AND THE MAIN FIELD OF STUDY INDUSTRIAL MANAGEMENT, SECOND CYCLE, 30 CREDITS STOCKHOLM SWEDEN 2018,
Applying a model for lateral transshipments in fast-fashion retail
OSKAR GRENMARK DANIEL OHLSSON
KTH ROYAL INSTITUTE OF TECHNOLOGY
transshipments in fast-fashion retail
by
Oskar Grenmark Daniel Ohlsson
Master of Science Thesis TRITA-ITM-EX 2018:164 KTH Industrial Engineering and Management
Industrial Management SE-100 44 STOCKHOLM
lagerflyttar inom snabbmodebranschen
av
Oskar Grenmark Daniel Ohlsson
Examensarbete TRITA-ITM-EX 2018:164 KTH Industriell teknik och management
Industriell ekonomi och organisation SE-100 44 STOCKHOLM
The highly variable demand of fast fashion causes retailers in the industry to face large uncertainties when allocating initial inventory batches across multiple loca- tions. Further into the selling season, inventory imbalances might arise as an effect of deviations from expected demand. To mitigate these imbalances, retailers can make use of lateral transshipments of inventory from locations with excess stock to those facing the risk of a stockout. Such transshipments require models for determin- ing what and how much to ship as well as when to ship it. This thesis investigates how such a model can be applied on replenishment warehouse level in a fast-fashion retail setting.
The research was conducted through a quantitative case study at Hennes &
Mauritz (H&M), one of the largest fast-fashion retailers in the world. An appropriate existing transshipment model based on the concept of service level was identified and adjusted to suit the characteristics of H&M. In contrast to the vast majority of models in literature, empirical probability distributions were used for dynamically modelling short-term demand. The proposed model was evaluated and found to suggest transshipments yielding significant revenue increase driven by lowered price reductions.
This thesis differs from existing literature by providing a unique case-study of how a transshipment model can be applied in practice and how it performs on em- pirical data from one of the largest fast-fashion retailers in the world.
Keywords: Lateral transshipments, service level, inventory control, supply chain management, fast fashion, retail, Hennes & Mauritz, H&M
Den kraftigt varierande efterfrågan på snabbt mode gör att aktörer i branschen står inför stora osäkerheter vid initiala lagerallokeringar. Längre in i försäljningscykeln kan lagerobalanser uppstå till följd av avvikelser från den förväntade efterfrågan. För att hantera obalanserna kan företag flytta lager från de regioner med lageröverskott till de som i närtid riskerar att få slut i lager. Sådana flyttar kräver modeller för att avgöra vad och hur mycket som ska flyttas samt när det ska flyttas. Detta examensarbete undersöker hur en sådan modell kan appliceras inom branschen för snabbt mode.
Studien genomfördes som en kvantitativ fallstudie i samarbete med Hennes &
Mauritz (H&M), en av världens största aktörer inom snabbmodebranschen. En lämplig existerande modell som baseras på konceptet om servicenivå identifierades och anpassades efter H&M:s egenskaper. Till skillnad från majoriteten av modeller i literature användes empiriska sannolikhetsfördelningar för att dynamiskt modellera kortsiktig efterfrågan. Den föreslagna modellen utvärderades och visades föreslå flyttar som genererar signifikanta intäktsökningar drivet av lägre prisnedsättningar.
Denna studie skiljer sig från existerande litteratur genom sitt bidrag med en unik fallstudie av hur en modell för lagerflyttar kan appliceras i praktiken samt hur den presterar på empirisk data från en av världens största snabbmodeaktörer.
Nyckelord: Lagerflyttar, servicenivå, lagerhantering, försörjningskedja, snabbt mode, detaljhandel, Hennes & Mauritz, H&M
1 Introduction 1
1.1 Background . . . 1
1.2 Problematization . . . 3
1.3 Purpose . . . 4
1.4 Research question . . . 4
1.5 Delimitations . . . 5
1.6 Expected contribution . . . 5
1.7 Disposition . . . 6
2 Literature review 9 2.1 Introduction to inventory theory . . . 9
2.2 Supply chain networks . . . 11
2.3 Lateral transshipments . . . 12
2.3.1 Proactive lateral transshipments . . . 14
2.3.2 Reactive lateral transshipments . . . 17
2.4 Summary of literature review . . . 20
3 Method 21 3.1 Research design . . . 21
3.1.1 Case selection . . . 22
3.1.2 Data collection . . . 23
3.1.3 Data analysis methods . . . 24
3.2 Research process . . . 25
3.2.1 Pre-study . . . 25
3.2.2 Literature review . . . 26
3.2.3 Data analysis . . . 26
3.2.4 Model evaluation - Selecting the model . . . 26
3.2.5 Model evaluation - Adjusting the selected model . . . 27
3.2.6 Model testing . . . 27
3.3 Quality of the Research Design . . . 28
3.3.1 Internal validity . . . 28
3.3.2 Construct validity . . . 28
3.3.3 External validity . . . 29
3.3.4 Reliability . . . 29
4 Findings and Analysis 31
4.1 Pre-study findings . . . 31
4.2 Model evaluation . . . 35
4.2.1 Business relevance . . . 36
4.2.2 Mathematical applicability . . . 36
4.2.3 Model evaluation - Selecting the model . . . 37
4.2.4 Model evaluation - Adjusting the selected model . . . 39
4.3 Model definition . . . 41
4.3.1 Algorithm . . . 41
4.3.2 Forecast method . . . 42
4.4 Model performance . . . 44
4.4.1 Forecast performance . . . 45
4.4.2 Method evaluation . . . 50
5 Discussion 59 5.1 The applied transshipment model . . . 59
5.2 Our findings in relation to the revised literature . . . 61
5.3 Discussion of the methodological approach . . . 63
5.4 Generalizability of the findings . . . 64
5.5 Sustainability . . . 66
6 Conclusion 67 6.1 Answer to the research question . . . 67
6.2 Contribution to academia and industry . . . 68
6.3 Limitations and Further Research . . . 69
References 72
2 Multi-period inventory levels while applying the EOQ model . . . 10
3 Example of a five-level multi-echelon system . . . 12
4 Lateral transshipments in a two echelon setting . . . 13
5 Illustration of the research process . . . 25
6 Simplification of H&M’s supply chain structure . . . 31
7 A replenishment warehouse stockout of a product triggers a decrease in sales performance . . . 32
8 Dimensions of importance in the model evaluation . . . 35
9 Illustration of the SLA method and the SLRP measure . . . 38
10 Illustration of the CDF consistency over weeks and service levels. . . 46
11 Illustration of the dispersion of outcomes above and below the trans- shipment quantity . . . 47
12 Performance scatter for different service levels . . . 48
13 Signal quality measures for different weeks and service levels . . . 51
14 Different demand outcomes and their respective cumulative probabil- ities . . . 54
15 Move quantity and net sales impact . . . 57
16 Season-total quantity and net sales impact for different SLLs . . . 58
List of Tables
1 Key characteristics for classifying the literature . . . 142 Outcomes corresponding to the four different service levels . . . 49
First, we would like to thank our supervisors at H&M for providing us with the exciting opportunity of writing this thesis with H&M. They have played a large role in framing the problem and providing invaluable information, advice, insights and validation throughout the thesis work. We also want to thank the whole Global Merchandising department at H&M for welcoming us as a part of their team during the course of this research.
