/ Department of Mechanical Engineering. Manufacturing Networks. Warehouse storage: cases or layers? J.J.P. van Heur. Where innovation starts

Transcription

1 / Department of Mechanical Engineering Manufacturing Networks Warehouse storage: cases or layers? J.J.P. van Heur Where innovation starts

2 Systems Engineering Group Department of Mechanical Engineering Eindhoven University of Technology PO Box MB Eindhoven The Netherlands Report Nr.: MN Warehouse storage: cases or layers? J.J.P. van Heur * Internship at the University of Wisconsin-Madison March 2, May 25, 2012 Supervisors: Ananth Krishnamurthy, Ivo Adan * Manufacturing Systems Engineering Group Department of Industrial & Systems Engineering University of Wisconsin-Madison, Madison, United States of America * Manufacturing Networks Group, Department of Mechanical Engineering Eindhoven University of Technology, Eindhoven, Netherlands Report: Nr MN Eindhoven, October 2012

3

4 Abstract This report studies two options to store products in a warehouse that supplies to supermarkets. The two options are to store the products in cases or in layers. Also the hybrid variant to use both options simultaneously is investigated. Therefore two existing warehouse systems are studied. If a layer is taken from the racks and it contains more products than needed for the pallet, the layer has to be split. In this report two different ways of splitting a layer are tested. An important decision is when to pick a layer and when to pick a case. Two ways of making this decision are designed and the results are discussed in this report as well.

5 2

6 Contents 1 Introduction 5 2 Background and motivation 7 1 SSI Schäfer warehouse system Witron warehouse system Motivation System description 11 1 The racks Robotic lift Conveyors to palletizer Palletizer Model description 15 1 Splitting a layer Case or layer decision Description of the models System components Pallet designs Validation of the models Results 23 1 α-splitting vs. β-splitting split on lift vs. separate splitting Optimizing α ref and β ref Conclusion Conclusions and recommendations 31 1 Recommendations Bibliography 33 A Example of α-splitting 35 B Example of β-splitting 37 C Model implementation 39 1 The split on lift method with α-splitting The split on lift method with β-splitting The separate splitting method with α-splitting The separate splitting method with β-splitting D Validation of the model 45 1 Assumption Explanation of the validation The split on lift method with α-splitting The split on lift method with β-splitting The separate splitting method with α-splitting The separate splitting method with β-splitting E α-splitting vs. β-splitting using the separate splitting method 53 F Split on lift method vs. separate splitting method using the α-splitting method 55 3 Contents

7 4 Contents

8 Chapter 1 Introduction Order picking is the most labour-intensive operation in warehouses with manual systems. So more and more companies nowadays are investing in automated order picking methods. These investments are done in the automated systems field but also done at the research side. A lot of improvement can still be reached in picking the products in a more efficient way. A general order picking station consists of a warehouse, where all products are stored. Furthermore it has an order picking operation. This order picking operation can be done by hand, but nowadays more and more companies are doing this automated. Automated means that the products are picked from the warehouse racks by a lift or by conveyor belts. After that, the products are picked from the warehouse racks and the products are transported to the palletizing station. At this station, the products are put on a pallet or a trolley. This again is possible in two ways: by hand or automated with a palletizing machine. A palletizing machine picks up a single product or a complete layer of products and places this on the pallet or in the trolley. This report considers warehouses that deliver pallets which contain a diversity of goods. Examples of such a warehouse are the warehouses that are used for supermarkets. These warehouses generally receive their goods in pallets containing products of just one product type. These pallets are broken up and put into the warehouse. When a supermarket needs products, it sends its lists of desired products to the warehouse. At the warehouse these different products are collected and placed on pallets. There are several ways to store the products in the racks. One way is to put every product in a separate case and store these cases in the racks. Another way is to store complete layers of products in the racks. This gives an advantage if more products of the same sort are needed. A complete layer is then picked from the rack and split into the number of products that are desired and the number of products that have to go back into the rack. The products that are not needed are placed back into the rack. One can imagine that when a lot of products of the same sort are used, it is better to store the products in layers and when only a few products of each sort is needed, it is better to store the products in cases. This paper focuses on comparing these two methods for several situations. Also the hybrid variant to use both storage methods simultaneously is investigated. A second question is studied about what the best way is to make the decision to either pick a layer or a case from the rack. As third question, two different methods of splitting the layer are compared. 5

9 First, the motivation and background of the research questions are explained in further detail. This is followed by the system description that is used for this research. In the following chapter this model description is given. As last the results are discussed. This is ended with a conclusion and some recommendations for future research. 6 Introduction

