Storage location assignment for differently sized SKUs in a manufacturing firm

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Storage location assignment for differently sized

SKUs in a manufacturing firm

Author

R. Smirnova (180415232/S3919226)

MSc Operations and Supply Chain Management (Dual Award) Newcastle, December 2019

Master thesis (Dual Award)

MSc Operations and Supply Chain Management (Newcastle University) MSc Technology and Operations Management (University of Groningen)

Supervisors

Dr De, A. (Newcastle University)

Dr Veldman, J. (University of Groningen)

Abstract

Storage location assignment is the area, improvement in which could bring massive savings to a company, as in combination with picking strategies, it contributes up to 60% to the warehousing costs. Researchers have suggested many solution mechanisms over the years, but those were mostly directed at the uniform-sized product allocation. In reality, however, due to the diversity of the offerings, unit sizes vary. Current research suggests a decision-support system that accommodates the differences in SKU sizes and suggests the allocation procedure that reduces pickers’ walking distance by up to 50%. Four (4) alternative tool variations are proposed depending on the company policies, warehouse layout and SKU dimensions. The generic version should be chosen if SKU split between several locations is not allowed. One of the customised options would be a solution in case of different shelf dimensions. Sharing alternative is recommended otherwise since it is appreciated to perform the best in any situation being it with big SKUs, wider aisles or higher demand.

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Acknowledgements

I would like to express my gratitude to both of my supervisors, Dr De (Newcastle University) and Dr Veldman (University of Groningen), for the support in conducting this project on the topic “Storage location assignment for differently sized SKUs in a manufacturing firm”. I would also like to express thanks to Company X, who was very kind to provide the opportunity to conduct research on their site and use their data set. Consultations received from the member of staff knowledgeable in the business function under analysis were of enormous help. Despite all the support, some of the results may not be accurate due to some data unavailability or non-suitability of its format to the project purposes. Additionally, because of the particular way of conducting business in Company X, such as the possible everyday SKU location change, and time constraints, some general assumptions had to be made to produce results. Those limitations, however, do not influence the quality of the decision-support system itself, which can be tested in the future with various data sets.

Table of figures

Figure 4.1. Warehouse layout used for the decision-support system ... 20

Figure 4.2. SKU length vs Box length ... 21

Figure 4.3. SKU allocation on the shelf when space sharing is not allowed ... 22

Figure 4.4. Border of the slot until where the distance is calculated ... 23

Figure 4.5. Conceptual model ... 26

Figure 4.6. New slot distance calculation on Rack 4 ... 29

Figure 5.1. Current layout in Company X ... 34

Figure 5.2.Warehouse shelf space utilisation ... 39

Figure 5.3. SKU five (5) wins more distance from relocation than SKU seven (7) loses) ... 43

Figure 5.4. Usage influence on the model variations behaviour ... 44

Figure 5.5. Aisle width influence on the tool variations behaviour ... 46

Figure C.1. Company X picklist example identifying the current SKU location ... 56

Figure D.1. SKU lengths calculation for non-uniform units ... 57

Figure E.1. Non-sharing model allocation sheet example ... 58

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Figure F.1. Four method’ distance result comparison ... 59

Figure G.1. Sharing model allocation results... 60

Table of tables

Table 4.1. Table of variables... 24

Table 5.1. Current distance calculation ... 35

Table 5.2. Four methods’ distance comparison ... 37

Table 5.3. Four methods’ shelf utilisation comparison... 39

Table 5.4. SKU allocation for Company X... 40

Table 5.5. SKU size change by 20% and 50% ... 42

Table 5.6. Sharing and customised sharing four (4) split model comparison... 44

Table 5.7. Four methods’ distance comparison (random usage generation) ... 45

Table 5.8. Four models’ distance comparison (different aisle widths) ... 45

Table B.1. Current layout sector, column and rack coding ... 55

Table H.1. Allocation result sheet for the multiple split model ... 61

Table of abbreviations

COI – Cube-per-Order-Index DSR – Design Science Research GA – Genetic Algorithm

In - Inch

I/O – Input / Output (point) KPI – Key Performance Indicator

MCDM – Multi-Criteria Decision-Making MTO – Make-To-Order

MTS -Make-To-Stock

OAT – One-factor-At-a-Time

RFID – Radio-Frequency Identification SKU – Stock Keeping Unit

SLAP – Storage Location Assignment Problem TSP – Travelling Salesman Problem

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1. Introduction

1.1. Motivation and context

Warehouses or storage units are critical parts of every manufacturing process or, globally, of every supply chain. 40% of the logistics costs in Europe are comprised of warehousing and inventory carrying (Mayer et al. 2009, EC 2015). Consequently, adequate warehouse management may contribute significantly to the cost, lead times and effort reduction. Order picking is the most labour-intensive and, therefore, expensive warehousing activity that has the potential to improve company performance significantly. Order picking is the warehouse function by which goods are extracted from the storage units to satisfy customer demand (Ashayeri 1989). In manual warehouses, it contributes up to 55-60% of the total warehouse costs (de Koster et al. 2007, Xie et al. 2018). Besides costs minimisation, order picking is also essential from the company image point of view since its efficiency directly influences order cycle times and service levels (Ashayeri 1989). Two categories order picking has been divided by researchers into are storage optimisation and picking optimisation (pickers’ behaviour, namely routing, picking pattern and method) (Giannikas et al. 2017). Storage optimisation is about layout design (warehouse dimensions) and storage assignment policy (random, class-based or full-turnover) (Bottani et al. 2012). While picking optimisation is about picking policy (discrete, batching, zoning), routing strategy (S-shaped, aisle-by-aisle, return) and material handling equipment (Bottani et al. 2012). Although order picking has been a focus of the researchers already for a few decades, some subject areas still require improvements (van Gils et al. 2019, Dijkstra 2017). As a result, storage optimisation and, specifically, the neglected variation of the storage assignment problem is the focus of this research.

1.2. The focus of this research

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The reason may be that the transition to the automatic storage retrieval system is very capital intensive (Ashayeri 1989). Also, companies may emphasise human decision-making and adaptability over the cheaper in long-term technology. This decision depends on the company policies, business nature and warehouse organisation. Sometimes even small mistakes can cause unrecoverable reputation damage.

SLAP is a widely researched topic suggesting product allocation solutions based on different constraints, such as picking policies, warehouse layouts, multi-criteria decision-making requirements, allocation policies, etc. The majority of the tools are based on simultaneous product allocation, where all products and slots have the same dimensions. It makes it easy to calculate distances and prioritise. However, these solutions are shown to be very inflexible when it comes to SKUs with different dimensions and space requirements (Shah 2018). Vertical travel is also acknowledged to be an under-investigated area (van Gils et al. 2019). As a result, the aim of this research is to suggest alterations to the SLAP solution taking differently sized SKUs and three-dimensional allocation into account. The current paper aims at developing a user-friendly SLAP system for the company that operates a warehouse with a high-level rack shop floor layout and offers products of various dimensions and volumes. The company used for the numerical example and constraint derivation (further referred to as Company X) uses return picking policy. This policy implies pickers to start and finish their journey into the aisle from the same side. Company X employs multi-level picking policy, where high-level picking is performed using the equipment, such as ladders. Storage sharing between different SKUs is not allowed since RFID tags identifying locations are attached to the racks under a specific part type. Finally, the warehouse area shall remain unchanged to keep rent costs constant. This research suggests the decision-support system for a full-turnover policy following the consecutive product allocation procedure.