Furthermore, we want to thank our supervisor at the division of Industrial Man- agement at KTH, Bo Karlson, for his guidance, help and support from start to finish.
Last, we want to express our gratitude to our opponents at KTH. They have provided valuable feedback and suggestions for improvement during the course of the seminar series conducted alongside our thesis work.
Oskar Grenmark Daniel Ohlsson
Stockholm, June 2018
1 Introduction
This chapter introduces the background to this thesis as well as the problematization, purpose and research question. Following that, the delimitations and limitations of the study are presented. The chapter ends with the expected contribution to literature and the case company, followed by the disposition of the thesis.
1.1 Background
The fashion retail industry is currently facing a vast transformation with regards to the progressing e-commerce trend and an ever-increasing competition. As a result, the already high variability in demand actors within the industry are facing has become increasingly unpredictable and it has become critical to be flexible, fast and able to adapt to rapid changes. On top of that, geopolitical turmoil and economic uncertainty contribute to this unpredictability. (McKinsey & Company and Business of Fashion, 2017) This vast transformation has caused large, slow-moving fashion retailers that historically have been acclaimed for strong sales and earnings growths to now struggle with weak growth digits and high stock levels destined to be sold at high discounts (PwC, 2017; Hoffbauer, 2017; Fortune, 2018).
Following these fundamental changes, decision makers within the industry need to focus on issues within their control (McKinsey & Company and Business of Fash- ion, 2017). One crucial focus area includes supply chain management (SCM) and inventory optimization, which can be critical success factors for retailers pressured by short product cycles and unpredictable demand patterns (Şen, 2008). In prac- tice, retailers are required to purchase according to a forecast while simultaneously adding buffer inventory with the purpose of covering demand upticks (Hillier and Lieberman, 2008). Consequently, retailers are facing the optimization problem of keeping down purchasing and inventory cost while simultaneously having enough inventory at hand to be able to meet demand fluctuations without ending up with unwanted excess inventory at the end of a product’s life cycle. Given the challeng- ing forecasting environment, trying to anticipate long-term demand perfectly at the early point of determining an initial purchase quantity could thus be argued is focus not well aimed for decision makers. One approach to partly address this issue would be to instead move focus towards increasing the flexibility of the options decision makers have at hand after the initial inventory allocations are made.
As a consequence of high demand variability, inventory batches allocated to dif- ferent regions will repeatedly either be too large or too small during the selling season, meaning that retailers might end up with either stockouts or unwanted ex- cess inventory for certain products. A way to avoid such situations is to use lateral transshipments for moving inventory from locations with excess inventory of a prod- uct to locations faced with stockouts of the same product. If lateral transshipments were to be made, overstocked regions would provide understocked regions with in- ventory, thereby mitigating the negative effects of inaccurate forecasts, including expensive excess inventory and lost sales opportunities. Using effective lateral trans- shipments will thus make inventory levels at locations of the same echelon better correspond to market performance and hence increase the ability to better serve the unaccounted demand behaviour. (Burton and Banerjee, 2005; Paterson et al., 2011) Multiple studies of such transshipment methods have been conducted, with Allen (1958, 1961, 1962), Gross (1963) and Krishnan and Rao (1965) as pioneers in the field some 60 years ago. The research area of lateral transshipment models has since received substantial attention in the supply chain literature as an effect of new possibilities arising from improvements within information technologies (Herer et al., 2006; Sanyal, 2012). Despite this, little attention has been devoted to the fast-fashion industry in the SCM literature (Şen, 2008). One of the leading actors in this industry is Hennes & Mauritz (H&M), a large Swedish fashion company founded in 1947.
With a portfolio of eight unique brands and more than 170 000 employees world- wide, H&M targets 69 different markets with its 4 700 stores and 44 e-commerce markets, making it one of the world’s largest global fashion companies (H&M, 2018).
The company has historically been a success story as one among the previously mentioned retailers with incredibly strong growth. During recent years however, H&M has been struggling with adapting to the retail industry transformation and has suffered from weak growth, high stock levels and consequently: high reduction costs. (Dagens industri, 2018) As a result, H&M has seen its stock price decline over 58 percent the last three years (Avanza, 2018) and has gone from a growth stock beloved by the people to one of the most criticized companies on Nasdaq Stockholm.
Some argue that the golden days of H&M have passed and are not likely to return, at least not in the near future (Dagens industri, 2017).
One of the largest issue areas in H&M’s operations as of today are high inventory levels (Hoffbauer, 2017). Not only are high inventory levels costly in terms of holding cost, but to make room for new seasonal collections excess inventory is sold at a
discounted price, thus affecting profitability as well as revenue. However, although high inventory levels might be present on aggregate, the same might not apply on product level across different markets or regions. Such inventory imbalances have been observed at H&M and are an effect of inaccurate sales predictions, which above has been established is essentially impossible to do more accurately in the current market environment of non-linear trends and constantly changing customer behaviour. To address these inventory imbalances, H&M is looking to make use of a lateral transshipment method. However, laying terms for such a method creates a need for assessing which products should be shipped, between which markets the transshipment should be made, what quantities to ship and at which point in time the transshipment should occur.
1.2 Problematization
The unpredictable nature of the fast-fashion market and the complexity that comes with a large amount of products in different sizes being sold at multiple locations makes it challenging to implement a strategy for lateral inventory transshipments in practice; indeed, it needs to be aligned with the nature of the products, their sales patterns, the market behaviour and the existing supply chain.
When considering making a lateral transshipment, a number of issues arise. First, there needs to be a signal that indicates when a transshipment of a certain product should occur between two specific markets. This amounts to identify when inven- tory imbalances are present, that is when one market is understocked and another is overstocked. A next-level issue here is to define what understocked and over- stocked means; such concepts need to be set in relation to some reference of what the desired stock level is. Second, when a transshipment signal is identified, a trans- shipment quantity needs to be calculated. Such a calculation includes predicting the post-transshipment reactions of the two markets in consideration, which will include theoretical assumptions and short-term forecasts, hence making the quantity calcu- lations - and as a result, the profitability calculations - of a lateral transshipment uncertain ex-ante.
