Warehouse Management Optimization Using A Sorting-Based Slotting Approach

: Purpose: Slotting is one of the main operations in warehouse management. It is based on the efficient allocation of slots for stock-keeping units (SKUs). Order picking and slotting represent a high percentage of total logistics costs; therefore, improving these activities leads to significant savings in overall performance. This paper aims to develop an allocation model integrating SKUs physical variables, warehousing design and operation (dimensions, layout, material handling equipment), and heterogeneous product demand. Design/methodology/approach: The modeling methodology considers two phases. First, an integer linear programming model for warehousing spaces assignment for SKUs considering priority and required orders is developed. Then, the total operation times using different strategies are calculated. Findings: The effectiveness of the model was verified through simulation using historical data. The results showed that the best performance in the total time of the slotting operation is achieved by using the ABC as a criterion for the classification of the SKUs and by sequentially assigning the row, level, column, and section. Practical implications: This approach can be adapted to different industrial sectors and serves as a basis for more robust models regarding the number of constraints or the incorporation of additional warehouse operating parameters.

Otherwise, there are several ways to study the picking strategies.The heuristics methods are the most common (Battista, Fumi, Laura & Schiraldi, 2014;Bustillo, Menéndez, Pardo & Duarte, 2016;Cano, 2019;Cano, Correa, Gómez & Cortés, 2019;Guerriero, Pisacane & Rende, 2015;Sukhov, Batsyn & Terentev, 2014;Zhang, Nishi, Turner, Oga & Li, 2016).This problem depends on the constraints and assumptions from each warehouse.The organizational structure sets the constraints on the operative and tactic decisions levels.For example, the order picking may be performed by using a picker-to-part or a part-to-picker method (Boysen & Stephan, 2013;Manzini et al., 2015).The warehousing management must define the strategies about methods, tools, configuration, and the constraints to develop the picking strategy (Kim & Smith, 2011).This paper works on the lack of studies considering integration between picking and slotting strategies to reduce total operation times that significantly affect warehouse performance.The integration of these strategies has not been widely studied and could improve the performance of warehouse management.
This paper aims to propose a warehousing management model considering the requirements given by a study case.Another purpose is to introduce a tool that can support the implementation of warehouse management strategies using correlated methods between slotting and picking to improve the performance and work around all the warehouse behavior.This paper is organized as follows: Section 2 presents a research background.Section 3 presents the research framework and methodology proposal referring to a mixed-integer linear model with a two-phase algorithm to solve it.Section 4 presents the proposed model formulation including assumptions, parameters, decision variables, and constraints.Section 5 exhibits the model application relating to a study case.Finally, in section 6, the analysis and results discussion are presented.