1.3. Structure of the thesis

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2. Literature review

The storage location assignment is not to be confused with the warehouse layout design. Warehouse optimisation is interlinked with the storage allocation problem since the number of racks based on the adequate storage allocation has to be known to optimise the warehouse size and vice versus (Shi et al. 2018, Venkitasubramony 2019). Even though the layout of the storage area influences the picking and storage policy combinations that would minimise walking distances, the selection of the best arrangement is not the focus of this paper. Neither is the selection of the best strategy combinations based on the given layout. This thesis only concerns about SKU allocation to the shelves taking design and other policy decisions as known variables, excluding the throughout discussion about the choice of the best routing policy as in Bahrami et al. (2017) and Petersen (2004), picking list construction and mid-route updating as in Giannikas et al. (2017) or clustering methods as in Yang (2016).

The allocation of the Stock Keeping Units (SKUs) to the storage places is commonly known as Storage Location Assignment Problem (SLAP) (Micale et al. 2019). Sometimes, it is also referred to as Inventory slotting or profiling (Pazour 2015, Reyes et al. 2018). According to Reyes et al. (2018), 81% of the papers published in academic journals of Scopus and Web of Science databases between 2005 and 2017 on this topic use either storage assignment or

storage location assignment to describe this issue often in combination with either problem or policy term. Product and space (al) location are other terms used in the literature (Heragu et al.

2005, Guerriero et al. 2013, Boysen 2013, Yu 2013, Yu 2014). The idea behind this concept, despite the title, is the same. Products are positioned to the shelves the way that minimises picker’s, is that a human or a machine, travel distances. Shorter distances consequently reduce retrieval and lead times, allow more efficient use of the facility spaces and reduce costs.

2.1. Storage policies

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is rather a rule for the storage allocation, and family-based is a customised class-based category. COI applies to both full-turnover and class-based policies. It compares the ratios of the storage locations needed to the number of retrievals and uses it as an allocation criterion instead of the most common one: demand. Every organisation may create its clustering criteria, such as size-based, weight-based or any other characteristic-based. The family-based strategy is one of them. If two criteria are to be combined, it leads to a multi-criteria heuristic allocation process. Micale et al. (2019) claim that these criteria are often in conflict, which leads to the suboptimum distance result. As a result, only three the most common policies are analysed in depth in this section: random, class-based and full-turnover policy.

2.1.1. Random policy

The random policy is the policy that allows product allocation on the rack wherever there is space available (Guo et al. 2016). For differently sized SKU problem, a slot with dimensions equal or more significant than SKU’s would have to be chosen, or SKU division between a few available spots considered. In case the second option is not permitted by company policies, the random allocation may result in some units not having a storage place at all. This policy usually allows the maximum storage sharing benefit (space utilisation) and, therefore, the lowest area costs. However, it often happens at the expense of the travel distance, which is also very challenging to determine accurately (de Koster 2007). Such a policy can only function in the computer-controlled environment since the system has to register the input location and communicate it to the picker. It is worth to mention that despite the clustering method or class-allocation criteria, products within the class (in a class-based policy) are assigned randomly to benefit from the space sharing (Yang 2016).

2.1.2. Class-based policy

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separate policies. The benefit of the class-based system over the other two is claimed to be the ability to combine the shorter walking distances, by using allocation criteria, with the minimum storage space requirement, by using random policy within the class (Yu 2013). Space needed is calculated from the average inventory point of view (Yu 2013). This assumption is challenged by Guo et al. (2016) addressing the issue of actual space required being higher than the average inventory. And indeed, in case a company employs a make-to-stock strategy rather than make-to-order, there will not be enough space for all products simultaneously. As a result, the suitable policy has to be chosen based on the replenishment cycles and the number of items in the class (Guo et al. 2016). The larger the category, random product allocation within it increases the distance travelled unless picklists are organised in sequence based on the current product position (Bahrami et al. 2017). The above finding is also confirmed by Guo et al. (2016). Additionally, if random locations of the most often picked products happen to be at the back of the class, this increases the total walking distance as well. The solution for better class-based benefit exploitation could be a two-stage storage allocation process: class-class-based and then full-turnover based within the class. It will tackle the complication of the full-turnover allocation problem having a high number of items (Rao et al. 2017) and give a possibility to use a second criterion.

2.1.3. Full-turnover policy

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main reason for academics to recommend class-based storage that combines short travel distance of the full-turnover and space benefits of the random.

2.1.4. The best policy does not exist

As a result, there is a debate in the literature based on what is the best storage policy minimising distance and retrieval times. Some argue that the class-based performs the best. Bahrami et al. (2017) claim that the best combination for the return routing policy (employed in the company) is the class-based allocation when orders in picklist are sequenced according to the location. Yu (2013) shows that in case of travel time model, class-based and random storage policies outperform the full-turnover one. And it is easier to allocate a smaller number of classes over thousands of individual SKUs, according to Rao et al. (2017). Others conclude that full-turnover policy is better (Peterson 2004 in Hsieh 2011, Rao et al. 2017). Consequently, the choice of the optimal SKU assignment policy is highly situational and depends on different factors, such as replenishment policy, demand pattern, company vision, etc. When it comes to footprint minimisation, there is an absolute winner. However, with distance, it is arguable. Every policy may be the best depending on the angle you judge from, performance indicators you consider the priority, the nature of demand, etc.

2.2. Methodologies for a storage location

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11 2.2.1. Methods used

Often SLAP is addressed through travelling salesman problem (TSP) (Altazari 2017, Ashayeri 1989, Theys et al. 2000). Given the number of locations (cities) and distances between each pair of them, the shortest route can be found. Even though only traversal routing fully mirrors suggested algorithmic situation, TSP can be easily adjusted for other policies. On the other hand, Theys et al. (2000) have pointed out that the exact algorithms are only beneficial for the warehouses with at most three cross aisles. His findings are supported by the results of ant colony algorithm outperforming TSP obtained by de Santis et al. (2018). For other warehouse types, there are various heuristic (practical) solutions suggested in the recent order picking planning literature published in high-quality journals. Previous work can be divided into three groups based on the methodology used: simulation (51%), mathematical programming (28%) and analytical models (21%) (van Gils et al. 2018). The first one seeks for a solution through the experimentation to identify the combination that scores the highest on the KPIs. The second refers to the mathematical equations that show the relationship, which cannot be easily observed and manually solved. And the third method predicts performance based on the problem parameters (van Gils et al. 2018). Because of the significant number of variables and the problem complexity, pure mathematical modelling or analytical approach is often not possible. A few examples of each are presented below to give a reader an idea of what methods are used in the literature to resolve similar problems.

2.2.1.1. Simulation

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simulation to allocate several slots to one product depending on the volume/demand; they also consider precedence rules and physical restrictions. This approach, however, restricts space utilisation, as it uses fixed-size locations.

