Efficient Product Rationalization within a
Single Product Portfolio
A Thesis Presentedby
Jackson Chou
to the faculty ofMechanical and Industrial Engineering
in Partial Fulfillment of the Requirementsfor the Degree of
Master of Science
in the field ofOperations Research
Northeastern UniversityBoston, Massachusetts
May 15, 2013
c© Copyright 2013 by Jackson ChouAll Rights Reserved
2
Table of Contents
Table of Contents 3
Abstract 6
Acknowledgments 8
1 Introduction 91.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . 101.2 Thesis Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.3 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Literature Review 142.1 Product Rationalization . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.1 Applied Mixed Integer Programming for Product PortfolioManagement . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.2 Benefits of Product Rationalization . . . . . . . . . . . . . 182.2 Gross Margin Return on Inventory Investment - GMROI . . . . . 18
2.2.1 Common Performance Measures . . . . . . . . . . . . . . . 192.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Mathematical Model 223.1 Fractional Programming . . . . . . . . . . . . . . . . . . . . . . . 223.2 Overall GMROI Model . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.1 Linearized GMROI Model with Auxiliary Variables . . . . 263.2.2 Overall GMROI Model with Dinkelbach’s Algorithm . . . 30
3.3 Individual GMROI Model . . . . . . . . . . . . . . . . . . . . . . 333.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4 Model Solutions and Analysis 374.1 Scenario Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Overall GMROI Model Solution . . . . . . . . . . . . . . . . . . . 384.3 Individual GMROI Model Solution . . . . . . . . . . . . . . . . . 404.4 Comparison of Model Results and Conclusion . . . . . . . . . . . 42
3
5 Discussion and Conclusion 475.1 Redistribution and Sales Margin Model . . . . . . . . . . . . . . . 485.2 Limitations and Extensions of Future Research . . . . . . . . . . . 50
Bibliography 52
Appendices 55.1 Appendix A: Overall GMROI Model Optimal Solution . . . . . . 56.2 Appendix B: Individual GMROI Model Optimal Solution . . . . . 65.3 Appendix C: Overall GMROI LINGO Code . . . . . . . . . . . . 74.4 Appendix D: Individual GMROI LINGO Code . . . . . . . . . . . 75
4
List of Figures
1.1 Company X’s Product Portfolio . . . . . . . . . . . . . . . . . . . 111.2 Company X’s Inventory Investment from each quintile group . . . 121.3 Product Hierarchy of a Product Portfolio . . . . . . . . . . . . . . 13
4.1 GMROI and Inventory Turnover as inventory investment is re-duced (Overall GMROI) . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 GMROI and Inventory Turnover as inventory investment is re-duced (Individual GMROI) . . . . . . . . . . . . . . . . . . . . . 42
5
Abstract
Product proliferation is a problem seen in many large consumer packaged
goods (CPG) companies. Effectively managing the supply chain when the prod-
uct portfolio is constantly growing is a complex task for management. Without
proper assessment of the product portfolio, companies can easily run into the
danger of adding products that only result in reducing profits. One approach to
effectively manage the product portfolio is stock keeping unit (SKU) rationaliza-
tion or product rationalization. SKU rationalization is an overall performance
assessment on the company’s product portfolio and focuses on reducing the in-
ventory cost by eliminating underperforming products. However, there is no uni-
versal performance measure for wholesalers and retailers to use. The definition
of an underperforming product may vary depending on management’s goals and
performance metric used. Although finding a suitable performance measure is
challenging, successful implementation of weeding out underperforming products
will improve inventory policies and the company’s supply chain operations will
run efficiently at a reduced cost, thus increasing profits. In this study, we explore
the feasibility of using the performance metric gross margin return on inventory
investment (GMROI) as the objective function and develop two product ratio-
nalization models: (1) Overall GMROI and (2) Individual GMROI. The models
maximize GMROI metrics at reduced inventory investment levels and portfolio
size, while ensuring certain inventory turnover level. The nonlinear fractional
6
overall GMROI model is solved by Dinkelbach’s Algorithm. While we are able
to solve the overall GMROI model for the global optimal, its recommended solu-
tions may not be practical. On the other hand, the individual linear (0-1) integer
GMROI model provided good solutions in terms of gross margin and inventory
turnover. The models were tested using the portfolio of 1120 products of a CPG
company.
7
Acknowledgments
I would like to express my sincere gratitude to my thesis advisor, Professor
Emanuel Melachrinoudis, for the advice, guidance, and most importantly his
time and support. His office was always open to me whenever I had questions
and provided me with reference materials for the completion of this thesis.
I would also like to thank the managers of the company that provided me the
data for this research. Without them, this thesis would not have been possible
and I would not have had the opportunity to develop my research abilities. Their
insights and expertise knowledge were also invaluable to the completion of this
thesis.
Lastly, I would like to express my gratitude to my parents for all the support
they have given me throughout my life. They have made great sacrifices in order
for me to receive a higher education, I would not be here without their love and
support.
Jackson Chou
Boston,USA
May 15, 2013
8
Chapter 1
Introduction
Effectively managing the supply chain of any large consumer packaged goods
(CPG) company has always been and will be a daunting task for management. As
these large CPG companies continue to grow and expand, so does their product
portfolio. Product proliferation, defined as “product line depth or “an increased
assortment within a product line [1], is a strategy that allows companies to attract
more consumers, leading to more demand and sales. At the same time, the
increase of product varieties adds to overall costs such as inventory carrying cost
and warehouse expenses [1]. Without proper assessment of the product portfolio,
companies can easily run into the danger of adding products that only result in
reducing profits.
