A Methodology to Incorporate Multiple Cross Aisles in a Non-Traditional Warehouse Layout. A thesis presented to. the faculty of

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1 A Methodology to Incorporate Multiple Cross Aisles in a Non-Traditional Warehouse Layout A thesis presented to the faculty of the Russ College of Engineering and Technology of Ohio University In partial fulfillment of the requirements for the degree Master of Science Akhilesh Mesa December Akhilesh Mesa. All Rights Reserved.

2 2 This thesis titled A Methodology to Incorporate Multiple Cross Aisles in a Non-Traditional Warehouse Layout by AKHILESH MESA has been approved for the Department of Industrial and Systems Engineering and the Russ College of Engineering and Technology by Dale Masel Associate Professor of Industrial and Systems Engineering Dennis Irwin Dean, Russ College of Engineering and Technology

3 3 ABSTRACT MESA, AKHILESH, M.S., December 2016, Industrial and Systems Engineering A Methodology to Incorporate Multiple Cross Aisles in a Non-Traditional Warehouse Layout Director of Thesis: Dale Masel Recent studies of warehouse layout designs show that the travel distance from the pick and deposit (P&D) points to a storage location in a unit load warehouse can be reduced by changing the angle of the cross aisles in the traditional warehouse layout design. These new designs are called as non-traditional warehouse layout designs. A method to incorporate multiple cross aisles in a non-traditional unit load warehouse with multiple P&D points is discussed in this thesis. Unlike other design in the literature, the aisles are arranged in a diamond shape to provide coverage across the entire floor of the warehouse. Travel distances are calculated for the designs proposed in this thesis under random storage assignment and class-based storage assignment and the results are compared with the traditional warehouse design for three different warehouse sizes. The results show savings in the travel up to 10.6% for random assignment and 8.3% for class-based storage assignment. The new layout requires only 2.5% more space for a small warehouse and 1.8% more space for a large warehouse.

4 4 DEDICATION I dedicate my thesis research to Industrial and Systems Engineering faculty and students at Ohio University, through all of your friendships and company, I was able to settle into a different country and still feel home. For that, I am forever grateful.

5 5 ACKNOWLEDGMENTS I d like to acknowledge my Grandfather, who recently passed away, for playing a pivotal role in pushing me to pursue my dream of earning a Master s degree and also to my parents, whom have helped shape me into the person I am. Without your patience, love, and encouragement, I wouldn t be here today.

6 6 TABLE OF CONTENTS Page Abstract... 3 Dedication... 4 Acknowledgments... 5 List of Tables... 9 List of Figures Introduction Background Motivation Objective Literature Review Traditional Warehouse Design with Cross Aisles Warehouse Routing for Order Picking Non-Traditional Warehouse Designs Single Command Operations in Non-Traditional Warehouse Designs Dual Command Operations in Non-Traditional Warehouse Designs Non-Traditional Warehouse Designs with Multiple P&D Points Methodology Description of Situation Notation... 34

7 3.3 Generating Cross Aisles in Diamond Layout Location of Storage Racks Location of Storage Racks Outside Cross Aisles Construction of Storage Racks Inside Cross Aisles Determining Travel Distance to Storage Locations from P&D Points Travel Distance to Zone I Travel Distance to Zone V Travel Distance to Zone III Travel Distance from I/O points to Storage Locations in Diamond Layout Modified Diamond Warehouse Layout Methodology Travel Distance Calculations from P&D point to all I/O Points in Modified Diamond Warehouse Layout Location of Storage Racks and Picking Aisles in a Traditional Warehouse Travel Distance from P&D point to Aisle I/O point in a Traditional Warehouse Travel Distance from I/O points to Storage Locations in Traditional Layout and Modified Diamond layout Results Random Storage Assignment Results Class Based Storage Assignment Summary Conclusion Implementation Future Work

8 References

9 9 LIST OF TABLES Page Table 4-1. Warehouse specifications Table 4-2. Random storage assignment results Table 4-3. Results for medium warehouse Table 4-4. Class distribution of small warehouse Table 4-5. Class distribution of medium warehouse Table 4-6. Class distribution of large warehouse Table pallet / SKU results Table 4-8. Equal pallet / SKU results... 69

10 10 LIST OF FIGURES Page Figure 1-1 Flying-V aisle design Figure 1-2 Fishbone-aisle design Figure 2-1 Aisle layout options Figure 2-2 MCAM illustration Figure 2-3 Sections in fishbone-aisle design Figure 3-1 Traditional warehouse design Figure 3-2 Diamond layout design Figure 3-3 Process for creating cross-aisle geometry Figure 3-4 Process to determine θ Figure 3-5 Determining the endpoint of storage racks outside the cross aisles Figure 3-6. Calculations to determine the number of storage locations on side Figure 3-7 Storage racks and picking aisles outside cross aisles Figure 3-8 Process to determine αα Figure 3-9 Determining the endpoint of storage racks inside the cross aisles Figure 3-10 Diamond warehouse layout Figure 3-11 Zones Figure 3-12 Input/output points for picking aisles Figure 3-13 Distance calculation between two I/O points in zone I Figure 3-14 Distance calculation from P&D to I/O point 1 in zone I Figure 3-15 Distance calculation between two I/O points in zone V... 45

11 Figure 3-16 Distance between edges of cross aisles Figure 3-17 Aisle I/O point distance calculation Figure 3-18 Distance calculation from P&D point to aisle 1 I/O point in zone V Figure Zone V aisle 1 travel from I/O point Figure 3-20 Travel path to zone III I/O point from P&D point Figure Travel path calculation to zone III Figure 3-22 Distance calculation from P&D to I/O point in zone III Figure Distance calculation from zone V exit point to zone III I/O point Figure 3-24 Travel distance calculation from zone V entrance point to exit point Figure 3-25 Travel path from I/O point to storage location Figure 3-26.Determining cross aisle length in modified diamond Figure Modified diamond layout Figure Distance calculations from P&D to I/O in modified diamond Figure 3-29 Storage racks and picking aisle locations in a traditional warehouse Figure 3-30 Aisle I/O points in traditional warehouse Figure 3-31 Travel path from P&D point to aisle I/O point in a traditional warehouse Figure 4-1 Öztürkoğlu et al. [6]non-traditional aisle designs with two P&D points Figure 4-2 Small warehouse with (a) diamond layout (38,400 ft 2 ) and (b) traditional layout (37,440 ft 2 ) Figure 4-3 Medium warehouse with (a) diamond layout (194,400 ft 2 ) and (b) traditional layout (190,080 ft 2 ) Figure 4-4. Large warehouse with (a) diamond layout (285,120 ft 2 ) and (b) traditional layout (279,840 ft 2 ) Figure 4-5. Comparison of random and class-based storage assignment

12 12 1 INTRODUCTION In general, many factors affect warehouse efficiencies such as layout design, storage locations, retrieval strategy and others. In recent years, non-traditional warehouse layout designs have been studied. The main aim of these designs is to reduce travel distance for warehouse operations. Accordingly, decreasing the travel distance within the warehouse can increase the efficiency of warehouse operations. 1.1 Background Warehouses play an important role in the supply chain. For instance, if a supplier were to send their products directly to all stores, transportation of these products is more expensive because many trips are required instead of one trip to a warehouse. It can be less expensive if they send their products directly to a warehouse, than making individual shipments to the stores. A warehouse also helps the supplier to accommodate variation in customer demand for the products, which may vary throughout a year. When the demand for the product is high, a supplier without a warehouse might not be able to deliver the products to the customer on time because the manufacturing plant may not have the capacity to produce at a high rate when demand is high. Also, manufacturers need a place to keep items produced when demand is low. In this type of situation, a supplier having a warehouse can store products in the warehouse. Based on the demand, these products are then shipped directly from the warehouse to the respective customer. A warehouse in which products are received, stored, retrieved and shipped on pallets is called a unit load warehouse [1]. For example, a manufacturer may have a primary

