The Impact of SKU and Network Complexity on Inventory Levels
by
Joseph McCord
B.S. Supply Chain Management & B.S. International Business
Robert H. Smith School of Business, University of Maryland, College Park, 2009
David Novoa Garnica
Dipl6me D'Ingenieur
Universit6 Pierre et Marie Curie, Paris VI / Polytech Paris-UPMC, 2009
SUBMITTED TO THE ENGINEERING SYSTEMS DIVISION IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING IN LOGISTICS
at the
ARCHNiES
MASSACHUSETTS INSTITUTE
OF I T CHNOLOWY
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
JUL 162015
June 2015
LIBRARIES
C 2015 Joseph McCord and David Novoa Garnica. All rights reserved.
The authors hereby grant to MIT permission to reproduce and to distribute publicly paper and electronic
copies of this thesis document in whole or in part in any medium now known or hereafter crated.
Signature of Author....
Signature redacted
Master of Engineering in Logistics Program, Engineering Systems Division
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Master of Engineig
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Dr. Bruce C. Arntzen
Executive Dir tor, Supply Chain Management Program
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7
1
.........................................
iDr.
Yossi Sheffi
Director, Center for Transportation and Logistics
Elisha Gray II Professor of Engineering Systems
Professor, Civil and Environmental Engineering
The Impact of SKU and Network Complexity on Inventory Levels
by
Joseph Cole McCord
and
David Novoa Garnica
Submitted to the Engineering Systems Division On May
8 th,
2015 in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering in Logistics
Abstract
Many firms introduce new distinct products more quickly than they remove old products, and some firms
have also established larger distribution networks to increase service levels or support new markets. This
research applies ordinary least-squares regression and a simulation approach to identify the relationship
between increased complexity and inventory levels relative to demand for a major fast-moving consumer
goods company. For this research complexity is defined as the number of SKUs in a brand and the
number of stocking locations for an SKU. We find that while increased complexity does translate into
increased demand variability, it does not correspond to higher inventory levels. While this research does
not isolate the exact reason for this disconnect, it could relate to the degree to which inventory targets
recommended by an optimization software are adhered to by planning staff. For similar companies which
are navigating inventory cost and complexity pressures, the research implies that there may not be a direct
relationship if the company does not strictly execute an inventory policy which bases safety stock levels
on forecast error.
Thesis Supervisor: Dr. Bruce Arntzen
Title: Executive Director, Supply Chain Management Program
2
Acknowledgements
The authors would like to acknowledge Dr. Bruce Arntzen for his guidance and oversight of this research
effort, staff at Unilever for their insight and feedback, and their SCM cohorts for an awesome year.
Joe & David
I'd like to thank Mom and Dad, Pop-Pop, Grandma, Liz, Jackie, and Pablo for their love and support in
getting me to Cambridge and throughout the year.
Joseph McCord
I would like to take this opportunity to thank my family and friends for their encouragement and support:
Anais, Melbis, Soledad, Mama, Papa, Camilo, Juan Pablo, Farid, Serge, Nathalie, Yohann, Uncles, Aunts
and all the others.
David Novoa Garnica
3
Table of Contents
Abstract .........................................................................................................................................................
2
Acknow ledge m ents .......................................................................................................................................
3
Ta ble of Contents ..........................................................................................................................................
4
Tables and Figures.........................................................................................................................................6
1. Introduction...............................................................................................................................................7
2. Literature Review ......................................................................................................................................
9
2.1 Supply chain com plexity......................................................................................................................9
2.2 SKU and network com plexity .......................................................................................................
11
3 M ethodology ............................................................................................................................................
13
3.1 General Experim ental Design ............................................................................................................
13
3.1.1 Unilever Operational Context .....................................................................................................
13
3.1.2 General Approach ..........................................................................................................................
14
3.2 Data Sources and Initial M anipulation.........................................................................................
14
3.2.1 Data Sources...................................................................................................................................14
3.2.2 Initial Data M anipulations ..............................................................................................................
16
3.3 Applied Definitions ............................................................................................................................
17
3.4 SKU Com plexity .................................................................................................................................
18
3.5 Network Com plexity..........................................................................................................................19
3.6 SKU and Netw ork Com plexity Sim ulation .....................................................................................
19
4.0 Data Analysis and Results......................................................................................................................21
4.1 Dataset Sum m ary Statistics...............................................................................................................21
4.2 SKU Com plexity .................................................................................................................................
25
4.3 Network Com plexity..........................................................................................................................27
4.4 Sim ulation Exercise ...........................................................................................................................
30
4.4.1 Simulation Scenario: Inventory Managed Weekly by Safety Stock Equation ............................
30
4.4.2 Simulation Scenario: Inventory Managed over Lead Time Using Safety Stock Equation .......... 32
4.4.3 Sim ulation Scenario: Inventory M anaged Using "ABC" M ethod ...............................................
5. Discussion ................................................................................................................................................
5.1 Original Research Question and Context .....................................................................................
33
36
36
5.2 Sum m ary of Outcom es......................................................................................................................37
5.3 Im plications of Findings.....................................................................................................................38
5.4 Lim itations .........................................................................................................................................
4
38
6 . C o nclu sio n ...............................................................................................................................................
40
R efe re n ce s ...................................................................................................................................................
42
5
Tables and Figures
16
Table 3-1. Cluster 2 M arket Dataset Sum m ary .......................................................................................
17
Table 3-2. A pplied D efinitions .....................................................................................................................
21
Table 4-1. Sum m ary of SKU-related Statistics.......................................................................................
22
Figure 4-1. Distribution of Demand by SKU, Cluster 1 dataset ..............................................................
Figure 4-2. Distribution of Demand by SKU, Cluster 2 Category A..........................................................23
23
Table 4-2. Sum m ary of Network-related Statistics ................................................................................