One approach to effectively manage the product portfolio is stock keeping
unit (SKU) rationalization or product rationalization. SKU rationalization is an
overall performance assessment on the company’s product portfolio and focuses
on reducing the inventory cost by eliminating underperforming products. How-
ever, there is no universal performance measure for wholesalers and retailers to
use due to the “multidimensional character of a retailer firm” [2]. The defini-
tion of an underperforming product may vary depending on management’s goals
and performance metric used. Common retail performance metrics are service
9
level, lost sales, product substitute percentage, gross margin, stock-turn, gross
margin return on inventory investment (GMROI) and sell-through percentage
[2], [3]. Although finding a suitable performance measure is challenging, success-
ful implementation of weeding out underperforming products will allow supply
chain operations to run efficiently at a reduced cost, improving the distribution
of products and reducing storage cost thus increasing the profits.
1.1 Problem Statement
The research done in this thesis was motivated from a real world problem fac-
ing a large CPG company. The company desired to remain anonymous, therefore
we will refer to it as Company X in this study. Company X is large CPG com-
pany and as with most CPG companies, maintaining a profitable product mix in
its product portfolio is one of the top objectives for management. The company
has a goal to improve the business performance and profitability growing in its
product portfolio. In addition, Company X is challenged with achieving working
capital targets, while maintaining a high level of customer service. This naturally
leads to a SKU rationalization exercise for Company X.
Figure 1.1 is a Pareto Chart that shows Company X’s current contribution of
total Gross Margin within a product portfolio consisting of 1120 different prod-
ucts. We can see from this chart that 80% of gross margin contribution is coming
from only 22% of the SKUs (246 out of 1120) in the portfolio. This phenomenon
is what we call the 80/20 rule or the Pareto principle, which states that about
80% of effects come from only 20% of the causes [7]. The 80/20 rule is widely
seen in business, especially within the CPG industries. As we venture further
along the Pareto Chart, we can see that the last 20% of products barely have
any effect on the total gross margin. Mapping the current status of the product
10
portfolio allows us to view the condition of tail (the worst performing SKUs or
in this case the last 20% of the product portfolio) and begin consideration on
products to trim and reduce.
Figure 1.1: Company X’s Product Portfolio
Figure 1.2 is a breakdown of the inventory investment supporting every quin-
tile group in the entire product portfolio. It makes sense to see that the majority
of Company X’s inventory investment is supporting the first quintile group of
products, which contributes $55.14 million dollars of the total gross margin in
the product portfolio. However, it is alarming here that the last three quintile
groups, or in this case, the last 60% of the product portfolio requires $9.15 mil-
lion dollars of inventory investment and only provides $6.47 million dollars of
the total gross margin. This inefficient use of inventory investment capital shows
why product proliferation may not always be profitable and increasing products
may result in reduction of profits. Company X has the opportunity to improve
its product portfolio and efficiently handle the inventory investment associated
11
with these products. The problem now is to determine the best combination of
products to keep in Company X’s portfolio.
Figure 1.2: Company X’s Inventory Investment from each quintile group
1.2 Thesis Motivation
Company X’s main objective is to increase the business performance and im-
prove profitability of its product portfolio. As illustrated in Figure 1.1 and 1.2,
there are opportunities for product rationalization at the tail-end of the portfolio.
Company X seeks to scale back on their inventory investment capital by elim-
inating these underperforming products in their product portfolio. Ultimately,
the reduced working capital will allow for higher profits and higher inventory
turnover in the product portfolio.
Companies in various industries have developed product portfolio optimiza-
tion models to effectively manage the inventory costs and reduce the amount of
products offered in their portfolio [11] [12]. While SKU Rationalization refers to
12
the elimination of products at the SKU level (where the difference of each SKU or
product may also include variants of the same product such as package size, ven-
dor, color, flavor, software, promotions, geographical location, etc.), the research
done in this thesis will be analyzing the elimination of products with only one
minor difference from each other. In other words, the products are exactly the
same but different characteristics such as flavor or the geographical location of the
product sold as illustrated in Figure 1.3. In this thesis, we explore the feasibility
of GMROI as a performance measure and objective function for the optimization
model. We concentrate on eliminating SKUs based on management’s goals and
objectives to maximize the GMROI within a single product portfolio.
Figure 1.3: Product Hierarchy of a Product Portfolio
1.3 Thesis Organization
The following thesis is divided into 5 chapters. Chapter 2 provides the litera-
ture review of SKU Rationalization and the GMROI performance metric. Chapter
3 presents different approaches of mathematical models for Product Rationaliza-
tion to be compared. Chapter 4 presents the comparison of different Product
Rationalization models under a scenario example. Finally, Chapter 5 summa-
rizes the thesis and presents future work and recommendation.
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Chapter 2
Literature Review
In this chapter, we describe the focus and general approach to SKU or Product
Rationalization and take a look at what companies in different retail industries
have done to create an efficient product portfolio. In addition, this chapter pro-
vides both literature and application of mathematical programming models to
solve the product portfolio problems. Finally, we will introduce the performance
measure GMROI and describe the uses of GMROI.
2.1 Product Rationalization
As mentioned in the previous chapter, product proliferation strategies require
careful analysis and assessment, otherwise retail firms run into the danger of
adding unprofitable products into their portfolios. Product proliferation problems
also arises from many other factors: firm’s desire of large product selections to
appeal to every consumer type, product proliferation strategy used as a barrier
to entry, increase in sales through minor product modifications, pressures from
functional areas within firm, improper management of product life cycles, demand
for unique products by resellers, and manager’s reluctance to prune products [1].
In fact, it is not uncommon to see CPG companies to have well over 50,000 SKUs
in their product portfolio [8]. In supply chain, product rationalization is a popular
14
approach to ease the undesirable and unprofitable effects of product proliferation
[1], [4].
One of the biggest challenges in product rationalization involves defining the
complexity costs incurred in the portfolio. There is no perfect way to accurately
account for the true costs associated with management and planning time, mar-
keting, operational costs, etc. Complexity cost is defined differently in each com-
pany, it is difficult to measure and is not always captured in standard accounting
systems [11]. For example, Hewlett-Packard (HP) defined their complexity costs
into two types: Volume-driven and Variety-driven. Volume-driven complexity
costs consist of material costs and variability-driven costs such as excess costs
and shortage costs [11]. Variety-driven costs are defined as resource costs, exter-
nal cash outlays, and indirect impacts of variety such as manufacturing, rework,
warranty-program expenses [11]. Even in the healthcare industry, complexity
cost is defined as the “impact that rationalization of a brand has on cash flow,
labor hours, machine hours, forecast accuracy, inventory, number of SKUs per
healthcare product, and sales per SKU” [9]. Therefore, product rationalization
requires management to strictly define their objectives and specifically eliminate
products that do not meet the threshold.