13 13 distribution center and this manufacturer may send products directly from the factory to the primary distribution center, which acts as the main supply of products to its subdistribution centers or its customers. In this distribution center, almost all the orders would be for full pallets. In this situation, pallets do not need to be broken down into carton quantities to fill the orders. Another situation in which full pallets are moved is the forward/reserve strategy. The products received from suppliers are first stored in a reserve area, which acts as a buffer zone for the stock keeping units (SKUs) in the forward area. The forward area is where products are picked based on the orders and then sent to the shipping area. When cartons are being picked in the forward area, full pallets are moved to the forward area from the reserve area to replenish the empty storage spaces. Thus, the reserve area shares some characteristics of a unit load warehouse. In warehouse operations, there are a variety of operating strategies that are used to increase the efficiency of the travel. For example, based on the demand, products can be divided into classes i.e., A, B, C [2]. Class A products fulfill most of the orders, Class B products fulfill few orders whereas Class C fulfills rare orders. Most of the Class A products are stored near the Pick & Deposit (P&D) point because typically approximately 80% of demand can be filled by Class A products [3]. Another strategy to increase efficiency is using dual-command operations. In single-command operations, products arrive at the warehouse, then a worker picks up a pallet and drives it to its storage location, then comes back to the receiving dock with an empty forklift [4]. In a single command, a worker also travels with an empty forklift to the

14 14 storage location to retrieve a pallet and drive it to the shipping area. In dual-command operation, a worker carries a pallet from the receiving area to a storage location to store the pallet then goes to another location to retrieve a pallet and drives it to shipping area [4]. In single command operations, a forklift is unoccupied for half of the travel. Empty travel of forklift can be reduced with the use of dual command operation, increasing the efficiency of workers. 1.2 Motivation The efficiency of travel can also be affected by warehouse design [5]. In a traditional warehouse, aisles are arranged in a rectilinear fashion with racks and aisles parallel to walls. To store or retrieve a pallet from a rack, the worker travels in a rectilinear path from the P&D point. Gue and Meller proposed new unit load warehouse designs which allow non-rectilinear travel: Flying-V and fishbone-aisle. Flying-V and fishbone-aisle designs are shown in Figure 1-1 and Figure 1-2 respectively. Figure 1-1 Flying-V aisle design

15 15 Figure 1-2 Fishbone-aisle design A flying-v layout can reduce expected travel distance by 10% -12% compared to a traditional warehouse layout and in the fishbone-aisle design, travel distance can be reduced by 20% [5]. For both flying-v and fishbone-aisle designs, the P&D point is centrally located at the bottom [5]. Later, non-traditional unit load warehouses with multiple P&D points were studied [6], [7]. These non-traditional multiple-p&d-point designs have two cross aisles. One of these layouts has four P&D points, which are centrally located on each side of the warehouse. In this case, instead of two cross aisles, a four cross aisle design might work better. The layout proposed in this thesis also has different P&D points, with four cross aisles. By allowing multiple P&D point designs for a non-traditional warehouse, designers have additional options for a designing the warehouse. Thus, this research can fill a gap in current research and gives some extra freedom for the warehouse designers.

16 Objective The objective of this thesis is to develop a methodology to incorporate multiple cross aisles in a non-traditional warehouse layout with multiple P&D points. This new layout is called the diamond layout. The expected travel distance from P&D points to storage locations will be calculated for the proposed layout and the obtained results will be compared with a traditional warehouse layout design and other non-traditional warehouse designs, Design C1 and Design C2 discussed in Öztürkoğlu et al. [6]. Öztürkoğlu et al. [6] determined the travel distances of non-traditional warehouse designs with multiple P/D points, C1 and C2 for three different sized warehouses, namely small, medium and large and compared the obtained results with a traditional layout design. Similarly, the travel distance in the diamond layout will be calculated for three different sized warehouses and the obtained results will be compared with traditional layout design and non-traditional designs C1 and C2. In the testing of non-traditional designs C1 and C2, products are assigned randomly to all storage locations. To do a fair comparison among three designs, it will be assumed that products are assigned randomly in diamond layout design and traditional design. The travel distance from the P&D points to all locations will also be calculated for class-based storage assignment in the diamond design and traditional design. The obtained results for class-based assignment in the diamond design will be compared only with the traditional design because travel distances in non-traditional designs C1 and C2 were not presented for a class-based assignment strategy.

17 17 2 LITERATURE REVIEW Gu et al. [8] discuss a comprehensive review of the design and performance of warehouses. They noted that five separate judgments have to be made in designing a warehouse: 1. modeling general warehouse construction 2. estimating overall size of the warehouse and its sub-divisions 3. selecting the material handling equipment 4. determining the operational policies 5. defining the layout designs of each sub-division During the design phase, warehouse designers should not ignore operational performance measures because they are strongly affected by the warehouse design [8]. The functionality of each department in the warehouse depends on the overall arrangement of the warehouse [8]. The main issues at this stage of design are to look after the storage and throughput requirements and to minimize the operational cost and construction cost. Gu et al. classify storage problems as: Pallet stacking arrangements Storage area layouts Automatic Storage/Retrieval System arrangements Storage area layout problems estimate the dimensions of aisles, the total number of aisles and the orientation of aisles in the storage area, which can help configure storage space. Automatic Storage/Retrieval System arrangements help determine the automation level and a total number of cranes require, which directly affect the storage area.

18 18 The performance of the warehouse is evaluated based on the maintenance cost, material handling cost, space utilization, and equipment utilization. 2.1 Traditional Warehouse Design with Cross Aisles Storage/retrieval strategies in warehouses can be categorize into two types: 1) single-command operations and 2) dual-command operations. Pohl et al. [9] discuss the efficiency of dual-command operations for three different layout designs (layout A, layout B, and layout C) in a traditional unit load warehouse. These three layouts are shown in Figure 2-1. Figure 2-1 Aisle layout options The objective of Pohl et al. is to define which of the three layouts best suits dualcommand operations. To do so, they develop a math models to determine the optimal travel path for these layouts. The P&D point for all three layouts is centrally located at the bottom of the layout. Layout A does not have any cross aisle and all the picking aisles are vertical to the P&D point. Layout B and layout C are almost alike; the only difference is that the picking aisles

19 19 in layout B are perpendicular to the wall with the P&D point and parallel to the wall with the P&D point in layout C. Layout B has a cross aisle, which is parallel to the P&D point and divides the warehouse into two halves. Layout C also has a cross aisle that also divides the warehouse into two halves. However, this cross-aisle is perpendicular to the wall with the P&D point. For single-command operations, layout A serves as a better option when compared to layouts B and C. Due to the cross aisles in layouts B and C, half of the picking locations are farther away from the P&D point when compared with layout A. However, in dualcommand operations, a middle cross aisle reduces the travel distance by generating additional routes for order picking. Assumptions include a random storage assignment strategy, and travel begins and ends at the P&D point. Pohl et al. model aisles as a set of discrete points with picking uniformly distributed among all aisles. Expected travel for dual-command operation is calculated as the sum of travel in single-command operation and travel between the storage locations. The results show that layout B and layout C are approximately 5% more efficient than layout A in dual-command. Pohl et al. conclude that layout C is favorable for small warehouses and layout B is favorable for large warehouses. However, there is less than 1% efficiency difference between layout B and layout C. Hu et al. [10] describe two types of storage systems (1) static-rack storage systems, and (2) mobile rack storage systems. They discuss order picking improvement with a cross aisle at the center in mobile storage systems.

20 20 Usually, cartons are stored in these racks and they are also called bin-shelving. In this, cartons are stored on a movable base that travels on rails, which are laid on the floor. Static-rack storage systems utilize approximately 40% of warehouse area whereas mobile rack storage systems utilize 85% of the system area. They describe the middle cross aisle models (MCAM) shown in Figure 2-2 and MCAM s routing algorithm. They compare the performance of an MCAM with mobile automated storage/retrieval system (M-AS/RS) for single-command operations. Their results show that an MCAM offers greater performance than an M-AS/RS in a simulation experiment. Figure 2-2 MCAM illustration 2.2 Warehouse Routing for Order Picking Retrieving items from storage locations in a warehouse to fill an order is called order picking. A worker travels from the P&D point to the storage location in a warehouse

21 21 to store/retrieve a product. Petersen [11] presents five order picking routing policies when a worker is retrieving multiple items on a trip. They are: 1. Transversal strategy 2. Return strategy 3. Midpoint 4. Largest gap strategy 5. Composite strategy A worker enters only the aisles which contain products for a particular order. In the transversal strategy, a worker enters from one end of the aisle, travels to the storage locations to retrieve products, then leaves from the other end of the same aisle. After retrieving products, the worker moves to next aisle to pick another product to fulfill the order. The return strategy is when the worker enters the aisle, travels to the storage locations to retrieve products, then exits from the same end of the aisle. In the midpoint strategy, the worker can only travel until the midpoint in an aisle to retrieve products and exits from the same end of the aisle. The largest gap strategy for routing is similar to midpoint strategy except for the worker travels until the largest gap between locations to be visited in the aisle. The composite routing design is the combination of both return and transversal routing strategy. Petersen s results suggest that the efficiency of order picking can be highly influenced by the choice of P&D location, the size of a warehouse, and routing policies. Optimal routing has shorter routes, but it does not follow a discernible pattern most of the time.

