The impact of required storage space on storage policy performance in a 3PL order picking warehouse: a simulation study Thesis

(1)

1

Thesis

The impact of required storage space on storage policy performance

in a 3PL order picking warehouse: a simulation study

Msc thesis Supply Chain Management

Faculty of Economics and Business, University of Groningen Department of Operations

Supervisor: dr. O.A. Kilic Second assessor: dr. N.D. van Foreest

By: Tim Wielens

(2)

2

Abstract

(3)

3

1. Introduction

Warehousing is a critical component of the supply chain with the responsibility to receive, store, retrieve, pack and transport SKUs between suppliers and customers. According to several studies, capital and operating costs of warehouses represent about 39 percent of the total logistics costs in Europe (Groothedde, as cited in Battista, Fumi, Laura, & Schiraldi, 2014) and are responsible for about 15 percent of the logistics costs in developed countries such as Germany (Handfield, Straube, Pfohl, & Wieland, 2013). Order picking has long been identified as the most labour or capital intensive activity in a warehouse that is taking up to half of the total operating expenses of a warehouse (De Koster, Le-duc, & Roodbergen, 2007).Therefore companies focus on maximizing efficiency of order picking. Factors that influence the order picking efficiency are operating policies, equipment, racking and layout of the warehouse (Dekker, De Koster, Roodbergen, & Van Kalleveen, 2004; Petersen, 1999). The operating policy with the greatest affect on order picking efficiency is storage assignment (Chan & Chan, 2011) and therefore the effect of storage assignment policies on the retrieval time is widely studied (De Koster et al., 2007; Gu, Goetschalcks, & McGinnis, 2007; Guo, Yu, & De Koster, 2015; Hausman, Schwarz, & Graves, 1976; Roodbergen & Vis, 2009; Rosenblatt & Eynan, 1989; Yu, de Koster, & Guo, 2015). However, there is a difference between conventional research (Hausman et al., 1976; Petersen, Aase, & Heiser, 2004; Rosenblatt & Eynan, 1989) and new research (Guo et al., 2015; Yu et al., 2015) about the space requirements for storing a class in a warehouse. This has motivated this research.

Selecting the appropriate storage assignment policy, like class based, random or full turnover based, is a way to reduce the travel time for storing/retrieving items. The average travel distance of a picking tour is linearly related to the travel time, which is often the objective in warehouse optimisation problems. Class based storage assignment divides the items into storage classes based on their turnover, where the highest turnover class is located closest by the pick-up/drop-off (p/d) point. This policy is often implemented in practice and also widely studied in literature (Chan & Chan, 2011; Hausman et al., 1976; Le-Duc & De Koster, 2005; Muppani & Adil, 2008; Petersen et al., 2004; Rosenblatt & Eynan, 1989). The conclusion of most articles is that the use of more classes reduces the average travel time for storing/retrieving items. All these articles assumed that the Required Storage Space (RSS) of a class equals the average stock level of all products in that class. However, an accurate measurement of the required space to store items is important for storage policy selection, warehouse design and travel distance evaluation (Guo et al., 2015).

(5)

5 new RSS to find the optimal travel times for different storage policies in an unit-load warehouse. Their conclusion was that a class based policy with a small number of classes is optimal which is contrary to conventional research. They recommend that further research should investigate the impact of RSS on the travel time performance of several storage policies in different warehouse layouts and systems. The novelty of this research is that it develops a storage assignment model and by simulations the minimal travel distances for storing and retrieving items in a two-block order picking warehouse while considering the RSS will be found. In addition, the impact of the space sharing factor on the travel distance will be investigated. The performance indicators of this research are the average travel distance and the stock overflow level per class, the latter one is the measure whether the RSS of a class is sufficient. The main objective is to minimize the average travel distance. The major difference between the study of Guo et al. (2015) and this research is that this research will develop a model for a two-block order picking warehouse and where Guo et al. (2015) created a model for an unit-load one-block warehouse. Through the contributions of this research, researchers and companies will better recognize the impact of the space sharing effect on the required storage space and so on the travel distance performance of storage policies.

In this thesis project, we aim to fill the aforementioned literature gap by answering the following research question: What is the impact of the space sharing factor on the required storage space and so on the travel distances of class based storage policies in a two-block order picking warehouse? The investigated system is a low-level picker-to-parts system, this implies that items are stored in racks and order pickers travel between the locations to pick all requested items of the order. A two-block layout is a rectangular layout with two sections and the picking aisles run parallel to the warehouse front-end where the P/D point is located. The goal of the research is to find the minimal travel distances for class based storage policies in a two-block order picking warehouse while considering the RSS. This will be accomplished by optimising the number and boundaries of storage classes. In addition, the impact of the space sharing factor on the travel distance performance of the storage policies will be investigated. This will be done by comparing the travel distance performance and stock overflows of class based storage policies that consider the conventional RSS with the performances of storage policies that consider the new RSS. The models of and Van den Berg (1996), Venkitasubramony & Adil (2016) and Caron et al. (1998)will be adapted to the new warehouse configurations. This research will extend the literature about the impact of the RSS on the performance of storage policies in a two-block order picking warehouse.

The remainder of this paper is organised as follows. After reviewing the relevant literature and describing the problem in the next section, the studied order picking warehouse will be described in section 3 together with the mathematical model. In section 4 the numerical study will be explained and section 5 presents the results of the simulations. The paper will be summarized and concluded in section 6 and in section 7 the limitations and further research directions will be provided.

2. Theoretical Framework

(6)

6

2.1 Warehousing

This paragraph first describes the role and activities of warehouses and thereafter clarifies the focus of the research. Warehousing is a critical component in the supply chain between the supplier and customer. The design and layout of a warehouse needs to be suitable for warehousing activities and appropriate storage policies and order picking operations need to be chosen to assure performance and minimize costs (Roodbergen, Vis, & Taylor Jr., 2015). Warehouses play an important role in the fulfilment of customer orders, they are responsible for meeting the expectations of customers that are set in the sales process (Guo et al., 2015). De Koster et al. (2007) defined order picking as the process of retrieving the required goods from storage to satisfy the orders of customers. Order picking has long been identified as the most labour or capital intensive activity in a warehouse that is taking up to half of the total operating expenses of a warehouse (De Koster et al., 2007). Companies therefore focus on to maximize the efficiency of order picking with the aim to reduce costs and to minimize the order throughput time. Factors that influence the order picking efficiency are operating policies, equipment, racking and layout of the warehouse (Dekker et al., 2004; Petersen, 1999). According to Tompkins (as cited in De Koster, Roodbergen, & Van Voorden, 1999), the travel time of an order picker is, in general, responsible for half the total order pick time. Bartholdi & Hackman (2011) also stated that travel time is the largest component of labour in a warehouse, however it does not provide added value. The travel distance depends on the aisle structure of the warehouse, position of pick-up/drop-off (p/d) point and operating policies (Venkitasubramony & Adil, 2016). Hence, reduction of the travel distances and so the travel times has a significant impact on the total order picking time.