Figure 4-4. Number of SKUs per Number of Nodes in Network, Cluster 1 Dataset...............................24
Figure 4-5. Number of SKUs per Number of Nodes in Network, Cluster 2 Category A Dataset.............25
Figure 4-6. Relationship between SKU Complexity and Stock Levels, Cluster 1 October 2014..............26
Figure 4-7. Relationship between SKU Complexity and Stock Levels, Cluster 2 Category B March 2015 ..26
Figure 4-8. Relationship between SKU Complexity and Stock Levels, Cluster 2 Category A April 2015.....27
Figure 4-9. Relationship between SKU Complexity and Stock Levels, Cluster 1 Category C April 2015.....27
Figure 4-10. Relationship between Network Complexity and Stock Levels, Cluster 1 October 2014 ........ 28
Figure 4-11. Relationship between Network Complexity and Stock Levels, Cluster 2 Category B March
29
2 0 1 5 .............................................................................................................................................................
Figure 4-12. Relationship between Network Complexity and Stock Levels, Cluster 2 Category A April 2015
29
.....................................................................................................................................................................
Figure 4-13. Relationship between Network Complexity and Stock Levels, Cluster 1 Category C March
30
2 0 1 5 .............................................................................................................................................................
Figure 4-14. Simple Base Stock Policy Simulation Weighted Days of Stock per Brand ........................... 31
32
Figure 4-15. Simple Base Stock Policy Simulation Nodes per SKU ..........................................................
32
Stock
.............................
of
Days
Weighted
Simulation
Time
Lead
Figure 4-16. Base Stock Policy with
Figure 4-17. Base Stock Policy with Lead Time Simulation Number of Nodes........................................33
34
Figure 4-18. 'ABC' Policy Weighted Days of Stock ..................................................................................
35
Figure 4-19. 'ABC' Policy Days of Stock against Number of Nodes per SKU ..........................................
38
Figure 5-1. Comparison of Actual and Simulated Inventory Levels .......................................................
6
1. Introduction
Any firm involved in the buying and selling of physical goods holds inventory for several
reasons. Inventory allows firms to meet the general demand of consumers and hedge against uncertainty
in demand or delivery lead times. While firms prefer to hold the minimum amount of inventory possible
while still meeting service goals, increases in supply chain complexity have the potential to raise
inventory requirements for equivalent service levels. Firms might increase the number of stockkeeping
units (SKUs) or the number of network locations to capture new markets, but these decisions increase
supply chain complexity and potentially inventory requirements to cover the added uncertainty of these
new markets. If firms better understood the approximate inventory increase attributable to these two types
of changes they would be better equipped to weigh the costs and benefits of adding new SKUs or adding
network locations. Instead of incurring higher inventory costs as complexity rises, firms would have the
ability to identify the point at which adding new SKUs or network locations is not worth the associated
inventory cost increases.
Given the ubiquity of inventory management pressures, this research is of broad interest across
firms, sectors and industries, particularly in low-margin, high-volume sectors such as consumer packaged
goods. Any firm which seeks to carefully manage inventory or supply chain complexity would find
commercial value in an understanding of the real world relationship between the two.
This research applied ordinary least-squares regression to cleaned historical datasets to identify
relationships between average point-in-time inventory levels and the number of distinct stock keeping
units in a brand or the number of stocking locations in the distribution network. To complement the initial
findings of this approach and deepen the understanding of the implications, the research team also
conducted a simulation based on hypothetical data. This simulation incorporated hypothetical
measurements of demand variability and inventory levels calculated under several inventory control
scenarios.
Initial results of the ordinary least squares regression indicated no correlation between either form
of complexity and inventory levels. However, subsequent iterations of this approach using data from
7
different operating markets produced modest indications of correlation. Examination of demand
variability figures in these datasets together with the simulation exercise showed that while higher
complexity does directly correlate to higher demand variability, this increased demand variability does
not directly translate to higher inventory levels.
These results have several implications. Firstly, as indicated by inventory theory, increased
complexity does correspond to higher demand variability. However, the failure of this increased
variability to directly relate to higher inventory levels could be caused by use of inventory management
heuristics by planning staff. Instead of adhering to inventory targets calculated by an inventory
optimization module, staff may prefer to respond to the complexity of managing hundreds of distinct
products by applying non-safety stock-based approaches such as the "ABC" method. The use of these
approaches instead of optimized values may effectively be the cost of increased complexity, although this
research does not indicate the exact point at which complexity might cause planning staff to prefer
simpler inventory control methods. This would also imply that when organizations apply inventory
control methods that do not incorporate variability factors they are effectively insulated against the
inventory effects of increased complexity on variability, although of course they are not insulated against
decreases in inventory fill rate when variability increases.
8
2. Literature Review
Through research and analysis, we sought to answer the following question: what are the effects
of network and SKU complexity on inventory levels? Answering this question requires first identifying
quantitative definitions of complexity as they apply to networks and categories of SKUs in a consumer
packaged goods (CPG) environment. Hypothesis development also requires a theoretical understanding of
how these factors should interact according to existing literature. These elements contribute to the
experimental design behind the research.
A literature review contributed to this research in several ways. First, it provided theoretical
backgrounds to definitions used, ensuring that the research aligns with the general literature on the topic.
It also provides guidance on potential experimental design approaches for inventory-related research.
Finally, the literature review contributed to our understanding of the current theoretical models related to
the relationship between supply chain complexity and inventory levels, which allowed the researchers to
formulate better hypotheses and inform the analysis approach.
Based on the research question itself, this review focuses on the following areas: the impacts of
supply chain complexity generally, SKU complexity (or proliferation) and its effects, and network
complexity and its effects. Additionally, the review includes formal definitions of network and SKU
complexity as well as less scholarly articles from trade magazines which look at the topic of supply chain
complexity.
2.1 Supply chain complexity
Supply chains naturally incorporate the possibility for complexity. Although industries differ
widely, the global spread of physical, informational, and financial flows ties together numerous firms and
products in complicated ways. The exact nature of this complexity, however, can take numerous forms.
Serdarasan, for example, identifies two broad categories of supply chain complexity: "static" - which
covers supply chain structure and component variety, and "dynamic" which addresses uncertainty and
randomness in supply chain activities (2013). De Leeuw further elaborates on these two broad categories
to note that "static complexity refers to the expected amount of information...necessary to describe the
9
state of a planned system," while dynamic complexity relates to a supply chain's tendency to deviate from
schedules (de Leeuw, Grotenhuis, and van Goor 2013). Seen this way, complexity in a supply chain can
arise from the volume of the activity taking place (such as number of partners, products, or locations) as
well as from the variety and unpredictable nature of these entities. For example, a supply chain that
manages 100 products would require more planning than one which handles 50, but additionally a supply
chain that manages 100 unique, diverse products would require more planning and management attention
than one which handles 100 relatively homogenous products.