22 22 Battini et al. [12] discuss the picking process in a warehouse by simultaneously considering travel distance and storage assignment in a warehouse. According to them, this idea can be used to determine the effects of different factors that result in different solutions. Their objective is to create a storage arrangement system, which can be used to determine a route to reduce the travel distance for a worker while processing the order. According to them, there are three main elements associated with creating a storage arrangement system. They are as follows: Defining the route between different departments in the warehouse Defining the route to different aisles within the department Defining the route to different pick locations within the same aisle Their methodology is applied in a wood and iron furniture warehouse. The iron furniture department area adopted a return routing policy and had ten storage locations with one aisle. The storage allocation and travel distance estimation (SA&TDE) methodology changed the way products are allocated to these 10 locations. Estimated travel distance was reduced from 8557 to 4585 m, which is approximately equal to 46.9%. Roodbergen et al. [13] discuss how to determine warehouse control policies and layout simultaneously considering different control policies. They study three different categories of management decisions that are tactical, operational and strategic concerns. They calculate the average time travel for any combination of layout parameters and control policies using Monte Carlo simulation. They consider traditional unit load

23 23 warehouse but according to them, this methodology can also be implemented to the nontraditional warehouse. They implement their concept in a warehouse located in Netherlands. Their results show that average savings of 53% in travel distance for a single order. Celik and Süral [14] discuss order picking under random and turnover-based storage policies in a fishbone-aisle unit load warehouse. According to them, expected travel distance in a fishbone-aisle warehouse increases with an increase in the size of picking list. Their objective is to determine the size of order picking list with which a traditional unit load warehouse can out-perform the fishbone-aisle design. They develop an optimized travel path for a multi-item picking list in a fishbone-aisle warehouse and a traditional warehouse. Their results show that a traditional unit load warehouse out-performs a fishboneaisle design by approximately 36% when the size of the order-picking list increases. When it comes to skewed demand, the performance of a fishbone-aisle design warehouse increases with the increase in the size of the order-picking list. Moreover, the fishboneaisle design out-performs a traditional warehouse when the demand is highly skewed. 2.3 Non-Traditional Warehouse Designs Gue and Meller [1] discuss the performance of a traditional unit load warehouse with a cross aisle and without a cross aisle. They state that a traditional warehouse without a cross aisle is better for single-command operations. This is because in single-command operations, the worker travels to a storage location to store/retrieve a pallet and comes back directly to the P&D point, which means the worker does not have to travel between aisles.

24 24 However, in dual-command operations, the worker travels between aisles to pick pallets so in this case, the worker may use the middle cross aisle. According to Gue and Meller, warehouse layout design has three basic steps. 1) aisle structure, 2) storage and retrieval operations, and 3) travel path within the warehouse. Almost all warehouse designs follow two basic rules while designing the warehouse: 1) All the aisles must be straight and parallel to each other and 2) All the picking aisles must intersect the cross aisle at 90 degrees. Gue and Meller [5] discuss two non-traditional warehouse layout designs, flying V aisle design and fishbone-aisle design (shown in figure 1.1 and 1.2.). The objective of both the layouts is to reduce expected travel distance from the P&D point to a storage location in a warehouse. The total travel from P&D point to storage location could be reduced by 8%-12% with flying V cross aisle design and 20% with the fishbone-aisle design [1]. As flying V aisle and fishbone-aisle designs are new to the industry, Gue and Meller [7] note common concerns from industry: Do building columns have any influence on the design? Can we implement these layouts if there is more than one P&D point? To what extent do these designs have an impact on storage density? Do these layouts fit for dedicated storage assignment? According to Gue and Meller [7], building columns must be considered while implementing non-traditional layout designs in the warehouse. Based on the information they gathered from warehouse designers, storage racks can be installed around building columns. They also state that they know a company that successfully implemented the

25 25 fishbone-aisle design. These non-traditional warehouse designs have slightly less storage space when compared to a traditional warehouse of the same area. Because these designs require more space than the traditional warehouse to store the same quantity of products, the new layout designs will also affect the storage density of a warehouse. They address the other concerns in their later research. They also discuss two warehouses where they successfully implemented the design. The first warehouse (Generac) has a centrally located P&D point, which they called the lay-down area. After the implementation of the fishbone-aisle design, operators responded positively. At the second warehouse where they implemented the fishbone-aisle design, management is also satisfied with the new design. They report the same production level with fewer workers. Clark and Meller [15] discuss to what extent the vertical (bottom to the top of the layout) travel affects the performance of flying V design and fishbone-aisle design. They discuss the methodology used to calculate the expected vertical travel in a non-traditional unit load warehouse. They also use Gue and Meller s [5] methodology to calculate the travel distance along the floor. To measure the effect of vertical travel in a non-traditional unit load warehouse, they divide the vertical travel into three different scenarios. First, the Automated Storage/Retrieval System (AS/RS) or forklift can only lift its forks once it reaches the exact storage location. Second, the AS/RS or forklift can raise its forks while traveling to the storage location i.e., chebychev scenario. According to them, this option is rarely used in practice with forklifts.

26 26 Clark and Meller s three-dimensional model shows the flying V design is better than a traditional warehouse design. Saying that, the advantage reduces with the increase in the storage shelf levels of the racks. When it comes to a fishbone-aisle design, there is a slight change in the advantage levels when compared to a traditional warehouse Single Command Operations in Non-Traditional Warehouse Designs Öztürkoğlu et al. [16] discuss three improvements to Gue and Meller [5]. They suggest three non-traditional unit load warehouse designs. Chevron design Leaf design Butterfly design Their results suggest that the chevron design can be good for a non-traditional unit load warehouse with less than 27 aisles. They find that expected travel distance decreases by % when the size of chevron warehouse increases from 19 aisles to 27 aisles. According to them, if there are more than 27 aisles in a warehouse, the leaf design offers more savings than the chevron design. In a warehouse with up to 51 aisles, the leaf design has 19.2% less expected travel distance when compared with a traditional unit load warehouse but it requires 6% extra space. Their result show that the leaf design is better than the butterfly design because the butterfly design requires more space than the leaf design and the expected travel distance is almost the same in many cases.

27 Dual Command Operations in Non-Traditional Warehouse Designs Pohl et al. [4] discuss how to design a warehouse with a fishbone-aisle layout for dual-command operation and compare the layout with a traditional warehouse layout. They assume random storage assignment and that the P&D point is centrally located at the bottom of the warehouse. They utilize math models to minimize expected travel distance. Travel distance to the storage location from the P&D point is the same as the travel distance to the location across the aisle. In a warehouse with the fishbone-aisle design, the two cross aisles divide the layout into three different sections. They consider three sections (shown in Figure 2-3) as three separate cases to calculate the expected travel distance. Figure 2-3 Sections in fishbone-aisle design The three cases are as follows: Travel within the section Travel between section 1 and section 2 Travel between section 1 and section 3

28 28 Travel between section 2 and section 3 will be the same as travel among section 1 and section 2 because of the symmetry of the warehouse. As discussed earlier, in singlecommand operation, a worker travels to the storage location from the P&D point to store/retrieve products. To accomplish dual-command operation, a worker travels between storage locations to store then retrieve products. According to Pohl et al., the addition of single-command travel distance and the travel distance between the locations gives the expected total travel for dual-command operations. Their results show that the expected travel distance in a fishbone-aisle layout for dual-command operations is 10%-15% less than traditional layout. In general, there are three different types of storage allocation policies in warehouses [17]. Random storage policy Turnover-based storage policy Class-based storage policy The objective of Pohl et al. [17] is to determine the efficiency of flying-v and fishbone-aisle design for both single-command and dual-command operations under turnover-based storage policy. In turnover-based storage policy, all the fast moving SKUs are stored in the same area near the P&D point. They compare the result with a traditional warehouse layout for turnover-based storage assignment in single-command operation and dual-command operation. They establish that the flying-v design is better than the traditional warehouse design for single-command operation when using a turnover-based storage policy. However, it does not perform well under dual-command operation.