The majority of models in the literature use advanced mathematical optimization to compute optimal transshipment quantities (see e.g. Seidscher and Minner (2013), Glazebrook et al. (2014) and Meissner and Senicheva (2018)), which appears to work satisfactorily when dealing with small inventory systems. However, when inventory systems grow large the calculations become increasingly computationally heavy and
are impossible to solve (Meissner and Senicheva, 2018). This results in trade-offs of optimality versus simplicity when calculating transshipment quantities.
Altogether, the essential problem in question is how to use the product sales data from the first week of allocation up until the state where a transshipment is to be evaluated to better understand how the market has adopted the product and how it will perform in the near future. A crucial part of this is to accurately forecast the near future, which likely will be more feasible to do accurately when the product is in the market compared to when the buying decision is made before initial allocation.
In addition, the optimality-simplicity trade-off is a challenge that needs analysis and adoption to the organization at hand.
The complex nature of the above formulated problems constitute the background from which this thesis originates and has given rise to the following purpose of this thesis.
1.3 Purpose
The purpose of this thesis is to apply a model for lateral transshipments suitable in a multi-echelon inventory system for fast-fashion retailers selling perishable products with high demand variability in multiple markets. It is further to evaluate the performance of the applied model on empirical data from a real-life case.
The aim is to identify an existing transshipment model in literature that is suit- able for fast-fashion retailers. Given such a model, eventual necessary adjustments will be identified to make it applicable for the case company, whereafter the purpose of this thesis can be fulfilled. In addition, the thesis should result in developed tools for identifying signals for transshipments, calculating transshipment quantities and estimating the subsequent effect on the income statement.
1.4 Research question
In order to operationalize the purpose of this thesis, the following research question was defined:
How can a feasible method for lateral inventory transshipments be designed in large multi-echelon inventory systems in a fast-fashion retail setting with perishable prod- ucts and a highly uncertain demand?
The research question was broken down into the following sub-questions:
• What signal indicates that a certain product should be shipped from one stock installation to another?
• What quantity of that product should be shipped?
• How can the method handle the challenge of a highly uncertain demand?
1.5 Delimitations
The H&M group has, as mentioned, a portfolio of several brands. Our thesis is however only focused on the core operations, i.e. the H&M brand. This reduces the complexity of the research as H&M’s brands are different with regards to market positioning, which in turn entails different customer behaviour and sales predictabil- ity. By only focusing on the core operations, data management was simplified and deeper insights of the company’s core operations was provided, which in turn served the purpose of the thesis well.
Another delimitation is that we only focused on inventory allocated to physical stores and not to the e-commerce platform, for which the operations are handled somewhat differently.
The final delimitation is that we considered stock levels as-is when deciding on whether to make a transshipment or not. Hence we do not incorporate regular replenishment and purchasing decisions as such decisions increase the complexity of the problem severely (Paterson et al., 2011).
1.6 Expected contribution
The fashion industry is somewhat unique in terms of its characteristics and the sup- ply chain challenges that follow. Little attention has been devoted to the fashion industry in the supply chain management literature in general (Şen, 2008) and to lateral transshipments and inventory optimization in particular (Caro et al., 2010).
Therefore, we aim to empirically contribute with a unique case study to the some- what neglected area of lateral transshipments within supply chain management in a setting with perishable products and highly variable demand. Furthermore, the existing literature is, to the best of our knowledge, mostly covering lateral trans- shipments in highly theoretical settings where advanced mathematical optimization is used. We aim to fill the gap in literature by concretizing theory, applying it on a
real-life case and evaluate the results. While addressing that gap, we simultaneously aim to contribute methodologically with our approach of solving a highly complex problem using existing research and applying it in practice.
Furthermore, the technical advancement and the amount of available data for or- ganizations increase rapidly which entails a persistent need for updated and renewed methods and models involving quantitative algorithms designed for data driven de- cision making. In addition to our particular contribution to the research on lateral transshipments, our thesis contributes to the development of quantitative problem solving in an industrial setting and can inspire for other applications within organi- zations as large as H&M, but also to smaller and less mature organizations.
Aside from the academic contribution, we aim to contribute to the operations of H&M by delivering a Python program with a fully implemented version of our applied transshipment model. The aim is to have a feasible transshipment model providing profitable transshipment suggestions, which thus will contribute to in- creasing H&M’s profitability, if successful.
1.7 Disposition
The outline of the thesis is as follows:
Introduction: This chapter introduces the background to this thesis as well as the problematization, purpose and research question. Following that, the delimita- tions and limitations of the study are presented. The chapter ends with the expected contribution to literature and the case company, followed by the disposition of the thesis.
Literature review: This chapter contains a review of relevant areas in literature related to this thesis. The section starts with introducing the fundamental advances in quantitative inventory and supply chain networks to further continue with a thorough literature review of previous research on the area of lateral transshipments within supply chain management. Last, a summary of the key takeaways will follow.
Method: This chapter describes the chosen research design and how it effec- tively made the problematization researchable. Moreover, the research process and the quality of the research design is presented. The chapter ends with a reflection on the research ethics.
Findings: This section presents findings from the activities in the research process described in the Method section. First, findings from the pre-study are presented, followed by findings from the model evaluation process. Second, the
resulting transshipment model is presented in detail as a step-by-step algorithm.
Last, evaluations of the performance of the model and the associated forecast is presented. Analysis and explanations of the findings are presented along with the results.
Discussion: This section contains a discussion of the choice of transshipment model and its estimated performance. We further discuss the findings in relation to literature, followed by the choice of methodological approach, research activities and how different choices could have affected the outcome. The section ends with a discussion on sustainability.
Conclusions: This section presents conclusive answers to the main research question and its sub-questions. In addition, contributions to academia and indus- try along with limitations of our thesis and opportunities for further research are discussed.
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2 Literature review
This chapter contains a review of relevant areas in literature related to this thesis.
The section starts with introducing the fundamental advances in quantitative inven- tory and supply chain networks to further continue with a thorough literature review of previous research on the area of lateral transshipments within supply chain man- agement. Last, a summary of the key takeaways will follow.
2.1 Introduction to inventory theory
Since the early days of the industrial revolution and the resulting complexity increase of businesses, managing and optimizing inventory has gained attention in multiple industries as well as in academia (Cerasis, 2015). No matter the product in question, an organization handling inventory needs to make assessments regarding balancing ordering quantity and timing to have enough available stock for their customers while minimizing costly oversupply (Hillier and Lieberman, 2008).