Additionally, however, there are alternative ways to categorize and define forms of supply chain
complexity. De Leeuw specifically identifies eight drivers of supply chain complexity drawn from prior
research which he applies to the development of a case study exercise. These include scaled indicators of:
upstream reliability, product diversity, size of orders, demand variability, management structure, speed of
response required, lack of information synchronization, and lack of cooperation between partners (De
Leeuw, 2013). These variables capture a range of perspectives on complexity which supported a
quantitative comparison of existing companies.
Jacobs also proposes an empirical definition of supply chain complexity which is designed to
support assessments of complexity at the product portfolio, company, or supply chain levels and cover
static and dynamic elements. He draws on similar histories of complexity research to develop a "General
Complexity Index" which produces a comparable indicator from three components: "multiplicity," which
considers the number of variants (SKUs or number of plants for example), "diversity" of those variants,
and "interconnectedness" of the variants (2013).
Despite their efforts to craft new empirical definitions, one common conclusion of Jacobs, De
Leeuw, and Serdarasan is that there is no universally accepted definition within academic literature of
supply chain complexity in general. Specifically, De Leeuw claims that the existing publications "show
that there is no commonly accepted or shared measure of supply chain complexity, although all studies
argue that supply chain complexity at least varies with uncertainty, variety and size" (2013). The lack of a
10
standard definition shows that there is space to tailor versions of a measurement for complexity to specific
problems.
2.2 SKU and network complexity
While supply chain complexity can cover numerous dimensions, SKU complexity (also called
proliferation) is a particular challenge for fast-moving consumer goods companies. Companies which
produce consumer products may feel pressure to develop new offerings to capture greater market share,
even if it adds new complexity. Specifically, Berman identifies seven predominant causes of product
proliferation which range from product offerings being a barrier to entry to managerial reluctance to
prune old products (2011).
Fortunately, firms do acknowledge SKU proliferation as being a significant problem. One
consulting firm found that "40% of retailers identified the impact of SKU proliferation as one of the three
top supply chain challenges they face" (Berman, 2011). One problematic effect of SKU proliferation is
the increase in the number of "slow-movers" - products that have drastically lower sales than the average.
These slow movers may "account for 40% of total items and less than 12% of sales" in the fast-moving
consumer goods industry (Garry, 2011). Burke notes that SKU proliferation is a longstanding trend for
many retailers. For example, "in the 1950s, a typical grocery store had about 5,000 items. In the 1990s, a
supermarket carried about 30,000 items. Today, if you walk into a mass retail store like Wal-Mart, they
may have over 100,000 different items" (Burke, 2007). The strategic importance and expected durability
of this trend indicate a strong potential value for a model which predicts the inventory impacts of this
SKU proliferation.
Several sources investigate the effect of SKU proliferation. Wan, Evers, and Dresner conducted
analysis of the effect of SKU proliferation (measured as the number of SKUs sold at various soft drink
bottler distribution centers) on operational performance (measured by fill rate) and sales using historical
records (2012). Their study finds that operational performance decreased with increases in the number of
SKUs, while sales volume initially increased but then began to decrease after a peak. This phenomenon is
also identified within marketing and finance literature as a "whale curve" of cumulative product (as well
11
as customer) profitability, in which the marginal profitability of successive new product introduction
eventually erodes (Sievanen, Suomala, and Paranko 2004). Rossetti and Liu developed a simulation
model to capture the effects of two types of SKU proliferation on operational performance (measured by
fill rate) within a network of hospitals (2009). Specifically, their model compares the effects of
introducing a product which is new to a particular hospital but already exists within the wider hospital
system versus introducing a product which does not exist within the broader hospital system. Their
simulation model shows that if SKU proliferation is comprised predominantly of products that are
entirely new to the system, fill rates trend downwards. These studies support initial hypothesis
development regarding SKU proliferation and inventory levels, and offer examples of empirical
definitions of complexity in action.
Network complexity has also benefitted from targeted research. Numbers of stocking locations,
numbers of distribution tiers or echelons, and relative size of inventory requirements feature strongly in
inventory modeling. One common model for the effect of network complexity on inventory requirements
is known as the "Square Root Law," as the theoretical inventory required for a network of 'n' facilities is
divided by the square root of n if inventories for a given market are consolidated into a single stocking
location (Evers, 1995).
Supply chain complexity presents significant threats to performance. Specifically, SKU
complexity (or proliferation) and network complexity present potential for direct impact on inventory
requirements. Significant research exists on these topics, offering expansive perspectives on definitions
and causes of supply chain complexity. Effort has also taken place to generate empirical, quantitative
measurements of complexity, which can support field analysis. Some of these efforts have also proven
direct relationships between complexity and operational performance in the field. While the existing
documentation adequately supports hypothesis formulation and the anticipated analysis, no existing
literature was found which indicates a known relationship between SKU proliferation and inventory
requirements.
12
3 Methodology
3.1 General Experimental Design
This section presents the operational context of the research partner and the approaches to
investigating the research question. The methods described in this section are designed to achieve the goal
of identifying the relationships between SKU complexity, network complexity, and inventory levels. The
operational context provides insight to the challenges faced by the research partner and summarizes the
research partner's supply chain as it concerns the research effort. The context also informs the general
experimental design by proscribing the kinds of information available and the applicability of certain
methods.
3.1.1 Unilever Operational Context
Unilever is a consumer packaged goods (CPG) firm headquartered in the UK and the Netherlands
with brand presence in 190 countries as of 2013. The firm has 14 "Billion Euro" brands as well as
numerous smaller brands (Unilever 2013). The brands cover several consumer categories, including
personal care (such deodorants and soaps), hair care (such as shampoos and dyes), savory foods, and
others. The mix of brands and product categories sold varies greatly between country markets in order to
tailor brands to local tastes. The specific formulations, sizes, and flavors offered also vary from one
market to another, and within a market over time.
Unilever does not manage retail sales, but produces finished products (or contracts production
from contract manufacturers) for sale and distribution to wholesalers and retailers. Unilever manages
production facilities and distribution centers to support these operations.
