LIST OF ACRONYMS° AGV: Automatic Guided Vehiclee AS/RS: Automatic Storage and Retrieval System¢ COI: Cube Per Order Index ¢ COL: Closest Open Location¢ DRP: Distribution Requirements Pla
Warehousing Operations -cc S1 1111111111159 1111111 krrrrrrree 2
Warehousing operations can be divided into several functions (See Fig 1.2) mainly:
Receiving, which consists of unloading of products from transportation vehicles to receiving docks, inspection of products for decencies or missing products, and updating warehouse inventory records to reflect changes.
Put-away can be described as a process of sorting pallet in pallet racking as well as storing goods information Some commonly storage policies used include random, dedicated, class-based and closest open location (COL) Which includes moving products from receiving dock to assigned storage locations, shipping dock or other areas in the warehouse, and moving products between these areas [1, 2, 3, 6|
Order picking is a process of retrieving articles from their storage locations in response to a specific customer request This is a fairly complex and costly process in warehouse management especially in warehouses with automated systems [1, 2, 3].
These authors estimate that order picking can account for up to 65% of the operating costs of a warehouse and thus its optimization is crucial to reduce costs Base on put- away or expiration day, some order picking policies is used such as first in first out(FIFO), last in first out (LIFO), first expire first out (FEFO) [2].
Shipping, which includes loading products onto transportation vehicles, inspection of products to be shipped, and updating warehouse inventory records It can additionally include sorting and packaging of products.
Schedule Carrier Unload vehicle Inspect for damage ig
Put-away Storage e Identify Product e Equipment e Identify Product \ e Stock Location Location ⁄ + Popularity e Move Products + Unit size e Update Records + Cube
Preparation e Information s Packing ự eô Walk & Pick e Labeling \ e Batch Picking e Stacking
Shipping e Schedule Carrier e Load Vehicle rou) e Bill of Loading e Record Update
Most common mode of pallet racking systems in Vietnam
Choosing right pallet racking system can make a huge cost saving in warehouse management A well-designed system can improve productivity and increase warehouse storage space by 40% or more, and help your operation adapt to changing inventory needs Subsection 1.1.1, 1.1.2, 1.1.3 and 1.1.4 are shown several type of pallet racking use in Vietnamese warehouse. e Selective Pallet Racking
Characteristics: This is the most popular racking system, which consists of beams linked to the vertical frame In standard designs, it reaches a height of 8 - 10m and can lift shelves up to 12m and in automatic operation systems, it can be as high as 30m.
Application: The system is suitable for large storage needs with all types of cargo handling in stock Contrary to the model of stacking goods, forklift truck can be accessed directly to each pallet and easily change cell height and intervals between beams to optimize shelf space. e Adjustable pallet racking for narrow aisles
Characteristics: This is an adjustable racking system which shelves are arranged close together to avoid wasting the aisle space, minimizing the space of cold storage - where warehouse space is proportional initial investment costs and operating costs.
The system has minimized the passageway and maximizing the height of the shelf (altitude above 10m).
- Can reach each pallet - Configured to be the maximum storage density, the highest efficiency - The rate of pallet filling is higher than other systems
- Save storage space, because of expanding storage space according to height.
- Difficulties in controlling vehicles when they need to import / export goods in high-density boxes because of limited visibility.
Fig 1.4 Adjustable pallet racking for narrow aisles e Mobile pallet racking system
Characteristic: The purpose of the system is to maximize the free space in the warehouse The system was design includes storage shelves placed on mobile racks.
This type of warehouse system is used when the storage space is very expensive, the need to save space.
- The system saves up to 90% of aisle space.
- Can access any pallet easily.
Operation: Shelves can be operated locally or via remote controllers, and crane vehicles are required to retrieve goods All shelves are equipped with a sensor system to ensure the shelves stop when encountering obstacles e — Dr¡ive-ln/Drive-Thru Rack
Characteristic: This system consists of racks designed so that forklifts can go deep into each shelf, pallet support rails are arranged higher than the height of the vehicle that can be easily moved In the process of warehousing or ex-warehousing, all pallets must be moved in order (from inside to outside, from top to bottom or vice versa).