2.2.1.2. Analytical

Analytical models have a closed-form solution and are usually design-oriented (Altarazi 2017). Venkitasubramony (2017) paper is one of the examples of analytical research. He suggests a SLAP model that considers 3D movements with a full-turnover policy in the forklift using environment. Venkitasubramony (2017) allows space sharing, considers area costs (storage dimensions are initially decision variables), employs traversal routing and makes slots the same size. Due to the routing policy choice, it is allowed to position products randomly within a level once it is defined. The novelty of his research is in adding space sharing and vertical travel considerations to the full-turnover policy.

2.2.1.3. Mathematical modelling and metaheuristics

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optimisation algorithm for class-based items allocation with fixed-size slots in 2D is used by Onut et al. (2008). Dijkstra (2017) employs dynamic programming to assign SKUs to equal-sized slots through exact route-length formulation in 2D. An alternative method of pallet allocation with different shelf heights and the possibility of placing two pallets in one slot on top of each other through random storage policy is suggested by Quintanilla et al. (2015). Yang et al. (2015) combine SLAP with storage/retrieval scheduling under shared storage policy in the automated system using variable neighbourhood search with randomly allocated fixed-size slots. Moshref-Javadi (2016) examines SLAP with congestion in aisles and interactions between family parts to locate them close in case of them being often sold together through four (4) different heuristic methods outlining vertical travel as an area for improvement. Other researchers suggesting alternative mathematical methods for SLAP are Battini et al. (2014); Manzini et al. (2015); Guerriero et al. (2015), who considers SKU compatibility; Pan et al. (2014) examining three-dimensional travel; and Manzini et al. (2019). This overview suggests that even though there is a variety of different methods created for the SLAP solution, there are still limitations. Most of the papers concentrate on two-dimensional storage units, standardised location/product dimensions and allocation criteria beyond just turnover.

2.2.1.4. MCDM

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items’ fragility. Product compatibility and correlation is the only second criterion that does not require trade-offs.

2.2.2. Closely related research

The most related paper to the current research, since differently sized SKUs are considered, is by Shah (2018), who has designed a model for forward-reverse storage with non-uniform unit loads. Even though there are similarities between Shah’s (2018) and this research, the approaches are still very different. Firstly, current research considers a three-dimensional allocation as opposed to the two-dimensional forward-reverse storage assignment in Shah (2018). Secondly, since Shah (2018) chooses between three pallet sizes that follow the ratio of 1B=0.5A=2C, it still eventually divides the total space into equal areas. Based on product demand ratios, the number and proportions of pallets for each product are defined constrained by the overall space limitation. Current research, however, allocates SKUs all of a different size, restricting space sharing. Thirdly, Shah’s research is directed at space utilisation and space division between products employing random policy (2018) while present work uses full-turnover strategy. Finally, the main focus of the research varies between “amount of each product” (Shah 2018) and “where to store this amount”.

2.3. Research gap

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15 2.3.1. SKU sizes and the need for a non-complex solution

Most of the papers mentioned in this review use slots of the same size; however, in reality, SKUs differ in their dimensions (Shah 2018). Zhang (2016) highlights the importance of SLAP research expansion into non-standardised storage locations, where stock levels of SKUs are taken into account to make it more realistic. The only paper that considers readjustments of the shelf heights to achieve the best space utilisation for differently sized units, in addition to the Shah (2018) mentioned above, is by Cardona (2019). She, however, considers pallets of the same length and width but of different heights as opposed to the heights of equal value and varying slot lengths. Cardona’s method of various shelf heights is unlikely to bring many benefits to the company with small pallet height differences or stacks constructed of the shallow boxes (2019). Space wastage is minimal anyway. In this case, once shelf heights are decided, the slots on the shelf will be of a different length, which is not the case in Cardona (2019). Additionally, both Shah (2018) and Cardona (2019) use a random allocation policy. It does not allow enough space to fit all SKUs at all times but targets service levels (accepted probabilities that all pallets can be stored). Their policy choice confirms the fact that the combination of both full-turnover policy and non-uniform slot allocation has not been introduced so far. Moreover, a non-uniform slotting itself has not been covered in the literature, as shown in Section 2.2.1 and Section 2.2.2.

What is more, most of the suggested tools are not user-friendly and are time-consuming, especially when it comes to the more complicated issue of non-standardised slots. For example, Bottani et al. (2012) indicate that simplified and faster SLAP tools have to be created to ensure quick and easy implementation for anyone without in-depth mathematical knowledge. Thus, a simple decision-support system is still to be designed.

2.3.2. Vertical travel

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addressed by a few recent authors (Micale et al. 2019, Venkitasubramony 2017). And still, resent review of van Gils et al. (2019) suggests vertical travel research expansion as an area of improvement to the allocation problem. The reason for 3D research still being a contemporary issue for research may be that the current database does not contain a universal solution. For instance, Venkitasubramony (2017) has addressed vertical travel distances for the forklifts using environment but where those can travel up/down and to the sides only (no parallel movements).

2.3.3. Research questions

As a result, the goal of this research, to develop a user-friendly decision support system for inventory slotting for the company having differently sized SKUs in a three-dimensional environment, is achieved by answering the following question:

Question1. Does full-turnover based policy result in better distance wins in comparison to the random one in case of differently sized SKUs?

As described in Section 2.1, depending on the KPIs company has in place, different storage assignment policies perform the best. When it comes to the distance minimisation for SKUs of the same size, random one tends to perform better (Yu 2013). The possibility of full-turnover policy to be more efficient in case of differently sized SKUs is high. It is justified by a very restrictive slot choice for the random allocation, taking different dimensions into account. The following questions will be answered by analysing a new SLAP solution:

Question 2. Is it possible to achieve a high shelf space utilisation when all SKUs are of different size?

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3. The practical setting of the problem

The scientific relevance of the problem presented in the previous section is followed by the practical constraints originating from the real-life scenario. The problem setting is suggested on the example of Company X situation and will behave as grounds for some rules, assumptions and constraints the recommended decision-support tool (solution) has to follow (Section 4.1). The general problem Company X is facing is a chaotic order picking rack-based storage area. The current product allocation system is based on the random policy, where each product is allocated to the free available spot, that are all of the same sizes. If space available is smaller than SKU (comprised of few boxes) dimensions, the product is split between few slots. In case a product is produced in several batches, each batch is treated as an independent entity. It results in one product being spread throughout the entire warehouse, which increases the distance in case the order amount is higher than the number of parts stored in one location. For instance, for a 10000-part collection, a picker may need to go to three different locations, where 4000 parts in each are stored. Pickers collect one order at a time before returning to the packing area. Picklists are organised to reflect the product sequence from the I/O point to reduce walking distances. The route lengths are difficult to measure since SKU locations may differ from day to day depending on the system availability. Therefore, Section 5.1 uses two-day location snapshots for the current situation analysis. To sum up, part types do not have specially designated areas, where they have to be always stored. Neither have those slots that would match product maximum stock level capacity. In the case of 179 products under analysis, picking procedure with current policies becomes time-consuming, confusing and inaccurate. Manual or “picker-to-part” strategy (Giannikas et al. 2017, de Koster et al. 2007, Manzini et al. 2015a, Bahrami et al. 2017, Reyes et al. 2018, van Gils et al. 2019) is used with return route policy, which requires an employee to enter and exit the aisle from the same side (van Gils et al. 2018).