The product categories and brands will often include numerous product variations, including
flavors/scents, packaging, and sizing, to differentiate the brands from competitor products, capture
additional market share, and appeal to retailers who are looking to offer a complete product offering to
their customers. For example, the manufacturer/distributor might offer the retailer a choice between 30
varieties of men's deodorant, even if the retailer only intends to purchase and display 10 of those 30.
13
These marketing pressures cause CPG firms to produce and offer more and more distinct SKUs
over time, under the assumption that any increases in product management costs are offset by greater
sales and profitability.
3.1.2 General Approach
The overall effort of this research is to determine whether SKU and network complexity influence
inventory levels. Intuition and existing literature suggest that as the number of SKUs or stocking locations
increase, the opportunity to pool variation in demand decreases, leading to increased safety stock
requirements for a given level of service (Evers 1995). To test the hypothesis that increased complexity
leads to increased inventory requirements within the sponsor firm's distribution network we applied
ordinary least squares regression between these two factors at several points in time within a single
market. The regression function was assumed to be a power function (non-linear) given the expressions
for the risk pooling effect behind the hypothesis. The approach was then replicated to other markets to test
the replicability of the original model.
3.2 Data Sources and Initial Manipulation
To conduct the analysis the team did not generate new data on Unilever's operations, but relied
on historical records accessed by Unilever staff from company servers which capture the critical elements
of complexity and inventory at points in time. The types and structures of data sources available therefore
governed the range of feasible methods. For the purposes of this document, direct references to specific
markets and product categories have been obscured as Cluster 1, 2, etc. for markets and Category A, B,
etc. for categories.
3.2.1 Data Sources
Unilever provided the analysis team with the following datasets for the initial analysis of Cluster
1 market operations:
14
*
Output from inventory optimization system (known as MIO - Multiechelon Inventory
Optimization) including approximately 23,000 records representing a historical snapshot
of the client's Cluster 1 operations as of October 4, 2014. Each record represents a single
SKU held at one of several dozen plants or distributions centers (DCs) within the market,
meaning that the data cover all SKUs currently managed in the system with several
records for each SKU. Each record identifies the SKU number, facility number, facility
echelon (plant, Pt tier DC, or 2 nd tier DC), average demand quantity, product category,
and product status (active, discontinued, promotional). The system is designed to use
SKU data to recommend optimal inventory levels, although the actual inventory targets
are controlled by staff. Therefore in this analysis the Cluster 1 MIO dataset was used
specifically as a record of historical demand.
*
Output from inventory records including approximately 21,000 records representing a
snapshot of the client's inventory quantities for each SKU as maintained at each facility
as of October 4, 2014. Attributes include the SKU number, facility number, and current
inventory quantity. While the inventory optimization system also includes inventory by
SKU and location in days of stock, for the Cluster 1 operations it was assumed that this
information was not up to date and would be more accurate coming from a separate
inventory system.
*
Output from sales records including approximately 264,000 records which capture
quantities of SKUs shipped to retailers by week for 40 weeks leading up to the main
October 2014 period for the Cluster 1 market.
The research partner also provided MIO outputs for several Cluster 2 categories for several points
in time. The research partner indicated that these datasets did not have to be complemented by separate
inventory and sales records as the quality of these fields in the Cluster 2 MIO database was sufficient.
With the availability of multiple dates, inventory levels could be averaged to avoid the potential
15
randomness of observing inventory levels at a single point in time. The Cluster 2 MIO data included the
following number of records:
Table 3-1. Cluster 2 Market Dataset Summary
Date
April 6/7 2015
April 14 2015
Category A
18,388
18,406
Category B
3,794
2,515
Category
3.2.2 Initial Data Manipulations
To facilitate the analysis process, the team prepared the Cluster 1 data in the following ways:
"
Inventory quantities were appended to the inventory optimization software outputs using
the common SKU numbers and facility codes. Unilever recommended that for any record
in the optimization software which did not have a corresponding record, inventory of 0
should be assumed.
*
Discontinued and promotional SKUs were removed from the analysis. At Unilever's
recommendation, discontinued and promotional SKUs would not follow normal
inventory management practices and would obscure any relationship in place for normal
SKUs. This process removed 1,750 out of 23,801 records.
"
A pivot table was constructed out of the inventory optimization records. This pivot table
lists a single record for each SKU, along with the brand, number of SKUs in the brand,
total brand demand (quantity), SKU daily demand quantity, % of brand demand
represented by the SKU, number of facilities (or nodes) where the SKU was held, the
number of tiers used to distribute the SKU, inventory quantity, and days of stock (DOS)
for the SKU (calculated as current inventory quantity/daily demand quantity). Days of
16
stock is considered a more accurate measure of inventory levels than inventory quantity
when looking across SKUs because DOS normalizes quantities by sales volumes and
some SKUs may have their inventory measured in different units (packs versus cases, for
example).
*
Total sales volumes were calculated for each SKU in the 8 weeks preceding the inventory
snapshot. Any SKU without any sales figures or sales figures totaling less than 5 units
was removed from the analysis. This reduced the number of active SKUs from 4,244 to
2,560.
For the Cluster 2 datasets the team applied a similar approach but did not have to append
inventory data from separate source or remove additional SKUs based on sales datasets. Also, because the
team had access to multiple inventory snapshots for the Cluster 2 categories, these snapshots were
appended to one another into the same spreadsheet with an additional field indicating their date.
3.3 Applied Definitions
While comparisons between inventory levels and "complexity" form the basis of this analysis,
formal quantitative definitions for these terms are required to execute ordinary least squares regression.
These definitions draw on the experience of prior research as well as the practicalities of the available
data. Table 3-2 summarizes the definitions developed for this research.