10 Chapter 2 Background and motivation In this chapter the background and motivation for this research are described. It all started with comparing two warehouse systems of two different companies. The warehouse systems of SSI Schäfer and Witron. So first, a description of both systems is given. 1 SSI Schäfer warehouse system The first step of the SSI Schäfer warehouse system is depalletizing the incoming pallets. Incoming pallets consist of products of one product type. These pallets are depallitized per layer. A single layer is put on a tray. These trays are transported to the warehouse racks where they are stored using a robotic lift called the Schäfer Tray Shuttle. This shuttle can only reach four meter in height. Because a shuttle can reach only four meters high, more shuttles are placed above each other. Every shuttle can carry two layers. Products have to go from one shuttle to another if they have to be stored in a place that is higher than four meters. An extra lift transports the products between the shuttles. When a layer is on the lift and has to go to the palletizing robot, the layer is first split into the desired number of products and the residue. The lift lowers until it reaches a bed of wheels. This bed is called the Casewheeler. The wheels of the Casewheeler fit into the recesses of the tray. The Casewheeler consists of 200 wheels which can be controlled individually. With a vision system the products are recognized and the system knows which wheels have to be moved in which direction to separate the desired products from the residue. Then the required products have to go to the palletizing robots in the right order. This is done with a network of conveyors. The palletizing robot builds the desired pallet with one product a time. Two different pallets can be palletized by the palletizing robot at the same time. 7 SSI Schäfer warehouse system

11 (a) Robotic lift (b) Casewheeler (c) Palletizer Figure 2.1: Parts of the SSI Schäfer warehouse system 2 Witron warehouse system The first step of the Witron warehouse system is also to depalletize the incoming pallets. Incoming pallets consist of one product type and are depalletized per layer. These layers are broken up in single products which are placed on a tray. There are two different tray sizes. These trays are transported to the warehouse racks by conveyor belts. At the warehouse racks the trays are stored in the racks using a robotic lift. The racks have an inventory of approximately two days. When a product is needed to ship to, for example, a supermarket, the robotic lift picks the product from the racks again and places it on a conveyor belt. This conveyor belt transports the product to a palletizing robot which builds the desired pallet. Figure 2.2: Overview of a Witron warehouse system 8 Introduction

12 3 Motivation The goal of this report is to compare these two warehouse systems. The main difference between the two systems is the way of storing the products. The products of the SSI Schäfer method are stored as layers in the warehouse and the products of Witron are stored as single products. So this report focuses on the question: which way of storage is better for various situations? Furthermore it is studied whether a hybrid variant, using both storage in layers and single product, is better in some situations. For these situations it is possible to choose different pallet designs. For example, it is possible to choose pallet designs containing mainly products of the same product types. On the other hand it is possible to choose pallet designs containing mainly products of different product types. 9 Motivation

13 10 Introduction

14 Chapter 3 System description In this chapter the system used for this research is described. This system is a warehouse to store goods. The type of warehouse that is used for this research, is a warehouse that is typically used for delivering goods to a supermarket. Such a warehouse receives pallets containing one type of products. These products are stored in racks in the warehouse. To pick up the products from the warehouse, an order picking system is used. An order picking system picks orders or in this case products in the desired order. For example, if it has to fill a pallet, it starts with picking first all products at the bottom layer. Then all products at the next layer are picked and so on. Completed pallets will leave the warehouse containing several different products. These pallets will go to the supermarkets. Figure 3.1 shows an overview of such a warehousing system. Figure 3.1: Overview of a warehouse layout 11