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4. Research Design

This thesis uses design science research (DSR) methodology to solve the problem shaped by the scientific gaps and practical scenarios. The deliverable of this paper suggests an artefact (Excel tool) that assists managers in solving storage location assignment problem and is easily adjustable to the company context. It meets the goal of DSR of creating generalisable knowledge applicable to real-life problems (Karlsson 2016, Goldkuhl 2012 in Peffers et al. 2018, Van Aken et al. 2016). The system is directed at improving emergent systems in the company. The tool principals are generic, which allows quick constraint adjustment to the customised ones. According to Hevner et al. (2004), DSR designs artefacts to solve organisational issues and can be presented in forms of software, formal logic or mathematics (optimisation proofs). This research uses mathematical modelling to develop some of the functions in the system as an input into the tool. The suggested model is validated in the artificial environment utilising simulation instead of real-life application since it saves time and money. In this paper, simulation on Company X storage space is done through Microsoft Excel software. As the nature of the current problem is not dynamic, static simulation is used to mimic the real-life scenario (Hubalovsky et al. n.a). A static simulation and mathematical modelling combined approach is chosen since the purely analytical or mathematical solution would be very challenging and time-consuming. The complexity is justified by the number of computations and constraints involved, and the format of the result required (visual allocation matrix) (Wieringa 2007). The choice of the research methodology is also justified by the goal of this paper to create a simple and efficient decision-support system. The tool is built with a formal logic approach. A detailed explanation of the Excel tool construction is provided in Appendix A through the pseudo-code expressed in a rule-based heuristic. The deliverable of this paper should:

1. minimise the total pickers’ walking distance;

2. consecutively allocate differently sized SKUs to the shelves ensuring the length fit to the available space;

3. provide comprehensive results of the shelf the item is assigned to, distance to the SKU from I/O point and the length allocated to each of the slots (usually the total length of the product);

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As a result, the remainder of this paper suggests the conceptual model for the solution with steps to follow to achieve an anticipated result (Section 4.1, 4.2 and 4.3). It validates its reliability on the real-life example considering a few variations of the model for the comparison (Section 5) and develops generalisability and theory (Section 6) (Holmström et al. 2009).

4.1. Assumptions and constraints the tool has to follow originated from

the practical problem description

1. Distance is the primary model success indicator, but utilisation for different tool variations will also be used to suggest grounds for multi-criteria decision-making.

2. The solution is built on a double-rack storage area layout, as shown in Figure 4.1, including the corresponding measurements. For the current distance calculation, the present arrangement of Company X (discussed in Section 5.2.) is used. While keeping the overall storage area constant, the new design enables the aisle width expansion, which prevents pickers’ blocking (van Gils et al. (2018), Pan et al. (2014), van Gils et al. (2019), Bahrami et al. (2017)). Picker blocking possibility had to be eliminated to maximise lead time and distance ratio, as the distance (current KPI) does not reflect time lost in a collision. In reality, pickers’ blocking affects the lead time, which is the customer service criteria aimed to be improved by the tool. As a result, the more time is reflected in the distance or, the more time influencing factors are eliminated, the more accurate is the distance result.

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3. The current paper studies a storage unit that consists of eight (8) racks. The analysis considers five (5) shelves per rack, which are flexible in their height. Input/Output (I/O) point is assumed to be at the north-west corner of Rack 1.

4. For the primary model, all shelves are of the same height, depth, and length. All aisles are equal in width too. For some alternative versions, shelf/level heights are modified; however, the rack dimensions remain the same.

5. Distance from I/O point to the 1st aisle is not considered since it is constant, and the purpose of this optimisation is to compare slot distances to each other. Thus, miles to slots on Rack 1 will be purely comprised of the lengths of already allocated SKUs and vertical travel where applicable (See Eq. (6) in Section 4.3).

6. Boxes, where maximum inventory quantity of a product is packed, are grouped into stacks, which dimensions are defined by box lengths, widths, and heights as well as shelf dimensions. Those stacks placed next to each other suggest the distance required on the shelf for a specific product ( See Figure 4.2).

Figure 4.2. SKU length vs Box length

7. Picking routing policy employed is return since the shop floor arrangement does not allow an alternative one. Only distance from the entry point to the product location is measured neglecting the distance back, which would only double the result each time.

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stack not occupying the entire shelf height (See Figure 4.3). RFID tags may be removed and replaced in case a SKU requires more space.

Figure 4.3. SKU allocation on the shelf when space sharing is not allowed

9. The allocation policy used is full-turnover (allocate a SKU to a specific permanent space equal to the maximum product volume). It is justified by the fact that sharing is not allowed and the tool seeks to simplify the current routing situation between several slots holding the same product type. Additionally, according to Battini (2014), in case the return routing policy, it is beneficial to use full-turnover strategy assigning the item with the highest turnover to the closest to the picking point slot. By doing so, the picker will have to cover shorter distances with higher frequency. Company X is ideal for the full-turnover policy implementation considering their flexibility to grow (vertically), and the importance of the product type to be located in one place. Company X demand is relatively stable, which mitigates the problem of hard implementation and frequent re-slotting indicated by Rao et al. (2017) and Tompkins et al. (2003). Additionally, due to space dimensions explicitly defined for the product allocated there, there will be minimum space wastage possibly resulting in the same benefit as space sharing. Nevertheless, the constraint of one stack being constructed from products of the same type only still exists (point 7).

10. If multiple slots have the same distance from I/O point, and both shelves can accommodate the length of the SKU, any of them can be chosen. Alternatively, the level that fits the SKU is selected.

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12. Maximum stock levels in combination with boxing policies are used to define storage space needed for a SKU and avoid space shortage at the highest demand peaks.

13. Although usually, in the literature, mileage is calculated to the middle of the slot, the distance here is calculated to the closest border of the available location. The reason is that slots are all of a different length, which are not known until SKUs are allocated (See Figure 4.4 below).

Figure 4.4. Border of the slot until where the distance is calculated

14. Not only horizontal but also vertical travel is considered. Shelves above human reach have to be accessed by ladders, which takes extra time (transformed into distance here).

15. Shelves with height less than ∂ (height of human reach without the ladder) have to be always preferred over the shelves located above ∂ due to Company X difficulties in using additional equipment to distract products from the upper levels.

16. Area costs shall not be considered in the present paper since warehouse dimensions are fixed.

17. Box dimensions differ depending on the product type; however, they are fixed per model, and no alternative packaging can be performed for a SKU except the assigned one. For instance, Product A will always go to Box 10, whereas Product B will only go to Box 9.