29 29 According to them, the cross aisle in flying-v is designed to address single-command operation under a random storage assignment policy. The fishbone-aisle layout has better performance when compared with a traditional warehouse layout for both single-command and dual-command operations under turnoverbased storage allocation policy. In a large warehouse, under turnover-based storage assignment for single-command operation, a fishbone-aisle layout offers 10-20% less expected travel distance than traditional design and 6-16% less for dual-command operation Non-Traditional Warehouse Designs with Multiple P&D Points Öztürkoğlu et al. [6] discuss a non-traditional warehouse with multiple P&D points. These P&D points are not located only on one side of the warehouse but are located on different sides. They propose four different layout problems, with multiple P&D points. They are: 1. P&D points are located at 1/3 and 2/3 of the same side of warehouse 2. One P&D point is located at the center of the top side of the warehouse, and the other point is located at the center of left side of the warehouse 3. One P&D point is located at the center of the top side of the warehouse, and the other point is located at the center of the bottom portion of the warehouse 4. P&D points are located at the center of all four sides of the warehouse Their results suggest that a non-traditional unit load warehouse with two P&D points at the bottom offers 9-12% savings, P&D points located at the center of top side and center of left side of the warehouse offer 6.1%, P&D points located at the center of top and

30 30 bottom side offer % travel distance savings when compared with the traditional unit load warehouse. According to them, there are no savings in travel when P&D points are located at the center of all four sides of the warehouse. Gue and Meller [7] discuss the performance of class-based storage policy for the flying V and fishbone-aisle warehouses. Their results show that the fishbone-aisle offers 10% improvement over a traditional unit load warehouse. However, they say that the flying V and fishbone-aisle designs should not be implemented in a warehouse where there is more than one P&D point. Moreover, it is common to have warehouses with multiple P&D in the industry. Gue et al. [1] discuss a non-traditional unit load warehouse which has various P&D points. For example, some warehouses contain two or more wrap machines, which means these machines can act as P&D points and in some cases multiple dock doors may serve as P&D points. The primary objective of a unit load warehouse is to move products from receiving to storage locations then from storage locations to the appropriate drop off point (shipping) and to minimize the total expected travel distance from a random storage location to random dock door. All the picking aisles in a fishbone-aisle design are positioned towards a single P&D point, but Gue et al. [1] consider a symmetric warehouse in which picking aisles are parallel to each other. For this reason, they ignore the fishbone-aisle design for their research. They also consider flying V layout with multiple P&D points, which they called as modified flying V, and one more design called an inverted V to test the performance.

31 31 They assume that the number of P&D points is the same as the number of picking aisles, and P&D points are located at the bottom of the warehouse. Their results show that the modified flying V cross aisle layout design can reduce the travel distance around 2-6% when compared with a traditional warehouse layout design. However, when it comes to the inverted V aisle layout, the results look disappointing. According to Gue et al. [1] the inverted V aisle design has negative improvement.

32 32 3 METHODOLOGY 3.1 Description of Situation Generally, in a traditional warehouse, all the picking aisles are parallel to the wall of the warehouse as shown in Figure 3-1. Figure 3-1 Traditional warehouse design This research proposes a new layout called the diamond layout. In the diamond layout, cross aisles are not parallel to the walls as shown in Figure 3-2. Figure 3-2 Diamond layout design

33 33 The way the diamond layout design is constructed is different from traditional warehouse layout design. To create and test the diamond layout, the methodology in this study can be categorized into three steps which are as follows: 1. Generating cross aisles 2. Determining storage rack locations 3. Determining travel distance to storage locations from P&D points Assumptions made for the design are as follows: 1. Width of the warehouse is greater than or equal to the height 2. Dimensions of warehouse are a multiple of 2[a+2p] 3. Storage locations are square 4. Single deep rack only Generally, if the width (w), height (h), aisle width (a), and pick face (p) of a warehouse are known, it is easy to design a traditional unit load warehouse. Similarly, with the same inputs, warehouse designers should be able to design a diamond layout. It is assumed that the width of the warehouse is greater than the height of the warehouse because if the height is greater than the width, the distances between the two P&D points increases and hence, the worker has to do additional traveling for every trip they make to/from storage locations to P&D points. Whereas, if the width of the warehouse is less than the height, the worker doesn t have to do additional travel for every trip. Moreover, to have an equal distribution of aisles and storage racks in the warehouse, the height of the warehouse is considered as a multiple of 2[a+2p] because one picking aisle (a) is necessary to retrieve products from two storage racks (2p) which are on

34 34 either side of the picking aisle. As mentioned in section 1.3, the diamond layout will be compared with non-traditional layout designs C1 and C2. Assumptions made for designs C1 and C2 are: single deep storage racks and all the storage racks are square. In order to have fair comparison, it is also assumed that in the diamond layout all the storage racks are single deep and are square (both dimensions of the storage location are the same) this is because most of the rack designs in the warehouses are square. 3.2 Notation In the methodology, the following variables are used. h w p a θ α i j k xx iiiiii DD nnnn height of warehouse width of warehouse pick face width and depth aisle width angle made by the cross aisle with warehouse wall where P&D point is located angle between cross aisles at the center of the warehouse index for aisle index for a storage location in an aisle index for a rack (each side of the aisle) travel distance from I/O point to storage location j in aisle i on side k distance from the P&D point to I/O point of aisle i in zone n 3.3 Generating Cross Aisles in Diamond Layout The first step is to determine the location of cross aisles in the warehouse. In a traditional unit load warehouse, the aisles that run along the longer walls of the warehouse

35 35 are used by the worker to navigate between picking aisles to store/retrieve products. The length of the aisle is same as the width of the warehouse, so it is reasonable to consider that the length of each cross aisle in the diamond layout (4 cross aisles) can be same as half the width of the warehouse. The process used to determine the geometry of the cross aisles is shown in Figure 3-3. Figure 3-3 Process for creating cross-aisle geometry As shown in Figure 3-3, to generate cross aisles for any given warehouse with height (h) and width (w), draw a semicircle with a radius w/2 on both larger sides of the warehouse. This is done because to have a cross aisle of length w/2, it is necessary to determine the end point of the cross aisle which starts from the P&D point. So, the points of the intersection of the two semicircles act as the end point of the cross aisles. The cross aisles begin at the midpoint of longer sides of the warehouse, where it is assumed the P&D points are located, and they extend to the point of intersection of the semicircles. 3.4 Location of Storage Racks After generating cross aisles, the next step is to position storage racks. The orientation of all storage racks in the diamond layout are not same. The shortest travel

36 36 between any two given points is achieved by traveling in a straight line. For this reason, it is better to have a straight picking aisle between the P&D points, so storage racks which are inside the diamond are oriented in the vertical direction. Also, the first picking aisle connects both the P&D points in the layout because the products which are on the either side of this picking aisle can be retrieved by a worker traveling from one P&D point to other without entering the cross aisles. Outside the cross aisles, storage racks are oriented horizontally because if they are oriented vertically, the worker needs to travel vertically downwards from the cross aisle to reach the storage location and then travel back up to reach the main cross aisle Location of Storage Racks Outside Cross Aisles To determine the exact location of storage racks and picking aisles, first, it is necessary to determine the angle made by the cross aisles with the walls of the warehouse. Consider triangle BCD in Figure 3-4. Figure 3-4 Process to determine θ

37 37 ssssss θθ = h/2 ww/2 θθ = ssssss 1 h ww (1) After determining θ, the next step is to define the location of storage racks outside the cross aisles. Using equation (1) and pick face width (p), the end location of the storage rack for picking aisle 1 can be determined using triangle BEF in Figure 3-5. Figure 3-5 Determining the endpoint of storage racks outside the cross aisles tttttt θθ = EF BE tttttt θθ = pp BE BE = pp tttttt θθ (2) The first row of storage rack starts at a distance of BE from the P&D point and extends until it reaches the wall of the warehouse. There may be empty space between the end of the storage rack and the wall of the warehouse because there might not be enough space there to have another full storage location. Picking aisles have racks on both sides. Because of the angled cross aisles, the storage rack on one side of the picking aisle has fewer storage locations than the other side.