Drive-In pallet racks: the process of warehousing and ex-warehousing is done from one side of the shelf, according to the Last In First Out method (LIFO)
Drive-Throught pallet racks: the process of warehousing and ex-warehousing is done from both sides of the shelf, according to First In First Out (FIFO) principle.
- Make good use of space because it does not take space for aisle - Allowing forklifts to move flexibly.
- Can increase storage capacity up to 75% compared to regular shelves.
Storage policy is related to assign products to storage locations when new products arrive in the warehouse Determining storage location - localization is understood as the process of selecting the optimal storage location among all positions in warehouse, so that the travel time is minimization, thus saving the total operating costs of the warehouse In addition, each storage location should be closely managed based on information such as type of goods, stored time, coordinates If storage policy is effective, there is shorter path will be found in determining storage location process for each cycle of pallet transferring in warehouse [1, 2, 7, 35]
In storage process, localization will be built based on the following strategy:
Random, dedicated, class-based and closest open location (COL) [1, 2, 3].
In arandom storage policy, each SKU (Stock-keeping unit - an inventoried item) is randomly assigned to an empty location in a warehouse [2] Random storage is a completely shared storage policy where all incoming storage pallets can be stored in any aisle and any open location in the rack Also, no grouping of storage location with the same SKU is usually made This makes random storage the easiest storing strategy to apply, since it makes no distinction between storage totes based on SKU features When a pallet is retrieved from for picking, it can be returned to a different rack location or even a different aisle [34, 35]
In dedicated (or fix slot) storage policy, each SKU is placed at a fixed position in stock This policy helps to manage and control system easier because each area in warehouse only contains one or a few type of items The storage locations are dedicated, meaning that each SKU is assigned a number of locations in the rack, where only that SKU can be stored This is referred to as dedicated storage [34] When dedicated storage is used, the COI (cube-per-order index) rule is a well-known ranking method, which takes the space requirements of the SKUs into account The COI is defined as the ratio of the number of storage locations assigned (or calculated) to an item With this measure, the SKUs with the smallest COI are positioned closest to the I/O point [34, 35]
Dedicated storage can be problematic, since the locations need to be allocated according to the maximum space requirement of each SKU The selected locations need to be reserved even when an SKU is out of stock These requirements induce the needed storage space [1, 21] For example, random storage needs about 70% of the space requirement of dedicated storage.
This result is based on the assumptions that the changes in inventory levels of different SKUs are independent, and most of the time the space requirement of an SKU is less than its capacity of inventory [21] In some applications with double-deep racks, it is possible to decrease the amount of rearrangements with dedicated storage by allowing only the same SKU to be stored in both front and back positions [20] In the installed system this strategy could not directly be applied because of the compartmented location Also it is expected that there will be several thousand SKUs in one aisle which makes it very difficult maintain the integrity of a dedicated storage location allocation An alternative approach to dedicated storage
Class-based storage policy is a combination of the above two methods Class- based storage partitions all products into two or more classes and reserves a block of storage locations within the rack for each class The class partition is based on some criterion, for example COI, duration of stay or turnover rate It can also be based on the affinity of items, meaning that items which have a higher chance of getting picked in the same order get stored close to each other.
This can be problematic though, since the items for the same order are not necessarily retrieved sequentially [22] If the turnover rate is used, the items with the highest turnover rate are allocated to the class whose storage zone is closest to the I/O point Inside the zone item locations are chosen according to an open location selection rule [4] Thus, class-based storage is a combination of dedicates and random storage policies The goal of using product classes is to achieve the potential effectiveness of full-turnover based storage while maintaining a part of the flexibility of random storage [34, 35] A higher number of classes can potentially impacted to large of travel time savings, but also increases the needed storage space For a single-deep rack it has been studied, that most of the gain from full-turnover storage can be obtained by using a small amount of classes For example 96% of the potential improvement can be got with 6 classes, and over 99% with 12 classes [34, 35] Using many classes can be hard to manage In practice, the number of classes is usually 2 — 3 After deciding the number of classes, there is the problem of deciding, how many and which SKUs belong to which classes Zoning, i.e the division of the storage rack into different zones.