18. All measurements are performed in inches.

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4.2. Variables

Table 4.1. Table of variables

Notation Description

𝒋 index for the vertical storage level (shelf) ∈ {1,2, … , 𝐽}, where 𝐽 is the total number of shelves

K number of shelves that can be reached by hand

∂ the maximum height that is reached by hand

V width of the aisle (passage between shelves)

C width of the rack (depth of the shelf)

m rack index number ∈ {1,2, . . 𝑀}, where 𝑀 is the total number of racks

Z rack length

n number of SKU/product type ∈ {1,2, … , 𝑁}, where 𝑁 is the total number of products

𝑳_𝒏 length of the slot for each SKU 𝑛 / length of the SKU n 𝑴𝒂𝒙 𝑻_𝒏 not yet allocated item 𝑛 with the highest priority

𝑴𝒊𝒏 𝑺 the slot with the shortest distance available

𝑷_𝒏𝒋𝒎 distance from I/O point to the specific slot/SKU 𝑛 at the specific shelf 𝑗 of the particular rack 𝑚

𝑭𝒏 frequency of product /SKU 𝑛 being picked 𝑰_𝒏 maximum inventory level of SKU 𝑛

𝑳𝒏𝒎𝒋 length of a SKU 𝑛 on shelf 𝑗, rack 𝑚

𝑽_𝒏 number of parts per box for the product/SKU 𝑛

𝑩𝒏 number of boxes per product/SKU 𝑛 𝒉_𝒋𝒎 height of the shelf 𝑗 on the rack 𝑚

𝑮_𝒋𝒎 vertical travel distance until the shelf 𝑗 on the rack 𝑚 𝑳_{𝒏.𝒂𝒍𝒍𝒐𝒄𝒂𝒕} length of SKU 𝑛 being allocated at the moment

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𝑳𝒏.𝒂𝒍𝒍𝒐𝒄𝒂𝒕.𝒓𝒆𝒎𝒂𝒊𝒏𝒊𝒏𝒈 the remaining length of the SKU 𝑛 being allocated at the moment after the first part has been placed (in case of the method with two locations per SKU)

𝑸_𝒎 the horizontal distance until turn into the aisle assigned to each of the racks 𝑚

𝐔_𝐣𝐦 the utilisation of the shelf 𝑗 on the rack 𝑚

4.3. Conceptual model

The following section describes the process of the data analysis and steps that are to follow to achieve distance minimisation with the differently sized SKU allocation. It can also be treated as a framework for the management-friendly model for re-slotting. The current model differs from the ones suggested in the literature by the following features:

1) it provides support for the data analysis (SKU length identification, priority sorting); 2) analysed data automatically appears as an input in the Excel tool;

3) it is the first user-friendly Excel-based SLAP tool;

4) it uses consecutive and not simultaneous allocation due to the unknown number of slots on the shelves before SKU allocation;

5) it can accommodate partial assignments; 6) it is easy and fast to use.

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26

unique in its consecutive allocation, where formulas have to be Excel tool friendly, mathematical expressions are created using a formal logic approach.

The ultimate goal of any SLAP problem is to minimise the overall travel distance/time (Ashayeri 1989), and the current issue is not an exception. The idea is to place the most frequently used items closer to I/O point to ensure the most often travelled route is the shortest. The objective function could be expressed as

𝑚𝑖𝑛 ∑𝑁_𝑛=1(𝑃_𝑛𝑚𝑗∗ 𝐹_𝑛); ∀ 𝑚 ∊ 𝑀, ∀ 𝑗 ∊ 𝐽 (1),

where 𝑃𝑛𝑚𝑗 is the distance until 𝑆𝐾𝑈/𝑠𝑙𝑜𝑡 𝑛 and 𝐹𝑛 is the frequency of 𝑆𝐾𝑈 𝑛 being picked per month.

The conceptual model is presented in Figure 4.5. The process is divided in two consecutive stages: Data Analysis and Slot Allocation.

1. Data Analysis is the first step to be performed, to prepare necessary measurements for products to be allocated. It can be divided in two phases: product data and layout data analysis.

a) Product data analysis: This step requires data retrieval from the company system to reflect products stored, quantities needed, monthly usage statements and packaging policies. Firstly, products have to be sorted based on the usage: the higher is demand for a part, the

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27

higher is the priority. Priority listing defines the sequence of the allocation. Secondly, if the number of elements per box differs per product (as in Company X), the number of boxes has to be defined per product type considering the maximum stock levels as in

𝐵_𝑛 = ⌈𝐼𝑛

𝑉𝑛⌉; ∀ 𝑛 ∊ 𝑁 (2),

where 𝐼_𝑛 is the maximum stock requirement and 𝑉_𝑛 is the number of parts per box for SKU

n. Maximum stock levels are used as a metric since full-turnover policy assigns a dedicated

space for a SKU, which shall fit the entire inventory even at its highest point.

Each shelf level has a constant height across all racks. For instance, if Shelf 2 on Rack 1 is 19.7 inches in height, so are all Levels 2 on the remaining frames. A decision on the shelf height has to be made taking potential constraints into account. First three shelves have to be less or equal to the height reachable by a human (∂) in Company X, as given in:

∑𝐾_𝑗=1ℎ_𝑗𝑚 ≤ ∂ ; ∀ 𝑚 ∊ 𝑀 (3),

where ℎ𝑗𝑚 is the height of the shelf 𝑗 on the rack m and K is the number of shelves reachable by a human.

Once the number of boxes per SKU and the shelf height are defined, knowing box dimensions, space requirements on the shelf for each SKU are calculated. The integer number of boxes that fit on the shelf in height is multiplied by the integer number of boxes that fit on the shelf in depth to define the number of boxes in one stack. The total number of boxes per SKU is divided by the number of cartons per stack to determine the piles' number. The integer number of stacks is multiplied by the length of a box to identify the overall distance required for a specific SKU on the shelf:

𝐿𝑛 = 𝑌𝑛∗ ⌈ 𝐵𝑛 ⌊ 𝑐 𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑜𝑥𝑛⌋∗⌊ ℎ𝑗𝑚 ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑜𝑥𝑛⌋ ⌉ ; ∀ 𝑛 ∊ 𝑁, ∀ 𝑗 ∊ 𝐽, ∀ 𝑚 ∊ 𝑀 (4),

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28

b) Layout data analysis: After measurements of the storage area are taken, the initial distances from I/O point until each shelf has to be identified following some rules:

1. The lower level shelves (reached without the ladder) are always prioritised over the upper levels. It is faster to walk to the furthest corner of Rack 8 than use ladder to the closest edge of Rack 1 (not all employees had training on ladder use). To enforce this rule, the dummy variable 10000 identifies vertical travel to the upper shelves as in:

𝐺_𝑗𝑚 = { 0, 𝑗 ≤K

10000, 𝑗 >K ; ∀ 𝑚 ∊ 𝑀, ∀ 𝑗 ∊ 𝐽 (5),

where 𝐾 is the number of shelves reached by a human without a ladder.

2. The travel distance until the slot is the summation of the following values:

1) the number of single racks passed multiplied by the length of the frame; 2) the number of aisles passed multiplied by its width;

3) the sum of SKU lengths already allocated to that shelf (in defining the initial distances this value is 0);

4) vertical travel 𝐺_𝑗𝑚.