38 38 It is assumed that the side closer to the vertical center of the warehouse is considered as side 1 (i.e., the longer side) and further from the center of the warehouse is considered as side 2 (i.e., the shorter side). To determine the number of storage racks in side 2 compared with side 1, consider triangle LMN in Figure 3-6. Figure 3-6. Calculations to determine the number of storage locations on side 2 tan θθ = LN LM LM = aa+pp tttttt θθ (5) Where, LM /p gives the number of additional storage locations on side 1 when compared with side 2. All the storage racks and picking aisles outside cross aisles are shown in Figure 3-7

39 39 Figure 3-7 Storage racks and picking aisles outside cross aisles Construction of Storage Racks Inside Cross Aisles To determine the exact location of storage rack inside the cross aisles, the angle between the two cross aisles (αα) is determined. As shown in Figure 3-8, From equation (1), αα = 180 2θθ αα = ssssss 1 h (3) ww Figure 3-8 Process to determine αα

40 After determining αα, the next step is to define the location of storage racks inside the cross aisles. By calculating SR in Figure 3-9 first storage rack location inside the cross aisles can be determined. Using equation (3) and pick face width (p), the location of the storage rack can be determined using triangle SRT in Figure 3-9. First, storage rack inside the cross aisles is placed at a distance of a/2 from the center of the picking aisle as shown in Figure Figure 3-9 Determining the endpoint of storage racks inside the cross aisles tan αα = ST 2 SR SR = pp tan αα 2 (4) Now, using equation (4), the first storage rack location inside the cross aisles can be determined. All the storage locations are positioned in the y-direction in the same way until they reach the other cross aisle. A diamond warehouse with all the storage racks is shown in Figure 3-10.

41 41 Figure 3-10 Diamond warehouse layout 3.5 Determining Travel Distance to Storage Locations from P&D Points After storage rack locations are determined, the next step is to estimate the travel distance from the P&D point to each storage location. To calculate the expected travel distance from one P&D point (receiving) to a storage location, and from a storage location to the other P&D point (shipping), the warehouse is divided into 6 zones, namely I, II, III, IV, V, and VI as shown in Figure Figure 3-11 Zones

42 42 Because of the design symmetry, the travel distance from P&D points to zones I, III, and V is the same as zones II, IV, and VI, respectively. The point of intersection of the center of the picking aisle and the edge of the storage rack is considered as the aisle input/output (I/O) point as shown in Figure A worker travels from the P&D point to I/O point of aisle i in zone j, then enters the picking aisle and travels to the storage location to store/retrieve product. Figure 3-12 Input/output points for picking aisles Travel Distance to Zone I To calculate the travel distance from the P&D point to storage locations in zone I, the first step is to calculate the distance between two I/O points in the zone. Consider triangle ZZ 11 ZZ 12 GG in Figure 3-13, where ZZ iiii represents I/O point j in Zone i.

43 43 Figure 3-13 Distance calculation between two I/O points in zone I sin θθ = Z 12G Z 11 Z 12 sin θθ = 2pp+aa ZZ ZZ = 2pp+aa sinθθ (6) Hence, the distance between two adjacent I/O points in zone I can be calculated using equation (6). The second step is to calculate the distance from the P&D point to the first I/O point in the zone. Consider the triangle BEZZ 11 in Figure Figure 3-14 Distance calculation from P&D to I/O point 1 in zone I

44 44 BZ 2 11 = BE 2 + EZ 2 11 Substituting equation (2) in (7), BZ 11 = BE 2 + pp + aa 2 2 (7) BZ 11 = pp tan θθ 2 + pp + aa 2 2 (8) The next step is to determine DD nnnn, the travel distance from the P&D point to I/O point of aisle i in zone n. This can be achieved by the sum of the distance from P&D point to the I/O point for aisle 1 and distance from I/O point 1 to the I/O point for aisle i. Combining equations (6) and (8) DD 12 = MZ 11 + ZZ DD 12 = 2pp+aa ssssss θθ + pp tan θθ 2 + pp + aa 2 2 DD 1ii = 2pp+aa sin θθ (ii 1) + pp tan θθ 2 + pp + aa 2 2 (9) The distance from the P&D point to any I/O point in zone I can be calculated using equation (9). As zone I and zone II are symmetric, travel distance in zone II can be calculated in the same way Travel Distance to Zone V In order to calculate the distance between two consecutive I/O points in zone V, consider triangle ZZ 51 ZZ 52 UU in Figure 3-15.

45 45 Figure 3-15 Distance calculation between two I/O points in zone V cos θθ = 2pp+aa ZZ ZZ = 2pp+aa cos θθ (10) To calculate the distance between the P&D point and the I/O point of aisle 1 in zone V, it is necessary to calculate the distance between the edges of the cross aisle (BJ in Figure 3-16). Figure 3-16 Distance between edges of cross aisles

46 Consider triangle JKO in Figure JO is obtained by subtracting the width of two aisles (a) from the length of the cross aisle (w/2). Then, cos αα 2 = KJ ww 2 2aa KJ = cos αα 2 ww 2aa 2 To find the distance from the P&D point to the edge of the cross aisle: JB = KB -KJ 46 JB = h cos αα 2 2 ww 2aa (11) 2 The next step is to calculate the distance from side of the cross aisle to the I/O point. Figure 3-17 Aisle I/O point distance calculation Consider triangle kzz 52 m in Figure 3-17 tan θθ = mzz 52 kzz 52 mzz 52 = tan θθ aa (12) 2 The final step is to calculate the distance from the P&D point to the I/O point from aisle 1 in zone V as shown in Figure 3-18.

47 47 Figure 3-18 Distance calculation from P&D point to aisle 1 I/O point in zone V From Figure 3-18 and equation (12), BZZ 51 + JZZ =JB 51 Substituting equation (11) in the above equation, BZZ = 51 h cos αα 2 2 ww 2aa - tan θθ 2 aa (13) 2 The travel distance from the P&D point to any I/O point in zone V can be determined by combining equations (10) and (13). BZZ 51 + ZZ = h cos αα 2 2 ww 2aa - tan θθ 2 aa + 2pp+aa 2 cos θθ DD 5ii = BZZ 51 + ZZ = h cos αα 2 2 ww 2aa - tan θθ 2 aa + 2pp+aa (ii 1) (14) 2 cos θθ The distance from the P&D point to any I/O point in zone V can be calculated using equation (14). This methodology can also be used to calculate travel distance in zone VI. As mentioned earlier, the point of intersection of a picking aisle and the edge of the storage rack is considered as the aisle I/O point. But, if the same procedure is adopted to aisle 1 in zones V and VI, the I/O point does not lie on the same line as all other I/O points.

48 So, it is assumed that the aisle 1 I/O point of zone V / zone VI lies on the same line of other I/O points in zone V and VI as shown in Figure Figure Zone V aisle 1 travel from I/O point To determine the travel from the I/O point of aisle1 to all storage locations in zone V and zone VI, consider triangle XJY in Figure tan αα = XY 2 XJ aa XJ 2 = +pp tan αα 2 (15) The distance from the I/O point of aisle 1 in zone V to all locations in that aisle can be determined by adding equations (12), and (15). DD 51 = tan θθ aa 2 + aa 2 +pp tan αα 2 (16) Travel distance from the I/O point of aisle 1 in zone V / VI to storage location j in can be calculated using equation (16).

49 Travel Distance to Zone III To reach an I/O point in zone III, it is not necessary for the worker to travel only in the cross aisle. The worker can travel in the cross aisle to an I/O point in zone V; then travel through a picking aisle in zone V to the far cross aisle; and then travel to an I/O point in zone III. Travel from the P&D point to an I/O point in zone III is shown in Figure Figure 3-20 Travel path to zone III I/O point from P&D point It is not necessary for the worker to travel to the end of the picking aisle in zone V to reach the zone III I/O point. So it is assumed that the worker travels to a certain point (g in Figure 3-21) the picking aisle which lies on the same line of the I/O point for zone III. This point is assumed to be the exit point of zone V.