Table 3-2. Applied Definitions
Definition
Rationale
SKU Complexity
Number of SKUs in a Brand
The datasets list the brands
associated with each SKU, but
there is no information on SKU
turnover within the brand
complexity is assumed to
increase with the number of
-
Term
SKUs
Network Complexity
Number of unique locations
used for an SKU
17
The datasets provide the
inventory levels at each location
where inventory is stored for
that product - this approach
assumes complexity increases
with the number of stocking
locations used, but cannot be
calculated for an entire brand
because individual SKUs within
the brand use distinct network
paths
Days of Stock (SKU)
Quantity of Inventory/Daily
Demand Quantity
Inventory levels can be
normalized to reflect underlying
demand, to support comparisons
between SKUs
Days of Stock (Brand)
Sum of Inventory
Quantities/Sum of Demand
Quantities for all SKUs in Brand
This calculation provides a
weighted inventory quantity for
an entire brand
Inventory on Hand (quantity)
Total inventory for all records
(locations) of an SKU
Within the inventory
optimization data, each record
reflects a distinct stocking of an
SKU
Daily Demand (quantity)
Total 'global demand' for all
'tier 1' records for an SKU
Within the inventory
optimization dataset, the field
for "global demand" reflects the
average daily demand for all
customer-facing distribution
centers supported by that facility
for that SKU, the sum of "global
demand" for all plant-level
facilities reflects the demand for
that SKU across the market
3.4 SKU Complexity
Starting with the cleaned dataset of inventory and demand records by SKU stocking location, the
team calculated total days of stock per SKU and subsequently total days of stock per brand. This
produced a list of each of the brands in the dataset along with the number of SKUs in that brand and the
total days of stock for that brand. Each brand was plotted against these factors in a scatterplot to support
regression analysis between observed inventory levels and SKU complexity. The two factors were
18
regressed using a power function rather than a normal straight line, because the hypothesized relationship
between the two variables operates on a power function.
For the Cluster 2 datasets which already included a usable figure for Days of Stock for each SKU
location, current inventory was calculated by multiplying Days of Stock and daily demand. Then for each
SKU and brand a weighted Days of Stock was calculated and regressed against brand size.
3.5 Network Complexity
Starting with the cleaned dataset of inventory and demand records by SKU stocking location, the
team calculated total days of stock per SKU. Subsequently the team also identified the number of unique
stocking locations employed per SKU (equal to the number of records) and the number of distinct
echelons or tiers used. This process produced a list of each of the SKUs in the dataset along with the total
network size and depth and days of stock for each SKU. Each SKU was plotted against these points in a
scatterplot to support regression analysis between observed inventory levels and network complexity.
3.6 SKU and Network Complexity Simulation
To help facilitate understanding of expected outcomes the team also conducted a simulation
exercise in parallel to the primary analysis. The decision to conduct this simulation was made when initial
analysis did not produce expected results, and the research team wanted to test proposed explanations.
The team developed a simulation to deepen understanding by showing what inventory levels would be
under various assumptions. Specifically, a simulation could show what expected inventory levels would
be if inventory levels were governed by policies which account for demand variance versus common
heuristics which ignore variance.
This exercise required construction of a dummy dataset with features similar to the Cluster 1
market SKU summary, including a similar distribution of SKUs to brands and a similar distribution of
daily demand across SKUs. In total, the simulation included 2,000 SKUs spread over 50 brands. While
some features of the dummy dataset mimicked actual datasets, a dummy dataset was required in order to
19
include hypothetical demand variance data not included in the actual dataset. The simulation included
demand variance measurements created under several assumptions: a coefficient of variation of 0.5 for all
products and increased by a factor of the square root of the number of SKUs in the brand. From this
hypothetical dataset several inventory scenarios could be developed under varying assumptions of
inventory control procedures, and days of stock calculations were developed using the same approach
applied to SKU and network complexity analyses described above.
20
4.0 Data Analysis and Results
This section presents the quantitative results of the analyses conducted to determine the link
between SKU and network complexity and observed inventory levels. The data analysis begins with
summary statistics for the datasets used in the analysis. Following this are the results of the simulation
and linear regression efforts for each dataset, including SKU and network complexity comparisons.
4.1 Dataset Summary Statistics
This section summarizes the datasets employed for the complexity comparisons. As described in
section 3, each iteration of the analysis used a set of several historical data sources provided by the
research partner. In each case, these data sources provide a sense of the scope of operations in a particular
market and inform expectations of what the impact of complexity would be on inventory levels. For
example, knowing the number of brands and associated SKUs in a market gives a sense of the overall
complexity in the product offering as well as the relative complexity within individual brands. Table 4-1
lists the SKU-related summary statistics for the datasets used and shows the comparative distributions of
SKUs and their demand across the local category offerings analyzed.
Table 4-1. Summary of SKU-related Statistics
Cluster 1 Oct 2014
Cluster 2 Category A
2015 (Multiple Dates)
No. Categories
6
1
No. Brands
77
415
No. SKUs*
2560
7368
Minimum
0
0
Maximum
Mean
6,481
134
20,460
Median
24
48
Standard
Deviation
310
Average
Daily
Demand for
SKUs
191
560
*No. SKUs: number of SKUs used in the analysis after certain SKUs were removed as described in
Section 3.
21
For specific markets, the distribution of demand across SKUs can be analyzed. Figure 4-1 shows
the average daily demand for each SKU ranked along the X-axis by their demand quantity for the Cluster
1 dataset.
7,000
6,000
a
5,000
M
E
4,000
3,000
0
a>
L.
Co o c0 o 00 0 C 0o
2,000
4-J
o Co 0 o D0C
1,000
CD
N*I
It
o
(.0
00
0
NI
'2-
W
00
0D
N~
Iq
W
00
0
N1
It
flo
00
0
SKU rank by demand
Figure 4-1. Distribution of Demand by SKU, Cluster 1 dataset
This distribution shows a strong skew toward a daily demand of zero units. While approximately
10% of SKUs have a daily demand of 500 units or more, more than half of the SKUs have average
demand of 25 units or less per day. This distribution represents a "long tail" of a high proportion of SKUs
which cumulatively represents a low proportion of total sales.
22
25000
20000
-
15000
E
10000
0
5000
4-J
0
W
N
n ry (Y
N,
c t :tqt t Lr) Lr) Lr) L) D
r
L
r-1
t0-j
0
r-4
N
r-j
t.0
UL)
H~
-j
D
.- 4
0
4
r,
Lfl
"
W0
"
C::
m
TH
"D
m Lr)
00
H(
0
kD
_4
D
-4
1.0
-1
1. LO-1
M
Lr
00
1H
mY
kw
00
-4
SKU rank by demand
Figure 4-2. Distribution of Demand by SKU, Cluster 2 Category A
that
Again this distribution shows a strong skew towards a daily demand of zero units, showing
that these demand
the pattern of a "long tail" is also applicable to this category. It should be noted
some SKUs do not
quantities specifically represent the global demands at level one facilities, and that
have a level one facility listed.