Since the goal is to compare miles to each other, distance from I/O point until Rack 1 is neglected: 𝑃_𝑛𝑗𝑚 = { ∑ 𝐿𝑛𝑚𝑗 + 𝐺𝑗𝑚 𝑁 𝑛=1 , 𝑓𝑜𝑟 𝑚 = 1 ((𝑛𝑒𝑥𝑡 𝑜𝑑𝑑 𝑛𝑢𝑚𝑏𝑒𝑟 𝑎𝑓𝑡𝑒𝑟 𝑚) − 1)𝑐 + 𝑣 ⌈𝑚 − 2 2 ⌉+∑ 𝐿𝑛𝑚𝑗+ 𝐺𝑚𝑗 𝑁 𝑛=1 , 𝑓𝑜𝑟 𝑚 > 1 ; ∀ 𝑚 ∊ 𝑀, ∀ 𝑗 ∊ 𝐽, ∀ 𝑛 ∊ 𝑁 (6),

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29 Example:

If the distance until Rack 4 Shelf 3 is calculated, where two (2) SKUs with lengths of 25 inches and 15 inches respectively are already allocated (Figure 4.6), the calculation will be as follows:

35.4 (rack width) * (5-1) (four (4) single racks have to be passed) + 78.75 (aisle width) * (4-2)/2 (one aisle is before turning into the next one) + 25+15 + 0 (Shelf 3 is still reachable by hand).

When the next slot allocation is performed, this is precisely the procedure performed that allows comparing distances of the available slots.

Figure 4.6. New slot distance calculation on Rack 4

2. Slot allocation is the second step to perform. The process includes the consecutive SKU allocation involving the distance between I/O point and the specific slot (every shelf’s best available slot after each product allocation) recalculation after each assignment to define the shortest possible distance:

max 𝑇𝑛 = min 𝑆

𝑃_𝑛𝑗𝑚 = 𝑃_{𝑛𝑗𝑚−1}+ {0, if last SKU is not assigned to the shelf 𝑗 of the rack 𝑚

𝐿𝑛, if SKU is assigned to the shelf 𝑗 of the rack 𝑚 ; ∀ 𝑛 ∊ 𝑁, ∀𝑗 ∊ 𝐽, ∀ 𝑚 ∊ 𝑀 (7).

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assigns 1st_{priority product to the closest slot and adds its length to the previous total} distance measure of the shelf it is assigned to. The procedure continues with the next SKU etc.

∑𝑁𝑛=1𝐿𝑛𝑚𝑗 ≤ 𝑍; ∀𝑗 ∊ 𝐽, ∀𝑚 ∊ 𝑀 (8),

where 𝑍 is the length of the rack, presents the space constraint to follow (total length of the SKUs on one shelf cannot exceed the length of the frame). Two alternative allocation methods are considered to meet the restriction. First, the entire SKU has to be located on one shelf and second, SKU can be divided between a maximum of two (2) locations. These constraints suggest the following equations dictating the rules on when the slot can be chosen:

1) ∑𝑁_𝑛=1𝐿_𝑛𝑚𝑗 ≤ 𝑍− 𝐿_{𝑛.𝑎𝑙𝑙𝑜𝑐𝑎𝑡} ; ∀ 𝑗 ∊ 𝐽, ∀𝑚 ∊ 𝑀 (9),

where 𝐿𝑛.𝑎𝑙𝑙𝑜𝑐𝑎𝑡 is the length of SKU 𝑛 being allocated, is applicable for a non-sharing model that states, that location cannot be chosen in case the available space on the shelf is smaller than the SKU length; and

2) ∑𝑁_𝑛=1𝐿_𝑛𝑚𝑗 ≤ 𝑍− 𝑌_𝑛 ; ∀𝑗 ∊ 𝐽, ∀𝑚 ∊ 𝑀 (10),

where 𝑌_𝑛 is the length of one box for SKU 𝑛, shows that slot can be selected if the space available is higher or equal to at least one box length of the SKU being assigned. Potentially, the second method may lead to higher space utilisation. Eq. (10), though, implies the second additional step before the usual procedure can be continued. The second shortest distance has to be identified, and this time that shelf should be able to fit the remaining length of the SKU:

∑𝑁_𝑛=1𝐿_𝑛𝑚𝑗 ≤ 𝑍 − 𝐿_{𝑛.𝑎𝑙𝑙𝑜𝑐𝑎𝑡.𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔}; ∀ 𝑗 ∊ 𝐽, ∀𝑚 ∊ 𝑀 (11),

where

𝐿𝑛.𝑎𝑙𝑙𝑜𝑐𝑎𝑡.𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 = 𝐿𝑛 − 𝑌𝑛∗⌊( 𝑍−𝐿𝑛𝑗𝑚

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(9), (10), (11) and (12) are valid at the moment of a specific SKU allocation only. Eq. (12) explains how the remaining SKU length is calculated, taking into account that only the integer number of boxes can be allocated to the first location.

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5. Results and discussion

In this section, four (4) allocation methods for differently sized SKUs are compared. Four (4) alternatives are all based on the principles of the conceptual model with slight variations that may originate from the company policies:

1)product sharing between several slots is not allowed; 2) different shelf heights are required;

3) splitting between several spots is permitted; 4) different shelf heights with sharing are possible.

The analysis is performed on the real-life storage location data set from Company X on 179 products. Methods are evaluated based on the distance wins in comparison to the current situation and utilisation differences between solutions. Due to the random policy use, product locations in Company X differ from day to day. Therefore, solutions are compared to the average distance data over two (2) non-consecutive days. Apart from the specific example, sensitivity analysis is performed on four (4) methods to obtain generalised conclusions and test the robustness of the tool suggested.

5.1. Result generation procedure

Even though the storage unit under analysis contains both stock (MTS) and make-to-order (MTO) SKUs, the current tool only concentrates on the allocation of the MTS products. The best locations are distributed between MTS units allowing the rest of the products to be placed to the remaining spaces according to the needs. This decision is justified by the fact that demand for make-to-stock products has high variability, which restricts a dedicated space assignment, that would only result in space wastage. As a result, before the decision-support tool is exploited, MTO stock is filtered out, resulting in 179 MTS products to allocate.

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may shift the result to either direction. However, due to the complete data unavailability, it is not possible in this case. This limitation is discussed in Section 6. For the result comparison, 131 SKU picklists for two (2) non-consecutive days (as explained before) are extracted from the system identifying the current locations (example of the picklist is provided in Appendix B). SKU numbers used for the comparison are adjusted for the sensitivity analysis since usage manipulation makes some of the products longer than the racks, which makes them unsuitable for the result generation. For distance comparison, a dummy variable used in Eq. (5) (10000) to prioritise lower shelves over the upper ones is neglected. Extra effort for upper-level picking is already considered in the top shelves product allocation, but in fact, those shelves have equal distances to the same rack lower levels. Distances to the named products for both current and new locations are calculated using Eq. (6) from the conceptual model.

Section 5.2. presents current distances pickers have to cover in a month, Section 5.3. demonstrates the comparison of the current results to the distances generated by four (4) solution methods, including the allocation results for the best performing alternative followed by the sensitivity analysis.

5.2. Numerical illustration

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34 Figure 5.1. Current layout in Company X

Since distance is calculated starting from I/O point, sector and column indices have to be coded to make them suitable for the formula (as shown in Appendix C). For instance, segment 4 of each rack becomes one (1) due to its proximity to I/O and columns change from H-A to one (1) to eight (8) respectively. Distance to every shelf is calculated from I/O point considering the real aisle width of 37.4 inches. Because currently company uses standard slot sizes for SKU allocation (which often requires SKU splitting into several parts) and different layout, adjustments to the Eq. (6) are needed:

𝑃_𝑛𝑚𝑗 = 𝑄_𝑚+ 13 ∗ ((𝑐𝑜𝑑𝑒𝑑 𝑐𝑜𝑙𝑢𝑚𝑛 𝑛𝑢𝑚𝑏𝑒𝑟 − 1) + 8 ∗ (𝑐𝑜𝑑𝑒𝑑 𝑠𝑒𝑐𝑡𝑜𝑟 𝑛𝑢𝑚𝑏𝑒𝑟 −

1)) (13),

where 𝑄_𝑚 is the horizontal distance assigned to each of the racks. Vertical distances are not considered, as explained in Section 5.1.