The focus of most research is on one of three operating policies to improve the efficiency of order picking: picking, routing and storage assignment. Picking policies involve assigning items to orders and routing policies determine the sequence in which the SKUs needs to be picked. A storage assignment policy is according to Goetschalckx & Ratliff (1990) a set of rules which determines where the incoming products will be located in the warehouse. A storage policy is considered as optimal if the time required for storage and retrieval is minimized while satisfying the constraints. The effect of storage assignment policies, routing policies and picking policies on warehouse performance are widely researched, however the focus of this research is on storage assignment policies. The reasoning behind this is that storage assignment has the greatest affect on order picking performance (Chan & Chan, 2011) and there is an interesting difference between conventional and new research about the space requirements for storing a class. The importance of storage assignment policies and some policies will now be discussed.

2.2 Storage assignment

(7)

7 turnover frequency (Heskett, 1963). The advantage of turnover based ranking is that it locates the high turnover products close by the P/D point and therefore minimizes the travel distance. The chosen method to rank the items is based on the turnover and more specifically the order frequency. The COI needs to be constantly reviewed and is therefore not an appropriate ranking method for this research.

Now, the several storage assignment policies are described together with their advantages and disadvantages. Thereafter, a literature review of the automated and traditional warehouses.

1. Random storage assignment stores all incoming products in one class. The products are stored arbitrary in one of the available locations and share one common class. The advantage is a better utilization of space, but it is more complicated to manage and workers cannot learn the layout (Bartholdi & Hackman, 2011; Gu et al., 2007).

2. Full-turnover based assignment is a policy where every item has its dedicated class and where products with the highest turnover are assigned to the location closed to the pick-up/drop-off (p/d) point. According to Bartholdi & Hackman (2011) and Gu et al. (2007) the advantages are that each product has a fixed location, more popular articles can be located close to the p/d point and workers can learn the layout. The disadvantages are that is does not use the space efficiently.

3. Class based assignment assign products to a storage class based on their turnover. The classes with the highest turnover are assigned closest to the p/d point and products are assigned randomly to locations within a class. The advantages are that high turnover products are located close to the p/d point while the flexibility and low space requirements of random storage are applicable (De Koster et al., 2007).

2.2.1 Automatic storage/retrieval warehouses

The first studies about storage assignment focused mostly on automated warehouses, therefore first a short review of automated warehouses is provided. Automatic storage/retrieval warehouses are warehouses that use computer controlled cranes for storing and retrieving items. These warehouses use parts-to-picker picking where the products are automatically brought to the picker. Hausman et al. (1976) were one of the first researchers that compared the performance of the three aforementioned storage assignment policies in an automatic storage/retrieval warehouse. They researched the two and three class based storage policy and concluded that class based storage assignment significantly reduced the crane travel times. Rosenblatt & Eynan (1989) searched for the optimal boundaries for class based automatic storage/retrieval systems (AS/RS) with the objective to minimize crane travel times. They showed that travel time decreases as the number of classes increases, but most of the reduction can be realized by using a small number of classes. Thereafter, several researchers also investigated the performance of storage policies in AS/RS warehouses (Goetschalckx & Ratliff, 1990; Khojasteh & Son, 2016; Kulturel, Ozdemirel, Sepil, & Bozkurt, 1999; Roodbergen & Vis, 2009; Yu & De Koster, 2009; Zaerpour, De Koster, & Yu, 2013).

2.2.2 Traditional warehouses

(8)

two-8 block or multiple block warehouses. The difference lays in the existence and the number of cross aisles in the warehouse. The narrowness of an aisle is also a difference, most researches neglect the travel distance from one side of the aisle to the other side (Caron et al., 1998; Le-Duc & De Koster, 2007; Venkitasubramony & Adil, 2016) and others incorporate them in their model (Hall, 1993). Some papers investigated an unit-load warehouse and others an order picking warehouse, the focus of this paper is on the latter one. An unit-load warehouse combines items into single units that can be moved easily and where each time one unit load is stored or retrieved. An order picking warehouse requires beside a storage assignment policy also a routing policy. The goal of a routing policy is to sequence the items on the pick list in such a way that it minimizes the travel distance of the order picker through the warehouse. There is a distinction between simple routing heuristics and optimal routing algorithms. A few routing heuristics are S-shape (or traversal), return, largest gap, mid-point and composite, for a graphical overview see appendix A. Every layout has his appropriate storage assignment strategies and routing policies.

Petersen (1999) and Petersen & Schmenner (1999) compared random storage with several implementations of class based storage policies in an one-block warehouse. The implementations were diagonal, within-aisle and across-aisle. By diagonal are the items stored in a diagonal pattern with the highest turnover items closest by the p/d point. By within-aisle storage are the highest turnover items stored in the aisle closest by the p/d point. Across-aisle storage assigns the products over the aisles with the highest turnover closest by the p/d point. They also identified appropriate routing policies for every storage assignment strategy. These studies concluded that the within-aisle implementation performs the best and the appropriate routing heuristics are composite, largest gap, mid-point or traversal. See figure 1 for an overview of the several implementation strategies. Petersen et al. (2004) compared order picking performance between random and class based storage and their interaction with routing policies. They investigated the optimal number and size of the classes and the best implementation strategy. They concluded that class based storage assignment reduces the travel distance significantly, but the performance gap decreases when the number of classes increases. They supported the aforementioned studies that within-aisle implementation with the traversal routing is the best strategy.

(9)

9 algorithm to minimize the travel times by finding the optimal formation of classes and allocation of storage locations with consideration that the use of storage classes reduce the storage space requirements. Several other researchers investigated the impact of routing policies in combination with storage policies on warehouse performance ( Lu, McFarlane, Giannikas, & Zhang, 2016; Petersen, 1997; Rao & Adil (2013); Ratliff & Rosenthal, 1983; Roodbergen & De Koster, 2001)

Figure1: Three implementations of class based storage assignment policy (Petersen & Schmenner, 1999)

Most studies focused only on the operating policies, but there are also studies that integrate the layout with the control policies Roodbergen et al. (2015) developed a methodology that simultaneously determines the layout of the warehouse and the best control policy and showed through simulation the improvement of performance of a warehouse. The goal of this research is to investigate the impact of required storage space on the performance of class based storage polices in a given warehouse layout. Optimizing the layout is not an objective, that is why the research focuses only on storage assignment with a given routing heuristic. The next paragraph will introduce the required storage space.