Harris (1913) was first to take a quantitative approach to this trade-off when he formulated the Economic Order Quantity (EOQ) model, which nowadays is consid- ered fundamental (Snyder, 2008). The EOQ approach seeks to minimize the setup cost, unit cost and holding cost when determining when and to what quantity an inventory should be replenished. Mathematically, the model can be described with the two formulas:
Q∗ =
r2dK
h (1)
t∗ = Q∗ d =
r2K
dh (2)
where Q∗ is the optimal ordering quantity, t∗ is the optimal cycle time, d is the constant demand rate and h is the cost of storing a product, referred to as holding cost in the literature. Using that demand is assumed known and deterministic, the model can be thought of as a balance between overstocking and ordering frequency;
a trade-off which since then have been reoccurring frequently in the supply chain literature. In the EOQ model, overstocking gets penalized by the holding cost and a non-optimal reorder point by the setup cost. Furthermore, to achieve an optimal order timing each batch cycle time is Q/d, implying that a new order should arrive exactly when the current stock runs out. See figure 2 for an illustration of a product’s
ordering pattern using the EOQ model. The optimal ordering quantity Q∗ and the corresponding optimal batch cycle time are found by defining an expression for the associated total costs and minimizing it analytically. Through that approach, (1) and (2) are obtained. (Hillier and Lieberman, 2008)
Figure 2: Multi-period inventory levels while applying the EOQ model (Hillier and Lieberman, 2008)
The way of modelling supply, demand, product cycles and inventory costs in this rather simple manner was the start of an area of quantitatively based deci- sions in inventory management and production scheduling. Numerous models and algorithms have later been formulated based on the fundamental ideas of the EOQ model and its principles. (Muckstadt and Sapra, 2010; Hillier and Lieberman, 2008) Although the model makes some limiting and simplifying assumptions, the model and the intuition behind it have been widely used in multiple industries including the automotive, pharmaceutical, and retail sectors (Agrawal, 2008).
The EOQ model is applicable on continually available products where demands are assumed constant. This assumption is however not reasonable for so called per- ishable products, which are products with short life cycles and declining demand over time (Hillier and Lieberman, 2008). Examples include newspapers or clothing going out of style or season. By relaxing these limiting assumptions, Arrow et al.
(1951) have been credited for formulating the well-known Newsvendor problem. The Newsvendor model optimizes inventory levels for perishable products and takes into account the risk of unsold stock being worthless after a certain period. The opti- mal solution thus addresses the expected cost of overstocking versus understocking together with the dimension of uncertainty in forecasts and demand by including stochastic optimization theory into the model. Arrow et al. (1951) derive the optimal
solution and find that
Q∗ = FD−1(S∗) (3)
S∗ = p − c
p + h (4)
where, adding to the notation of the EOQ model, p is the price of the product, c the shortage cost, S∗ the optimal service level and FD−1 is the inverse cumulative distribution function of the stochastic demand D. Service level is defined as the probability that demand during a predefined period will be met with the current inventory. Using equation 3, an organization can calculate the needed inventory to maintain a sought service level, making the service level a powerful and intuitive managerial concept to determine stock levels. For example a high service level (closer to 100%) can be set if understocking is more costly than overstocking and vice verca for a lower service level (closer to 0%) (Hillier and Lieberman, 2008). Equation 4 is thus the optimal weighting in the trade-off given a fixed p, c and h.
The holding and shortage cost can however be difficult to determine or even esti- mate for a company having a complex supply chain and diversified product catalog.
In that case, the service level can instead of equation 4 be set subjectively based on the sought level of service to customers implied by the strategy of a company.
According to Hillier and Lieberman (2008) alternative measures commonly used in- cludes: "the average number of stockouts per year" and "the average percentage of annual demand that can be satisfied immediately". The usage of service levels as a performance measure (which in general is defined as the percentage to which a certain goal is aimed to be realized) has gained popularity as supply chains have gained complexity and other measures have become increasingly difficult to calculate or estimate. Diks et al. (1996); Rădăşanu (2016)
2.2 Supply chain networks
In practice, ordering, storing and selling goods at the same location is rarely the case. Instead companies’ supply chains are often structured as networks using a downstream flow of products along nodes with production or buying units at the top, distribution centers at the mid levels and customer-facing stores as the last level. (Diks et al., 1996) These multi-stage models of inventory networks are called multi-echelon systems (Muckstadt and Sapra, 2010). An example of such a network with five levels is given in Figure 3.
Figure 3: Example of a five-level multi-echelon system (Gumus and Guneri, 2009)
First to study the multi-echelon network structure was Clark (1958). Later on, Clark and Scarf (1960) added to Clark’s previous research and derived an optimal inventory policy for a two-level system of nodes. They take on a recursive approach for solving the optimal base-stock level at each echelon using cost functions penal- izing over- and understocking at each node, in turn ensuring optimal stock levels (Clark and Scarf, 1960). Much like the EOQ model, the multi-echelon inventory network laid terms for a large research field and numerous articles on developments of the Clark and Scarf model have been published (Gumus and Guneri, 2009).
During the most recent decades, the focus on scientific inventory management has increased as digitalization has enabled organizations to have larger and more complex network structures while maintaining the needed information exchange and visibility in the inventory system (Gumus and Guneri, 2009). As the network size increases, the inventory optimization problem however becomes infeasible to han- dle and often impossible to solve. Therefore, an approach used by many is to use heuristics that achieve close-to optimal solutions but with significantly lower com- putational time (Axsäter, 2003).
2.3 Lateral transshipments
Paterson et al. (2011) provide an extensive review of the plethora of existing research on inventory models with lateral transshipments. They explain lateral transship- ments as “stock movements between locations of the same echelon” and argue that the literature on the subject treats two different classes of transshipments: proac- tive and reactive transshipments. In the literature, these are also termed preventive and emergency transshipments, respectively. The former are transshipments that take place periodically at fixed points in time with the purpose of proactively redis-
tributing stock levels into a balanced state to avoid stockouts or unwanted inventory imbalances, whereas the latter may be made at any point in time to meet observed excess demand. The areas of proactive and reactive transshipments, their sub-classes and the research on the respective areas will be presented briefly below.
Figure 4: Lateral transshipments in a two echelon setting (Paterson et al., 2011)
In the literature, lateral transshipments are also referred to as lateral resupply, reallocation of stock, substitutions and stock transfers (Paterson et al., 2011). It is indisputable that the inclusion of the opportunity to move inventory between stock installations adds complexity to an inventory system, thus making supply chain optimization more challenging; beyond decisions of optimal ordering policies there is a need to determine optimal transshipments, which certainly will affect ordering and replenishment decisions. As a result, many papers on the subject make assumptions, simplifications and limitations to the inventory systems considered (Paterson et al., 2011). These limitations may for example regard the structure of the inventory systems, including the number of echelons, the number of stock installations within each echelon, whether lead times are negligible or if the retail locations in the systems are identical or not. A full list of the key characteristics separating the literature on lateral transshipments according to Paterson et al. (2011) is presented in Table 1.