Research Background
Some researchers and practitioners have studied and proposed warehouse management techniques to improve and optimize warehouse performance.Some previous work had focused on two main factors: (i) spaces assignment and (ii) picking strategies (Duque-Jaramillo et al., 2020;Zhang, 2016;Zhong et al., 2022).For the space assignment, some authors based on the Product Allocation Problem (PAP).PAP consists on to locate the SKUs inside the warehouse slots by reducing cost, operation time, and used slots and increasing the service level (Lorenc, Kuźnar & Lerher, 2021;Lorenc & Lerher, 2020;Scheffler, Wesselink & Buscher, 2021).
In this topic, Millstein, Yang and Li (2014) developed a model to improve the quality and efficiency of the inventory grouping.The model optimized the number of groups and SKUs assignment according to service level.The authors developed a support decision-making tool that offset the service level inventory cost and more decision factors.Huang, Wang, Batta and Nagi (2014) introduced an integrated two phases model for slot selection and space determination with products carried from supplier to warehouse and stored for an indeterminate time.The objective was to reduce the inbound and outbound transportation costs as well as the total cost of operation, including the location and variable costs.The authors mentioned that the picking and slotting problem is closely related to the warehouse selection and sizing problem.Zhang et al. (2016) pointed out an application in the real world where the challenge was to search free slots for products and manage them.They developed an integrated strategy that combined PAP with the capacitated lotsizing using COI rule allocation based on priority.This was achieved by formulating an integer linear programming model to optimize the total cost of production, setup storage, handling, and reserving places.Alqahtani (2023) developed an analytical hierarchical process model to solve the storage allocation and assignment problem using COI as the ABC analysis criterion.The storage area was partitioned according to the class-based policy.However, SKUs were randomly assigned within a class.Zhang, Shang, Alawneh, Yang and Nishi (2021) proposed a joint production planning and randomized storage strategy to increase space utilization by using IoT systems.The model minimized the total cost of both operations by determining the production quantity, inventory level, and storage assignments.However, the class-based storage assignment policy was not considered.Yiğit and Esnaf (2021) proposed a technique to sort the inventory combining ABC analysis, a fuzzy C-Mean cluster algorithm and analytic hierarchical process for a multicriteria inventory classification.The authors considered most companies used ABC inventory classification, but they pointed out as a weakness the use of popularity as single criterion.The model included nominal and non-nominal variables like the criticality factor and average unit cost.Yan, Zhang, Liu, Lv, Zhang and Li (2021) presented a multi-objective algorithm combining an NSGA II genetic algorithm and an ABC method for neighborhood search to optimize warehouse schedule considering aisle switching time.The model aimed to minimize the total competition time and total delay penalty.This work was based on an automated warehouse and did not use the COI classification in its algorithms.Silva, Roodbergen, Coelho and Darvish (2022) proposed a methodology to predict the optimal size of an ABC warehouse product allocation.They considered warehouse layout, demand characteristics, and storage and routing policies.To solve the problem, they used machine learning models and demonstrate a performance increase by comparing ABC with random storage.The authors explored a PAP but just considered ABC as the unique slotting methodology and no routing optimization.
The picking strategies cover the methodologies to prepare the order including the routing methods to reduce operation times (Bustillo et al., 2016;Cano, 2019;Guo, Wu, Shen, Starner, Baumann & Gilliland, 2015).Zhang (2016) mentioned several solutions for correlated storage assignment strategy.The author developed some picking strategies using picker-to-parts methods in a warehouse section.These strategies were based on the correlation between SKUs and search the best results in warehouse operation.This approach could help to reduce travel distances for order pickers and improve the efficiency of the picking process.
Yener and Yazgan (2019) performed a literature review and proposed a mixed-integer quadratic model considering variables like consumption, capacity, and travel distances.They focused on three issues: (i) the effectiveness of warehouse design (ii) picking assignment zones and (iii) order picking process aiming to reduce the picking time.
Yuan, Li, Wang, Dou and Pan (2021) introduced a slotting methodology for zone-based robotic picking distribution systems.The authors included the mathematical formulation to solve the slotting problem but, due to the problem complexity they developed a four phases hybrid heuristic.One of them included correlated items picking analysis according to SKUs correlation.Boysen and Stephan, (2013) analyzed a PAP under a pick-by-order policy.The objective was to allocate the SKUs making the least possible picker effort.The authors also designed a multiple-aisle warehouse configuration.This configuration could change aisle parameters allowing a more complex analysis.They stated that the picking and slotting strategies combination is a critical factor in warehouse operations due to it can have a significant impact on picking efficiency and order accuracy.Schuur (2015) described some cases where COI classification was not the best decision.However, the COI strategy could be combined with a wave picking strategy to improve the overall performance of the warehouse.He also stated that there were other slotting strategies that could be combined with picking strategies.
An approach for warehouse management and design systems was introduced by Manzini et al. (2015).It involved demand patterns with SKUs lifetimes.The authors formulated a mixed-integer linear model based on costs and used two policies (picker-to-part and part-to-picker) with SKUs assignment using the lifetime as a popularity criterion.They concluded there were several different ways to combine picking and slotting depending on the characteristics of the warehouse operation.Guerriero et al. (2015) presented a mathematical model for multi-level PAP.The objective was to reduce the inventory delivery times and logistic costs and guarantee the service level by combining slotting and picking strategies.The problem was represented using mixed-integer linear programming and compatibility constraints according to product classification.The solution was found with an iterated local search-based heuristic and cluster-based heuristic.Kuo, Kuo, Chen and Zulvia (2016) developed a methodology to zone warehouses and allocate space (synchronized zone order picking) based on logistics management policies combining picking and slotting strategies.Their goal was to reduce cost, travel distances, and lead times and increase customer satisfaction and warehouse utilization.To solve these problems, they used Particle Swarm Optimization metaheuristics and genetic algorithms.Kung and Liao (2017) developed a PAP solution methodology to maximize the result based on the demand behavior and minimize the impact on marginal benefit with a non-linear model focusing on the problem of competitive facility location with network effects.Pferschy and Schauer (2018) developed a methodology to work with non-standard warehouses structure.They used a heuristic solution algorithm based on a fair graph model considering the order batching and grouping them for picking.
Wang, Zhang and Fan (2020) developed a storage location assignment mechanism by exploiting data characteristics from item orders seeking to minimize the total travel distance.They generated different instances with ABC classification that allow for improving the picking performance by a data-based approach.Although the authors considered classification methodologies advantageous, they did not consider them a strategy to solve the problem.
Pacheco, Møller-Clausen and Bumann (2023) indicated the pros of ABC classification for reducing operational waste in distribution warehouses.The authors integrated three conceptual modeling tools and a quantitative tool based on successive correlation vectors and matrices.The ABC classification provided a structure for allocations and reduced the waste on transportation during the picking process.The work did not use other classification methodologies, such as COI, to demonstrate waste reduction.Fontana and Nepomuceno (2017) proposed a multi-criteria decision model for classifying the products and solving the storage location assignment problem in a multi-layer warehouse.The model assigned a fixed location for each product considering several criteria, such as the demand level and the decision-maker preferences.Due to the above, the model goal was optimizing the slotting or picking operations, and it was not possible to obtain and compare the total times of picking orders.
Wang, Man, Zhao, Zhang and Zhao (2022) proposed a storage assignment optimization model using Adaptive Genetic Algorithm in order to reduce goods movement and travel distance and improve order-picking efficiency.The model addressed the robotic mobile fulfillment systems problem in a warehouse with a fishbone rack layout.The model considered the working distance and aisle balance but did not consider the correlation between orders on storage assignment.
Mirzaei, Zaerpour and de Koster (2021) considered product affinity as a relevant variable for improving warehousing management, assigning multiple correlated products to the same inventory cluster, and reducing retrieval time.They proposed an integrated cluster allocation (ICA) policy based on both product turnover and affinity.Although the model could reduce the total retrieval time compared to class-based policies, this was true when applied to robotic mobile fulfillment systems.Viveros, González, Mena, Kristjanpoller and Robledo (2021) developed a mathematical programming model to minimize the total travel distance addressing the multi-level storage locations assignment problem for SKU pallets.They proposed a sequential decomposition method of the problem whose solution depends on the storage location type, the storage strategy, the number of SKUs, and the warehouse size.However, the model was applicable in warehouses where it was possible to vary the height and the size.
Most of the authors proposed models to provide a solution in specific cases considering the reduction of operating costs and focusing on one of the two activities that significantly affect warehouse performance.But a smaller number of them worked with combined slotting and picking strategies.Integrating slotting and picking strategies could improve picking efficiency and reduce errors and costs.However, there is not enough research on this integration, and some possible barriers to performing this integration are related to data accuracy, the flexibility of the slotting strategies, and the trained force (Khullar, 2021).Silva, Coelho, Darvish and Renaud (2020) jointly analyzed storage location and order-picking problems by considering four routing policies.The proposed metaheuristic worked efficiently for small instances and improved traditional solutions for large warehouses and picking operations.The results of this work highlighted the importance of jointly analyzing picking and slotting problems.The SKUs allocation policy should be periodically updated according to the seasonality of sales, the products expiration date, among other factors.  1 summarizes the main contributions to warehouse management optimization previously mentioned, highlighting the optimization problem (space assignment and picking strategies, individually and jointly), the proposed technique, the optimization objective function, and the authors.The joint management of slotting and picking is important because the two processes are interrelated and complement each other to improve efficiency and productivity in logistics systems.Some of the main reasons for combining slotting and picking are to optimize workflow, reduce picking times, minimize picking and storage costs, and improve picking accuracy (Echeverria-Garcia, Espinoza-Alarcon & Quiroz-Flores, 2022).There is no single best combination of picking and slotting, as the optimal solution depends on the specifics of the warehouse and the order profile.However, the use of ABC classification and COI has not been widely studied and could improve the standardization of picking and slotting strategies, considering bulk conditions.