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N°-Column N°. “Coded sector” and “Coded column” columns represent the coding transformation presented in the previous paragraph. The full current distance table can be found in Appendix D.

Table 5.1. Current distance calculation SKU

name

Location Rack Actual

sector Shelf Actual column Coded sector Coded column Distance SKU1 342-03-01-B 42 3 1 B 2 7 477.05 SKU8 342-01-01-D 42 1 1 D 4 5 659.05 SKU10 342-02-01-A 42 2 1 A 3 8 594.05 SKU11 343-01-02-G 43 1 2 G 4 2 580.7

5.3. Solution and its variations

This section suggests the comparison of results for all four solution alternatives to the storage allocation problem with differently sized SKUs to show the differences. The generic version considers shelves of the same height, whereas customised examines height variance changing identically for all racks. For instance, a change of lower shelf on Rack 1 from 20 inches to 35 would lead to the same adjustment on the remaining seven (7) racks. In case level height alterations, allocations for the shelves with different dimensions would have to be executed separately from the primary process using the same tool. Sometimes, it is beneficial to split SKUs between locations to potentially maximise space utilisation; therefore, sharing version is proposed as well. Space utilisation is outside of the scope of this research but maybe a promising area for work extension and, therefore, is provided as post hoc analysis.

• The generic version is based on the condition that each SKU gets one fixed position equal to the maximum stock level dimensions. Item cannot be divided between several spots. For instance, if the closest available slot is 10 inches and the length of the SKU being allocated is 15, it has to be allocated elsewhere. This model follows the procedure explained in Section 4.3 using Eq. (9), which ensures that SKU can only be assigned to the slot if the space available is greater or equal to the product length.

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due to their packaging requirement (must be stored in pallets) have to be assigned separately. The current alternative to the tool is only valid if products that should go to the lowest level are known. Once the height for the lower shelf is decided, the number of shelves that are under the human reach limit has to be checked. In this work, the change from 20 to 35 inches is assumed, which causes level three (3), which is usually within human reach, to be above (>∂). Even if the lower border of level 3 is still low enough, the upper limit may be out of reach and dangerous from the health and safety point of view. This alteration also makes results more comparable, since prioritised (human height) shelves in different models have a similar total height (60in vs 55in).

• Sharing version only differs from the generic that instead of Eq. (9), Eq. (10) is used, which allows partial SKU allocation to the closest available spot if its length is greater or equal to the current SKU box length. Present work restricts division of a SKU between maximum of two (2) locations, which means the shelf of the second pick has to accommodate the remainder of the SKU. As a result, the integer number of boxes is allocated to the first location, and the rest is allocated elsewhere.

• The customised sharing method is a combination of sharing and customised. Lower shelf allocation is performed separately due to the height differences and sharing between the maximum of two slots is allowed for the remaining levels.

5.3.1. The comparison of all variations

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5.3.1.1. Distance

The routes from I/O point to the locations assigned by each of the variations are measured to compare to the distances pickers currently have to cover per month. 131 SKUs are considered. These results are distracted from the current routes calculated in Section 5.2. The difference identifies the distance win of each method compared to the initial situation. Positive or negative, the distance win is multiplied by the monthly usage of the SKU. The summation over 131 SKUs for each method separately allows routing length comparison to the initial values:

∑131_𝑛=1(𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒_𝑛 − 𝑁𝑒𝑤 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒_𝑛) ∗ 𝐹_𝑛 (14) ,

where 𝐹𝑛 is the frequency of SKU 𝑛 being picked. Eq. (14) presents the total distance covered by pickers within a month for 131 SKUs.

Table 5.2. presents the process for monthly distance wins calculation for each of the methods on the example of three SKUs, and the overall wins for the entire analysis (fully presented in Appendix D). The total distance displayed is the result of the Eq. (14). Total win indicates the win of the named method over the average total initial distance.

Table 5.2. Four methods’ distance comparison SKU name Initial distance 1 Initial distance 2 Usage Generic distance Sharing distance Customised distance Customised sharing distance SKU159 581 629 72 555 556 582 582.44 SKU163 721 721 60 564 563 598 598.22 SKU173 363 363 31 580 579 938 144.3 Total distance 27874554 29994080 14804794 14764372 16361223 1574027 Total win 48.8% 48.9% 43.4% 45.5%

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space-size fit. However, the difference in this specific situation between sharing and not is negligible. It can be explained by the perfect size fit of current data set even without sharing. The relatively poor performance of the customised versions can be explained by a large number of first shelf items. It enforced the furthest rack exploitation even if otherwise it would remain unoccupied. Another reason for their lower performance may be that the total height of human reach shelves is five (5) inches smaller for the customised options. As a result, it allows fewer product allocations to the closer shelves sending SKUs to the further racks, which have distance disadvantage but the allocation priority over the closest top shelves. Results demonstrate that sharing versions always outperforms non-sharing both in customised and the-same-shelf-height alternatives. It is essential to note, that sometimes generic version is the only option possible for the company to use based on their policies and goals. Nevertheless, despite the fact which one out of four (4) versions company prefers, from the results it can be appreciated that the tool identifies a new allocation that reduces the travel distance up to 50%. To conclude, the decision-support system suggests product distribution that implies shorter walking distances to the pickers. However, the exact percentage win may not be as accurate, due to the current distance calculations being based on the continually changing two-day locations only. The allocation procedure sheet can be seen in Appendix E.

5.3.1.2. Utilisation

Apart from the given example of distance comparison, utilisation of the shelves for each method is also compared based on the ratios of occupied shelf space to the rack length. This research studies the total unoccupied space per model alternative:

𝑈𝑗𝑚 = ∑(𝑍 − ∑ 𝐿𝑛𝑗𝑚) 𝑁 𝑛=1 , ∀𝑚 ∊ 𝑀 (15). 𝐾 𝑗=1

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(total height of those is similar to the first three shelves in the alternatives). Table 5.3 compares the utilisation results of four (4) methods.

Figure 5.2.Warehouse shelf space utilisation

Table 5.3. Four methods’ shelf utilisation comparison

Version Generic Sharing Customised Customised

sharing

Shelf Occupied Free Occupied Free Occupied Free Occupied Free

1A 424 1.2 424.6 0.6 425.16 0.04 425.16 0.04 1B 422.8 2.4 425.2 0 424.8 0.4 424.3 0.9 1C 424.1 1.1 424.5 0.7 2A 424.4 0.8 424.4 0.8 425.16 0.04 425.16 0.04 2B 421.4 3.8 424.7 0.5 425.1 0.1 423.6 1.6 2C 425.1 0.1 424.5 0.7 3A 423.9 1.3 423.6 1.6 425.16 0.04 425.16 0.04 3B 419.8 5.4 423.4 1.8 424.4 0.8 424.8 0.4 3C 421.2 4 423.5 1.7 Average 2.23 0.93 0.24 0.50

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provides a high lower shelf utilisation, and the latter contributes towards the remaining occupancy) has not been confirmed. The reason may be that, in this specific situation, sharing caused a partial SKUs allocation, which box lengths did not match the remaining spaces as perfectly as in the generic version. For instance, if in the sharing version, the next priority SKU is split and placed on the shelf despite the ideal fit, in the generic only the SKU with length match would fit. This result shall not be taken as a rule and should be tested on a different data set. The current analysis, however, confirms that the sharing version improves utilisation factor in comparison to the generic one.