From these characteristics, Paterson et al. (2011) highlights pooling as a key feature of a transshipment policy. By pooling inventory, stock installations in the same echelon level share the total available inventory and can thus lower inventory levels and its associated costs while simultaneously being able to serve customers or lower echelons to the same extent by using lateral transshipments within the eche- lon. Complete pooling refers to the setting where all inventory at a stock location is available to be shipped, whereas partial pooling is used when a share of the stock needs to be kept to cover future demand at the location from where the transship-
Number of items 1, 2 or any number M Number of echelons 1, 2 or P
Number of locations (depots) 2, 3 or any number N Identical locations Yes, (identical) costs or no Unsatisfied demands Backorder or lost sales
Timing of regular orders Continuous review or periodic review Order policy (R, Q), (s, S), (S − q, S), General or Other Type of transshipments Proactive or reactive
Pooling Complete or partial
Decision making Centralized or decentralized
Transshipment cost structure Per item, per transshipment, both or none
Table 1: Key characteristics for classifying the literature (Paterson et al. 2010)
ment is to take place. In addition to pooling, timing of regular orders is used by Paterson et al. (2011) as a key classifier and is divided into continuous and periodic review. Periodic review models were developed first, with Allen (1958, 1961, 1962), Gross (1963) and Krishnan and Rao (1965) being pioneers in the field. Since then, both periodic and continuous review models have received much attention in the lit- erature. The two types of transshipment methods are accounted for below, starting with the area of proactive lateral transshipments.
2.3.1 Proactive lateral transshipments
The aim of redistributing inventory proactively is often to balance inventory lev- els among all stock installations in an echelon such that they are better suited to face expected demand. Since these transshipments are done proactively, they can be coordinated such that handling costs are minimized. These costs are generally large in the retail sector, making proactive transshipments useful for retail applica- tions. (Paterson et al., 2011) The existing research on proactive models all focus on a periodic review setting, since such ordering policies leave natural opportunities for deciding on lateral transshipments with the purpose of balancing stock levels throughout the system. Some articles, however, regard transshipments separately from ordering decisions which Paterson et al. (2011) refer to as standalone redistribu- tion. The method for determining when to perform a lateral transshipment is either static or dynamic, where the latter is more challenging to implement but provides larger flexibility. Allen (1958, 1961, 1962) presents a static model with transship- ments occurring at the beginning of the order period while Agrawal et al. (2004) introduce a method that determines the transshipment moment dynamically. They
show that lost sales due to unmet demand can be significantly reduced by the use of up-to-date information on retail inventory levels. The method relies on dynamic pro- gramming and can be computationally heavy and complex as the inventory system grows, which is why the authors, for simplification, also suggest a myopic heuristic comparing redistribution of inventory for pairwise adjacent sub-periods. The heuris- tic is suggested to be used in conjunction with the dynamic programming approach in order to obtain close to optimal results in an effective manner. The approach presented is fairly easy to implement compared to other models in the literature, however the objective is merely to minimize lost sales and does not take profits into account.
In contrast to the simplifying assumption of negligible transshipment times made by several papers (see for example Das (1975), Lee and Whang (2002) and Herer et al. (2006)), Jönsson and Silver (1987) allow positive transshipment times in their proposed model considering a two-echelon system with multiple retailers. The ware- house orders according to a base-stock policy meaning that units are replenished one at a time. Their research results in approximations for average inventories and back- orders to be used for determining order quantities in a setting where the aim is to satisfy a managerially determined service level requirement. They also conclude and illustrate that transshipments are more favourable in settings where high demand variability, long order cycles, many retailers, high service levels and short lead times are present. (Jönsson and Silver, 1987) The conclusion of transshipments being more advantageous when demand is highly variable is further supported by Tagaras and Vlachos (2002). Using a simulation approach for finding an optimal redistribution point, they conclude that proactive lateral transshipments are beneficial in general, especially when demand is highly variable.
Meissner and Senicheva (2018) present a model for proactive lateral transship- ment problems in multi-location inventory systems with multiple opportunities for transshipment within each order cycle. The model considers demand as lost if a stockout occurs, i.e. there is no opportunity to backorder. The objective of the optimization is to maximize the expected profit of the entire network of stock in- stallations for the upcoming periods by finding an optimal policy that decides where to transship from and to as well as the number of units to redistribute. However, due to the complexity of real-world settings, the mathematically optimal solution is impossible to find in practice. In the same faith as in Agrawal et al. (2004), Meiss- ner and Senicheva (2018) find a near-optimal policy by using approximate dynamic programming. The proposed algorithm is shown to be near-optimal in both small-
and large-scale and that it performs better than state-of-the-art models in literature as, for example, the Transshipment Inventory Equalization (TIE) model introduced in (Banerjee et al., 2003) and (Burton and Banerjee, 2005). The TIE model is compared to a simple reactive method named Transshipment Based on Availability (TBA), which is shown in Banerjee et al. (2003) to be more effective in preventing stockouts in a setting where demand is backordered in case of shortages, although Burton and Banerjee (2005) show that the TIE policy achieves lower costs for the inventory system on aggregate.
With the aim of more accurately handling retail demand, Lee et al. (2007) com- bine the advantages of proactive and reactive transshipment policies by introducing the Service Level Adjustment (SLA) model. The authors define the SLRP measure (Service Level during Remaining Period) calculated as the probability of a stockout not occurring during a predefined period as
SLRP = P (Demand during period < Current inventory) (5) where current inventory denotes the on-hand stock less the safety stock. By taking the concept of safety stock under consideration while using the service level con- cept, Lee et al. (2007) introduce a transshipment method incorporating an already established strategy for handling the variety in demand experienced by retailers (Rădăşanu, 2016). Different approaches for estimating appropriate safety stock lev- els is in turn discussed by Rădăşanu (2016) who further argues that safety stock optimization is imperative for companies striving to increase savings and improve inventory turnover.
In the SLA model, a decision maker initially makes assessments of upper and lower SLRP levels. Then, the inventory level needed to maintain the desired service level for the remaining period is calculated for all products and retailers. If a retailer is above the upper level while another simultaneously is below for the same product, a transshipment of surplus stock is made from the first retailer to the second in order to achieve inventory levels corresponding to the desired service levels at each location. Assuming that demand is normally distributed and independent among retailers, Lee et al. (2007) show that the SLA policy outperforms both the TIE and TBA methods considered by Banerjee et al. (2003) and Burton and Banerjee (2005).
In particular, the SLA method performs better as the transportation cost per unit is lowered, suggesting that the method is more effective when implemented in larger organizations with sophisticated supply chains (Lee et al., 2007).