There are two general approaches in product rationalization. The first ap-
proach is redundant product rationalization, where the strategy is to focus on
the top to medium ranking products (based on the performance metric used) and
seeks to eliminate products that do not “satisfy a unique customer need” [8].
In doing so, the process is believed to redistribute the sales from the eliminated
products among the remaining products in the portfolio.
The second approach is tail-end pruning, which is the common and tradi-
tional method of product rationalization [8]. Tail-end pruning aims to eliminate
15
the bottom ranking products, which is generally the tail from the initial Pareto
analysis of the portfolio. As seen in Figure 1.2, the Pareto analysis of Company
X, you will always expect the 80/20 rule when mapping the product portfolio
based on some revenue metric. We observed that the last 60% of the Company
X’s product portfolio required more inventory investment than margin return.
However, companies may also exhibit negative volume and negative return from
their bottom ranking products because of excess product returns. Pruning the
bottom ranking products will lead to overall lower revenue and margin, however,
the aim is to have the reduced costs outweigh the revenue and margin loss [5].
2.1.1 Applied Mixed Integer Programming for ProductPortfolio Management
The study and practice of applying integer programming models for product ra-
tionalization has long been researched in various industries. Most notably, the
pharmaceutical industry often experiences product proliferation where the SKU
differences are multiple dosage forms of the same medicine such as film-coated
tablets or sugar-coated tablets [8]. In literature, the use of stochastic program-
ming has been proposed as an approach to properly manage pharmaceutical prod-
uct portfolios [10]. Although the stochastic programming approach determines
which project to undertake based on expected net present value, the decision of
eliminating and keeping a product can be seen as such projects. The framework
has two stages, the first stage deals with decision that must be made immediately,
the “here and now” decisions [10]. After the decisions are made, a second stage
deals with uncertainty, the “wait and see” decisions [10].
In the computer hardware and software industry, HP tackled their product
portfolio problem with integer programming to improve business performance
and effectively reduce operational costs. However, due to HP’s sheer size of
16
data set and order history, the formulated integer programming problem was
too large to solve by standard linear programming methods. Instead, HP found
that the problem can be formulated as a parametric maximum-flow problem
in a bipartite network and developed a new, exact algorithm that solves their
parametric maximum-flow problem [11].
John Deere & Company (Deere), the leading manufacturer of agricultural ma-
chinery in the world, believed their product lines included too many configurations
available for customers that resulted in reduced profits. In Deere, configuration
is defined as a “feasible combination of features available on a machine” such as
engine type, transmission, and horsepower etc. [12]. To efficiently build their
product portfolio, Deere developed a mixed integer programming model to select
configurations that maximizes shareholder value added [12].
As we have seen in the previous two industrial applications, mixed integer lin-
ear programming (MILP) can be applied to achieve optimal solutions in product
rationalization. However, in order to even attempt to build a MILP problem, the
data quality must be high and accurate since complexity costs must be incorpo-
rated into the model [8]. The binary decision variables in the MILP model would
indicate whether to keep the product or eliminate from the portfolio. An MILP
model can be formulated with either maximize or minimize objective function.
The maximization objective function will result in an optimal solution that indi-
cates the best products to keep in the portfolio. Alternatively, the minimization
objective function will output the optimal solution that indicates the worst per-
forming products in the portfolio. The flexibility of the objective function and
constraints would be based on management’s aspiring goals.
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2.1.2 Benefits of Product Rationalization
The process of product rationalization may be challenging but the benefits are
quite rewarding. In June 2010, Novartis, a pharmaceutical company, had around
14,000 different SKUs in its product portfolio. By applying both redundant prod-
uct rationalization and tail-end pruning, Novartis was able to reduce about 1100
SKUs in their active product portfolio that would result in a reduced inventory
capital of $20 million USD [8]. HP’s product portfolios consist of 2,000 laser
printer SKUs, 15,000 server and storage SKUs, and over eight million customiz-
able combinations of notebook and desktop products [11]. Through the process of
product portfolio management, HP was able to reduce their LaserJet SKU count
by 40%, resulting in annual profits of $20 million [11]. Deere’s product portfolio
consisted of multiple product lines. Each product line carried thousands to mil-
lions of different configurations for its products. By developing a mixed integer
programming model, Deere was able to reduce its configuration set that allowed
for reduced costs, which ultimately lead to increased profits of millions of dollars
[12].
Each of the companies mentioned above had invested time in analyzing and
assessing their current product portfolio to effectively prune out their worst per-
forming products or simply inefficient products. By doing so, the companies
felt the positive impact of product rationalization and improved their business
performance immensely due to the reduced inventory capital.
2.2 Gross Margin Return on Inventory Invest-
ment - GMROI
As with all types of models, whether it be mathematical programming, simu-
lation modeling, or forecasting – if the data input is inaccurate, then the output
18
from the model will be useless. For supply chain, an important issue is defining
a performance measure for analyzing the decision variables. Since there is no
universal performance measure, supply chain practitioners have used several dif-
ferent measures in analyzing retail performance. The following section describes
some of the common performance metrics and how it relates to GMROI.
2.2.1 Common Performance Measures
Gross margin is a common performance metric used across all businesses.