50 50 Figure Travel path calculation to zone III Figure 3-22 shows the travel distance calculation from P&D point to an I/O point in zone III. Because of the symmetry of the warehouse, ZZ 52 f = gz 32 (shown in Figure 3-21). So by determining, ZZ 52 f travel distance from zone V exit point to zone III I/O point can be determined. Figure 3-22 Distance calculation from P&D to I/O point in zone III

51 51 From Figure 3-22, From equation (2), be = Therefore, pp tttttttt ZZ 52 f = be + ZZ 11 n czz 52 ZZ 52 f = pp + ZZ tttttttt 11n [aa + 2pp] (17) To determine ZZ 11 n consider triangle ZZ 11 nzz 12 in Figure 3-22 From equation (6) Therefore, cccccccc = ZZ 11n ZZ ZZ 11 n = ZZ cccccccc ZZ = aa+2pp sinθθ ZZ 11 n = aa+2pp cccccccc Substituting equation (18) into equation (17). sinθθ ZZ 11 n = (aa + 2pp) cot θθ (18) ZZ 52 f = pp + (aa + 2pp) cot θθ [aa + 2pp] tttttttt pp tttttttt + (aa + 2pp) cot θθ (aa + 2pp) pp tttttttt pp tttttttt + (aa + 2pp)(cot θθ 1) + (aa + 2pp) 1 tttttttt 1 ZZ 52 f = (aa+2pp)(1 tttttttt)+pp (19) tttttttt

52 The next step is to determine the distance between the exit point of zone V and the end point of the picking aisle. This can be achieved by determining ZZ 32 k in Figure Figure Distance calculation from zone V exit point to zone III I/O point As ZZ 32 k = ZZ, 12 f consider ZZ 12 f in Figure ZZ 12 f = 3aa 2 + 3pp cb From equation (13), ZZ 12 f = 3aa + 3pp czz ZZ 51 bb ZZ 51 bb = h cos αα 2 2 ww 2aa - tan θθ 2 aa 2 Therefore, ZZ 12 f = 3aa + 3pp czz h cos αα 2 2 ww 2aa tan θθ 2 aa (20) 2 To determine czz 51 consider triangle czz 51 ZZ 52 in Figure 3-22.

53 53 tttttttt = czz 51 czz 52 Therefore, Substituting equation (21) into equation (20) czz 51 = tttttttt czz 52 czz 51 = (aa + 2pp)tttttttt (21) ZZ 12 f = 3aa + 3pp (aa + 2pp)tttttttt + 2 h cos αα 2 2 ww 2aa tan θθ 2 aa (22) 2 The next step is to determine the travel distance from a zone V I/O point (e. g., ZZ 52 in Figure 3-24) to the exit point (g in Figure 3-24) in the same aisle picking aisle. Figure 3-24 Travel distance calculation from zone V entrance point to exit point determined. By calculating gzz 52 the required travel in zone V to reach zone III can be

54 54 From Figure 3-24, gzz 52 = ZZ 12 f + h 2 3aa 2 + 3pp gzz 52 = ZZ 12 f + (h 3aa 6pp) (23) To generalize the formula for all the aisles in the zone, i is substituted in equation (23). From equation (22), gzz 5ıı = ZZ 12 f + h (2ii 1)(aa + 2pp) (24) ZZ 12 f = 3aa 2 + 3pp (aa + 2pp)tttttttt + h 2 cos αα 2 ww 2 2aa tan θθ aa 2 Therefore, gzz 5ıı = 3aa + 3pp (aa + 2pp)tttttttt + 2 h cos αα 2 2 ww 2aa tan θθ 2 aa + h 2 [(2ii 1)(aa + 2pp)] (25) The final step is to sum the lengths of these segments to calculate the distance between the P&D point and the I/O point of the aisle in zone III, which can be determined by adding equations (14), (19) and (25) as shown in equation (26). DD 3ii = h cos αα 2 2 ww 2aa tan θθ 2 aa + 2pp+aa (ii 1) + 2 cos θθ (aa+2pp)(ii 1)(1 tttttttt)+pp + 3aa + 3pp (aa + 2pp)tttttttt + tttttttt 2 h cos αα 2 2 ww 2aa 2 tan θθ aa + h (2ii 1)(aa + 2pp) 2

55 DD 3ii = h cos αα 2 2 ww 2aa tan θθ 2 aa (aa+2pp)(ii 1)(1 tttttttt) + 2pp+aa (ii 1) + + pp + 2 cos θθ tttttttt tttttttt 3aa+6pp 2 (aa + 2pp)tttttttt h + cos αα 2 2 ww 2aa + tan θθ 2 aa + h (2ii 1)(aa + 2pp) 2 DD 3ii = 2pp+aa (aa+2pp)(ii 1)(1 tttttttt) (ii 1) + + pp + 3 (aa + 2pp) (aa + 2pp)tttttttt + h cos θθ tttttttt tttttttt 2 (2ii 1)(aa + 2pp) 55 DD 3ii =(aa + 2pp) ii 1 (ii 1)(1 tan θθ) pp tan θθ 2ii h + cos θθ tan θθ 2 tan θθ (26) 3.6 Travel Distance from I/O points to Storage Locations in Diamond Layout After determining travel distances from the P&D point to all aisle I/O points, the next step is to calculate the travel distance from an I/O point to an individual storage location in that aisle. To reach a storage location in an aisle, it is assumed that a worker travels down the aisle to the point of intersection of the midpoint of the pick face with the center of the picking aisle, then travels a distance of a/2 to the face of the storage rack as shown in Figure Figure 3-25 Travel path from I/O point to storage location

56 To simplify travel distance calculations from an I/O point to the storage location, each storage location is allocated with a number and numbering starts at the end by the I/O point as shown in Figure The first storage location in side 2 is given the same location number as the storage location in the opposite rack because travel distance from the I/O point to these locations is same. Travel distances from the aisle I/O point to the midpoints of the storage locations in an aisle follows a series as shown below. pp, 3pp, 5pp, 7pp, 9pp, [(jj 1)2+1]pp Therefore, travel distance from an I/O point to storage location can be determined using the following equation. 56 xx iiii = aa 2 + [(jj 1)2+1]pp 2 = aa+[(jj 1)2+1]pp 2 (27) where, a/2 is distance from center of picking aisle to storage location. 3.7 Modified Diamond Warehouse Layout Methodology In order to check if additional storage space can be fit into the diamond layout by reducing the sharp angle at the intersection of the cross aisles. Slight changes are made to the diamond layout design. The new design is called a modified diamond layout design. As shown in Figure 3-2, there may be only one storage location where the cross aisles intersect with each other. In the modified diamond, the picking aisle which is used to retrieve product from that storage location becomes the new cross aisle. The storage racks which are outside of the new cross aisle are extended towards it and these storage racks would be the same length. This new design is shown in Figure 3-26.

57 57 Figure 3-26.Determining cross aisle length in modified diamond It is assumed that there will be only 3 rows of racks next to the newly formed cross aisle so that the length of the side of the cross aisle is 2(a+2p) which means the length of the cross aisle also decreases. In the modified diamond, the length of each cross aisle is not equal to w/2. To determine the length of the cross aisle, consider triangle bcd in Figure sin θθ = bd bc sin θθ = h 2 (aa+2pp) bc h bc 2 = (aa+2pp) sin θθ The methodology used to determine the storage rack locations inside and outside the diamond layout can be adapted to determine storage racks in the new modified diamond warehouse because all the construction principles of the modified diamond are the same as the diamond layout. The modified diamond layout is shown in Figure 3-27.