2.3 Required storage space

This paragraph introduces the required storage space (RSS) and describes the difference between previous mentioned research and new research about the RSS of a class. Most previous mentioned articles concluded that the use of more classes reduces the average travel time for storing/retrieving items, but this is inconsistent with reality where usually only a few classes are used (Roodbergen & Vis, 2009). These studies assumed that the Required Storage Space (RSS) of a class equals the average inventory level of items in that class. A class consists of multiple items that are randomly located in the same region and share common storage space. The replenishment of the items is at different moments in time, so any available location in a class can be used for storing incoming items. Conventional research assumed deterministic demand and that the replenishment is based on the classic economic order quantity (EOQ) model and as a result, the RSS equals half the order quantity i.e. the average inventory level.

(10)

10 fluctuates. Class-based storage reserves less storage space than dedicated storage but there is a risk of inventory overflow. He solved this problem by calculating the minimum storage space that would guarantee that for a certain probability the total inventory of a class does not exceed the available storage space. He calculated the required space for a class by imposing a risk level on stock overflow and concluded that space requirements increases when number of classes increases. He stated that the travel time significantly reduces for 1 to 6 classes and travel times hardly reduce when number of classes is larger than 10. The article did not state that too many classes degrade the travel time performance.

Yu et al. (2015) were the first that demonstrated that too many classes degrade the performance of systems. They showed that the average inventory level of a class as the required storage space for a class is not an accurate reflection of the RSS. Yu et al. (2015) found that the required storage space of a class is larger than the total average inventory level of items in that class and decreases when there is an increase in the number of items per class that share storage space. Thus, the opportunity for space sharing between different SKUs in the same class affects the RSS. The required space per class in only equal to the average inventory of a class if the number of items per class is infinite. Yu et al. (2015) also stated that the RSS of items depends on several factors, like the number of items sharing the space, skewness of demand, inventory replenishment policies and the ratio of order to holding costs. They stated that if the number of classes increases, the number of items per class decreases and thus more space per item is required, because the opportunity of space sharing decreases. Thus the travel distance decreases by assigning SKUs into different classes based on their turnover (turnover ranking effect) and simultaneously increases because of the growth in RSS (space sharing effect). Eventually the space sharing effect exceeds the turnover ranking effect, this means that the increase in travel time due to the reduced space sharing is larger than the decrease due to turnover ranking.

Yu et al. (2015) developed a model to minimize the travel times for storing and retrieving items while considering the required storage space of items. They showed that the optimal number of classes is relatively small and that the required space for a warehouse with a finite number of items is at least 30 percent more than the total average inventory level. Guo et al. (2015) were one of the first that used the new RSS in their research. They developed a generalised travel distance model that investigate the impact of RSS on storage policy performance in an across-aisle unit-load one block warehouse. Venkitasubramony & Adil (2016) developed a model for designing a single-block order-picking warehouse with class based storage in both horizontal and vertical dimensions while considering the real RSS. Guo et al. (2015) recommended that future research should investigate the impact of RSS on the performance of storage policies in different warehouse layouts and systems. This is due the fact that the results of conventional research could significantly differ when they use the new RSS based on both the space sharing effect and turnover ranking effect. There is a gap in literature about storage assignment policies that consider the new RSS.

2.4 Problem Description

(11)

11 narrow aisle low-level picker-to-parts system, that implies that the picker drives along the aisles and the locations to pick the products that are requested by customers (De Koster et al., 2007). The narrow-aisle means that the travel distances are measured along the centre of the aisle, so the distance from one side to the other side of the aisle is not taken into account. The warehouse is graphically shown in figure 2.

Figure 2: Warehouse layout

The novelty of this research is that a class based storage assignment model will be developed that minimizes the travel distance in a two-block order picking warehouse while considering the RSS. This study applies a within-aisle class based storage policy to assign products to the classes and the traversal heuristic for routing the order pickers. These policies are optimal according several studies and are widely applied in practice These policies aim to reduce the expected number of visited aisles, because when an aisle is entered it needs to be fully traversed. Several studies showed the positive impact of cross aisles on the performance of warehouses (Roodbergen & De Koster, 2001), but the existing models that consider new RSS focused mostly on one-block warehouses. By the use of simulations the minimal travel distances will be achieved by optimising the number of classes, partition of classes i.e. number of aisles per class and boundaries of storage classes. Petersen et al. (2004) stated that a proper partition strategy can result in lower throughput times. The impact of space sharing on the RSS and on the travel distance will also be investigated. The models of Van den Berg (1996), Venkitasubramony & Adil (2016) and Caron et al. (1998) will be adapted to the new layout and system. As mentioned by Guo et al. (2015) an accurate measurement of RSS is important for storage policy selection, one-way travel distance evaluation and warehouse design. The model will consider an RSS that is more accurately and therefore researchers and companies will recognize a more realistic impact of the RSS on the travel distance, warehouse design and storage policies. The main assumptions about the warehouse conditions are as follows:

(12)

12 2. Each location stores only one SKU at the time, so a certain location cannot store two different

SKUs at the same time.

3. If there are multiple loads of an SKU, the loads will be assigned to multiple locations in the same class if there are locations available in that class.

4. The quantities of products that are stored in the aisles that belong to a specific class are picked before the stock of these products in the overflow aisles are picked.

5. Orders are picked by order, thus an order picker collects the whole order before starting with the next one.

6. The capacity of an order picker is 20 products. When the capacity is reached and the order is not completed, the picker first travels to the p/d point and drops the pallet and then picks a new pallet and proceed with the order.

7. Classes are allocated on a whole aisle basis, thus the storage locations of one aisle can only be allocated to one class but one class may be allocated to multiple aisles.

8. Loads are not relocated.

9. The picking tour starts and ends at the p/d point and the picked items also need to be dropped here.

10. All the picking aisles are equal in width.

3. Methodology

In this section the methodology is discussed. First, to be able to perform the numerical analysis the mathematical models will be formulated. The model consists of two parts, the storage assignment model and the routing heuristic. The storage assignment will be optimized in order to minimize the travel distance and the routing heuristic is fixed. First, the conventional RSS storage assignment model will be developed and thereafter the model will be extended with the new required storage space. At the end the routing heuristic will be formulated and the mathematical models were programmed in Excel Visual Basic for Applications in order to run the simulations. Section 4 will explain the process of simulating the model. The numerical study will be based on data of a third party logistics service provider (3PL) which is HST group and is located in Enschede, the Netherlands.