However, gross margin only takes into account the sales price of the products sold
and does not incorporate any inventory management. Gross Margin is defined
as:
Gross Margin = Revenue− Cost
Inventory Turnover is another common metric in business that measures the
efficiency of inventory management [3]. Higher turnover represents efficient use of
inventory investment and results in lower inventory carrying costs due to inven-
tory ”turning” at a high pace. Inventory turnover has variations of calculations,
however, research done in this thesis is calculated as:
Inventory Turnover =Total Units Sold
Average Inventory in Stock
Gross Margin Return on Inventory Investment (GMROI) is a performance
measure that takes into account both the revenue and inventory unit impact. GM-
ROI was first introduced to give management the flexibility to increase profit lev-
els by making decisions based on gross margin percentage or inventory turnover.
GMROI is defined as:
GMROI =Total Gross Margin
Average Inventory Cost
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where the total gross margin and average inventory cost are calculated within the
same period of time (for example, within the last 52 weeks). The Turn and Earn
ratio is another variation of GMROI:
Turn and Earn Ratio = Gross Margin %× Inventory Turnover
Ultimately, GMROI can be interpreted as the amount of money earned per
dollar invested in inventory [3]. For example, if the product portfolio has a
GMROI of 5, this means for every dollar invested in inventory, you are earning five
dollars. GMROI has been used as a performance measure for analyzing sourcing
decisions [3], [13]. While GMROI has been used to generate profit insights, to our
best knowledge, the performance metric has not been applied to mathematical
programming for product rationalization decisions.
Although the idea behind GMROI is novel, the performance metric is consid-
ered bias. GMROI can make a product with high margin dollars look worse, and
a low margin product look great. The reasoning behind this is due to the average
inventory cost in the denominator of the GMROI ratio. If two products have
the same inventory investment, the higher gross margin would make the product
the better one. However, this does not take into the account of the inventory
productivity. Even though the higher gross margin product has a better GMROI
metric, the inventory turnover for that product may be lower than the product
with the lower gross margin. GMROI does not truly differentiate between high
margin/low turnover and low margin/high turnover products.
2.3 Conclusion
In this chapter, the general process and approach to product rationalization
20
are discussed. Product rationalization is one approach to solving the product pro-
liferation problems seen in every large retail firm. One of the largest challenge in
product rationalization is determining the true costs associated with each prod-
uct. There are two approaches to product rationalization. First is redundant
product rationalization that seeks to eliminate redundant products within the
top to medium ranking products. The second approach, known as tail-end prun-
ing, tackles the bottom ranking products of the portfolio.
The use of mixed integer programming to solve product rationalization prob-
lems was also discussed, showing several examples of what companies in different
industries have done to efficiently manage and build their product portfolios.
Given the management’s goals and objectives, mathematical programming can
be used to determine the optimal combination of products to keep in the portfo-
lio. Finally, we introduced several performance metrics typically used in supply
chain as well as GMROI, the primary performance measure to be used as the
objective function for the optimization model formulated in the next chapter.
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Chapter 3
Mathematical Model
In this chapter, we introduce several mathematical models for product ra-
tionalization with the GMROI performance metric. As we have defined in the
previous chapter, product rationalization is an overall assessment of the product
portfolio with a goal to reduce inventory cost by pruning underperforming prod-
ucts. Therefore, this problem can be formulated as a type of resource allocation
problem through the use of binary decision variables from Integer Programming
(IP). To be more precise, because the performance metric GMROI is in the objec-
tive function, our model becomes a Fractional Programming (FP) problem with
binary decision variables. In the following sections of this chapter, we show sev-
eral different formulations for this Fractional Programming problem as described
below.
3.1 Fractional Programming
When a mathematical programming problem is to maximize or minimize a ratio
of two linear functions, subject to linear constraints, we define this as a Frac-
tional Programming problem. Fractional programming is a special structure and
class of Non-linear Programming (NLP), and when the problem consists of both
22
continuous and discrete variables, the problem becomes a mixed integer non-
linear programming problem (MINLP). Therefore, a mixed integer linear frac-
tional programming problem (MILFP) is a special structure of MINLP problems.
Fractional Programming problems typically have the form:
FP : Max:α +
∑i nixi
β +∑
i dixi
s.t. Ax = b
xi ≥ 0
where A is an m × n matrix, x is the decision vector, and α and β are scalars.
In linear fractional programming problems, every local minimum (maximum) is
a global minimum (maximum). The following lemma from Chapter 11.4, “Lin-
ear Fracational Programming [16] gives some important properties for obtaining
global optimal solutions.
Lemma 3.1.1. Let F (x) = (α +∑
i nixi)/(β +∑
i dixi), and let S be a convex
set such that β +∑
i dixi 6= 0 over S. Then, F (x) is both pseudoconvex and
pseudoconcave over S.
Due to the above lemma, there are multiple implications for the fractional
programming problem. The following lemmas are based on the theorems in “Non-
linear Programming: Theory and Algorithms in Bazaraa et al. [16].
Lemma 3.1.2. Since F(x) is pseudoconvex and pseudoconcave over S, then it is
also quasiconvex, quasiconcave, strictly quasiconvex, and strictly quasiconcave.
Proof. Based on Theorem 3.5.11, “Generalizations of a Convex Function” [16].
Lemma 3.1.3. Every local optimal solution of F(x) is a global optimal solution
over the feasible region S.
23
Proof. By Theorem 3.5.6, in “Generalizations of a Convex Function” [16].
Therefore, based on lemma 3.1.3, we are able to obtain a global optimal
solution for the FP problem with 0-1 binary variables by using MINLP solvers
able to handle pseudoconvex and pseudoconcave objective function such as the
branch and bound algorithm [17]. We now formulate the overall GMROI product
portfolio problem in the MILFP form.