Summary statistics can also be provided for the networks employed by the SKUs in a market.
Table 4-2. Summary of Network-related Statistics
Cluster 1 Oct 2014
Cluster 2 Category
A 2015 (Multiple
Dates)
53
68
1
51
58
2
11
48
3
9
34
4
6
31
5
0
14
0
0
1
4
2
I
No. Unique Locations
No. Locations
Serving as
Layer*
6
7
Minimum
23
No. Locations
for an SKU
*
Maximum
10
12
Mean
5.1
2.5
Median
6.0
2.0
Standard Deviation
2.3
1.1
Many facilities serve as layer 1 facilities for some SKUs and as layer 2, 3, or 4 facilities for others.
Table 4-2 shows the comparative network arrangements for the markets analyzed. The data show
that individual SKUs can use a wide range of networks to reach customers - while some SKUs only have
inventory at one facility, others may have inventory at up to 10. Figure 4-4 shows the distribution of
SKUs by the number of nodes in their network for the Cluster 1 market. Again, this chart shows a
significant range in the networks used by various SKUs, suggesting the possibility for complexity of
operations.
800
700
600
500
4
400
6
300
Z
200
100
0
1
2
3
4
5
7
6
8
9
10
Nodes in Network
Figure 4-4. Number of SKUs per Number of Nodes in Network, Cluster
24
1 Dataset
3000
2500
2000
4
6U
Z
1500
1000
500
0
1
2
3
4
5
6
8
7
9
10
11
Nodes in Network
Figure 4-5. Number of SKUs per Number of Nodes in Network, Cluster 2 Category A Dataset
Figure 4-5 shows the distribution of network sizes for the SKUs in the Cluster 2 Category A. This
distribution has a stronger skew towards lower values than the Cluster 1 categories. On average, Cluster 2
SKUs in this category flow through fewer distribution locations than Cluster 1 SKUs, even though the
maximum number of location is higher for Cluster 2 Category A.
4.2 SKU Complexity
This section summarizes the results of regression analysis for each dataset in the exercise,
specifically for the comparisons between SKU complexity and days of stock. Figure 4-6 below shows the
scatterplot, line of best fit (to a power curve) and r-squared for this comparison within the Cluster 1
dataset from October 2014. As seen in the chart, the weighted days of stock per brand do not follow the
expected relationship compared to increasing complexity: the company appears to hold more inventory
with a greater variance for brands with fewer SKUs, with relatively stable inventory levels for brands
with more than 75 SKUs. Behind the scatterplot, brands with a small number of SKUs in some instances
have a single SKU with very low demand which drives up the weighted average of the brand. For larger
brands these low demand SKUs are more likely to be balanced out by SKUs with higher demand
quantities. Figures 4-7 through 4-10 repeat this pattern across different time periods, markets, and
categories.
25
1200
2
R = 0.047
0
1000
0
0
800
0
600
0
0
00
0*
400
OD
Z-
0
150
100
50
0
200
SKUs per Brand
Figure 4-6. Relationship between SKU Complexity and Stock Levels, Cluster 1 October 2014
70.00
0
60.00
R2 =0.0605
50.00
40.00
cc
(A
0
0
30.00
0
20.00
PC.......... ..........
10.00
0.00
0
10
20
30
50
40
60
70
# SKUs in Brand
Figure 4-7. Relationship between SKU Complexity and Stock Levels, Cluster 2 Category B March 2015
26
70.00
R2 = 0.0406
60.00
50.00
0
4
40.00
0E
30.00
m
1%
0
Z)
20.00
1W0
10.0
0.00
150
100
50
0
200
250
300
No. SKUs in Brand
Figure 4-8. Relationship between SKU Complexity and Stock Levels, Cluster 2 Category A April 2015
300.00
R2 = 0.0485
0
250.00
200.00
V)
150.00
0
100.00
50.00
a
w
0.00
0
50
100
150
200
250
300
# SKUs in Brand
Figure 4-9. Relationship between SKU Complexity and Stock Levels, Cluster 1 Category C April 2015
4.3 Network Complexity
This section summarizes the results of regression analysis for each dataset in the exercise,
specifically for the comparisons between network complexity and days of stock. Similar to the
comparisons of inventory levels to SKU complexity, network complexity does not appear to act as an
27
.
. ....
.
..
....................
. . ....
. . ..
influencing factor. For these analyses, because individual SKUs within a brand will take different paths
not make
through the research partner's distribution network, measurement of network complexity does
each axis.
sense at a brand level. Instead, all scatterplots show individual SKUs measured against
As shown in Figure 4-10, SKUs display a very wide range of inventory levels at each discrete
do not follow a
network size. As shown by the line of best fit, the distributions across network sizes
discernable pattern.
Figures 4-11 through 4-13 show this same scatterplot for varying time periods, markets, and
the two factors, these
categories. While they display a similar lack of the expected relationship between
of nodes
comparisons do show a more patterned trend of declining inventory levels as the number
increases.
500
R
450
2
0.0033
8300
0 200
00
100
0
2
4
8
6
12
10
Network Size
2014
Figure 4-10. Relationship between Network Complexity and Stock Levels, Cluster 1 October
28
.
..
........
...
160.0
R2=
0.0493
140.0
120.0
S
100.0
S
80.0
60.0
6
40.0
".
..-.-.
.
20.0
0.0
0
8
7
6
5
4
3
2
1
# Nodes in SKU
Category B March 2015
Figure 4-11. Relationship between Network Complexity and Stock Levels, Cluster 2
160.00
R2
0.0732
140.00
120.00
100.00
80.00
0.0
60.00
40.00
20.00
0.00
0
2
4
6
8
10
14
12
# Nodes in SKU
A April 2015
Figure 4-12. Relationship between Network Complexity and Stock Levels, Cluster 2 Category
29
.
. .. ..
. ......
.....
..
...
.
. ...........
....
.. ..............
...