Methodology
This methodology is based on a two-phase algorithm.The first phase manages classic slotting strategies for warehousing management by assigning priority to each SKU.Also, it is supported in an integer linear programming model for warehousing spaces assignment for the SKUs considering priority and required orders.The second phase calculates the strategies total operation time for the selected periods.
ABC classification and Cube per Order Index (COI) were the selected methodologies for priority classification.The assignment strategies were based on an adaptation of the Traveling Salesman Problem (TSP) and establishing six different slot assignment sequences (SAS).The TSP aimed to assign each SKU to the empty slot with the lower travel time and the SAS defined different path patterns (Khalil, Li, Wang & Khan, 2016;Nalivajevs & Karapetyan, 2019).Moreover, the following conditions were considered: 1.The warehouse was divided into sections, rows, columns, and levels.A section is each of the areas into which a warehouse is divided according to the storage or handling requirements of the products.A row is the set of rack locations arranged horizontally along the aisles.A column is a set of spaces arranged one above the other in a row.The level number corresponds to the increasing order of the vertically available spaces in a column.There were twenty-four alternatives to organize the sequence in which the spaces will be assigned under a structured order, changing the section, row, column, and level (Table 2).
2. There were six paths in the tridimensional perspective.The calculated travel times were measured considering Manhattan distances.
3. Only evaluated the sequences and paths that gave priority to the exit of the warehouse and/or reduce traveled distances, considering the warehouse structure.It depends on some factors like: (i) the vehicle speed is faster when is empty and (ii) the location of the entry and exit gates.The modeling methodology is in Figure 1.The inputs include internal factors from company decisions referred to the warehouse design configuration and external factors associated with product characteristics.Since the proposed model is applied to different operational warehouse parameters, a two-phase approach is used.The first phase focuses on defining the operational strategies regarding priority methods, space requirements, and slot allocation.