Zone sizing is commonly chosen based on an ABC-analysis In case of two classes, the A class is reserved 20% and the B class 80% of rack area With three classes, the sizes for A, B and C classes are 20%, 40% and 40%, respectively [33, 34, 35] The classes are usually L-shaped or rectangular In Fig 1.4 typical example of zone division is presented for three classes.
With double-deep racks, zoning is not as simple If the zones were allocated according to Fig 1.4, each zone would require its own rearrangement area The fill level of each zone would need to be controlled so that there would always be a chance to move a tote in an allowed location Even so, the zone positioning of this figure might not work well double deep rack This is due to the previously mentioned issue that the back positions have a higher retrieval costs than front positions Instead of storing fast
Fig 1.7 A typical Zone positioning for three class in a Square in rack
METHODOLOGY 0 a 12 2.1 Assumption and Layout €S1ỉ1n (1111111 EEEEESsesssssssssse 12
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The system is built based on some special characteristics of cold store for preservation of aquatic products but we can adjust it to suit different types of storage. e The capacity of system are 480 storage locations, each location contain 1 SKU (stock keeping unit — an inventoried item) System containing 6 types of frozen shrimp which are named Al, A2, A3 A4, A5 and A6. e Goods are organized into the pallet Each pallet is a SKU This is the smallest item in system Pallet is placed on single pallet racking and order picker can reach all items in the rack regardless of rack’s height. e Pick out time is undefined for all SKUs in system.
For frozen shrimp products, the requirement in storage process is if goods were come first, it will be sorted in pallet racking first (FIFS) and travel distance for each moving cycle is the shortest to prevent damage under wrong temperature In retrieval process, pallet is removed base on import day, the oldest good in system is the earliest move out.
This requirement is necessary to ensure the goods are not in warehouse too long.
Warehouse layout and Routing . - c+<<<<<<ssssseeeeesss 12 2.2 Forklift Truck — System configuration and kinematic modeling
Caron, Marchet, and Perego found that the layout design greatly affected to order picking distance [7] According to their study, layouts affect over 60% of the total distance traveled in storage Therefore, designing layout is an important foundation task before building the management algorithm.
From assumptions were presented in section 2.1.1, warehouse system with 1 single pick aisle and 2 storage aisles is recommended (see Fig 2.1) Warehouse space is divided into 16 pallet racking (16 lines) The line consider in this paper include 5 tiers (A, B, C, D and E) and 6 bays (are distinguished by the digits from 1 to 8), totally 40 storage locations is located at each line These lines are named Roman numerals I to XVI The design help to be easily reach all items in the pallet racking and access to depot by using 2 separate Input and Output points
2.2 Forklift Truck — System configuration and kinematic modeling
The forklift is proposed in this thesis is a standard industrial forklift with a spin- turn mechanism provided by CLARK Company (see Fig 2.2) The car was designed with 4 wheels including 2 caster wheels in front, one dummy caster wheel at the right rear and one wheel at the left rear, which is used for driving and steering the forklift.
The forklift car has three basic motions (3 DOF), a straight-forward motion, rotation around the vehicle's axis (center of 4 wheels), and vertical translation along the elevation The forklift can be operated in the narrow aisle racking warehouse That mean the turning radius is less than the aisle dimension [6].