700.00
R 2 = 0.0403
600.00
500.00
C
400.00
0n
0
300.00
*
4
4
200.00
0
2
4
100.00
0.00
*
I
4
4
4
6
A?
8
10
I
I
LI:
12
14
A6
16
18
# SKUs in Brand
Figure 4-13. Relationship between Network Complexity and Stock Levels, Cluster 1 Category C March 2015
4.4 Simulation Exercise
Using the hypothetical dataset described in Section 3.6, scenarios were developed using varying
assumptions of inventory control policies. This was conducted to show the expected outcomes if
inventory levels were in fact managed according to various known inventory control policies.
4.4.1 Simulation Scenario: Inventory Managed Weekly by Safety Stock Equation
The first scenario developed applied a simple base stock inventory control policy. This policy
assumed a weekly review period and calculated inventory levels as cycle stock [half of weekly demand
over the review period) plus safety stock (k -- a normalization factor for an assumed desired cycle service
level of 0.95) times the standard deviation of demand]. Figure 4-14 shows the results of this scenario in
terms of the days of stock and number of SKUs for each brand.
30
--ainval
14
R2
=
-
-
- -
.. ...........................
0.9495
12
...............
10
2 05 8
..
--
= 3.1149xO.
'
8
0
40- 6.-
.1,
0
2
200
100
0
400
300
SKUs in Brand
Figure 4-14. Simple Base Stock Policy Simulation Weighted Days of Stock per Brand
The number of SKUs and weighted days of stock measurements show high correlation through
regression against a power function, which is to be expected because the inventory component of days of
stock contains a parameter for safety stock based on the square root of the number of SKUs. This
simulation presents a scenario in which inventory is highly driven by the increase in variance of demand
caused by the increase in SKUs within a brand. Figure 4-15 shows a similarly clear correlation between
Days of Stock and nodes per SKU.
6
R'= 0.9866
5
0..
43
2
0
0
2
4
6
10
8
Number of Nodes
31
12
- -
N--
--
-- --
--
- -I- .
-
- -
-
-
-
-
-
-
-
I---
-
Figure 4-15. Simple Base Stock Policy Simulation Nodes per SKU
4.4.2 Simulation Scenario: Inventory Managed over Lead Time Using Safety Stock Equation
The second scenario developed expanded on the first by setting the review period as the
manufacturing lead time of the SKU and finding the base stock level. Figure 4-16 shows the weighted
days of stock and SKUs per brand for the 50 brands in the simulation.
18
R2 = 0.5483
16
0
..
14
.a
12
y
6
8
4
0
1
y=5.9533x
10
.......
........
8
0
6
4
S2
COQ
0
200
100
300
400
SKUs in Brand
Figure 4-16. Base Stock Policy with Lead Time Simulation Weighted Days of Stock
This simulation shows the effect of adding an additional variable to the inventory equation. The
fit of the data to the power function has declined, with the r-squared value now at 0.54. The effect of the
number of SKUs in a brand on inventory levels has decreased with the addition of lead times. As shown
in Figure 4-17, for network complexity the r-squared drops more precipitously, because the data is not
aggregated up from SKUs to brands.
32
.
.........
.
.
. . ............
.....
-
-
-,-.
- -- -
- ----
-
--l-N., NNn- -:-
-
-0-
...................................
18
16
16 0R' = 0.0066
*
12
.
14
10
I
U
8 U
6
0
0
2
4
6
10
8
12
Number of Nodes
Figure 4-17. Base Stock Policy with Lead Time Simulation Number of Nodes
4.4.3 Simulation Scenario: Inventory Managed Using "ABC" Method
The third scenario included an inventory policy which ignores demand variance by setting
inventory targets based on relative demand volume. Known as an "ABC method," this approach might be
employed in settings where planning staff have more SKUs than they are able to manage rationally, so
they manage higher volume products carefully and low volume products with less attention. Typically a
small subset of the high volume products are responsible for the vast majority of total demand, while the
situation can
majority of products are cumulatively responsible for only a limited portion of demand. This
be observed in Figure 4-1 of the 'long tail' featured in the Cluster 1 dataset. In this scenario, the products
target of two
responsible for 70% of total demand (375 out of the 2,000 SKUs) were assumed to have a
weeks of demand, the next 25% a target of three weeks of demand, while the long tail representing 5% of
total demand (957 of 2,000 SKUs) were given a target based on a normal distribution with a mean of
of this
eight weeks of demand and a standard deviation of three weeks. Figure 4-18 shows the results
scenario.
33
....
................
.
.
......
70
*
80
60
50
*
0
-; 40
0
0
3>
0
0
100
300
200
400
SKUs in Brand
Figure 4-18. 'ABC' Policy Weighted Days of Stock
The policy produces a scatterplot with no overall correlation between the two factors, as the
inventory policy is based entirely on demand, and not on the variance of demand. However, brands with
fewer products appear to be more likely to be influenced by 'C' products with high inventory levels,
while larger brands appear to be able to average 'C' products with 'A' and 'B' products. Figure 4-19
again shows the lack of correlation introduced by this type of inventory control method. Additionally,
while the correlation is similarly small, the ABC method causes a wider range in days of stock to occur
than the safety stock method with multiple sources of variance.
-M"w
-
-
-
-
--
-
-
34
200
180
160
140
D
120
CL
.S
100
0
0
o
R2 = 0.0034
80
III
I
60
0
0
40
*
I
20
80
0
0
2
4
6
10
8
12
Number of Nodes
Figure 4-19. 'ABC' Policy Days of Stock against Number of Nodes per SKU
35
.
......................
5. Discussion
This section interprets the previously presented results regarding the relationship between
complexity and inventory levels. The findings are briefly summarized and put into context of the original
research question as well as the broader research context on applied inventory science. Additionally, this
section includes commentary on the limitations of this research and the extent of its broader applicability.
5.1 Original Research Question and Context
The overall effort of this research was to answer the question of whether SKU or network complexity
drive inventory levels. With quantitative definitions set for these factors, the research focused on two
questions:
"
Does a having a higher number of distinct SKUs in a brand coincide with higher amounts of
inventory held for the same expected service level?
*
Does use of a larger distribution network (measured in number of stocking locations) coincide
with higher inventory held for the same expected service level?