3.1 Mathematical Model

The mathematical model will be developed and explained in depth in this section. The mathematical models were programmed in Excel Visual Basic for Applications (VBA) in order to run the simulations. VBA enables the user to build user-defined functions and to automate processes. This study applies a within-aisle class based storage policy although the products need to be ranked before they can be assigned to classes. This ranking can be done in several ways as mentioned in the literature. Rao & Adil (2013) and Yu et al., (2015) used the order frequency i.e. the expected number of retrievals to rank the items and this research also use this method. This ranking method in combination with the demand curve is the first requirement to optimally divide the products over the aisles. The ABC-demand curve of Hausman et al. (1976) is a plot of ranked cumulative percentage of ABC-demand per unit time. According to Yu et al. (2015) the ABC curve can be expressed as follows:

(13)

13 Where i is the item index in the ranked sequence of all items, Y the total number of products in the warehouse, D(j) is the order frequency of item j for period t and s is the shape factor of the demand curve. When s = 0.317 it means that the first 20% of the products contribute to 60% of the total demand. A lower s means that the demand is more skewed and if s is a large value it means that demand is hardly skewed. The within-aisle storage assignment ensures that the most frequently ordered products will be assigned to the aisles close by the p/d point. The variables that have an impact on the storage assignment and the performance of the model are the number of classes applied in the warehouse, partition of classes i.e. the number of aisles per class and the class boundaries. The aisles are allocated to classes on a whole aisle basis, so the locations in an aisle cannot be allocated to multiple classes however one class could be allocated to multiple aisles. The first class is allocated to at least the first aisle in the warehouse and the second class is allocated to the aisle(s) after the first class aisle(s) and so on. Class based storage assignment reserves less storage space than the maximum inventory level of a product, so there is a probability that the reserved space is not sufficient i.e. risk of stock overflow. The key performance indicators (KPIs) of this study are the travel distance and the stock overflow.

 The travel distance is defined as the average travel distance for storing or retrieving a pallet in the warehouse.

 The stock overflows are defined as the percentage of times that a load arrives for a particular class but there are no open locations in that class and therefore it must be stored in the overflow storage.

Every warehouse has a fixed number of aisles and due to the fact that this study assumed that aisles are allocated to classes on a whole aisle basis, the maximum number of storage classes in a particular warehouse can be easily determined by counting the number of aisles. The capacity of the warehouse can be calculated by multiplying the number of aisles with the number of locations per aisle. The number of storage locations or capacity of a particular class can be determined by multiplying the number of storage locations of an aisle with the number of aisles allocated to that particular class, which is expressed in equation 2.

(2)

Where Sk is the number of storage locations for class k, C the number of storage locations in an aisle and Ak the number of aisles that are allocated to class k. The warehouse is divided in two sections, therefore the aisle is broken into two sub aisles however these aisles will be considered as one whole aisle. The aforementioned stock overflow level indicates the percentage that the inventory level of class k exceed the available storage space of class k. The stock overflow level can be expressed as follows based on Van den Berg (1996):

(3)

(14)

14

3.2.1 Conventional RSS

The storage assignment model with conventional required storage space will be developed first, this is due to the fact that the new RSS is an extension of this model. The conventional required storage space of item i equals the average inventory level of item i (Qi). The required number of locations (Ri) for item i is the average inventory level of item i divided by the maximum number of items i per pallet (Pi).

(4)

The average inventory level of class k (Qk) is the sum of the average inventory levels of all the individual products in class k. The three variables of this study affect the inventory level and space requirements of a class. The number of classes and the partition of classes determine the available storage space per class. The boundary of a class (Xk) i.e. the last assigned product to class k determines the number of products assigned to that class. The difference between the conventional RSS and the new RSS is the boundary of classes, this is due to that space requirements per product differ between the models. This will be explained in depth in the new RSS model. Equation 5 formulates the total average inventory level of class k:

(5)

Where is the last item in class k and the last item of the previous class. The required storage locations of class k is the sum of the required storage locations of all the individual items of class k, which is expressed as follows:

(6)

The process of assigning the products to the classes is as follows: First the number of classes are determined and thereafter the number of aisles per class. The first class is allocated to at least the first aisle or may be to more aisles. The next class is allocated to the aisles behind the aisles of class 1 and so on. The items with the lowest index and thus the highest order frequency are assigned to the first class until the sum of the average inventory levels of products reached the capacity of the class. The products that did not fit in the first class will be assigned to the next class until the capacity of this class reached and this will proceed until all aisles reached their capacity or until all products are assigned to classes. For some graphical overviews of a 3 class-based storage assignment, see appendix C. As mentioned in the theoretical background, most articles used this measure for determining the space requirements of a class.

3.2.2 new RSS

(15)

15 thus the probability of a stock overflow must be less than 1- α. As aforementioned, this research uses the model of Van den Berg (1996) for determining the percentage that the total inventory of a class exceeded the available storage space of a class i.e. the stock overflow level.

Van den Berg (1996) stated that due to variable demand and supply the inventory level fluctuates. The conventional RSS needs a factor that incorporates the fluctuation of the inventory level in a class with the aim to enlarge the space requirements of a class when the inventory level largely fluctuates. The distribution of the inventory level of a class is approximated by a Normal distribution with a average and variance. The variance indicates the fluctuation of the inventory level, where a low variance means that there is little fluctuation in the inventory level and a high variance means large fluctuation in inventory. The variance will be added to the conventional RSS model for determining the required space of a class. The formula for the variance of class k is the sum of the variances of all products in class k.

(7)

The new storage assignment process will be as follows: products will be assigned to a class until the sum of the average inventory reached the capacity of that class or until the sum of the variances reach a chosen variance level. The chosen variance level will determine the allowable variance in inventory level and indirectly affect the space sharing opportunities in a class. A low level allows that the sum of variances of the products need be small, otherwise products are assigned to the next class. As a result the number of products in a class will be smaller compared to when the conventional space requirements are used. When the variance level is high it results in that the new required space equals the conventional RSS. The new required storage locations of class k is the same formula as the conventional RSS (equation6) only with an additional constraint where the sum of the variances must be smaller than the chosen variance level for that class.