O-X-Y and o-x-y are the frame and the body coordinates of the forklift, respectively (see Fig 2.3) Let v and ỉ be the velocity of the forklift in the x-direction and the rotational angle of the x-axis with respect to the X-axis Let 6 be the steering
13 angle of the driving wheel Under the assumption that the wheels do not slip, let OICR be the instantaneous center of rotation of the forklift Finally, let | and a be the length of the forklift and the offset of the center of the driving wheel from the centerline. driving ` ` wheel
Fig 2.2 An industrial forklift truck Fig 2.3 Kinematics model of a forklift h, = l (2.1) sind
Then, from assumption that all wheels of forklift are not slippage, the following relationship can be derived: oa — Vv ở=-#=— h hcosỏ+a (2.2)
Where V, is the velocity of the driving wheel with the following formula below:
Where 7; and @, are the radius of the driving wheel and angular velocity of the driving wheel, respectively Therefore, the linear velocity of the forklift becomes:
Finally, the kinematics relationship between two input variables {w,,6) is the rate of change of the steering angle, and three generalized variables {X, Y, 8} becomes:
X =vcosO=r,0, 6055152 oso (2.5) Y =vsinỉ =r„ứ, cos + SẺ sing (2.6) Q= mẻ (2.7)
Apply states space model, 2 input variables and n states variables can be written as a (2, n) chained form model with the following form: x, =U, x, =U,
Combining the kinematic model (2.5) and the structure of the chained form (2.8), the coordinate transformation to obtain the chained form are: x, =X (2.9) x, = sind (2.10)
Thus, the velocity after being transformed becomes: u, =v, Ccos@ (2.14) lo, cos 9 —3v, sin sin’ ổ
Based on these velocity values, the distance and time weights will be calculated inSection 2.3.1
Auto — Localization Algorithm . - 1111111 EEEESSsssssssssssse 16
We focus on the ABC storage (class-based storage) and COL policy since they are basic policies for developing continuous cluster method Per mention at section 1.2.1, ABC storage policy is a combination of dedicated and randomized policy (see Fig 2.4).
Randomized policy is used for sorting SKU (stock keeping unit) within a class, and dedicated policy is used among different classes Under COL policy, SKU is sorted into storage location where is closest to the I/O point [2, 3, 4].
Pallet Pick racking aisle ae mạ Depot Depot
Under ABC storage policy, warehouse space is divided into three classes (see Fig.
2.4) Each class contain goods with the same parameters (same good type or same travel distance) In storage and retrieval process, goods will be sorted on each class with priorities in turn are A, B and C In each class, goods are arranged randomly into a certain location.
All storage locations of class A are considered to have the same distance and they have same priority in storage process, although the actual distance of each storage
16 location to I/O point is different from the others So if goods is stored in the same class, the travel distance is not really optimal This argument is correct when the number of pallets is smaller than the number of available storage location in class A.
To increase the efficiency of the algorithm, the ABC storage and COL policy are combined together That mean each class is divided into several smaller classes, each of which is called a cluster (see Fig 2.5) The radius of cluster is the travel distance from storage location on racking to I/O point In storage and retrieval process, SKUs are priority arranged into the cluster which has smallest radius By this method, the storage location is found always has travel distance less than the ABC class method If the number of clusters in each class is greater, the algorithm is more efficient To see the effectiveness of the algorithm, a warehouse system is simulated and analyzed in the following section 3 Continuous cluster method is a combination of ABC storage (class- based storage) and Closest Open Location policy — COL [2, 3, 4]
In detail, each class of ABC policy is divided into several smaller classes, each of which is called a cluster In Fig 2.5, Fig 2.6, each cluster is represented by a different color, the cells with the same color have same value d,, The radius of cluster is the travel distance from storage location on racking to I/O point In storage and retrieval process, SKUs are priority arranged into the cluster which has smallest radius By this method, the storage location is found always has travel distance less than the ABC class method.
If the number of clusters in each class is greater, the algorithm is more efficient.
Denot Fig 2.5 Continuous cluster concept
Node Output point Input point
Fig 2.6 Storage location under Continuous cluster policy
In storage process, pallets are transferred from I/O point to storage location in turn by 3 axes in space as Line (x axis), Bay (y axis) and Tier (z axis) [7] The travel distance of pallet in each circle can be computed as follows: dị = Xị + Jị +2, (2.16)
Where, ””— bx, 7 x, Tự — l ˆ 9) 5= |E;~ 2 (2.17) (Xi 3 Z ),(x, _“ ) are coordinates of I/O point and storage location.