3.2 Overall GMROI Model
The following formulation is a MILFP problem that maximizes the overall
GMROI of the product portfolio. As described in the previous chapter, GMROI
is a ratio of gross margin and average inventory investment. Therefore, we will be
maximizing the product portfolio that will give Company X the best income for
every inventory dollar spent. Since product rationalization requires a decision to
eliminate or to keep a product, we use binary decision variables for each product
where a “0” indicates the decision to eliminate the product and “1” indicates
to keep the product in the portfolio. In addition, each product is attributed
with several parameters for constraint and performance purposes. The following
formulation is a 0-1 fractional programming problem:
Index:Notation Meaning
i index for products
24
Parameters:Notation Meaning
mi Gross Margin in dollars for product ici Average Inventory Investment in dollars for product isi Total Units Sold (Last 52 weeks) for product igi Average Inventory Units (Last 52 weeks) for product iIC Available Investment Capitalb Inventory TurnoverN Desired product count in new product portfolio
Variables:Notation Meaning
xi Decision to invest in product i
Overall GMROI Model:
Max :
∑i(mi × xi)∑i(ci × xi)
(3.2.1)
s.t.∑i
ci × xi ≥ IC (3.2.2)
∑i(si × xi)∑i(gi × xi)
≥ b (3.2.3)∑i
xi ≤ N (3.2.4)
xi ∈ {0, 1} (3.2.5)
In the parameters table above, each product will have an attribute of the
gross margin, average inventory investment, units sold, and average inventory
units. The product’s attributes will allow the model to determine the optimal
mix of products to keep depending on management’s goals and objective. When
making product rationalization decisions, we want to make sure we are analyzing
products that are considered active and not waste time on products that are (1)
already in the process of being discontinued, and (2) new products that were
25
recently introduced. Therefore, the products included in the decision variables
are sold within the last 52 weeks.
The objective function (3.2.1) is maximizing the overall GMROI of the product
portfolio. In other words, we are looking for the best combination of products
that will provide the highest ratio by dividing the sum of mi (total gross margin)
by the sum of ci (total average inventory cost). The constraints of the model
are based on management’s goal in operating under a reduced investment capital
(3.2.2), achieving a higher or same level of inventory turnover (3.2.3), and the
desired number of products in the new product portfolio (3.2.4). Equation 3.2.5
is the constraint that restricts our decision variables (xi) to binary.
One thing to note in this formulation is the investment capital constraint
(3.2.2). Due to the structure of maximizing a ratio, if we let the investment
capital constraint to be a less than or equal, this causes an issue where the
model will simply maximize the overall GMROI metric by choosing products
with extremely high margin product and combining this selection with low margin
products towards the tail-end of the portfolio. By setting the capital constraint
to be greater than or equal, this allows us to analyze the portfolio’s GMROI as
we reduce investment capital at certain levels. The optimal solution will never
equal to this investment capital reduction, instead, the optimal solution will arrive
closely above the investment capital parameter, IC. We show this behavior in
the next chapter when comparing model solutions.
3.2.1 Linearized GMROI Model with Auxiliary Variables
Solving the GMROI model in its MILFP form becomes inefficient and does not
scale well depending on the size of the product portfolio. Since our model consists
of 1,120 different products, we can reformulate the overall GMROI model with
26
a linear objective function to solve the model efficiently. In order to linearize
the objective function, we use a global 0-1 fractional programming approach
developed by Wu [14] :
Theorem 3.2.1. A polynomial mixed 0-1 term z = xy, where x is a 0-1 variable,
and y is a continuous variable taking any positive value, can be represented by the
following linear inequalities:
(1) y - z ≤ K - Kx
(2) z ≤ y
(3) z ≤ Kx
(4) z ≥ 0
Where K is a large number greater than y.
Proof. (a) Suppose z = xy, K is a large number greater than y, then:
1. y − z = y − xy = y(1− x) ≤ K(1− x) = K −Kx,
2. z = xy ≤ y(∴ x = 0 or 1),
3. z = xy ≤ Kx,
4. z = xy ≥ 0
Conditions (1) to (4) are satisfied for x = 0 or 1.
(b) Suppose conditions (1) to (4) are true. If x = 0, then from conditions (3) and
(4), we have z = 0. If x = 1, then from conditions (1) and (2), we have z = y. It
is thus concluded that z = xy. If value of y is less than 1, then K = dye = 1.
Following Wu’s theorem, we can transform the fractional programming model
to a linearized formulation by creating the same auxiliary variables:
y =1∑
i(xi × ci)
27
y becomes the denominator of the GMROI ratio (or in this case, the Average
Inventory Cost), then the objective function becomes:
GMROI = mi × xi × y
Now we introduce the second auxiliary variable:
zi = xi × y
∴ GMROI = mi × zi.
We now have a linear objective function that is equivalent to optimizing the
overall GMROI of the product portfolio. The next step is to incorporate the
same conditions from Wu’s proof into constraints in the linearized optimization
model.
Index:Notation Meaning
i index for products
Parameters:Notation Meaning
mi Gross Margin in dollars for product ici Average Inventory Investment in dollars for product isi Total Units Sold (Last 52 weeks) for product igi Average Inventory Units (Last 52 weeks) for product iIC Available Investment Capitalb Inventory TurnoverK Arbitrary large number (1, in our case)N Desired product count in new portfolio
28
Variables:Notation Meaning
xi Decision to invest in product iy Dummy decision variable treated as 1
Average Investment Capital
zi Auxiliary variable
Linearized GMROI Model:
Max:∑i
mizi (3.2.6)
s.t.∑i
xici ≥ IC (3.2.7)
∑i
xisi − b∑i
xigi ≥ 0 (3.2.8)
∑i
xi ≤ N (3.2.9)
∑i
ciy = 1 (3.2.10)
zi ≤ Kxi (3.2.11)
Kxi + y − zi ≤ K (3.2.12)
zi ≤ y (3.2.13)
xi ∈ 0, 1 (3.2.14)
zi ≥ 0 (3.2.15)
y ≥ 0 (3.2.16)
The linearized problem has the same functional constraints as the previous
overall GMROI model (Section 3.1) where we want to operate under a new re-
duced investment capital while also reaching a desired inventory turnover. The
objective function (3.2.6) is equivalent to equation (3.2.1) due to the conditions
from Wu’s theorem which is represented in the dummy constraints of the model
29
(Equations 3.2.1–3.2.16). The addition of a new set of decision variables (zi)
does not add to any computing time. However, while this method allows for the
use of regular linear programming (LP) and mixed integer programming (MIP)
solvers, the binary variables in the model can become computationally complex
when dealing with thousands of variables.