3.2.3 Routing heuristic

There are several heuristics for routing the order picker through the warehouse, but for this layout and the applied within-aisle storage assignment the traversal or s-shape routing heuristic performs the best according literature. The travel distance consists of the within aisle travel distance and the across aisle distance. The within-aisle distance is the distance travelled in an aisle and the across-aisle distance is the distance from the p/d point to the enter/exit point of an aisle. The applied policies aim to reduce the across-aisle distance in a picking tour. Caron et al. (1998) stated that an even number of aisles per section is preferred to avoid additional travel when a large number of locations need to be visited in a picking tour, thus when all aisles need to be entered. If an odd number of aisles per section need to be visited, the traversal policy will be modified the same as Caron et al. (1998) did. The reasoning behind this modification is to incorporate return travel in the aisle with the largest gap each time an odd number of aisles per section need to be visited. Without this modification the picker ends their picking tour in a lateral cross aisle, so he needs to traverse an additional aisle to return to the middle cross aisle. The products are already assigned to the classes, however the probability of a pick in a specific aisle m need to be formulated. The demand curve of equation 1 is used to determine the demand distribution of the products. The cumulative probability of picks till a particular aisle can be expressed as follows, similar to Venkitasubramony & Adil (2016):

(16)

16 Where m is the particular aisle, M is the total number of aisles in the warehouse and s is the shape factor of the demand curve. The probability of a pick in specific aisle m can be expressed as follows, similar to Venkitasubramony & Adil (2016):

(9)

The research of Venkitasubramony & Adil (2016) assumed that every aisle is a class, thus the number of aisles is also the number of classes. Every aisle has his own index and thus a different pick probability. In this study, a class may be allocated to multiple aisles. The probability of a pick in an aisle when multiple aisles belong to the same class is equal for all aisles of that class, this is due to the fact that the products are randomly stored in a class. The within-aisle travel distance can be expressed as follows, based on Venkitasubramony & Adil (2016) and Caron et al. (1998):

(10)

where

indicates the probability that Z independent picks are not in the mth aisle. Where Li is the length of an aisle and We the width of a cross aisle and Z the average number of picks in a tour. Equation 10 calculates the expected number of visited aisles multiplied by the within-aisle distance. The expected across-aisle distance is twice the distance from p/d point to the enter/exit point of the farthest aisle, because the picker also needs to return to the depot. The across-aisle distance can be modelled as follows, based on Venkitasubramony & Adil (2016) and Caron et al. (1998):

(11)

where

indicates the probability that the farthest aisle entered is one of the two sub aisles, thus the probability that the pick is in one of the two sections. Where Wi is the width of the stocking aisles inclusive the depth of locations. For a graphical overview of the distances, see figure 2. The total travel distance per order is the sum of the travel distance within an aisle and the travel distance across the aisles which is similar to Venkitasubramony & Adil (2016) and Caron et al. (1998).

(12)

3.2.4 Optimising the model

(17)

17 a large extent the number of products and the space sharing opportunities in that class. If the number of classes is small and the number of aisles per class is large it results in large classes. The large classes ensures that there is a lot of space sharing opportunities and this will result in small number of stock overflows. If the number of classes increases, the aisles per class decrease and the capacity of a class also decrease. Small classes results in fewer space sharing opportunities and that results in more stock overflows compared to the first situation. The number of classes, partition of the classes and the number of products per class must be well balanced to minimize the travel distance while keeping the number of stock overflow under control. A stock overflow causes additional travel distance, because the pallets need to be stored in the farthest aisles in the warehouse in case of a overflow. For a summary of the notations, see Appendix B

4. Numerical study

The storage assignment model and the routing heuristic are formulated in the previous section and this section will describe how the validity of the model will be numerically tested. First the studied company and system will be described, then the historical data analysis will be performed which will be used as input for the mathematical models. At the end the process of the simulations of the mathematical models will be explained and the next chapter will discuss the results of the numerical study.

4.1 Company and system

The company is HST group which is an all-round logistics service provider and is located in Enschede, the Netherlands. They have different kinds of disciplines and their offered services are sea freight, air freight, road transport, warehousing and e-fulfilment. The numerical study focused on the warehousing department of HST. The studied warehouse is dedicated to one customer and they currently assign the products randomly over the aisles. The storage racks are arranged in a parallel-aisle layout and are divided in two section, where parallel-aisles changes are possible on both end sides of the racks and at a cross aisle in the middle. There are 8 aisles in the warehouse and an aisle consists of two racks so there are 16 racks in the warehouse. The left section of the warehouse has a capacity of 420 storage locations per aisle and the right section 328 locations. The total capacity of an aisle is 748 storage locations. The p/d point is located opposite the middle cross aisle. All items enter and leave the warehouse via the p/d point. The system works as follows: the products enter the warehouse in containers, first the products are sorted and placed on pallets. When a pallet arrives at the p/d point, a reach truck retrieves and transports it to any given open location. When a customer request some products, an order picker travels with a truck to the different locations and aisles to pick the products till the order is complete or capacity of pallet is reached and then drops the pallet at the p/d point. The capacity of a pallet is set at 20 boxes.

4.2 Historical data analysis

(18)

18 the return heuristic when the number of pick locations per aisle is larger than 3. The average number of locations in a picking tour is 26 in 2016, which is more than 3 pick locations per aisle so the applied traversal policy is justified.

First the ABC demand formula of equation 1 is applied to check the demand distribution and to check the contribution of each product to the total order frequency. As showed in figure 3, 20% of the products contribute for almost 60% of the total demand, so the shape factor s of the curve is 0.317. The SKU with the lowest index, thus with the highest order frequency has a frequency of 139 and the SKU with the highest index has been ordered once in 2016. The total inventory level and the storage and retrievals over the year have been examined to analyse how demand and supply are matched. Figure 4 shows the total inventory level over the year and figure D1 in appendix D present the cumulative numbers of stored and retrieved products over the year. Both figures show that most products gradually enter the warehouse between mid February and the end of August and that most products leave the warehouse in a relative short period of time (July -October). This indicates that the products are seasonally bounded and this correspond to the type of products. This seasonality causes that that the average inventory level and variance are larger compared to non-seasonally bounded products. The distribution of the inventory level was approximated as a normal distribution and this is also numerically tested. The graph in figure D2 in appendix D confirms that the inventory level is normally distributed. Figures D3 and D4 in Appendix D show the inventory level over the year for a single SKU.