Proactive lateral transshipment policies integrated in ordering policies as planned and systematic balancing of inventories have not been extensively implemented in practice until recent years (recent years referring to the last two decades) (Herer et al., 2006). Herer et al. (2006) state two key reasons for this: the lack of visi- bility in supply chains along with limitations of IT infrastructure and the lack of practically oriented, realistic models capturing the theoretical benefits of proactive models. Although Herer et al. (2006) argued this more than a decade ago, there has, to the best of our knowledge, not been much more evidence of such documented implementations in the literature since. However, an earlier case study on lateral transshipments was conducted by Mercer and Tao (1996) where they studied a food manufacturer pressured by unpredictable buying patterns from a large grocery re- tail chain. They show that lateral transshipments serves to decrease lost sales in a setting of identical products, high service levels, high demand variability and short lead times compared with the planning horizon. In contrast to other papers, they do not include ordering policies since they themselves are manufacturing the product under consideration and also, they do not make assumptions regarding a demand distribution. Instead they consider how much to produce and use a managerially set warehouse inventory target as a multiple of weekly sales, which is forecasted using simple time series modelling in terms of exponential smoothing. It was highlighted that the manufacturing company had not used formal statistical forecasting methods and therefore were in need of a simple method that fitted into the current organiza- tional practice. In the transshipment quantity calculations, the authors account for variations in demand by multiplying the standard deviations of the demand fore- cast with a predetermined safety factor. This can be compared to the service level concept used by Lee et al. (2007), which also is a tool for setting the risk level while dealing with demand uncertainty. An additional distinction from other papers is that the method evaluation was based on actual demand outcomes where lost sales could be directly counted. The authors acknowledge that the results thus could have been influenced by relative sizes of local demand.
2.3.2 Reactive lateral transshipments
Reactive, or emergency, transshipments are transshipments made when there is a stockout or risk for a stockout at one stock installation while another has sufficient stock available for redistribution. Research shows that reactive transshipments are most suitable in settings where transshipment costs are low in relation to holding and shortage costs. An example of such a setting is the spare parts environment,
which also is the environment where lateral transshipments historically has been used to the most extent. (Paterson et al., 2011; Meissner and Senicheva, 2018) The area of reactive transshipments has been thoroughly researched and several different settings have been considered. A main divider is that of review timing; both periodic review and continuous review models have been studied. Furthermore, research has been done on systems with both centralized and decentralized decision making, where the former aims to maximize profits for the whole system in contrast to the latter where profits are maximized at each sales location. Here the latter will not be considered as the case studied in this thesis regards a centralized system.
One of the most cited and frequently occurring papers in this area is that of Robinson (1990). Building on the pioneering work of Krishnan and Rao (1965), who proposed reactive transshipments at the end of a single replenishment period, he developed an inventory model with the objective of minimizing expected net present value of current and future costs. By solving a linear program through Monte Carlo integration, Robinson (1990) finds a heuristic base stock order-up-to point that is close to optimal.
Robinson’s model is reactive in the sense that transshipments are allowed after demand has been observed but before it needs to be satisfied. This is not the case in our setting as consumers in the retail industry generally have low patience for stockouts; a survey of over 71 000 consumers shows that only 15% of consumers that are faced with a stockout delay their purchase until the item is replenished (Corsten and Gruen, 2004). Hence, in fast-fashion retail demand needs to be satisfied at the time of observation, otherwise the demand will generally be considered lost.
Robinson (1990) further concludes that it often is worthwhile to modify the whole inventory policy to capture the maximum effect of the possibility of lateral transshipments. A similar conclusion was drawn by Burton and Banerjee (2005).
In contrast to the static setting in Robinson (1990), Archibald et al. (1997) allow an unlimited number of reactive transshipments any time during a period. They analyze a multi-period, periodic review model of two stock installations and model the problem as a Markov decision process. This work is extended by Archibald (2007) and Archibald et al. (2009) to a multi-location setting.
Herer et al. (2006) propose a method in a similar setting to that of Robinson (1990), but where multiple, non-identical retailers are allowed in contrast to the setting with only two non-identical or multiple identical retailers that Robinson (1990) considers. Similarly to Robinson (1990), Herer et al. (2006) base their model on an order-up-to policy which is proven to be optimal in their setting. Further,
they propose a transshipment model based on a network flow framework and a more general cost structure than that of Robinson (1990), compared to which it is also shown to be more robust. Moreover, Herer et al. (2006) highlight the limitations of their proposed model; they argue that it is not clear how the optimality of the order-up-to policy is affected by relaxing the assumption of negligible transshipment lead times and allowing them to be positive. It is further argued that it is not clear what the optimal transshipment model is in such a setting, as it might be beneficial for a retailer to hold back inventory instead of transshipping it.
Taking it one step further than traditional reactive models, Paterson et al. (2012) introduce enhanced reactive lateral transshipments on the form of a mixture between proactive and reactive transshipments. The reactive part identifies the transship- ment opportunity, but the transshipment quantity is set by proactive procedures.
The method is shown to improve service level while reducing safety stock and overall costs. On a similar note, Seidscher and Minner (2013) provide an integrated trans- shipment model of both proactive and reactive character through a semi-Markov decision problem formulation based on redirecting demand to a warehouse with suf- ficient inventory level. The inventory system considered has multiple locations and is under a one-for-one continuous review policy. They compare proactive and reac- tive transshipments and show that proactive transshipments are most beneficial in networks with intermediate opportunities of demand pooling compared to the sole use of reactive transshipments.
Glazebrook et al. (2014) propose a hybrid lateral transshipment method that allows proactive transshipments to prevent future shortages, but also reactive trans- shipments for meeting immediate shortages. The method is proposed for an automo- tive spare parts environment setting but the generality of the method is highlighted;
the authors claim its potential for wide implementation through an easy-to-compute quasi-myopic heuristic. The hybrid method is shown to be superior to other policies when a large share of the transshipment cost is fixed. The improvement is driven by fewer and larger transshipments making more efficient use of the resources, in relation to which the sustainability impact of the result also is highlighted.
A more recent study on reactive transshipments is that of Yao et al. (2016), who apply a stochastic dynamic programming approach to a setting with demand modelled as Poisson processes in two locations. They find the optimal ordering and transshipment policy for the inventory system and also provide a heuristic that is asymptotically optimal when the demand rate T in their Poisson process approaches infinity. An interesting conclusion is that the profit contribution for the initially
ordered quantity and the transshipment quantity is in the order of T and √ T , respectively. Consequently, when considering a setting with high-volume and fast- moving products, the initial stocking quantity is a significantly more important contributor to profits compared to what can be derived from transshipments.
2.4 Summary of literature review
Most research on the area of lateral transshipments has been done on reactive trans- shipments and most applications have been done in spare parts environments, such as the aircraft or automotive industry. Some models are static with periodic re- view and transshipment decisions at predetermined points in time, while others are dynamic with periodic or continuous review, making it possible for dynamic deter- mination of when transshipment decisions are to be made. Many models are highly theoretical in the sense that a vast amount of assumptions and variables need to be considered. This includes assumptions on demand distributions, opportunities for backordering, transshipment cost, ordering cost, holding cost and shortage cost.