SAS
This phase establishes the warehouse conditions for the problem formulation and each specific application case.
The second phase focuses on measuring and analyzing the different allocation strategies and their contribution to improving the picking activity.The model outputs are the times for the different allocation strategies in each analysis period.

Model Characteristics
The model was applied in the distribution center of a baked and packaged food company in the city of Medellin (Colombia), with 22,204 slots.The assumptions, notations, definitions, mathematical formulation, and constraints are presented in this section.

Model Assumptions
The following assumptions were established to apply this model: 1.The demand of each SKU is known for each period (months).
2. The SKUs do not need special warehousing conditions.3. The slot sizes are homogeneous.
4. Any pallet can be stored in any slot.5.The dimensions and weights of the pallets are similar.
6.The warehouse layout is known.7. The picking orders are made in pallets.
8. The vehicle loading and unloading times are not considered.

Notations and Definitions
The notation definitions, index parameter sets and decision variables for this model are defined as follows.
Figure 1.Proposed model structure p, s, r, c, l, i: index for periods, sections, rows, columns, levels, and item, respectively.Parameters Table 3 presents the input parameters to define the warehouse conditions and configurations.Lowering time from the level l to the floor Table 3. Model parameters configuration

Sets
Table 4 shows the sets for defining the objective function limits for summations.

Mathematical Formulation
The objective function (3) minimizes the strategies times ST p for each period p. Equation (4) calculates each ST p according to the parameters sets and decision variables.Also, Equations ( 5), ( 6) and ( 7) calculate the distances for row (d r ), column (d c ), and section (d s ).