15 The depalletizing part of the process is not considered to make the models not too complex. This chapter describes the model elements, which includes the storage in the racks, retrieving the products from the warehouse, the transport of these products to the palletizing robot and the palletizing of the pallets that go to the supermarkets. In the upcoming sections all parts of the warehouse are described that are used for modeling such a warehouse. 1 The racks The products are stored in the racks until they have to move on to a supermarket. In general there are two ways for storing these products in the racks. The first one is to store each product separately and the second one is to store a layer of each product a time. The advantage of storing every product separately is that it is faster to retrieve a single product from the warehouse racks. But if several products of the same type are needed, the automatic lift has to go back and forth multiple times through the racks. So in that case it can be better to pick a full layer. The lift takes the full layer from the rack, splits that layer and places the residual back into the rack. So the robotic lift has to go back and forth twice for every number of products less than one full layer and has to go back and forth once if it has to pick up a complete layer. This method takes more time than the first one if it has to pick up one or two products. For some products one knows that one always needs more than one product so it is desired to store these in layers. For other products one knows that one always need only one or two products so it is better to store these as single products. For this research also warehouse racks are modeled that can store cases and layers. So in these racks you have both ways of storages. Products are placed or retrieved according to one of these two possibilities, depending on parameters such as the number of products required for one simulation. More about this will be explained in chapter 4. 2 Robotic lift Products are retrieved from the racks by using an automated robotic lift. The automated robotic lift can carry one product or one layer a time. In case we pick a single product, the lift starts in its initial position and then picks a product from the rack. This is followed by moving back to this initial position where the product is placed on a conveyor belt. The lift can now pick up the next product. In case we pick a layer, the lift start in its initial position, picks a layer from the rack, moves back to its initial position where the layer is split. The desired products are placed on the conveyor belt. The remaining products are placed back in the rack after which the lift moves back to initial position. There are two different methods to split the layer. Both methods are described in detail in chapter 4. 3 Conveyors to palletizer Products are transported from the racks to the palletizer by a conveyor belt. This conveyor belt has a continuous flow so products don t have to wait before the previous product has left the conveyor belt. Products in a layer move as single products. The first products is placed on the conveyor belt. The next one is placed after the first one has moved away far enough to place the second one, and so on. 12 System description

16 4 Palletizer The products are transported from the racks to the palletizing robots by conveyor belts. The palletizing robot picks the products one by one and places them on a pallet. Even if a complete layer arrives at the palletizing robot the products are palletized one by one. 13 Palletizer

17 14 System description

18 Chapter 4 Model description According to the warehouse described in chapter 3, several models of different warehouses are modeled in MATLAB. This chapter explains which assumptions and decision are made to make the models work properly and in a realistic way. An important decision is in which situations the robotic lift picks a layer from the rack and in which situations does the lift pick a case. Two different methods are developed to make this decision. Both methods will be explained in the upcoming section. Furthermore two different methods of splitting a layer are developed. These two methods are described in detail. These two decisions give in total four different models. These four models are described in the last section. The prior section describes the assumption and decision of the system components which are described in the previous chapter. 1 Splitting a layer For the splitting of the layer an existing technique is used. This is the technique that is currently used by SSI Schäfer. This technique is implemented in the model and is called the split on lift method. One has also developed a new technique which should produce better results. Both techniques are implemented and compared. In the upcoming paragraphs both techniques are explained. 1.1 Split on lift method This method is developed and used by SSI Schäfer. The robotic lift has a tray on which layers are placed. This tray is connected to the robot and is used to split the layer. The robot starts in its initial position. The initial position is located at the end of the racks where products arrive from the depalletizer and depart to the palletizer. The robotic lift picks up a layer from the racks and moves back to its initial position. The tray, on which the layer is placed has about 200 cut outs. The lift lowers to the bottom on a bed of wheels. 15 Splitting a layer

19 These wheels fit in the cut outs and raises the layer somewhat. These wheels are all independently controlled. A vision system recognizes all the products in the layer. The wheels start to move in such direction that the products that are needed, move to the conveyor belt. The products that have to go back in the racks, stay on the tray. When all desired products have left the tray, the robotic lift places the remaining products back in the racks. A flow diagram of this system can be found in figure 4.1. Figure 4.1: Flow diagram of robotic lift 1.2 Separate splitting method The disadvantage of the split on lift method is that the robotic lift is not in process when the products are split. The robotic lift is the bottleneck in the system, so it is desired that the lift should keep moving. An alternative for this splitting method is shown in figure 4.2. (a) Split on lift (b) Separate splitting Figure 4.2: Overview of both splitting methods Figure 4.2a shows the split on lift method. The splitting is done on the lift. In figure 4.2b the alternative method, called separate splitting, is shown. Now the lift puts the layer on a conveyor belt and can continue its work with picking up a next layer. The layer moves over a conveyor belt to a splitting station. The layer is split after which the desired products move further to the palletizing robot and the residuals move back to the lift. When the lift is available, the lift will return these products into the racks. In figure 4.3 the flow diagram of this method is shown. The lift now does not have to wait until the splitting process is finished and it can keep moving. 16 System description