58 58 Figure Modified diamond layout Travel Distance Calculations from P&D point to all I/O Points in Modified Diamond Warehouse Layout. The travel distance from the P&D point to all I/O points in the modified diamond warehouse is same as the diamond warehouse except for picking aisles which are on either side of the warehouse centerline. To determine the travel distance from the P&D point to these I/O points, consider triangle ZZ 13 ZZ 14 g in Figure Figure Distance calculations from P&D to I/O in modified diamond

59 59 ZZ = ZZ 13 g 2 + gzz 2 14 ZZ 13 ZZ 14 = ZZ 13 g 2 + (aa + 2pp) 2 where, ZZ is the distance from the last I/O point on the cross aisle to the I/O point which is on the side of modified aisle. From equation (5), ZZ 13 g = aa+pp tttttt θθ ZZ 13 ZZ 14 = aa+pp tttttt θθ 2 + (aa + 2pp) 2 (28) The total distance can be calculated by adding equation (9) and (28) DD 14 = 2pp+aa sin θθ + pp tan θθ 2 + pp + aa aa+pp tttttt θθ 2 + (aa + 2pp) 2 (29) The distance from the P&D point to I/O point for the aisles which are on the side of the modified diamond cross aisle can be calculated using equation (29). 3.8 Location of Storage Racks and Picking Aisles in a Traditional Warehouse As mentioned earlier, in a traditional unit load warehouse, aisles which run along the longer side of the warehouse are used by the worker to navigate between picking aisles to store/retrieve products as shown in Figure 3-29.

60 60 Figure 3-29 Storage racks and picking aisle locations in a traditional warehouse As discussed earlier, the shortest travel between any two given points is achieved by traveling in a straight line. For this reason, it is better to have a straight picking aisle between the P&D points. The first storage racks are placed at a distance of a/2 from the center of the facility so that picking aisle 1 runs between two P&D points as shown in Figure The storage rack in picking aisle 2 is placed next to the storage rack of the preceding aisle (aisle 1). Since all the picking aisles in the traditional warehouse are parallel to storage racks, all storage racks can be defined using the same procedure. Similar to the diamond warehouse, to have an equal distribution of aisles and storage racks, the width of the traditional warehouse must be (2n-1)(a+2p) and the height must be (2a+np) where n=1,2,3,

61 Travel Distance from P&D point to Aisle I/O point in a Traditional Warehouse A worker travels from the P&D point to the aisle I/O point, then enters the picking aisle and travels to the storage location to store/retrieve a pallet. I/O points are shown in Figure Figure 3-30 Aisle I/O points in traditional warehouse After determining the aisle I/O points, the next step is to calculate the travel distance from the P&D point to aisle I/O points. The travel path from a P&D point to I/O point is shown in Figure Figure 3-31 Travel path from P&D point to aisle I/O point in a traditional warehouse

62 62 To reach an I/O point, a worker travels from the P&D point to the midpoint of the cross aisle, then travels for a distance of [aa + 2pp] (ii 1) in the cross aisle and then travels to an I/O point which is at a distance of a/2 from the center of the same cross aisle. Therefore, travel distance from the P&D point to the I/O point of aisle 1 can be calculated using equation (30). = aa + [aa + 2pp](ii 1) + 2 aa 2 = aa + [aa + 2pp](ii 1) (30) where, ii = 1,2,3, 3.10 Travel Distance from I/O points to Storage Locations in Traditional Layout and Modified Diamond layout The methodology used in the diamond layout to determine the travel distance from an aisle I/O point to a storage location can be used to calculate the travel distance in the traditional layout and the modified diamond layout. In both the traditional layout and modified diamond layout, a worker travels to the point of intersection of the midpoint of the storage location and the center of the picking aisle, then travels to the midpoint of storage rack, which is at a distance of a/2 from the center of the picking aisle as shown in Figure 3-25.

63 63 4 RESULTS The primary objective of testing is to compare the diamond warehouse with the traditional warehouse and other non-traditional warehouse designs. The other nontraditional models are Design C1 and Design C2 discussed in Öztürkoğlu et al. [6] shown in Figure 4-1. In designs C1 and C2, one P&D point is located at the center of the top side of the warehouse, and the other point is located at the center of the bottom portion of the warehouse which is same as diamond layout design. Figure 4-1 Öztürkoğlu et al. [6]non-traditional aisle designs with two P&D points The first step in calculating the results is to determine the number of storage locations in the diamond warehouse based on the warehouse dimensions, aisle width, and pick face width using the methodology described in section 3. After determining the number of storage locations in the diamond warehouse, the next step is to identify the dimensions of the traditional warehouse that can accommodate the same number of storage locations as in the diamond warehouse. A traditional warehouse with the same dimensions as the warehouse for the diamond layout has a few additional storage spaces. To make a fair comparison between the diamond warehouse and

64 64 the traditional warehouse, it is assumed that the number of storage locations is same in both the warehouses, so the traditional warehouse will be slightly smaller. Finally, the methodology to determine the travel distance from the P&D point to all storage locations is used to calculate the expected travel distances in both the warehouses. Travel distance to a storage location is calculated as the distance to first P&D point (receiving) plus the distance to the second P&D point (shipping). Travel distance is calculated for three different sized warehouses: small, medium and large. All the warehouse specifications are shown in Table 4-1. Dimensions are all given in feet. Diamond warehouse dimensions (wxh) Table 4-1. Warehouse specifications Traditional warehouse dimensions Pick face (wxh) width (p) Aisle width (a) Number of Locations Warehouse size Small 240x x Medium 540x x Large 648x x (a) (b) Figure 4-2 Small warehouse with (a) diamond layout (38,400 ft 2 ) and (b) traditional layout (37,440 ft 2 )

65 65 (a) (b) Figure 4-3 Medium warehouse with (a) diamond layout (194,400 ft 2 ) and (b) traditional layout (190,080 ft 2 ) (a) (b) Figure 4-4. Large warehouse with (a) diamond layout (285,120 ft 2 ) and (b) traditional layout (279,840 ft 2 ) The obtained results are categorized into two sections: Random storage assignment Class-based storage assignment 4.1 Random Storage Assignment Results In this approach, products are randomly assigned to all the storage locations in the warehouse. Travel distance to all storage locations is calculated under random storage

66 assignment for all the warehouses mentioned in Table 4-1 and the results are shown in Table Warehouse size Table 4-2. Random storage assignment results Expected Travel Diamond Diamond Traditional Additional warehouse (ft) warehouse (ft) Savings Space required Small % 2.5% Medium % 2.2% Large % 1.8% The results show that the travel distance savings increases with an increase in the size of the warehouse. Also, the additional space required for storage locations in the diamond layout decreases with an increase in the size of the warehouse. In a small warehouse to accommodate 764 storage locations, the diamond layout warehouse (38,400 ft 2 ) is 2.5% bigger that traditional layout warehouse (37,440ft 2 ) and in the large warehouse, to accommodate 6550 storage locations, the diamond layout warehouse (285,120 ft 2 ) is just 1.8% bigger than a traditional layout warehouse (279,840 ft 2 ). Table 4-3 shows the results of the diamond layout, the modified diamond layout, design C1 and design C2 for a medium size warehouse. Table 4-3. Results for medium warehouse Layout Savings Additional Space Required Diamond 8.1% 2.2% Modified Diamond 8.1% 2.2% Design C1 2.9% 8.2% Design C2 9.8% 11.7%

67 67 The results from Öztürkoğlu et al. [6] show that the non-traditional warehouse design C1 for a medium-sized warehouse with 4320 storage locations offers 2.9% improvement in travel, but requires 8.2% additional space when compared with the traditional warehouse. Design C2 provides 9.8% travel savings but requires 11.7% of extra storage space. For the medium-sized warehouse, the diamond warehouse has 4406 storage locations whereas, for the same size warehouse, the modified diamond has 4412 locations. As shown in Table 4-2, the diamond warehouse and the modified diamond both offer 8.1% savings when compared with a traditional warehouse. 4.2 Class Based Storage Assignment For the class-based assignment, products are divided into three classes based on their demand. To determine the expected travel distance, first, it is necessary to estimate the number of pallets for each class. This was done by multiplying the total number of storage locations in the warehouse with the percentage of SKUs in each class. According to Pareto s law, 85% of turnover will be a result of 15% of the material stored [3], It is assumed that class A products, which are high-demand products, fulfill 80% of the demand; class B fulfills 15%; and class C fulfills 5% of the demand. It is also assumed that 20% of the SKUs are class A, 30% are class B, and 50% are class C. Two strategies are used for determining the number of locations assigned to each class: 1 pallet / SKU and equal pallets for all the classes. The total number of pallets for each class in 1 pallet/sku is determined by multiplying the total number of locations in the warehouse with the percentage of SKUs that are allocated to the class. Demand per