3.2.2 Overall GMROI Model with Dinkelbach’s Algorithm
Dinkelbach developed an algorithm to solve fractional programming problems
with optimal solutions by solving multiple subproblems in MILP form [15]. The
algorithm has been shown to solve at most O(log(nM)) subproblems in the worst
case [6]. In addition, Dinkelbach’s algorithm has been proven that it has super-
linear convergence rate [17]. In this subsection, we show the steps of Dinkelbach’s
Algorithm and how to formulate the MINLP GMROI model to solve using this
algorithm.
Algorithm 3.2.1. Dinkelbach’s Algorithm
• Step 1: Set initial x ∈ S, such that λ = λ1 = N(x)/D(x) (can also set
λ1 = 0).
• Step 2: Solve the MILP F(λ) = max{N(x)−λD(x)} to obtain the optimal
x solution.
• Step 3: If objective value of problem F(λ) ≤ δ (optimality tolerance), stop,
we have obtained the optimal solution in x. Else, set λ = N(x)D(x)
and go to
Step 2.
Recall from section 3.1 that the Fractional Programming objective function
is formulated as:
α +∑
i nixiβ +
∑i dixi
30
To implement Dinkelbach’s algorithm, we need to reformulate the problem into a
linear objective function, thus allowing the algorithm to solve a sequence of MILP
subproblems as described in the algorithm. First, let us consider the numerator
linear function and the denominator linear function:
N(x) = α +∑i
nixi
D(x) = β +∑i
dixi
Reformulating FP’s linear objective function along with linear constraints:
Max: F (λ) = N(x)− λD(x)
s.t. D(x) > 0
x ∈ {0, 1}
We denote z(λ) as the optimum objective value of F (λ). Let x∗ be an optimal
solution of FP and let λ∗ = N(x∗)/D(x∗). Then the following is known [6]:
z(λ) > 0 if and only if λ < λ∗ ,
z(λ) = 0 if and only if λ = λ∗ ,
z(λ) < 0 if and only if λ > λ∗
We can see that by solving the z(λ) = 0, we will obtain the optimal solution
equivalent to solving the original FP problem in the ratio form of N(x)/D(x).
Therefore, we reach an optimal solution when:
F (λ∗) = max{N(x)−λ∗D(x)|x ∈ S} = 0, if and only if λ∗ = N(x∗)D(x∗)
= max{N(x)/D(x)|x ∈
S}, where S is the feasible region of F (λ).
Below is the formulation of the overall GMROI problem (section 3.2) using Dinkel-
bach’s Algorithm:
31
Index:Notation Meaning
i index for products
Parameters:Notation Meaning
mi Gross Margin in dollars for product ici Average Inventory Investment in dollars for product isi Total Units Sold (Last 52 weeks) of product igi Average Inventory Units (Last 52 weeks) of product iIC Investment Capitalb Inventory TurnoverN Desired product count in new product portfolioλ Intial parameter for arbitrary F(x) solutionδ Optimality tolerance (usually 0.01)
Variables:Notation Meaning
xi Decision to invest in product i
GMROI with Dinkelbach’s Algorithm:
Max: F (λ) =∑i
(mixi)− λ∑i
(cixi) (3.2.17)
s.t.∑i
xici ≥ IC (3.2.18)
∑i
(sixi)− b∑i
(gixi) ≥ 0 (3.2.19)
∑i
xi ≤ N (3.2.20)
xi ∈ {0, 1} (3.2.21)
Here we have two new parameters: λ and δ. λ is the overall GMROI of the
product portfolio since λ =∑
i(mixi)/∑
i(cixi). δ is the optimality tolerance for
the stopping rule when taking the difference between∑
i(mixi) and λ∑
i(cixi).
The optimality tolerance is determined by the user, for the GMROI problem, we
set δ = 0.01.
32
We set our initial λ = 0 to start the algorithm and solve the MILP, thus at
every iteration of Dinkelbach’s algorithm, λ will continue to update at each solved
iteration until λ is at a value that makes the objective value of F (λ) equal to 0.
The optimal solution of x from this λ is equivalent to the optimal solution to
the original FP model. Based on the optimal condition described above, Dinkel-
bach’s algorithm allows us to solve a sequence of MILP subproblems to obtain a
global optimal solution for the overall MINLP GMROI model. Although the al-
gorithm requires scripting, the code is simple (only requires IF and ELSE logical
statements) and using the algorithm allows us to move away from NLP solvers.
Dinkelbach’s algorithm has been shown to use less computing memory compared
to using MINLP solvers [17].
3.3 Individual GMROI Model
In section 3.2, we have shown one approach of maximizing the GMROI for
product rationalization with two different methods of solving the GMROI model.
The second approach is to take account of the individual GMROI ranking of
products. The rationale behind this approach is because maximizing the overall
GMROI of the portfolio also masks the sensitivity of the individual items in
the portfolio. By combining the summation of margin in the numerator (mixi)
and the summation of the average inventory cost in the denominator (cixi), the
relationship between a product’s margin dollars and average inventory cost is
segregated in the overall GMROI model. Therefore, the overall GMROI can easily
be maximized by taking in a few products that are highly profitable, allowing for
the combination of less profitable products.
Furthermore, due to the structure of the GMROI model (MILFP), the 0-1
global fractional programming problem will always require a MINLP solver or
33
an algorithm to reach an optimal solution. The following formulation is less
complex and looks into maximizing the margin dollars of the product portfolio
by the individual GMROI ranking of products.