20 Figure 4.3: Flow diagram of the separate splitting method 2 Case or layer decision If products are stored in both cases and layers, a decision has to be made when to pick a layer and when to pick a case. Two variants of making this decision are studied. The first one is to decide beforehand whether products of a certain type are stored in layers or in cases. This means that all products of that type are stored either in the cases rack or in the layer rack. When products of that type are needed, the products have to be picked from the corresponding rack. This method is called α-splitting. The second one is to store, some of the products of a type in layers and the rest in cases. The decision from which rack the products will be picked, is made when these products are needed. This method is called the β-splitting. Before that both methods are described in detail, some more information about the simulations is given to give a better understanding of both methods. For a simulation a certain number of pallets is selected with the same or different pallet designs. The number of products that are needed for these pallets is determined. Twice the required number of products is placed in the racks. So the size of the racks depends on the number of products that are needed for that simulation, i.e. for loading a certain number of pallets. Now both methods are described in more detail in the upcoming paragraphs. 2.1 α-splitting The first way is to decide about the storage method before storing the products. This decision is made based on the expected demand for every product. According to this demand an α i is introduced for each product i. This α i specifies the fraction of product type i of the total number of products. α i is defined as follows: total demand for product i α i = (4.1) # pl # cl In this equation, # pl is the total number of products that fit on a single layer, and # cl is the number of layers which have at least one product of product type i for that particular simulation. The total demand of product i is the total number of products of product type i to fill all pallets that are executed in that particular simulation. For every simulation, new α i s are calculated. So this α i represents the fraction of product i on the layers which have at least one product of type i. α i is a value between 0 and 1. So for products with an high α i, it may be better to store them as layers because a high α i implies that a layer mainly consists of products with product type i and then it is better to pick a layer than to go back an forth in the racks several times to pick all products one-by-one. Therefore, a reference α, called α ref is set, where α ref is a number between 0 and 1. Every α i is compared to this α ref and if 17 Case or layer decision

21 α i α ref then the products of product type i are stored as layers and if α i < α ref then the products of product type i are stored as cases. An example of determining these α i and comparing them to α ref is given in appendix A. 2.2 β-splitting Deciding on the α i for a product of a certain product type has as disadvantage that a product type that has a large α i, also can be needed only for one or two products in a layer. In that situation it would be better to pick it in cases from the warehouse. So an alternative way is to store for every product, some products in cases and some in layers and decide which one is picked when you get the order. For an order a pallet configuration is created by a computer. According to this pallet configuration a β ij is calculated for each product i on layer j of the pallet in the following way: β ij = total number of cases of product i in layer j total cases in layer j (4.2) This β ij indicates the fraction of the demand of the products of type i in layer j. If β ij is high, then it is best to pick a layer. So therefore β ij is compared with a reference β in the same way as for α-splitting. So if β ij β ref then product i is picked from the layer warehouse and if β ij < β ref then product i is picked from the case warehouse. An example of determining these β ij is given in appendix B. For returning the products into the warehouse, 1 β ij is compared with β ref. If 1 β ij < β ref, then the residue is returned into the case rack. In that case the residue is smaller than the minimal number of products that is picked from the layer rack, so it would make no sense to return these to the layer rack. If 1 β ij β ref then the residue is returned into the layer rack. An example of determining these β i j is given in appendix B 3 Description of the models With the two different splitting methods and the two different ways of deciding to pick either a case or a layer, four different models can be built. These four different models are: 1. The split on lift method with α-splitting 2. The split on lift method with β-splitting 3. The separate splitting method with α-splitting 4. The separate splitting method with β-splitting In general all these four models have the same structure. Only the components that are influenced by the methods are modeled differently, such as the racks and the lift. How these components are modeled is described in the upcoming section. A step-by-step model implementation of the Matlab models can be found in appendix C. 18 System description

22 4 System components This section describes how the different components, introduced in Chapter 3 are modeled for the different methods. So a description of the racks, the robotic lift, the conveyors to palletizer and the palletizer is given in the upcoming paragraphs. 4.1 The Racks Figure 4.4: Layout of the racks First the essential parameters of the racks are lined out. One of the important design parameter of the racks is how the products are ordered in that rack. For all different models the products are ordered according to the same method. In figure 4.4 it is shown how a rack is ordered containing products of two different product types. The products or layers of the two product types are alternately placed. 1 stands for a product of product type 1 and 2 stand for a product of product type 2. If there are more different product types used for simulation, these are placed in a similar way. On the left hand side a rack is shown that is filled with single products and on the right hand side a rack is shown that is filled with layers. A single layer of a pallet contains eight products. This means four products in the length direction and two products in the width direction. When products are stored in layers, such a complete layer is placed in the racks. The width direction is the one that faces the outside of the rack. The depth of a case warehouse rack is just one product. So racks with layers are deeper than racks with single products. For filling up the warehouse typically twice the desired number of products are placed in the racks. In the models using the α-splitting, three different situations of creating the racks have to be distinguished: all products are stored as cases, all products are stored as layers and products are stored as cases and as layers. When all α i are smaller than α ref, all products are stored as cases. Two racks are modeled which are both filled with cases. The width and the height of the racks are based on the number of products that have to be stored in the racks. For the racks filled with cases, the height and the width are of the same length. These height and width are chosen such that all products fit in the racks. When all α i are bigger than α ref, all products are stored as layers. Two racks are modeled 19 System components

