0.79	0.74	0.128	0.733	0.24	0.756	0.83	0.855	0.733	0.181	0.793	0.111	0.091	0.863	0.39	0.847	0.85
Rank	10	7	9	16	11	14	8	5	2	11	15	6	17	18	1	13	4	3
MARCOS-CRITIC	0.322	0.556	0.34	0.309	0.339	0.355	0.37	0.482	0.449	0.325	0.32	0.476	0.309	0.285	0.463	0.354	0.428	0.451
Rank	14	1	11	16	12	9	8	2	6	13	15	3	16	18	4	10	7	5
MARCOS-CILOS	0.591	0.685	0.573	0.477	0.624	0.491	0.625	0.685	0.649	0.607	0.477	0.667	0.45	0.436	0.656	0.504	0.636	0.651
Rank	11	1	12	15	9	14	8	1	6	10	15	3	17	18	4	13	7	5
MARCOS-MEREC	0.326	0.412	0.268	0.228	0.293	0.362	0.309	0.643	0.493	0.236	0.191	0.371	0.272	0.185	0.536	0.389	0.502	0.512
Rank	10	6	14	16	12	9	11	1	5	15	17	8	13	18	2	7	4	3
TOPSIS-IDOCRIW	0.945	0.947	0.937	0.756	0.895	0.896	0.947	0.965	0.955	0.946	0.844	0.95	0.121	0.095	0.956	0.936	0.953	0.954
Rank	10	7	11	16	14	13	7	1	3	9	15	6	17	18	2	12	5	4
TOPSIS-CRITIC	0.483	0.5	0.466	0.55	0.492	0.52	0.568	0.555	0.514	0.529	0.57	0.638	0.465	0.445	0.535	0.475	0.509	0.531
Rank	14	12	16	5	13	9	3	4	10	8	2	1	17	18	6	15	11	7
TOPSIS-CILOS	0.648	0.566	0.401	0.826	0.836	0.789	0.666	0.843	0.559	0.422	0.565	0.426	0.656	0.177	0.787	0.647	0.725	0.807
Rank	10	12	17	3	2	5	8	1	14	16	13	15	9	18	6	11	7	4
TOPSIS-MEREC	0.53	0.5	0.465	0.464	0.406	0.549	0.496	0.739	0.567	0.46	0.439	0.509	0.411	0.355	0.609	0.539	0.588	0.588
Rank	8	10	12	13	17	6	11	1	5	14	15	9	16	18	2	7	3	3
VIKOR-IDOCRIW	0.093	0.07	0.075	0.948	0.093	0.818	0.063	0.051	0.001	0.081	0.893	0.033	0.995	1	0.003	0.656	0.009	0.004
Rank	7	11	10	3	7	5	12	13	18	9	4	14	2	1	17	6	15	16
VIKOR-CRITIC	0.811	0.378	0.768	0.561	0.681	0.769	0.34	0.374	0.415	0.329	0.511	0.018	0.821	0.932	0.578	0.776	0.532	0.309
Rank	3	13	6	9	7	5	15	14	12	16	11	18	2	1	8	4	10	17
VIKOR-CILOS	0.315	0.403	0.673	0.352	0.051	0.336	0.275	0.038	0.393	0.623	0.51	0.581	0.401	1	0.113	0.399	0.181	0.081
Rank	12	6	2	10	17	11	13	18	9	3	5	4	7	1	15	8	14	16
VIKOR-MEREC	0.481	0.523	0.838	0.772	0.701	0.468	0.644	0.012	0.18	0.786	0.952	0.574	0.735	0.97	0.052	0.461	0.15	0.174
Rank	11	10	3	5	7	12	8	18	14	4	2	9	6	1	17	13	16	15

.

Based on the model validation results, it can be concluded that A8 was the best-ranked 13 times, while the same alternative was the worst-ranked five times. On the other hand, A14 was the best-ranked eight times, while it was the worst-ranked 22 times. The ranking of all alternatives, as well as the method combinations in which each alternative was best-ranked or worst-ranked, are presented in

Table 17. Best- and worst-ranked alternatives using different combinations of methods.

Methods	Best-Ranked	Worst-Ranked
A1
A2	ARAS-CRITIC
	ARAS-CILOS
	MARCOS-CRITIC
	MARCOS-CILOS
A3
A4
A5
A6
A7
A8	ARAS-CILOS	MAIRCA-IDOCRIW
	ARAS-MEREC	MAIRCA-CILOS
	COCOSO-CILOS	MAIRCA-MEREC
	COCOSO-MEREC	VIKOR-CILOS
	CODAS-MEREC	VIKOR-MEREC
	MABAC-IDOCRIW
	MABAC-CILOS
	MABAC-MEREC
	MARCOS-CILOS
	MARCOS-MEREC
	TOPSIS-IDOCRIW
	TOPSIS-CILOS
	TOPSIS-MEREC
A9		VIKOR-IDOCRIW
A10
A11
A12	COCOSO-IDOCRIW	MAIRCA-CRITIC
	COCOSO-CRITIC	VIKOR-CRITIC
	CODAS-CRITIC
	CODAS-CILOS
	MABAC-CRITIC
	TOPSIS-CRITIC
A13		CODAS-CRITIC
		CODAS-CILOS
A14	MAIRCA-IDOCRIW	ARAS-IDOCRIW
	MAIRCA-CRITIC	ARAS-CRITIC
	MAIRCA-CILOS	ARAS-CILOS
	MAIRCA-MEREC	ARAS-MEREC
	VIKOR-IDOCRIW	COCOSO-IDOCRIW
	VIKOR-CRITIC	COCOSO-CRITIC
	VIKOR-CILOS	COCOSO-CILOS
	VIKOR-MEREC	COCOSO-MEREC
		CODAS-IDOCRIW
		CODAS-MEREC
		MABAC-IDOCRIW
		MABAC-CRITIC
		MABAC-CILOS
		MABAC-MEREC
		MARCOS-IDOCRIW
		MARCOS-CRITIC
		MARCOS-CILOS
		MARCOS-MEREC
		TOPSIS-IDOCRIW
		TOPSIS-CRITIC
		TOPSIS-CILOS
		TOPSIS-MEREC
A15	ARAS-IDOCRIW
	CODAS-IDOCRIW
	MARCOS-IDOCRIW
A16
A17
A18