The assumed mechanism of this relationship lies in the increase in total variance caused by splitting
independent sources of unpredictability (such as demand). If a firm decides to produce and sell 20 distinct
SKUs for a brand which previously included 10 distinct SKUs, the coefficient of variation and the
difficulty of predicting demand for each individual SKUs increases. If the firm operates any inventory
control model that includes a factor for demand uncertainty, an increase in variance produces an increase
in the quantity of safety stock required to meet desired service level targets.
While this overall relationship is generally assumed to hold true, the client firm has not been able to
identify a strong correlation previously, and a direct link between SKU proliferation and inventory levels
has not been described specifically in existing literature.
A replicable methodology which identifies this relationship would allow firms in any consumerbased industry to estimate the inventory-related costs of increased complexity.
36
5.2 Summary of Outcomes
As described in Section 4, correlations were found for three datasets, each representing inventory
carried as part of distribution operations for the research sponsor. Each dataset included inventory and
demand quantities for individual SKUs managed under brands and categories.
Ordinary least squares regressions for the Cluster 1 market dataset of 77 brands found no or
negative correlation between the number of SKUs and days of stock held in the network. This lack of
correlation was driven by extremely high days of stock held for low demand, or "long tail" products,
which for brands with fewer SKUs played a comparatively larger role. This pattern was repeated in
similar analyses for separate datasets covering different time periods, markets, and categories.
Least squares regression analysis of SKUs comparing inventory levels to network complexity
found a similar lack of explanatory power. SKUs across time periods, markets, and categories showed
significant variance in their inventory levels even at the same number of network locations.
Additionally, a simulation was created to gain insight into the deviations observed between actual
and hypothesized results. A simulation of a theoretical "ABC" inventory control method which ignores
demand variation generated a distribution with a similar pattern to the Cluster 1 dataset. This observation,
combined with knowledge of operating practices in this market indicate that planners set inventory levels
in a manner closer to the "ABC" method than to optimal inventory models. Figure 5-1 provides a graphic
comparison between the actual results from the Cluster 1 dataset and the simulated outcomes. From left to
right, the figures include actual comparison of number of SKUs per brand and days of stock, simulated
days of stock under an inventory control system where variance in demand is only driven by the number
of SKUs, and simulated results under an ABC inventory control method.
37
so
014
e70r
ltd
n
60
11
840
105
~40
30
10
CA)
10
0
5.
mliainso
inig
1
0100
0
)L0
0
0)
0
0
SKUs in Brand
20D
10D1
00
200
100
300
S~th
Levels
and Simulated Inventory
5-1. Comparison of Actual
Figure
aibliy4oeete
ohgerdmn
opeiydeaorepn
300
400
400
N~WSICUnnBrand
i
alr
fti
inase
5.3 Implications of Findings
These results have several implications. Firstly, as indicated by inventory theory, increased
complexity does correspond to higher demand variability. However, the failure of this increased
variability to directly relate to higher inventory levels could be caused by use of inventory management
heuristics by planning staff. Instead of adhering to inventory targets calculated by an inventory
optimization module, staff may prefer to respond to the complexity of managing hundreds of distinct
products by applying non-safety stock-based approaches such as the "ABC" method. The use of these
approaches instead of optimized values may effectively be the cost of increased complexity, although this
research does not indicate the exact point at which complexity might cause planning staff to prefer
simpler inventory control methods. This would also imply that when organizations apply inventory
control methods that do not incorporate variability factors they are effectively insulated against the
inventory effects of increased complexity on variability.
5.4 Limitations
Several factors limit the ability to extend the results of this research. Firstly, while the data
analyzed represent multiple geographies and product categories, they only represent the experiences of
one firm within the consumer packaged goods industry. Other firms in the same industry or firns in other
industries may operate more centralized inventory control methods which would affect the relationship
between complexity and inventory levels in more direct ways. The independence of demand for products
within a brand would also vary between industries and would influence the variability of demand
associated with addition of SKUs or network locations to a brand.
38
.............
. ...
........
-
--------
Also, in complex settings, there could be many sources of complexity and variability. This
research focused on changes in inventory levels attributable to SKU and network complexity, and
regressed SKU levels and inventory levels against an equation which assumed independence of demand
between products. Other unexplored sources of complexity which could drive inventory levels could be
production or sourcing lead time variance, frequency of product mix change, and overall variance of
demand within brands.
-
Additionally, the data used for this research reflects operations within a limited time period
specifically from October 2014 to April 2015. Potentially this time period reflects unusual demand or
inventory patterns for the firm which are not typical.
39
6. Conclusion
This research focused on the role of complexity in driving inventory levels at a global fastmoving consumer goods firm. Specifically, it sought to answer the questions of whether increases in SKU
and network complexity correspond to increases in the days of stock held.
In summary, the research effort found that these specific forms of complexity do not strongly
correspond to associated increases in inventory levels. Instead, changes in demand variability associated
with the increased complexity do not translate into increases in actual inventory levels, and the inventory
levels held follow expected patterns under inventory control models which do not include demand
variance as a factor. This implies that there is no direct effect of complexity on inventory levels.
While the observed inventory levels are similar to expected levels under the simulations
conducted for this research, the research partner should undertake internal efforts to determine the exact
methodologies used by planners to set inventory targets. This could inform change management
approaches to encourage planners to use recommended optimal inventory levels more frequently.
Several related questions remain uninvestigated in this research. One important factor related to
the concept of the cost of complexity could be the impact on service levels - if inventory levels remain
unchanged even when variability increases, the assumption would follow that associated service levels
would decline. This could then translate into a useful "cost" measure when looking at the impact of
complexity. It may also be useful, through difficult, to determine at what level of complexity staff prefer
to apply simpler heuristics over optimal inventory management methods. Additionally, another way to
examine "cost" might be to look at the difference between actual and ideal inventory levels under
increasing levels of complexity. This could provide another perspective of the impact of increasing
variability.
Another line of valuable insight could come from investigating the role of other forms of
complexity in this context. Other forms of complexity could include overall variance of demand within
40
product categories or brands, frequency of product turnover within brands, or variability between
customer demand patterns.
Additional research could also investigate these relationships in other industries. Potentially, in
sectors with greater centralization and automation of inventory targets, more direct relationships between
complexity and inventory levels might exist.
41
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