23 which both are filled with layers. The depth of the racks is equal to the length of a layer. The width of the layer is placed at the side were the robotic lift picks it from the warehouse, which is also shown in the right rack of figure 4.5. Again the height and the width of the layer racks have the same length but because of storing layers, less layers can be placed in the width then in the height. If one or more α i is bigger than α ref and one or more α i is smaller than the α ref, it mean that products are stored as layers and as cases. In this situation, one rack is created to store layers and one racks is created to store cases. These racks don t have to be of the same size. The size of these racks depends on how many cases and how many layers have to be stored in these racks. In the models using the β-splitting, products of every product type are stored in both cases and layers. The ratio between the number of products that are stored in cases and layers depends on the α i of that product type. For example if the α i of product type i is 0.75, then 75% of the products that are stored for product type i are stored as layers and 25% of the products are stored as cases. These products are divided over two racks to make the models comparable. 4.2 Robotic lift Together with the racks, a matrix is created with the pickup time per product. The product that is closest to the initial position of the robotic lift has the shortest pickup time. The motion of the robotic lift is modeled as Chebychev motion. This means that the robotic lift can move with the same speed in the x and the y direction. Figure 4.5: Examples of Chebyshev motion An example of Chebychev motion is shown in figure 4.5. The products which have the blue spot, have to be picked from the racks. The red arrows show the motion of the robotic lift from its initial position. According to this, the pickup time of a product or layer can be described as following: max(x, y) pick up time = with v = v x = v y (4.3) v With x and y the distance that the lift has to travel in the horizontal and vertical direction. According to this formula all pick up times are calculated and placed into the matrix. If the robotic lift has to pick a product from a case or a layer rack, the matrix with the pick up times is used to pick the closest corresponding product or layer from the rack. When the robotic lift has to pick a layer from the racks, there is first searched for a layer that has to exact number of desired products. When such a layer is available, the closest one is picked. If such layer isn t available, then there is searched for the closest full layer. If there even is not a full layer available there is searched for the closest layer which has at 20 System description

24 least the desired number of products. Because twice the number of desired products are in the racks it never occurs that there is no sufficient layer available. When a residue of a layer has to be returned into the rack by the robotic lift, this residue is placed at the closest free spot in the layer rack. Free spots occur because that other products are retrieved from the racks. In case of β-splitting, it also has to be determined to which rack it will return. If the residue is smaller than β ref times the number of products on a layer, then the residue is returned to the case rack because it makes no sense to return it to a layer rack because it will never be used again. If the residue is bigger than β ref times the number of products on a layer, then the residue is returned to the layer rack. The residue is returned to the closest free spot. 5 Pallet designs For the validation of the models and for generating the results, some pallet designs have to be defined. To make it easy to compare the models, the pallet designs only have two layers each containing eight products. Furthermore the designs only make use of two different product types. One product type represent products that are used quiet often and the other type represents products that are used more rarely. This also called the fast and slow movers in an production line. In total nine different pallet designs are used. These pallet designs are shown in figure 4.6. Figure 4.6: Pallet configuration used for the simulations There is chosen to use nine different pallet designs. For these pallet designs some random compo- 21 Pallet designs