68 68 pallet is determined by dividing the percentage of demand for that class by the number of pallets in that class. For equal pallets per class, the number of pallets is obtained by dividing the total number of pallets in the warehouse by the total number of classes. Class A products have a high number of pallets per SKU, but have fewer SKUs when compared other classes. Class C products have a low number of pallets per SKU, but have more SKUs when compared with other classes. After estimating the demand for each class, the probability of visiting each location is calculated. The class distribution of the small, medium, and large warehouses is shown below in Table 4-4, Error Reference source not found. and Error Reference source not found., respectively. Class Percent of SKUs Table 4-4. Class distribution of small warehouse 1 pallet / SKU Equal pallets / class Percent Number Number of of of Demand Pallets Demand/Pallet Pallets Demand/Pallet A 20% 80% % % B 30% 15% % % C 50% 5% % % Class Percent of SKUs Table 4-5. Class distribution of medium warehouse 1 pallet / SKU Equal pallets / class Percent Number Number of of of Demand Pallets Demand/Pallet Pallets Demand/Pallet A 20% 80% % % B 30% 15% % % C 50% 5% 2204 <0.01% 1469 <0.00%

69 Class Percent of SKUs Table 4-6. Class distribution of large warehouse 1 pallet / SKU Equal pallets / class Percent Number Number of of of Demand Pallets Demand/Pallet Pallets Demand/Pallet A 20% 80% % % B 30% 15% % % C 50% 5% 3625 <0.00% 2185 <0.00% 69 Demand per pallet decreases as warehouse size increases, since there are more locations. Also, the demand is more skewed with 1 pallet/sku (A is higher, C is lower). The expected travel distance to a location is calculated by multiplying the probability of visiting the location with the travel distance from both P&D points to that location. The travel distance results of class-based storage assignment for all the warehouses are shown in Table 4-7and Table 4-8. Table pallet / SKU results Expected travel in diamond warehouse for 1 pallet / SKU (ft.) Expected travel in traditional warehouse for 1 pallet / SKU (ft.) Warehouse size Savings Small % Medium % Large % Table 4-8. Equal pallet / SKU results Warehouse size Expected travel in diamond warehouse for equal pallet / SKU (ft.) Expected travel in traditional warehouse for equal pallet / SKU (ft.) Savings Small % Medium % Large %

70 70 Similar to random storage assignment, class-based storage results also show that the diamond layout offers savings in travel distance from the P&D points to storage locations that traditional layout. Also, savings in the diamond layout again increases with an increase in the size of the warehouse. The percentage of travel distance savings in classbased storage assignment is less than random storage assignment because in random storage assignment, the probability of visiting is same for all the storage locations. In classbased storage assignment, workers make most of the trips to class A products which are located near P&D points because of high demand. Also, the distance between P&D points in the diamond layout is more than the traditional layout because of these reasons the travel savings in class-based assignment is less than random storage assignment. The medium size modified diamond warehouse offers 4.27% savings over the traditional warehouse when using class-based assignment. Öztürkoğlu et al. [6] only discussed random storage assignment, so a comparison with these results is not possible. 4.3 Summary Under both random storage assignment and class-based storage assignment, the diamond warehouse has an increase in the percentage of savings in travel with an increase in the number of storage locations. Results also show that the percent of additional storage space required for the diamond warehouse decreases with increase in the area when compared with traditional warehouse. These results are graphically shown in Figure 4-5.

71 71 Travel Savings in Random Storage PERCENTAGE Travel Savings in Class Based Assignment with Equal Pallets/Class Travel Savings in Class Based Assignment with 1 Pallet/SKU Additional Area required STORAGE LOCATIONS Figure 4-5. Comparison of random and class-based storage assignment Based on Figure 4-5, the additional area required decreases with an increase in the number of storage locations. Also the travel distance savings increases with an increase in the storage locations. Whereas, for class based assignments, savings in travel increases and slightly decreases.

72 72 5 CONCLUSION Results show that in a unit load warehouse with two P&D points, the diamond layout has a lower expected travel distance from P&D points to all storage locations under random storage assignment when compared with the traditional warehouse layout and the non-traditional warehouse design C1. The diamond layout also out-performs the traditional layout design under class-based storage assignment; Öztürkoğlu et al. [6] didn t calculate the travel distances for designs C1 and C2 under class-based storage assignment. Under random and class-based storage assignment, the percentage savings in travel from P&D points to the storage locations increase as the size of the warehouse increases. The percentage increase in space required for the warehouse decreases with the increase in the size of the warehouse. The diamond layout could be a better option for warehouse designers when they are designing a unit load warehouse with two P&D points (shipping and receiving) which are centrally located at the top and bottom side of the warehouse. This is because the diamond layout reduces the worker travel distance while moving pallets from the receiving point to a storage location and then from the storage location to the shipping point. 5.1 Implementation To implement the diamond layout, the warehouse should be a unit load warehouse, which means all the orders in the warehouse are pallet loads. The diamond layout can also be implemented in a section of a larger warehouse that handles only unit loads (e.g. reserve). In order to implement this design, the width of the warehouse (where P&D points are located) should be greater than or equal to the height of the warehouse.

73 73 Because of the presence of cross aisles in the design, the building columns should be placed in such a way that they do not affect the travel in the layout. Gue and Meller [7] implemented fishbone aisle design in a warehouse. They suggested that warehouse designers should be able to install building columns in a non-traditional warehouse. After determining the dimensions and the location of the building columns, the next step is to arrange racks in a warehouse. To create the layout, it is necessary to know the dimensions of pick locations or storage racks and aisle width. Once all the required information is gathered, a CAD drawing of the warehouse should be created, and the number of storage locations and aisles are determined. After finalizing the CAD drawing, the next step is to draw the layout on the floor and estimate the storage rack capacity and the warehouse designers should be able to install the storage racks accordingly. 5.2 Future Work As this research estimated the travel distance from P&D points to storage locations under random and class-based storage assignment for single command operation, future researchers can evaluate the performance of the diamond design for dual command operation. This research work can also be extended by eliminating the assumptions such as the length of the cross aisles is half the width of the warehouse because this research work does not focus on determining the optimal end point of cross aisles. Another area future researchers can look into is how the diamond layout design performs when the design is implemented in a warehouse which does not handle unit loads. Future researchers can also extend this

74 work by determining a methodology to modify the diamond layout design if P&D points are centrally located on all four sides of the warehouse. 74

75 75 REFERENCES [1] K. R. Gue, G. Ivanović and R. D. Meller, A unit-load warehouse with multiple pickup and deposit points and non-traditional aisles, Transp. Res. Part E Logist. Transp, Jul. 2012, Rev., vol. 48, no. 4, pp [2] S. S. Rao and G. K. Adil, Class-based storage with exact S-shaped traversal routeing in low-level picker-to-part systems, Int. J. Prod. Res., Aug. 2013, vol. 51, no. 16, pp [3] R. Riedel, Facilities planning 4th edition by J.A. Tompkins, J.A. White, Y.A. Bozer and J.M.A. Tanchoco, Int. J. Prod. Res., 2011, vol. 49, no. 24, pp [4] L. M. Pohl, R. D. Meller and K. R. Gue, Optimizing fishbone aisles for dualcommand operations in a warehouse, Nav. Res. Logist., Aug. 2009, vol. 56, no. 5, pp [5] K. R. Gue and R. D. Meller, Aisle configurations for unit-load warehouses, IIE Trans., Jan. 2009, vol. 41, no. 3, pp [6] Ö. Öztürkoğlu, K. R. Gue and R. D. Meller, A constructive aisle design model for unit-load warehouses with multiple pickup and deposit points, Eur. J. Oper. Res., Jul. 2014, vol. 236, no. 1, pp [7] R. Meller and K. Gue, The application of new aisle designs for unit-load warehouses, in NSF Engineering Research and Innovation Conference, 2009.

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77 77 [15] K. A. Clark and R. D. Meller, Incorporating vertical travel into non-traditional cross aisles for unit-load warehouse designs, IIE Trans., Dec. 2013, vol. 45, no. 12, pp [16] Ö. Öztürkoğlu, K. R. Gue and R. D. Meller, Optimal unit-load warehouse designs for single-command operations, IIE Trans., Jun. 2012, vol. 44, no. 6, pp [17] L. M. Pohl, R. D. Meller and K. R. Gue, Turnover-based storage in nontraditional unit-load warehouse designs, IIE Trans., Oct. 2011, vol. 43, no. 10, pp

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