Model Constraints
The following constraint sets were defined: Eq. ( 8) defines the type of decision variables.Equation ( 9) defines the upper limits for periods total, SKUs, sections, rows, columns, and levels indexes.Equation (10) defines the maximum spaces that can be assigned.Equation ( 11) indicates the total assigned SKUs in period p. Equation ( 12) refers to the combination of total assigned SKUs regarding total spaces.Equation ( 13) defines that the total SKUs in period p are less or equal to the maximum warehousing capacity.Finally, Equations ( 14), (15), and ( 16) limit the distance to the rows, sections, and columns, respectively. ( (16)

Application Software and Algorithm
The model was applied using Microsoft Excel © and written in Visual Basic for Application (VBA).The algorithm used to solve the integer linear programming problem of warehousing space assignment is as follows: a) Step 1: Define input parameters (Table 3).

b)
Step 2: Define demand for each period (Table 4).c) Step 3: Classify each SKU (ITEM p ) under ABC and COI classification methodologies for each period.

d)
Step 4: Calculate slot needs for each SKU in the period under each classification methodology.e) Step 5: Assign one by one SKU to free slots under SAS (Table 2).
f) Step 6: Calculate the time for each SKU and the total time for the strategy, for each period under each classification and each SAS.g) Step 7: Compare the strategies in each period and get the best solution.

Model Application in a Real Case
Model application with real data is presented in this section, by setting the warehouse and vehicle characteristics and the orders selection criteria.

The Warehouse Configuration
Table 5 shows the warehouse configuration and dimensions.The warehouse layout is shown in Figure 2. The orders are selected considering the SAS from Table 2 and the following conditions: • The section is the last factor to change.The warehouse entry and exit doors are on the same axis, which is perpendicular to the section changes direction.Hence, section one must be assigned before section two.
• The rows assignment is from the nearest to the doors to the farthest, according to route conditions shown in Figure 2 (orange and green lines) and the forklift speed.
• The columns assignment is in ascending order (1 to 66).Items with higher priority must be allocated near the entry or exit doors.
• The levels assignment is from bottom to top.Items with higher priority must be allocated near the floor.

The Vehicles
Table 6 shows the vehicle characteristics used in this study case.There is only one forklift type with one pallet capacity.

Results Analysis
The application was made considering two periods in one year (semester 1 and semester 2) and the SKUs demand behavior (stational and regular).

Classification Methodologies Comparison
Classification methodologies comparison is made by matching ABC and COI by position in the priority list.Table 8 exhibits this comparison for the two semesters.Only 30 SKUs are in the same position (13.39%) in semester 1.In semester two, there is less coincidence (9.79%), although the total SKUs are higher.
Furthermore, the three groups of the ABC classification are compared with the COI classification considering the total SKUs that are in the same location in both methodologies (Table 9).There are high coincidence percentages between categories, the lowest is for category B in semester 1 (92.13%), and the highest is for category C in semester 1 (98.11%).

Time Results Analysis
The times were calculated by applying the mathematical model and compared in seven different scenarios regarding the SAS.We run the model 30 times, and Table 10 shows the summary for the time results (in hours) for semester 1 and semester 2, including all the SAS.For both semesters the best order to assign the slots is the proposed model because it is the nearest strategy to the TSP classification travel time used as a benchmark time.In that sense, for established orders the best two configuration assignments are the SAS 2 and the SAS 5, getting an operation time near to the TSP.These two SAS change the columns and section factors in the last positions.Only the first and second step changes varying the rows and the columns.

Times per Item and Cumulative Times
Figure 3 and Figure 4 present the results of cumulative times for semester two with ABC and COI classification for all SAS, respectively.It is noted that the TSP, SAS 2 and SAS 5 lines are close because these strategies behavior are similar.Moreover, the cumulative line slopes are related to the ABC classification.The times for the B-class SKUs are higher than A-class SKUs because the assigned slots are nearer to entry and exit doors, but there are a lot of pallets that increase the final time.Regarding the C-class SKUs, the travel times are lower, but longer than A-class SKUs travel times.For this reason, the quantity and participation are quite significant in final times results strategies involving the location.