25 sition are chosen to investigate the influence of different pallet designs on the four different models. Some pallet designs like design 1, 2 and 7 contain the same number of products of product type 1 and the same number of products of product type 2. For these configurations it is possible to invesigate the effect of distributing the products over the layers. The advantage of pallet designs 1, 2 and 7 is that the total number of product type on a pallet is equal to the number of products on a layer. This means that the residue of the first layer can be used for the second layer. Other pallet designs don t have this advantage. So by comparing pallet designs 1, 2 and 7 with the other designs shows the influence of the reuse of residues on the mean time to create a pallet. For the simulations multiple different pallet designs are used. The reason to use multiple pallet designs for the simulation is to see how the models react if more pallets are used with different pallet designs. The effect of multiple pallets designsis that in the long term all residues are reused again. Every residue occurs in at least one of the pallet designs. So it avoids that residues are placed in the rack and will be used never again. 6 Validation of the models Now that all aspects of the model are defined, it is time to validate the four different models. For validating the models there is chosen to draw a flowchart during the execution of the models. Every step that is executed is drawn in a figure with a corresponding color. So when the model gives a total time for filling several pallets, it is possible to check in the flowchart if this gives the same time. Furthermore it is easy to check if all product are picked in the order that is desired. The validation is done for all four models. In particular, the following will be checked for each the models: Are cases and layers picked from the closest free spot? Are residues returned to the closest free spot? Does the robotic lift pick all products in the right order? Are the two different splitting techniques implemented in the right way? The validation shows that all these steps are done in the right order and in the way it is defined. The complete validation including the flowcharts can be found in appendix D. 22 System description

26 Chapter 5 Results Now that the model is defined and the validation is done, it is possible to show the results. The best way to compare the four models is to compare the two design parameters that are defined in chapter 4. This gives us the following comparisons: split on lift vs. separate splitting α-splitting vs. β-splitting For the results the following assumptions are made for the time parameters: Time to split layer = 10 seconds Time to transport for separate splitting = 20 seconds Time to travel to palletizer = 30 seconds Time to palletize products = 5 seconds 23 The time to pick and return a layer is dependent of the place of the product or layer in the warehouse. It is assumed that the robotic lift travels with a speed of 6 m/s. More about these assumptions can be found in section 1 of appendix D. For the simulation, nine different pallet designs are used (see figure 4.6. These pallet designs can be found in chapter 4.5. First the models are executed for 50 pallets of the same pallet design. This is done for all nine pallet designs. These simulations can be used to show whether it is better to store products in cases, layers or cases and layers. In practice it will never occur that all pallets have the same design. Therefore the models are also executed using all nine pallet designs in a random order and using these nine designs eleven times. This gives simulations with in total 99 pallets. The results of these simulations are discussed in this chapter.

27 Our performance of interest is the average time to palletize or load a pallet. We will show and investigate the average loading time of a pallet over the first n pallets as a function of n,running from n = 1 up to the total number of pallets to be loaded. For the α-splitting models there are three plots for every model. One where all products are stored in cases, one where all products are stored in layers and the one where the products are stored in both cases and layers. For the β-splitting models it is possible that there are more plots for a model because in the β-splitting it is not possible to distinguish only three situations. For the β-splitting it is for example, possible that a single product of product type 1 on layer 1 is picked from the case rack and three products of product type 1 can be picked as layer. But it also possible that they are all picked as layers or as cases. This gives three different situations only for product type 1. Together with product type 2 it is possible to have more than three different situations. In total there are three questions examined in this report which will be discussed in the upcoming sections. Is it better to store products in cases, layers or cases and layers and whether does the splitting technique (α vs. β splitting influence this? Is it better to split layers on the lift or is it better to do that on a separate splitter? What is the optimal α ref and β ref for the models? It starts with the comparison between the α and β-splitting. In these comparison it also becomes clear whether it is better to store products in cases, layers or cases and layers. Followed by the comparison between the split on lift and the separate splitting. As last there is taken a look at how to find the optimal α ref and β ref. 1 α-splitting vs. β-splitting This comparison can be done for either the split on lift method as for the separate splitting method. Both methods give approximately the same results. In any case, both methods give the same conclusions. So in this sections the results for the split on lift method are given. Some more results from the separate splitting method can be found in appendix E. The simulations with the split on lift are done for both the α-splitting and the β-splitting method. These simulations are done for all nine pallet designs. The interesting results are discussed here. The first one to discuss is pallet design number 3 (figure 4.6). The corresponding average times are shown in figure 5.1. In the left figure again for both methods three situations are plotted. These are the situations for both α-splitting and β-splitting where the products are stored only in layers, only in cases and in cases and layers. These figures show that storing the products in cases is the slowest one. The β-splitting is slower than the α-splitting. The reason for this is that for the β-splitting always a layer and case rack is created and then, when a product is picked from the rack, the decision is made upon β ref whether to pick a case or a layer. The α splitting fills in this situation two racks with cases because it is for the corresponding α ref not possible to pick in layers. So the travel times for the α-splitting will be shorter because there are two racks with products that are close to the robotic lift. So on average this splitting method is faster for this pallet design. To take a closer look at the other situations a plot is made in which the two situations with storing in layers have been removed. This is the left figure of figure 5.1. This figure shows that picking in layers 24 Results