Index:Notation Meaning
i index for products
Parameters:Notation Meaning
mi Gross Margin in dollars for product ici Average Inventory Investment in dollars for product isi Total Units Sold (Last 52 weeks) of product igi Average Inventory Units (Last 52 weeks) of product iIC Investment Capitalb Inventory TurnoverN Desired product count in new product portfolio
Variables:Notation Meaning
xi Decision to invest in product i
Individual GMROI model:
Max :∑i
(mi
ci)xi (3.3.1)
s.t.∑i
xici ≥ IC (3.3.2)
∑i
xisi − b∑i
xigi ≥ 0 (3.3.3)
∑i
xi ≤ N (3.3.4)
xi ∈ {0, 1} (3.3.5)
34
While the Individual GMROI model has a linear objective function, this re-
quires management or decision maker to generally know how many products to
eliminate from the portfolio. As indicated in the parameters table above, N is the
remaining product amount in the portfolio after elimination. If management has
no idea how many products to eliminate, the parameter N becomes a decision
variable in Equation 3.3.4.
3.4 Conclusion
The structure and convex properties of a Fractional Programming problem
was described in this chapter. Due to the implications of the lemma 3.1.1, this
allows us to obtain global optimal solutions when solving MILFP using MINLP
solvers. Two approaches of applying mathematical programming into product
rationalization using the GMROI performance measure were presented. The first
approach is maximizing the GMROI of the overall product portfolio, making the
objective function into a sum of ratios. Unfortunately, the combinatorial nature
of this MINLP model does not scale well when decision variables reaches into the
thousands. Thus we introduce two alternative methods of solving the maximum
GMROI product portfolio problem.
The first method reformulates the MINLP GMROI model into a linearized
objective function based on Wu’s theorem and introducing auxiliary variables
into the model. The second method to solving the overall GMROI model uses
Dinkelbach’s algorithm which solves multiple MILP subproblems to reach the
optimal solution. Although the Dinkelbach’s algorithm involves some coding, the
algorithm allows us to obtain a global optimal solution without the use of MINLP
solvers.
The second approach is maximizing the sum of individual GMROI of the
35
product portfolio. The model is a MILP that takes into account of the individual
GMROI and total gross margin dollar of each product in the product portfolio.
The individual GMROI model has a linear objective function and is less complex
compared to the MINLP GMROI problem. In addition, the individual GMROI
model avoids segregating the relationship between a product’s margin dollars and
average inventory cost. The overall GMROI model inherently causes the product
to lose the link between the margin dollars and average inventory cost due to
the fact that the objective function is a summation of margin over summation
of cost as opposed to sum of individual margin over individual cost. Therefore,
the overall GMROI can easily be maximized by taking in a few products that
are highly profitable, allowing for the combination of less profitable products.
We show this in the next chapter when we compare solutions from the overall
GMROI model and the individual GMROI model.
36
Chapter 4
Model Solutions and Analysis
Chapter 4 discusses the solutions obtained from the two primary GMROI
models: (1) Overall GMROI model and (2) Individual GMROI model. In the fol-
lowing sections, we provide a scenario example and compare the optimal solutions
from each model based on that same scenario. We then discuss the differences
between the overall GMROI and individual GMROI and show which model is
better in practical sense.
4.1 Scenario Example
Company X is seeking to improve their business performance by reducing their
inventory investment in one of their product portfolios. In order to do so, the
company hopes to identify and discontinue some of the underperforming products
within a single product portfolio. The product portfolio consists of 1120 different
products, where some products are the same type but have minor differences
such as flavor, color, region, retailer, etc. All products considered for elimination
in the portfolio are in their active status, sold within the last 52 weeks, and do
not include recently introduced products. During the last 52 weeks, 80.1 million
units of the products in the portfolio were sold, generating $72 million dollars
gross margin while requiring a $33 million dollars inventory investment at the
37
average inventory units level of 18 million units. In other words, the current
GMROI of the product portfolio is at 2.16 and the inventory turnover is at 4.51.
As mentioned in the individual GMROI model (Section 3.3), the desired num-
ber of products to eliminate is based on management’s goals. Management may
never know exactly how many products to eliminate or where to cut the tail of
the Pareto chart. If management does know the minimum or exact number of
products to keep in the new product portfolio, we will have a parameter input for
N , otherwise, N becomes a decision variable and the individual GMROI model
will also solve for the optimal number of products to eliminate in the product
portfolio.
For the purpose of comparing the two model solutions, we will assume man-
agement has some idea of how many products to eliminate; the model will cap
the new product count to be N = 672, which is 60% of the original product port-
folio size, 1120. In addition to reducing the portfolio size, management wants the
product portfolio to have a greater than or equal inventory turnover than before,
b = 4.51. We also want to reduce our inventory investment, we start solving
the model with a reduced capital of 10%, IC = .90 × 33 million and continue
reducing investment capital by 10% until we reach a 60% reduced capital.
4.2 Overall GMROI Model Solution
For the scenario example shown in this section, we use Dinkelbach’s algorithm
to obtain the optimal solution. For the initial algorithm parameters, we have
λ = 0, and δ = .01. Table 4.1 is a summary of the 6 different scenarios where
the available inventory capital is changed for each model solution. The optimal
solutions for which products to keep and eliminate can be found in Appendix A.
Increasing the overall product portfolio’s GMROI will require a loss of gross
38
Table 4.1: Overall GMROI Solutions Summary
margin dollars. At the same time, since the product portfolio is working with
a reduced inventory investment, the amount of capital saved can help alleviate
the margin dollar lost. As we eliminate the underperforming products from the
portfolio, both GMROI and inventory turnover increases. However, management
will need to decide at which point to stop reducing the inventory investment,
as shown in Table 4.1 and Figure 4.1. For example, comparing the differences
between scenario 3 and 4, Company X needs to decide whether an increase of
GMROI from 2.84 to 3.11 is worth the $4 million gross margin loss.