Slotting Strategies Difference
This section presents the analysis of time differences between ABC and COI slotting methodologies considering the best results for the second semester.The differences are calculated by subtracting the ABC from the COI times.
Figure 5 shows the time differences (hours) for the three best strategies considering the accumulated participation of the ABC classification.The points that are up from the zero line indicate that COI time is higher than ABC.Analogy, the points below the zero line indicate that the ABC time is higher than COI.It is possible that for the first SKUs in the priority list, there is no time difference between the two classification strategies because the SKUs are in the same location for both strategies.A difference in positions in the priority list implies a time difference between the two strategies, and it is probable that this difference persists for the next SKUs.The difference magnitude is determined by participation position on the priority list and location.The differences between ABC and COI are higher until 80% of the accumulated participation of SKUs is reached (i.e., for A and B classes).
The time differences between ABC and COI strategies in SAS 2 are mostly higher (points of the yellow line above and below the zero line).However, this does not have a major impact on the cumulative time because the positive values are balanced out.However, it can be a critical factor if SKU demand is dynamic and/or most of the SKUs are A or B class.

Conclusions
This paper presented an allocation model integrating SKUs physical variables, warehousing design, and operation (dimensions, layout, material handling equipment), and heterogeneous product demand.The study assumed that there was no policy for slotting allocation and therefore had no benchmark for results.The implementation of the strategy could serve as a basis to formulate improvements in performance in warehousing management.The joint application of sorting-based slotting and picking models with priority lists can be helpful when each SKU has different behavior.This condition could generate priority lists for products that require more attention in the supply chain.
Traditional allocation strategies achieve adequate fulfillment of warehouse management objectives, but there are differences and variations between priority lists, implying different times for each SKU.Theoretically, COI performs better when the volume and frequency of orders are heterogeneous, while ABC works better with homogeneous products and material handling equipment.Although the COI strategy is not one of the grouping strategies, it can work if there is a greater difference between locations in a group.However, it is necessary to consider storage constraints to stock SKUs according to their classification.
According to the results, the optimal strategy to reduce distances according to the priority lists is the TSP adaptation for both periods.The two best SAS are SAS 2 and SAS 5.This result is due to the fact that the entry and exit doors are on the same axis, and the assignment must be made from the closest slots to the entry or exit doors with higher priority SKUs to the furthest slots with lower priority SKUs.It is necessary to evaluate more than one alternative.In this case, SAS 2 is too close to TSP matching, and depending on the warehouse handling equipment, this decision will affect real-world performance.
In this study, the times are cumulative, and the strategy is evaluated in the total operation time.For each SKU there is a time difference between strategies due to its position in the priority list.A proper strategy evaluation must take into account the cumulative number of SKUs in the analysis period.
The main contribution of this work is the development of an adaptable methodology to operational changes to improve storage management efficiency using slotting.This methodology can be adapted to other industries.Although this work has been validated on a specific case, it can also be adapted to changes in current warehouse operation parameters, becoming a basis for developing more robust models with different constraints or variables sets.The approach proposed in this paper contributes to the state of the art in warehouse optimization, specifically to the need for models that integrate multiple slotting and picking techniques with a solid academic foundation and application in real-world logistics operations.
Future work includes considering other objective functions of sustainable operations (economic, social, and environmental) and incorporating uncertainty treatment techniques.This study could be extended in several aspects, aiming to generalize the studied problem, considering the warehouse design, including new technology and equipment used in picking and slotting activities, using data analysis, and new modeling techniques.

Figure 3 .
Figure 3. Cumulative times for ABC -SAS semester two

Figure 5 .
Figure 5. Differences between COI-ABC times for each SKU in semester 2

Table 1 .
Main contributions to warehouse management optimizationTable

Table 4 .
Sets and limits.

Table 7 .
Table 7 shows the ABC classification per semester.The total SKUs increases from 224 to 286, because of stational demand behavior.ABC Classification per semester

Table 9 .
Classification coincidence per location