Through modelling these variables and making assumptions on related factors, it is possible to numerically simulate, quantify and compare the performance of different models given these assumptions, which is a method many papers use to make claims on the performance of their models.
Furthermore, a large amount of models try to optimize a whole supply chain network, effectively adding significant complexity to the calculations. This involves integrating replenishment decisions and ordering policies into the equations. While adding complexity if integrated to the models, many ordering and replenishment policies provide ease in calculations of transshipment quantities when the policies involve optimal inventory levels, for example when considering an order-up-to S policy. Thus, when optimal inventory levels are given or calculated, required and offered transshipment quantities can often be calculated by simply taking the differ- ence between the optimal inventory levels and the current inventory. However, when lacking such optimal levels the issue becomes far more ambiguous and complex.
The literature shows a significant lack of case studies and implementation exam- ples of practically oriented transshipment models. It is evident that mathematically optimal solutions for these problems in large inventory systems are computation- ally impossible to reach, which is why many papers suggest approximations as a substitute for optimal solutions. Although the complexity is decreased, theoretical assumptions and variable modelling are still issues for practical implementation.
3 Method
This chapter describes the chosen research design and how it effectively made the problematization researchable. Moreover, the research process and the quality of the research design is presented. The chapter ends with a reflection on the research ethics.
3.1 Research design
The purpose of this thesis was to investigate how lateral transshipments can be ap- plied in a multi-echelon inventory system for fast-fashion retailers selling perishable products in a market with high demand variability. In order to effectively address the problem formulation and fulfill the purpose, we adopted an inductive research approach designed in the form of a case study of H&M.
According to for example Yin (2009) and Blomkvist and Hallin (2015), the pur- pose of a case study is to understand complex phenomena. Yin (2009) argues that case studies are suitable for research questions of how and why character focusing on contemporary events and in settings where control over behavioural events is not required. Furthermore, case studies allow for retainment of holistic characteristics of real-life events in, for example, organizational and managerial processes (Yin, 2009). Based on this, our assessment is that a case study design aligns well with our purpose and research question since inventory management in the fast-fashion industry is highly complex and the need for a holistic perspective with sound busi- ness judgment is of highest importance to H&M as case company, but also to the generalizability of the resulting model.
On the same note, the inductive approach was chosen as it lets the empirical material guide the choice of theory to apply to the case of interest (Collis and Hussey, 2013). Although we aim to ultimately propose a model that is generalizable to some extent, the model needs to be adapted to our case of interest, i.e. H&M. As a result, we consider it suitable and reasonable to depart in the empirical material in the pursuit of understanding the dynamics of the H&M operations. Therefore, the inductive approach was considered suitable for our purpose as it allowed us to use the existing literature complementary to the data analysis and let the data provide guidance for the choice of method to apply to our case. Our research thus departed in an understanding of the case company and the empirical material through data analysis, after which the existing literature on lateral transshipments was thoroughly
reviewed with the aim to find a model that fits the needs and characteristics of the case company while simultaneously fulfills the purpose of our research.
Throughout the process of writing this thesis, we have been immersed in the H&M organization by conducting our research at H&M’s global head office in Stock- holm, Sweden. Specifically, we have been a part of the Central Analysis Team at the Global Merchandising department. Using this setup, we have been able to continuously gather data and insights through informal interviews, workshops and conversations far too extensive to fully provide as transcripts here. This has also limited the need for formal interviews for data collection, which have provided us with the time to focus on deeper and more extensive data analysis. This setup and focus has, in our opinion, served the purpose of this thesis well as the research is of highly quantitative character.
3.1.1 Case selection
With a portfolio of eight unique brands and more than 170 000 employees world- wide, H&M targets 69 different markets with its 4 700 stores and 44 e-commerce markets, making it one of the largest global fashion companies in the world (H&M, 2018).
The company has historically been a success story with incredibly strong growth.
During recent years however, H&M has been struggling with adapting to the retail industry transformation and has suffered from weak growth, high stock levels and consequently high reduction costs. In addition, H&M is currently facing difficulties with inventory imbalances and is therefore, for our purpose, a highly suitable case of a large fast-fashion retailer with a multi-echelon inventory system to study. There are only a few fast-fashion retailers of comparable size and character in the world, which makes this case somewhat unique and as a result makes it suitable for a single-case study, as advised by Yin (2009). Moreover, we believe that studying the area of lateral transshipments using a large fast-fashion retailer such as H&M is more valuable than it would have been using a smaller actor. The rationale behind our belief is that a smaller retailer will not face as large inventory imbalances and will not have the same distribution network as a larger one. In turn, this will likely not make room for as many potential opportunities for lateral transshipments and the opportunities that actually arise will to a smaller extent be large enough for a transshipment to be profitable, as the unit transshipment cost for a smaller player likely will be higher. Hence, the H&M case is highly suitable for a study of this character.
3.1.2 Data collection Databases
Databases were a crucial source of data for the analysis laying ground for the result- ing model presented in this thesis. The data which our proposed method is tested on came exclusively from H&M databases of historical sales and inventory data for different regions.
Literature review
The main purpose of the literature review was to gather data on previously de- veloped transshipment models, match the data with our analysis of the needs and characteristics of H&M and apply one model to the case company.
To search for relevant articles, books and research papers, Google Scholar and KTH’s databases were the main online sources. To navigate through the vast amount of literature available in the field, we only used well-cited articles from renowned journals and drilled down further through their references. Through this approach, we were able to use a time-efficient work flow and simultaneously narrow down the plethora of research to a first selection of the most relevant models in literature while also reaching higher validity and reliability, as argued by Collis and Hussey (2013).
Examples of keywords and phrases used to find relevant sources include, but was not limited to, ”lateral transshipments”, ”inventory theory”, ”inventory manage- ment”, "inventory control", "supply chain management", ”multi-echelon”, ”inventory systems” and ”supply chain optimization”.
The literature review process is described in more detail in the next section.
Interviews and workshops
To identify the important factors to consider when identifying and existing model for lateral transshipments suitable for fast-fashion retail, there was a need for a deep and thorough understanding of the H&M operations, fashion retail sales and how H&M is working with inventory management, purchasing and forecasting. To fill that need, we continuously held informal interviews, workshops and conversations with managers and analysts working at the Global Merchandising department. Such interviews and conversations have fitted this study well since the primary purpose for the interviews was not to gather empirical data but rather to obtain a holistic picture of the relevant processes, norms and methods within H&M. Understanding retail sales in general and at H&M in particular as well as how it relates to inventory
management laid terms for what data was collected, analyzed and how the data was used in the research process. Moreover, weekly meetings/workshops with our H&M supervisors have been a crucial part for fully understanding the current situation on a qualitative level as a complement to the data analysis, but also for continuously aligning our progress with competent H&M employees to ensure that our conclusions and choices are reasonable from the perspective of the case company. Their opinions and guidance have also provided validity and reliability to our results.