28 Figure 5.1: Average times for 50 pallets of pallet design 3 is faster than picking in both cases and layers and that the α-splitting is faster than the β-splitting. The other pallet designs show the same trend. For all pallet designs is the α-splitting faster than the β-splitting. And for all pallet designs it is best to store the products in layers. Let us continue with the simulations with the mixed pallet designs. For these simulations, all nine designs are used eleven times. So in total the simulation is done for 99 pallets. The results of this simulation can be found in figure 5.2. Figure 5.2: Average times for 99 pallets for the 9 pallet designs For the α-splitting method again the three different situations are plotted and for the β-splitting simulations are executed for β ref = 0, 0.25, 0.5, 0.75, and 1. For large β ref more products are picked as cases. So are all products picked as cases for β ref = 1. So the lines in the left figure for β ref = 0.75 and 1 are the slowest ones because these correspond to picking in cases, which one is also the slowest one at the α-splitting method. So storing in cases is again the worst way to store the products. In the right figure again the lines corresponding with storing in cases are removed to have a better look at the other situations. This figure shows that storing in layers for α-splitting is best but it is only slightly better than picking according the β-splitting method with β ref = Further two more situations with β-splitting are faster than storing in cases and layers with the α-splitting method. 25 α-splitting vs. β-splitting

29 2 split on lift vs. separate splitting This comparison can be done for either the α-splitting method as for the β-splitting method. The results from the β-splitting method are more interesting and give a broader view of this comparison. Therefore are the results that are given in this section created using the β-splitting method. Some more results using the α-splitting method can be found in appendix F. The simulations with the β-splitting are done for both the split on lift and the separate splitting method. These simulations are done for all nine pallet design which can be found in figure 4.6. The interesting results are discussed here. The first one to discuss is pallet design number 6 (figure 4.6). The corresponding average times are shown in figure 5.3. Figure 5.3: Average times for 50 pallets of pallet design 6 In the left figure for both the split on lift and the separate splitting method, all three situations (storage in cases, layers, cases and layers) are plotted. The β ref is chosen in such a way that these three situations can be distinguished. For some pallet configurations it is possible to have more ways to retrieve the desired products in both cases and layers. The lines of the storage in cases lie on top of each other again. This is quite obvious because the difference between the two models is that at the separate splitting method, the layers are split in a different way. If all products are stored and retrieved in cases, this won t make any difference. So storing in cases and retrieving in cases is the worst situation. These situations gives higher average times because only two product types are used. The average number of products per product type on a layer is equal to four. For picking four products it is better to pick a layer than to pick four single products. For four single products, the robot lift has to move back and forth four times and for picking and returning the layer the robotic lift has to move back and forth only twice. In the right figure the same plot is shown only without the retrieval in cases. As seen before, using the separate splitting method gives better results than the split on lift method. This is as expected. For the separate splitting method the robotic lift can keep moving and doesn t have to wait until a layer is split. For this situation it is better to retrieve the products in both cases and layers. These simulations give a much lower average time to finish a pallet. The difference why storing in cases and layers is better than storing in layers for this product type is there because there is only a single product of product type 2. For storing in layers the robotic lift has to move back and forth twice to pick that single product and for storing in cases and layers the robotic lift has to move back and forth only once because the products of product type 2 are stored as cases. If we take a look at the average times for pallet design 8 as shown in figure 5.4 it is clear that for that pallet configuration it is better to retrieve all products in layers. So for these simulations it depends on the pallet configuration whether it is better to retrieve the products in layers or in cases and layers. 26 Results

30 Something surprising is that for the split on lift method the cases and layer retrieval start at a high value. The reason for this is that with configuring the warehouse, a certain number of products is stored in the racks depending on the total number of pallets that have to be filled. This number of products is not necessary a multiplication of the number of products in a layer. So in these situations a residual is stored as last in the racks. This residual has exactly the number of products that is needed for picking the first products so the robotic lift picks these products first according to the pickup rules. Figure 5.4: Average times for 50 pallets of pallet design 8 The results of the other seven designs show that it depends on the design whether it is better to store the products in cases and layers or to store them only as layers. In general storage in layers is better when the residue can be used again. Picking the residue takes less time, because it is stored close due to free spots and a residue doesn t have to return into the racks. Further simulations are performed using the mixed pallet designs. For these simulations all nine designs are used eleven times. So in total the simulation is done for 99 pallets. The results of this simulation can be found in figure 5.5. Figure 5.5: Average times for 99 pallets for the 9 pallet designs For both methods five simulations have been done. The simulations are executed for β ref = 0, 0.25, 0.5, 0.75, and 1. For large β ref more products are picked as cases. So all products are picked as cases for β ref = 1. The right figure shows that the simulations with β ref = 0.75 and 1 have the largest average time. The right figure shows the same simulations only without β ref = 0.75 and 1 to have a better view for which β ref the models performs best. The lowest average times are reached with a 27 split on lift vs. separate splitting