Figure 3: ABC demand curve Figure 4: Inventory level over 2016

4.3 Numerical study

This section will explain the process of simulating the models. First the current situation of the warehouse will be simulated to evaluate the travel distance performance of the current (random) storage and these results will be used as benchmark. Thereafter the products will be ranked on descending order frequency and will be assigned to classes based on this ranking while taken the required storage space into account. The performances of class based storage policies with conventional RSS will first be simulated and then analysed to find which number and boundaries of classes are optimal. The number of classes that will be investigated range from 2 to 7, this is due the fact that this research allocate only whole aisles to classes and literature also stated that the use of a few classes is optimal. Petersen et al., (2004) stated that a 30/70% or 40/60 % distribution of products over the classes performs the best in a two class based policy, thus the first 30% of SKUs will be assigned to the first class and the remaining 70% to the second class. Le-Duc & De Koster (2005)

0% 20% 40% 60% 80% 100% 0,0 0,1 0,2 0,3 0,4 0,5 0,5 0,6 0,7 0,8 0,9 Cu m fr ac tion o f o rd e r fr e q u e n cy

Cumulative product index

ABC demand curve

(19)

19 and Teunter, Babai, & Syntetos (2010)also stated that for each next class, the class size increase. Several class partitions including the ones from literature will be simulated for each number of classes. For a graphical overview of several class partitions for a three class based warehouse, see Appendix C. Thereafter the travel distance performances of storage policies considering the new RSS will be simulated and analysed. Again several number of classes and class partitions will be simulated but now with the new space requirements with the aim to minimize the travel distance.

5. Results

This section will present the results of the numerical study. First the results of the current storage assignment will be described, second the results of the conventional RSS will be analysed and the need for the new RSS will be highlighted. Third, the performances of the new RSS and the optimal number of classes and boundaries will be determined. At the end, the results of the two studies will be compared to investigate the impact of the space sharing on the travel distance performance and to compare the number of stock overflows between the two RSSs.

5.1 Current situation

The warehouse currently stores the incoming products randomly over the warehouse, so in the simulation the products are randomly assigned to the aisles. The number of pallets that are stored in 2016 is 8,953 pallets and the total travel distance for storing all pallets is 885,815.6 meter and the average distance per pallet is 98.94 meter. The total number of pallets that are retrieved is 7484 and the total travelled distance is 2,210,392.4 meter, i.e. more than 2,200 kilometre and the average distance per pallet is 295.3 meter. When the average distance will decrease by a small number, it has a significant impact on the total travelled distance in the warehouse. The travel distances of the current situation are used as benchmark for the developed models. During the simulations, the total capacity of the warehouse was almost reached which is illustrated in the peak in figure 4. The next sections simulate class based assignment so the products are assigned to a fixed class and the space sharing opportunities will become smaller. So the fluctuations in inventory can only be compensated by the aisles that are allocated to that particular class and the overflow aisles. To ensure that stock overflows of a class can always be stored in the overflow aisles, an additional assumptions is made that state that capacity of the overflow storage is infinite.

5.2 Performance of conventional RSS

(20)

20 level. For the three class based assignment were three class partitions simulated and the partitions are respectively 1/2/4 aisles, 1/3/3 aisles and 2/2/3 number of aisles allocated to the different classes. See appendix C for examples of class partitions. The average distances of the three class partitions are presented in figure 5. The travelled distance of partition 3 is respectively 2.4% and 1.8% smaller compared with partition 1 and 2.

Figure 5: Average travel distances for the three class partitions of 3 class-based storage

Table 1 shows the number of products in each class and the percentage of stock overflows per class for the three partitions of the 3 class-based storage assignment. The last two columns show the total number of SKUs in the warehouse and average percentage of stock overflow in the warehouse. The average stock overflow in the warehouse is almost the same for the thee partitions, but the differences per class are much larger. The percentage of stock overflow for partition 3 is 6 percentage points lower for the first class and at least 10 percentage points lower for the second class compared to the other partitions. Concluded, a proper class partition strategy have a significant impact on the travel distance and the percentage of stock overflows within a given number of classes. This conclusion corresponds with Petersen et al. (2004).

Class 1 % stock overflow Class 2 % stock overflow Class 3 % stock overflow Total % stock overflow Partition 1 287 46,5% 1310 28,7% 2493 0,0% 4090 22,0% Partition 2 287 46,5% 2041 18,9% 1762 0,0% 4090 20,6% Partition 3 903 40,2% 1426 8,9% 1761 0,0% 4090 20,6%

Table 1: Number of products and % stock overflows per class for 3 partitions of 3 class-based storage assignment

For every number of classes several class partitions were simulated and the minimal travel distances per number of classes are presented in Figure 6. The figure shows that when seven classes are applied it results in the minimal travel distances. The improvement in travel distance is on average more than 50 meter per pallet. The major drawback of applying a large number of classes is the increasing risk of stock overflows when the number of classes increases. The products will be divided over more classes, so the number of products per class will decrease and the capacity of a class also decrease. So as a results, the number of space sharing opportunities in a class decrease and therefore the risk of a stock overflow will increase.

244 246 248 250 252 254 256 1 2 3 A vg . Tr av e l d istan ce p e r p al le t Class Partition

(21)

21

Figure 6: Overview of travel distance performances for every number of classes

Table E 1 in appendix E is the extended version of table 1, because all number of classes and class partitions that are simulated are included. The table shows for every class and class partition the number of products and percentage overflow per class and the average travel distances. For every number of classes the first classes have the highest overflow percentages. This means that the most frequently ordered products have the largest variance in inventory level or it could be that they enter the warehouse at the same moment. The first class is for any number of classes at least 35% and the stock overflow level gradually decreases for every next class. The table shows that when the number of classes increases, the percentage of stock overflows per class also increases. If two classes are applied, the percentage of stock overflow for the first class is 34% and when seven classes are applied the stock overflow level per class is 46%,34%, 21% and 11% for the classes 1 to 4 respectively. The difference in total number of stock overflows between these two storage assignments is 57 pallets. So for a two class based storage only the space requirements for the first class are not sufficient, but for a seven class based storage are the space requirements for four of the seven classes insufficient. Thus the more classes that are applied in a warehouse, the more often it occurs that the assigned storage space is not enough for that particular class. This is due to the fact that classes contain less products when the number of classes increases so there are less space sharing opportunities between the products. It is clear that for each number of classes the average inventory level as RSS is too small. Concluded, the average travel distance is minimized when 7 class based storage assignment is applied, but the drawback is a high stock overflow level. The required storage space needs to be larger than the average inventory level of products to reduce the risk of stock overflow. The next section will consider the new RSS with the aim to minimize the travel distance and the stock overflow.