.

5.3. Theoretical and Managerial Implications

Order picking is one of the most demanding and crucial processes in e-commerce, as it directly impacts delivery speed and accuracy. A poor bonus distribution system can reduce employee motivation and negatively affect the overall efficiency of the process. By optimizing the reward system, numerous positive effects can be achieved:

• Increased delivery speed.
• Reduced commissioning errors.
• Adaptation to seasonal fluctuations in demand.
• Optimization of operating costs.
• Increased employee satisfaction and reduced worker turnover.
• Improvement in service quality and increased revenue.

The practical implications of this research primarily relate to its direct application in e-commerce warehouses, regardless of size, market, or product structure. The approach utilizes a unique set of indicators that arose as a synergy of theoretical and practical knowledge. It enables an objective and quick assessment of bonuses for employee satisfaction, management, customers, and company owners. The model offers each system the possibility to further adjust the measurement process to its specific needs. Based on the results obtained from applying the proposed model, it is possible to define preventive and corrective measures to enhance the efficiency of inefficient order pickers. Specifically, the application of the DEA method enables the identification of a benchmark for each order picker, highlighting the most efficient ones as reference points for performance improvement.

The theoretical implications of this study are numerous. First and foremost, this model addresses a clear gap related to reward and incentive models for order pickers in e-commerce. The model provides an excellent foundation for further research, expansion, modification, and the testing of its applicability in other markets and companies. On one hand, the model was developed for a specific system, but on the other, it simultaneously provides the opportunity to adapt to the different requirements of decision-makers.

6. Conclusions

This study unequivocally highlights the critical role of order picker efficiency in e-commerce warehouses, particularly under the intense workload conditions driven by seasonal fluctuations. Companies face significant challenges in the preparation and sorting of shipments, where the efficiency of order pickers directly impacts operational performance and service quality. The proposed model was developed and implemented in four phases. In the first phase, the application of the DEA method facilitated a quantitative evaluation of the efficiency of 56 order pickers based on three input and five output variables. The second and third phases involved ranking the order pickers using the IMF SWARA and COPRAS methods. In the fourth phase, a bonus distribution model was designed based on the obtained results, incorporating four distinct scenarios. This model ensures a fair and transparent allocation of bonuses, thereby incentivizing warehouse workers to enhance their performance. A comprehensive sensitivity analysis and model validation confirmed its stability and reliability. The proposed methodological framework addresses a notable gap in the literature, as previous studies have largely overlooked the detailed assessment of order picker efficiency and the distribution of performance-based incentives. The findings of this research offer valuable insights for refining reward systems and supporting data-driven managerial decision-making in logistics. Furthermore, the proposed model can be adapted for use in other sectors that assess worker efficiency. Its implementation has the potential to improve operational performance in logistics companies while simultaneously increasing employee satisfaction.

Based on these findings, this study provides both theoretical and practical contributions. The significance of this research is particularly evident in its integration of theoretical advancements, existing literature insights, and practical constraints observed in real-world systems. The primary limitation of this study lies in the relatively small sample size used for model validation. Additionally, this study is based on a single domestic warehouse, e-commerce company, which naturally limits the empirical generalizability of the findings. While the proposed multi-stage framework and evaluation criteria are conceptually grounded in established performance measurement theory, caution is warranted when extrapolating specific efficiency and bonus allocation results to other operational contexts. Future research should consider multiple warehouses or e-commerce settings to validate the framework and enhance external applicability. Future research could focus on testing the model on larger datasets, across diverse markets, and exploring additional factors influencing the efficiency outcomes. Employee surveys, combined with advanced statistical analyses, could further refine the model and enhance its applicability. Additionally, the integration of more sophisticated analytical techniques and machine learning approaches could offer a more precise assessment of order picker efficiency. Simulation modeling also represents a promising direction for future investigations. A crucial aspect of future research should be the refinement of employee compensation strategies, not only in terms of bonus distribution methodologies, but also considering the broader economic implications, company performance metrics, worker satisfaction, and wider social and economic impacts. Moreover, the development of a dedicated software tool could streamline the practical application of this model, making efficiency assessments and bonus allocations more accessible and scalable.