31 β ref of Both the separate splitting as the split on lift method have the lowest average time. This is followed by β ref = 0 and β ref = Furthermore the conclusion can be made that the separate splitting gives lower average times then the split on lift method. But changing the β ref has a larger impact then changing the method of splitting. So the best result can probably found by optimizing the β ref. More about this can be found in section 3. 3 Optimizing α ref and β ref The results of the previous simulations show that the results depend on the chosen α ref and β ref. So there have been done some more simulations to find out which are the best values for α ref and β ref. To determine the best α ref the time to pick one pallet is determined for α ref is 0 to 1 with an interval of 0.1. These simulations are done for all nine pallet designs. The results of these simulation are shown in figure 5.6. Figure 5.6: Average times for the 9 pallet design for all α ref This figure shows that the highest α ref give the worst average times. The average time to palletize a pallet is going up when α ref increases. This corresponds to the storage in cases from which we have seen before that it is the worst way to store products. The best α ref is an α ref of approximately 0.2. This α ref gives the lowest average times to palletize a pallet. To determine the best β ref the same simulations has been done only with a model using the β-splitting method. The results of these simulation are shown in figure 5.7. This figure also shows that for the highest β ref the average time is worst which also corresponds to picking the products in cases. A β ref of approximately 0.2 gives the best results. 4 Conclusion Now that all simulations have been done, the conclusions can be made up. For the comparison between the α and β-splitting the simulation show that the α-splitting is slightly better than the β-splitting, but it depends on the chosen α ref and β ref which one gives the best results. 28 Results

32 Figure 5.7: Average times for the 9 pallet design for all β ref The best results are achieved by storing the products in layers with the α-splitting method followed by the β-splitting method with a β ref of For the comparison between the split on lift method and the separate splitting method it is clear that the separate splitting method is the best method. This method is better, because the robotic lift is the bottleneck of the system. The separate splitting method takes over a part of the load of the robotic lift. The robotic lift doesn t have to split the layer anymore but can immediately continue with picking the next layer. The simulation have shown that the results depend on the corresponding α ref and β ref. For the α-splitting the best results are achieved for an α ref of approximately 0.2. This corresponds in most of the used pallet designs with storing the products in layers in the racks. For the β-splitting the best results are achieved as well for an β ref of approximately Conclusion

33 30 Results

34 Chapter 6 Conclusions and recommendations This report looks at warehouse systems that typically are used for supermarkets. These warehouse systems receive pallets with goods of typically only one product type and they sent out pallets of goods of various product types. The system is simplified to do research on whether it is better to store the products in the racks as single cases, as complete layer or a combination of them both. We have distinguished ways to split the layer. One splits the layer on the robotic lift and the other one splits the layer at a separate splitting station. Furthermore two ways of deciding whether the products are stored as cases, layers or cases and layers are distinguished. The decision on which type of storage is used, is based on the fraction of products of a certain product type is needed. One method makes this decision before the warehouse racks are filled (α-splitting). The other method makes this decision when it has to pick a certain product from the rack d (β-splitting). These different methods give in total four models. These four models are validated with a flowchart. In the flowchart all desired properties of the models are validated and we have seen that the models work like they should do. The results of the models show that the model with the separate splitting station gives lower average times per pallet. The robotic lift is the bottleneck and this model facilitates the robotic lift which explains why the average times are lower. Furthermore does the α-splitting give slightly better results than the β-splitting. From the α-splitting we can conclude that for the pallet designs that have been investigated, it is best to store the products as layers. Furthermore the results show that the average times are strongly dependent on the chosen reference α and β. Further research shows that the best results can be obtained by choosing a reference α and β of Recommendations Furthermore there are some recommendations for future work to continue with these models. So it is desired to look at some different warehouse designs. In this report the products are placed alternately. But maybe it is better to place to products which are most frequently used closer to the point where the products go to the palletizing robot. Another improvement is to do simulations with pallet design which contain more different product 31 Recommendations