5.3.2. The winning combination’s allocation values

Findings show that the sharing version provides the highest distance wins and the best utilisation; therefore, it is suggested for implementation to Company X. Consequently, the allocation results for this option are presented below in Table 5.4. Since it is a sharing version and some shelves would accommodate only parts of the SKU, the number in brackets indicates what length of the specific SKU is allocated to the rack. Additionally, SKUs are presented in the order they have to be placed on the shelf starting from the closest to the I/O point side. The result presentation tab can be found in Appendix G.

Table 5.4. SKU allocation for Company X. Due to the different layouts used, the names of the shelves are different as well. They are defined by a number and a letter: the number identifies the rack and the letter – the level, starting with A from the bottom.

Shelf SKUs Shelf SKUs

1A SKU1(165.2), SKU17(28.4), SKU21(56), SKU36(17.7), SKU37(30), SKU42(11.8), SKU49(76.5), SKU73(36), SKU123(3)

5A SKU43(11), SKU50(21.3), SKU53(17.7), SKU56(45), SKU77(14.2), SKU83(103.5), SKU117(5.9), SKU124(15), SKU135(45), SKU171(7.5)

1B SKU2(127.3), SKU11(112.5), SKU32(40), SKU40(28.4), SKU49(117)

5B SKU44(96), SKU78(30), SKU87(5.9), SKU89(5.9), SKU91(22.5), SKU99(40), SKU109(15), SKU119(15), SKU134(6.7), SKU142(16),SKU155(7.5), SKU161(27)

1C SKU3(42.6), SKU4(11), SKU5(42.6), SKU9(56.8), SKU16(35.4), SKU19(21.3),

SKU24(21.3),SKU29(123), SKU60(67.5), SKU107(3)

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41 2A SKU(418.4), SKU(5.9) 6A SKU65(47.4), SKU85(30), SKU93(90),

SKU143(18),SKU158(27), SKU179(7.1)

2B SKU7(28.4), SKU10(200), SKU46(52.5), SKU58(11.8), SKU62(22.5), SKU74(51), SKU92(58.5)

6B SKU66(37.5), SKU81(39.5), SKU92(9), SKU97(22.5),SKU103(22.5), SKU111(15), SKU121(54), SKU168(18)

2C SKU(67.5), SKU12(52.5), SKU20(90), SKU41(211.5), SKU133 (3)

6C SKU67(7.5), SKU71(126), SKU113(15), SKU125(15), SKU136(7.5), SKU146(15), SKU159(7.1),SKU163(5.9), SKU166(13.5)

3A SKU13 (60), SKU23(17.7), SKU28(17.7), SKU35(60), SKU48(11.8), SKU51(45), SKU60(99), SKU100(22.5), SKU105(5.9), SKU108(67.5), SKU160(7.5), SKU164(9)

7A SKU94(14.2),SKU101(22.5),SKU106(22.5 ),SKU116(7.1),SKU120(58.5), SKU169(6), SKU173(6)

3B SKU14(28.4), SKU18(28.4), SKU22(29.5), SKU31(40), SKU39(15), SKU41(31.5), SKU52(42.6), SKU63(7.5), SKU69(7.1), SKU72(126),SKU114(13.4),SKU126(49.5 ), SKU166(4.5)

7B SKU95(22.5),SKU102(22.5), SKU107(27), SKU130(7.1), SKU132(5.9), SKU138(15), SKU149(36)

3C SKU15(192), SKU55(17.7), SKU61(11.8), SKU68(21.3), SKU75(14.2), SKU80(30), SKU90(22.5), SKU98(81), SKU145(15), SKU156(7.5), SKU162(7.5), SKU169(3)

7C SKU96(85.5),SKU139(15),SKU150(31.5), SKU175(6)

4A SKU25(21.3),SKU33(265.5),SKU115(5.9) ,SKU118(22.5),SKU141(15),SKU154(31.5 ), SKU177(9)

8A SKU127(15), SKU140(15), SKU152(15), SKU165(9), SKU170(13.5)

4B SKU26(15), SKU30(117), SKU59(45), SKU79(30), SKU88(99), SKU131(7.1), SKU137(15), SKU148(16),SKU164(13.5), SKU172(18)

8B SKU128(49.5), SKU167(18)

4C SKU27(21.3), SKU34(33.5),SKU38(28.4), SKU47(28.4), SKU54(45), SKU70(11.8), SKU73(90), SKU104(22.5), SKU112(15), SKU122(15), SKU133(18), SKU151(5.9), SKU157(27), SKU178(3)

(43)

42 5.3.3. Sensitivity analysis

Sensitivity analysis is performed to confirm the robustness of the decision-support system and potentially identify circumstances in which one or another alternative would work the best. The main goal of the analysis is to evaluate the importance of the input parameters that influence results (Thiele et al. 2014). It is achieved by varying some of the settings, such as usage and aisle width. The most common one-factor-at-a-time (OAT) method is used, which keeps all values at original values while changing only one of them to identify its influence (Thiele et al. 2014).

5.3.3.1. SKU size manipulation

The first parameter changed is the size of SKUs. This variable can be manipulated through the maximum stock requirements. The purpose of varying this parameter is to see whether product sizes influence the advantage sharing model has over the other ones. The stock requirement is 150% of the average usage per month; therefore, usage is the variable that is changed in reality.

5.3.3.1.1. Unchanged allocation priority

The initial analysis is based on increasing and decreasing values by 20% and 50% to see the differences. Table 5.5 presents the results.

Table 5.5. SKU size change by 20% and 50%

Generic Sharing Customised Customised sharing

120% usage 43.6% 44.2% 31.1% 45.6%

100% usage 48.8% 48.9% 43.4% 45.5%

80% usage 53.4% 54.4% 42.6% 41.5%

50% usage 61.9% 63.1% 48.9% 48.5%

(44)

43

unit; however, it may be enough for just a part of it. With larger SKUs, splitting may provide a higher total distance win to the bigger SKUs than the loss caused by the smaller less prioritised units shuffled to the back (see Figure 5.3 below). While in a generic version, due to the large volumes, SKUs have to be allocated to the furthest still empty shelves that have enough space for the whole unit. In case those SKUs have the highest demand, the frequently walked longer distances will significantly contribute to the total distance growth. In the case of larger SKUs, the customised sharing alternative appears to perform the best, since it allows later priority SKUs to fill the lower shelf gaps following the generic allocation. It also allows greater wins for the bigger SKUs on the upper shelves with the sharing model. High lower shelf utilisation also contributes to the better result.

Storage location assignment for differently sized SKUs in a manufacturing firm