5.3 Performance of new RSS

The previous paragraph showed clearly that the average inventory of a class as the required space is too small and this section will simulate and analyse the impact of the new RSS on the travel distance performance. As aforementioned a variance level per class has to be chosen for determining the allowable variance level of a class. Several number of classes and class partitions combined with different variance levels are simulated to investigate the affect of the variance level on the space requirements and the number of stock overflows per class and on the average travel distance. The addition of the variance level causes that the space requirements of a product increase and that the number of products per aisle and/or class are smaller than the previous section. This has as

50 75 100 125 150 175 200 225 250 275 300 1 2 3 4 5 6 7 A ve rag e t rav e l d istan ce Number of classes

Average distances per class

(22)

22 consequence that all aisles in the warehouse will be allocated to classes, so there are no aisles available for storing overflow. An additional assumption is made that ensures that overflow pallets can always be stored. The assumed distance for storing/retrieving products at the overflow storage is 100 meter and the capacity of the overflow aisles are infinite.

Variance Class 1 Overflow Class 2 Overflow Class 3 Overflow Class 4 Overflow Avg* Partition 1 1 425 19,0% 1023 8,5% 1441 1,2% 1201 0,0% 8,5% (2/2/2/2) 2 343 12,5% 858 3,2% 1450 5,1% 1439 0,0% 5,5% Partition 2 1 61 0,0% 584 13,8% 1402 16,6% 2043 0,0% 9,4% (1/2/2/3) 2 98 3,4% 590 6,6% 1408 15,5% 1994 0,0% 7,0% partition 3 1 343 11,4% 1779 9,8% 1429 0,0% 539 0,0% 7,3% (2/3/2/1) 2 425 19,0% 1520 0,0% 1441 0,0% 704 1,1% 5,9%

Table 2: Number of products and percentage stock overflows per class for 3 partitions of 4 class-based storage assignment * Avg = average stock overflow in the warehouse

Table 2 shows the number of products and stock overflows per class for a 4 class based storage assignment and the last column is the average overflow percentage. The variance level has an impact on the number of products per class and on the stock overflow level per class, so almost every class partition has been simulated with different variance levels to analyse the performance differences. Table 2 shows that the average stock overflow level of partition 1 of a 4 class based assignment decreased with 3 percentage points by only changing the variance level and thus the class boundaries. The class partition also affect the stock overflow level, because the class partition determine together with the number of classes the capacity of a class. Table 2 shows that partition 2 of a 4 class based storage assigned a small number of aisles to the first classes compared with the other two partitions and therefore a small number of SKUs is stored in these classes. These first classes op partition 2 have less stock overflows compared to the other partitions, but the last two classes of partition 2 have meanwhile higher overflows. Table 3 shows that the average pick travel distance for partition 2 is smaller than for partition 3, but partition 1 which allocated two aisles to every class performed better in terms of overflows and travel distances than the other two partitions. So the class partitions need to be well balanced to minimize the stock overflows and of course to minimize the travel distance.

variance Storage (m) Retrieval (m) Partition 1 1 97,18 264,55 (2/2/2/2) 2 98,87 266,01 Partition 2 1 99,30 268,22 (1/2/2/3) 2 98,00 266,17 partition 3 1 97,13 274,24 (2/3/2/1) 2 98,44 269,32

Table 3: Average distances for several partitions of 4-class based storage

(23)

23 to the travel distance. The 5 class-based storage with class partition 1 for instance shows that the travel distance is higher when the stock overflow level is lower. When the chosen variance level is low, the space requirements of a class are significant higher compared with the conventional RSS and thus the number of products per class will be smaller. The height of the variance level determines thus for a large extent the space sharing opportunities. Due to the decrease in number of products per class, the risk of stock overflow will decrease but this has as downside that the travel distance per pallet will increase because the product density per aisle is lower than the conventional RSS. So the variance level need to be carefully chosen to reduce the number of stock overflows but the travel distance also need to be kept in mind.

5.4 Conventional RSS vs. New RSS

This section shortly discuss the performance differences between the conventional RSS and the new RSS. The travel distances for retrieving a pallet is significant lower for the conventional RSS, but the stock overflow level is much higher. The difference in travel distance when a 6 class based policy is applied is on average almost 20 meter per pallet and the difference in stock overflow is at least more than 10 percentage points. So a warehouse managers need to think carefully about both effects before determining the space requirements of classes. If the objective is to minimize the stock overflows then 3 or 4 classes need to be implemented. If the objective is to minimize the travel distance then the number of classes should be between 6 and 8.

6. Conclusion

This thesis examined the impact of the required storage space on the travel distance performances of class based storage assignments. A storage assignment model that considered the required storage space has been developed and by simulation the average travel distances per pallet are minimized. Setting the cumulative average inventory level as the required space of a class resulted in large number of stock overflows. There was a need to enlarge the space requirements of a class, this has been achieved by adding a variance level to take the fluctuation of inventory into account by determining the required storage space of class. The variance level affect the number of products per class, the number of stock overflows per class and also the travel distance.

(24)

24

7. Discussion

There are some minor limitations of the study, the first one is the assumption that first the products in the assigned aisles of a class are picked before the products of the reserve storage will be picked. This limitation causes that the travel distance of the simulations are smaller than when First in First out (FIFO) policy is used, which is mostly applied in practice. A second limitation are the additional assumptions to ensure that there is sufficient space for the stock overflow. In practice it is impossible to have infinite overflow capacity, so future research need to restrict the overflow capacity. The third limitation is that aisles are allocated to classes on a whole aisle basis. The class partitions and class boundaries are due to this limitation sub optimal, so future research should loosening this assumption to find the optimal boundary of classes. The last limitation is the used data for the numerical results. Most SKUs enter the warehouse between the beginning of February and early July and most SKUs are picked from July till October, so the products are seasonally bounded. There are some doubts if these results could be generalized and to ensure the validity of the model it need to be tested on a new data set.

(25)

25

8. Bibliography

Bartholdi, J. J., & Hackman, S. T. 2011. Warehouse & Distribution Science.

http://www.covesys.com/docs/appnotes/warehouse_and_distribution_science.pdf.

Battista, C., Fumi, A., Laura, L., & Schiraldi, M. M. 2014. Multiproduct slot allocation heuristic

to minimize storage space. International Journal of Retail & Distribution Management,

42(3): 172–186.

Brynzer, J. 1996. Storage location assignment: Using the product structure to reduce order

pickin times. International Journal of Production Economics, 47: 595–603.

Caron, F., Marchet, G., & Perego, A. 1998. Routing policies and COI-based storage policies in

picker-to-part systems. International Journal of Production Research, 36(3): 713–732.

Chan, F. T. S., & Chan, H. K. 2011. Improving the productivity of order picking of a

manual-pick and multi-level rack distribution warehouse through the implementation of

class-based storage. Expert Systems with Applications, 38: 2686–2700.