Total travel distance for an order of n SKUs: b=Sad, k=] (2.18)
However, above arguments only in the ideal case, in fact the forklift cannot move at three sides of the space that always has a rotation angle (Turning Radius) between the two axes x and y Therefore the actual distance forklift to move is constructed as follows: t: Total time t,: Total running time í,: Total lifting time d,,: Expected distance v.=u,: Running speed in straight line và =u, : Running speed in curve line
R: Turning radius n,: Number of turning radius in actual rout v„„: Average loading speed/unloading speed x,,y,: X and y coordinates of the Node z,: Height of storage locations (i = 1, 2, 3, 4, 5) n Number of picking product k : Number of Node on forklift truck route
Expected distance are determined from the IN terminal to the center of each slot in 2D warehouse layout (see Fig 2.7) The expected distance can be estimated by Euclidian distance.
In practice, it is faster that the forklift follows a continuous path rather than making a rigid 90° turn so turning radius is essential Each node is presented by 3 coordinates
(x,,y,.z,) and the turning angle can be calculated:
P| lỉ| = 0, forklift truck continue to go straight
~ (1: forklift truck begin to turn at Node (i — 1) From Eq (2.19) and Eq (2.22), d,, —2Rn, R 0.5n,7rR
Estimate total loading and unloading time base on the height of storage racks. t= (2.24)2.Z,
The total time is needed to transfer from I/O point to all storage locations can be calculated The total time after calculated are stored In 5x6 matrix During storage process, system using this matrix to find which location has lowest time index to sort pallet. d,, —2Rn fn 0.5n.7R 22, (2.25)
So travel distance are used in this article can be computed by the formulas below: đ, =X, +y, +2, + offset (2.26)
Fig 2.7 The mapping model in simulation
Fig 2.8 Travel distance index for rack S-III
Where, (x, ,.Z,) , (x, y„.Z/) are coordinates of I/O point and storage location Offset is the distance need to be added to suitable with layout in section 2.1.
2.3.2 Storage and retrieval strategy base on A-star Algorithm
For frozen shrimp products, the shorter duration of sorting, the less risk of failure of goods, so pallet should be entered into inventory under FIFO and continuous cluster method For FIFO policy, if goods are shipped to warehouses before, it will be sort in pallet racking before With continuous cluster method, each pallet was added into appropriate storage location whose time to I/O point is the shortest and it’s represented by distance index is đ, To apply those policies, A* algorithm was propose to find the optimal storage location.
First published in 1968 by Peter Hart, Nils Nilsson and Bertram Raphael, A* is an informed search algorithm, meaning that it solves problems by searching among all possible paths to the solution (goal).
Operating cost function, g(ứz) — Actual operating cost having been already traversed Heuristic function, ứ(ằ) — Information used to find the promising node to traverse, the heuristic function must be admissible.
Figure 3.8 demonstrates how to determine an optimal storage location using the star algorithm:
The g(n,.,) (choose fromd,) in this flow chart represents the exact travel distance of the path from the starting point to any vertex n,,,, — which is defined as a shortest node in each step of the loop and A(n,,,,)represents the heuristic estimated distance from vertex ứ„ „ to the selected storage location x and 4, value is calculated
22 using the Euclidean distance formula Each time through the main loop, it examines the vertex n that has the lowest (1) with each: s(„„)+h(n,„) < g(x) (2.28)
One more node in the shortest path is found The main loop repeat until latest node is determined — which represent selected storage location The auto-localization algorithm base on A-star approach is clear It is easy to implement and allows very fast route computations since this method only cares about the start and end of each row and ignore the time dependent between forklifts However, when system was performed by 2 forklifts, various drawbacks are caused by deadlock and traffic jam have a deteriorating effect on the system performance (see Fig 2.6).
2.4 Dynamic Routing by time windows method
This section illustrate the routing task with time windows algorithm After the storage location is defined base on continuous cluster method, Time windows help to finding the shortest distance path and conflict free between an origin node and a destination node in a system, based on scheduling restrictions (time windows) for each one of the path nodes The main purpose is optimization of the total travel distance of the transportation task so the operation cost is minimization This section is referred to [21, 22, 23, 24, 25, 27]
Considering a number of routes which forklift can reach, there are many route is for a pair of points (origin and destination), a cost value, a duration and time intervals
[a,.6,] The routing is defined as the routes sequence done by a number of
12 1 forklifts, P is defined as being the set of routes and I o the set of intermediary points.