Our H&M supervisors have been the Global Head of Controlling and a Business Analyst at the Global Merchandising department. Together they have many years of experience from controlling and driving the H&M sales operations and therefore they know the business inside and out. As a result, they have the background and competence to contribute with assessments and validation regarding logic, reason and feasibility.
3.1.3 Data analysis methods
The data analysis was highly quantitative, where we applied statistical methods and probability theory to gain insights of product and demand behavior as well as to evaluate the applied transshipment model. As a complement, a qualitative analysis was needed in order to understand the broader spectrum and to obtain a holistic view of how the different parts of a retail sales company are connected and which factors are relevant to consider for a transshipment model.
H&M’s databases contain enormous amounts of data. In order to effectively analyze the relevant data, it was initially reduced to only include a subset of the H&M assortment for a few markets and for one selling season. This provided the opportunity to visualize the data in an understandable way and draw qualitative conclusions laying ground for how to proceed with further statistical analysis. After prototyping the initial version of the model on the reduced data set, the model was then scaled up to a larger data set and further analyzed and adjusted.
The analysis was initially conducted using Microsoft Excel. However, the com- putational power of Excel is limited when the formula complexity and amount of data increases. To cope with this limitation, we only used Excel for prototyping the model on the smaller data set. This enabled us to continuously discuss the model with our supervisors and visualize the structure of the model in an intuitive man- ner. When the model was accepted by and aligned with our supervisors, we used the programming language Python to allow for larger data sets, higher flexibility and consequently wide implementation, analysis and tests of the model.
3.2 Research process
The research area and focus of the thesis were agreed upon in conjunction with our supervisors at H&M and our academic supervisors, but the project idea originated from the need of balancing inventory levels within H&M as thoroughly described in the introductory section of this thesis.
After aligning the purpose of the thesis with our supervisors, the research was initiated with a pre-study consisting of efforts to gain an understanding of the cur- rent situation, the important factors to consider for a transshipment model and building a business case for the project. Followed by the pre-study, the existing literature on the area of lateral inventory transshipments was reviewed. Along with the literature review, continuous data analysis was done as new insights and wisdom were obtained. Given the findings from the pre-study, the initial literature review and the data analysis, our understanding of H&M’s operations and needs with re- gards to a transshipment model was clear, which enabled us to holistically evaluate different transshipment models from the literature to potentially apply to the H&M case. Consequently, the model evaluation process consisted of two steps: selecting the model and adjusting the model. The last two phases of the research process consisted of testing the model performance and, based on the test results, drawing conclusions regarding its applicability to fast-fashion retail and H&M. During the whole process, we have also worked with developing a fully implemented version of the transshipment model in a Python program. This did not only provide value to H&M at the end of the thesis work, but also to the activities within the research process as the tool could be used to analyze, test and evaluate the model.
The research process is visualized in Figure 5, below which each step is further elaborated on.
Figure 5: Illustration of the research process
3.2.1 Pre-study
During this phase, analysis of historical sales and inventory data was conducted in order to estimate the potential revenue increase a lateral transshipment strategy
would provide. The analysis also provided valuable insights with regards to how sales and inventory patterns behave during a product life cycle and which the potential main drivers of a feasible and profitable lateral transshipment could be. Further, this part of the research provided findings regarding assumptions to make in the transshipment model as well as resulted in identified initial important factors and dimensions to consider when evaluating models in the literature. The pre-study con- sequently laid a solid foundation for being able to effectively conduct the following phases of the research.
3.2.2 Literature review
The literature review formed the initial approach to solving the problem and was partly used to, in accordance with (Yin, 2009), position our study within the existing research and to define a precise, accurate and insightful research question. It was also used to gain deeper knowledge in the field of supply chain management in general and in the lateral transshipments field in particular. Moreover, the literature review was used to gather data on previously developed lateral transshipment models that we later on would evaluate as potential fits to our empirical setting. In addition, it provided further insights and guidance on what factors to consider when evaluating models as potential fits for the H&M case and thus added value to the mapping of the important factors and dimensions that was initiated in the pre-study.
3.2.3 Data analysis
Through the analysis methods presented in the research design section, the collected data was analyzed with the purpose of understanding what characteristics the em- pirics demand of a successful transshipment model. This was done iteratively in conjunction with the literature review and informal interviews and workshops with our supervisors in order to incorporate new insights and knowledge of both quanti- tative and qualitative character into the analysis. As a result of the pre-study, the initial literature review and the data analysis, we had gained the understanding and tools to screen the literature for an appropriate model to apply to the H&M case.
3.2.4 Model evaluation - Selecting the model
The first step of evaluation consisted of screening the literature for a model to con- sider for the H&M case. The assessment of which models to consider relevant was done using the identified dimensions of importance. Based on our understanding of
the H&M needs and characteristics in conjunction with the dimensions of impor- tance, we selected one model as the most suitable model for applying to the H&M case.
3.2.5 Model evaluation - Adjusting the selected model
After selecting the model, we identified what adjustments were needed for the model to be tailored to our case of interest. This was done by analyzing the dimensions of importance for which the selected model was considered to be relatively weak on or by logically adjusting the parts that were not a great match for the H&M needs. These suggested improvements were then used as modifications to the se- lected model, which in its entirety then was tested on the H&M case.
3.2.6 Model testing
When a model was chosen and adjusted according to the empirics, several tests were conducted in order to evaluate the performance of the model on H&M sales and in- ventory data. The performance testing was divided into two categories: forecast and method performance. The rationale for splitting the testing was that we found the forecast to be a crucial part for the implementation of a transshipment method, making it interesting and valuable to analyze and evaluate the forecast performance in isolation. The forecast evaluation was in turn divided into two categories: con- sistency and dispersion. These measures are explained in connection to the forecast evaluation results in section 4.4.1.
The transshipment model test was in turn divided into evaluating the signal quality and the quantity estimation. A good model should be able to identify good transshipment opportunities, but should also accurately estimate transship- ment quantities that yield profitable transshipments for each identified transship- ment opportunity, which is why these two measures were chosen to be evaluated.
All steps in the evaluation was conducted using k-fold cross validation, which is a technique for evaluating quantitative models. It consists of dividing the data set upon which the model is built into k subsets and using k − 1 subsets for training the model and the remaining subset for testing the trained model. This procedure is then repeated k times, where the test set is changed each time. Last, the k results are averaged. Through this approach, the whole data set gets represented into the test result. (James et al., 2015)