De Koster, R., Le-duc, T., & Roodbergen, K. J. 2007. Design and control of warehouse order

picking : a literature review. European Journal of Operational Research, 182(2): 481–

501. De Koster, R., Roodbergen, K. J., & Van Voorden, R. 1999. Reduction of walking time in the

distribution center of De Bijenkorf. In M.G. Speranza and S. Stähly (Ed.), New trends in

distribution logistics: 215–234. Berlin: Springer.

Dekker, R., De Koster, M. B. M., Roodbergen, K. J., & Van Kalleveen, H. 2004. Improving

order-picking response time at Ankor’s warehouse. Interfaces, 34(4): 303–313.

Goetschalckx, M., & Ratliff, H. D. 1990. Shared Storage Policies Based on the Duration Stay of

Unit Loads. Management Science, 36(9): 1120–1132.

Gu, J., Goetschalcks, M., & McGinnis, L. F. 2007. Research on Warehouse Operation: A

Comprehensive Review. European Journal of Operational Research, 177(1): 1–21.

Guo, X., Yu, Y., & De Koster, R. B. M. 2015. Impact of required storage space on storage

policy performance in a unit-load warehouse. International Journal of Production

Research, 54(8): 2405–2418.

HALL, R. W. 1993. Distance Approximations for Routing Manual Pickers in a Warehouse. IIE

Transactions, 25(4): 76–87.

Handfield, R., Straube, F., Pfohl, H.-C., & Wieland, A. 2013. Trends and Strategies in Logistics

and Supply Chain Management. Hamburg: DVV Media Group GmbH. www.bvl.de.

Hausman, W. H., Schwarz, L. B., & Graves, S. C. 1976. Optimal storage assignment in

automatic warehousing systems. Management Science, 22(6): 629–638.

Heskett, J. L. 1963. Cube-per-order index-a key to warehouse stock location. Transportation

and Distribution Management, 3(1): 27–31.

Khojasteh, Y., & Son, J.-D. 2016. A travel time model for order picking systems in automated

warehouses. International Journal of Advanced Manufacturing Technology, 86: 2219–

2229.

Kulturel, S., Ozdemirel, N., Sepil, C., & Bozkurt, Z. 1999. Experimental investigation of shared

storage assignment policies in automated storage/retrieval systems. IIE Transactions,

31(8): 739–749.

Le-Duc, T., & De Koster, R. M. 2005. Travel distance estimation and storage zone

optimization in a 2-block class-based storage strategy warehouse. International Journal

of Production Research, 43(17): 3561–3581.

(26)

26

Lu, W., McFarlane, D., Giannikas, V., & Zhang, Q. 2016. An algorithm for dynamic

order-picking in warehouse operations. European Journal of Operational Research, 248: 107–

122. Muppani, V. R., & Adil, G. K. 2008. Class-based storage-location assignment to minimise pick

travel distance. International Journal of Logistics Research and Applications, 11(4):

247–265.

Petersen, C. G. 1997. An evaluation of order picking routeing policies. International Journal

of Operations & Production Management, 17(11): 1098–1111.

Petersen, C. G. 1999. The impact of routing and storage policies on warehouse efficiency.

International Journal of Operations & Production Management, 19(10): 1053–1064.

Petersen, C. G., Aase, G. R., & Heiser, D. R. 2004. Improving order-picking performance

through the implementation of class-based storage. International Journal of Physical

Distribution & Logistics Management , 34(7): 534–544.

Petersen, C. G., & Schmenner, R. W. 1999. An evaluation of routing and volume-based

storage policies in an order picking operation. Decision Sciences, 30(2): 481–501.

Rao, S. ., & Adil, G. K. 2013. Class-based storage with exact S-shaped traversal routeing in

low-level picker-to-part systems. International Journal of Production Research, 51(16):

4979–4996.

Rao, S., & Adil, G. K. 2013. Optimal class boundaries, number of aisles, and pick list size for

low-level order picking systems. IIE Transactions, 45(12): 1309–1321.

Ratliff, H. D., & Rosenthal, A. S. 1983. Order-Picking in a Rectangular Warehouse : A Solvable

Case of the Traveling Salesman Problem. OperationsResearch, 31(3): 507–521.

Roodbergen, K. J., & De Koster, R. 2001. Routing order pickers in a warehouse with a middle

aisle. European Journal of Operational Research, 133: 32–43.

Roodbergen, K. J., & De Koster, R. B. M. 2001. Routing methods for warehouses with

multiple cross aisles. International Journal of Production Research, 39(9): 1865–1883.

Roodbergen, K. J., & Vis, I. . A. 2009. A survey of literature on automated storage and

retrieval systems. European Journal of Operational Research, 194: 343–362.

Roodbergen, K. J., Vis, I. F. A., & Taylor Jr., G. D. 2015. Simultaenous determination of

warehouse layout and control policies. International Journal of Production Research,

53(11): 3306–3326.

Rosenblatt, M. J., & Eynan, A. 1989. Deriving the Optimal Boundaries for Class-Based

Automatic Storage/Retrieval Systems. Management Science, 35(12): 1519–1524.

Teunter, R. ., Babai, M. ., & Syntetos, A. A. 2010. ABC Classification: Service Levels and

Inventory Costs. Production and Operations Management, 19(3): 343–352.

Van den Berg, J. P. 1996. Class-based storage allocation in a single-command warehouse

with space requirement constraints. International Journal of Industrial Engineering,

3(1): 21–28.

Venkitasubramony, R., & Adil, G. K. 2016. Design of an order-picking warehouse factoring

vertical travel and space sharing. The International Journal of Advanced

Manufacturing Technology, 1–14.

Yang, C.-L., Phuong, T., & Nguyen, Q. 2016. Constrained clustering method for class- based

storage location assignment in warehouse. Industrial Management & Data Systems,

116(4): 667–689.

(27)

27

Yu, Y., de Koster, R. B., & Guo, X. 2015. Class-Based Storage with a Finite Number of Items:

Using More Classes is not Always Better. Production and Operations Management,

0(0): 1–13.

(28)

28

9. Appendices

9.1 Appendix A: Routing heuristics

Figure A1.1: routing heuristics (Petersen, 1997)

9.2. Appendix B: Model notations

The used notations for mathematical models

Index of the ith item (classification based on their order frequency) m Index for aisle number

M Number of aisles

s Demand skew factor

Sk Number of storage locations of class k D(j) Order frequency of product j

Y Number of products in the warehouse

Pi Maximum number of product i packed on a pallet C Number of storage locations per aisle

The impact of required storage space on storage policy performance in a 3PL order picking warehouse: a simulation study Thesis

Thesis