Figure 4.1 shows the improvement in GMROI and Inventory Turnover as
we reduce the available inventory investment capital. GMROI increases almost
linearly at each 10% reduction of the original investment capital, whereas the in-
ventory turnover increases also but not at the same rate for each 10% reduction,
showing a sharper increase after the 10% and 30% reduction. As the invest-
ment capital reduction increases further, the marginal improvement of inventory
turnover gradually decreases. The turnover constraint for this model (Equation
3.2.19) only requires the new product portfolio to have a greater than or equal
inventory turnover than the original product portfolio. Although the constraint
may be redundant in our scenario example since we expect inventory turnover to
39
Figure 4.1: GMROI and Inventory Turnover as inventory investment is reduced(Overall GMROI)
always increase as we reduce inventory investment and number of products in the
product portfolio. This is due to the fact that low inventory turnover products
are usually tied to underperforming products (in terms of gross margin dollars).
However, this can be a potential deciding factor for management as they take
inventory turnover into account. For example, management may have inventory
turnover targets of 6 or higher, therefore the inventory turnover constraint will
lead to choosing a combination of products that produce both high turnover and
margin dollar profit.
4.3 Individual GMROI Model Solution
The solutions presented in this section are from the individual GMROI model.
The model is an MILP problem with binary decision variables. However, the
parameter N can be a decision variable when management does not know the
exact amount to reduce and the problem will have an integer decision variable in
40
N along with the binary decision variables of products. Table 4.2 is a summary of
the solutions output from the individual GMROI model. The optimal solutions
for which products to eliminate and keep can be found in Appendix B.
Table 4.2: Individual GMROI Solutions Summary
Recall the objective function for the individual GMROI model (Equation
3.3.1). The model solves for the best combination of products that will maxi-
mize the sum of individual GMROI of the products in the portfolio. Since the
objective value given is the sum of individual GMROI ratios, we recalculate the
overall GMROI of the product portfolio to compare the solutions obtained from
the overall GMROI model. From Figure 4.2, the optimal solutions as we take
away investment capital are more consistent than the solutions seen in Figure
4.1.
As expected, GMROI and inventory turnover increases as inventory invest-
ment capital is reduced. Substantial improvements in both GMROI and inventory
turnover is evident when the initial inventory investment capital is reduced (Sce-
narios 1 through 4). However, the last two scenarios results in identical optimal
solutions. In other words, further reduction in the inventory investment amount
will not yield a better solution in terms of GMROI and inventory turnover unless
the number of products in the portfolio decreases. Management may even include
41
Figure 4.2: GMROI and Inventory Turnover as inventory investment is reduced(Individual GMROI)
the fourth scenario (40% reduction) as the same solution as the last two scenarios
due to the fact that the differences are .03 in GMROI, .02 in inventory turnover,
and .38 gross margin dollars.
4.4 Comparison of Model Results and Conclu-
sion
In terms of GMROI and inventory turnover, the summary of the results shown
in Table 4.2 is similar to the summary from Table 4.1. For example, in the first
three scenarios, both of the model’s optimal solution output in the new portfolio’s
GMROI and Inventory Turnover are extremely similar. The only major difference
is in scenario 2, where inventory turnover for overall GMROI is .09 higher than
individual GMROI’s inventory turnover. However, there are also several differ-
ences in the solution output. While the GMROI and Inventory Turnover metrics
may be similar, the gross margin dollar of the new product portfolio from the
individual GMROI’s model is more consistent than the overall GMROI model.
42
Since the individual GMROI’s objective function takes the GMROI performance
of each product into account, we see a more consistent decrease in gross margin
dollars of the portfolio as available investment capital is reduced.
Table 4.3 is a snippet of the decision variables from the two models for sce-
nario 3 (reduced capital of 30%), both of the model’s optimal solution eliminates
products from the top 10 gross margin products in the portfolio. However, com-
paring the GMROI metric from the two models (Table 4.1 and 4.2), the overall
GMROI model provides a better GMROI and gross margin than the individual
GMROI model from scenarios 1 to 3. Although the overall GMROI eliminates
the two worst performing products (in terms of GMROI) in Table 4.3, it also in-
cludes some of the lower GMROI products (Styl205 Clr004 and Sty173 Clr017).
The logic and validity of the optimal solutions from the overall GMROI model
depends on the scenario and how the constraints are formed in the mathematical
programming model.
Table 4.3: Optimal solutions for the top 10 products in Gross Margin dollars
The Individual GMROI model is a more conservative approach and places
emphasis on the individual GMROI of the products. We exhibit this in Table
4.1, where the last two scenarios (40% and 50% reduced capital) have a vast
difference in the gross margin dollars retained. Although the overall GMROI
43
model may be analytically optimal, some of the rationalization decisions do not
make business sense and result in lower total margin dollars when compared to
the individual GMROI model. Table 4.4 provides an example where the worst
gross margin products are kept in the overall GMROI solution, but are eliminated
in the individual GMROI model.
Table 4.4: Optimal solutions for the bottom 10 products in Gross Margin dollars
When maximizing the overall GMROI, the model does not eliminate the worst
performing products seen in the bottom ranking of the product portfolio. In fact,
the optimal solution is to drop some of the most profitable products (in terms of
margin dollars) from the portfolio. This is due to the fact that when optimizing
the overall GMROI of a product portfolio, the performance metric can easily be
maximized by choosing only a few products that give a high overall GMROI per-
formance. The model can simply include products that have the highest gross
margin and lowest inventory cost, allowing the combination to include the worst
performing products in margin dollars. Therefore, maximizing the overall GM-
ROI of the product portfolio will mask the sensitivity and performance of the
individual products that are considered underperforming.
44
Depending on the situation and management’s objective, the overall GM-
ROI model will require the decision maker to check the optimal solution of each
product to see if it makes business sense (as evident in Table 4.4). The overall
GMROI model is essentially mixing a high margin dollar product with a low cost
dollar product, thus allowing for a “high” GMROI portfolio. For example, in Ta-
ble 4.4, the overall GMROI model cannot differentiate between Sty356 Clr004’s
margin dollars and Sty505 Clr050’s inventory cost. In fact, the overall GMROI
model may possibly be mixing and matching Sty356 Clr004’s margin dollars with
Sty505 Clr050’s inventory cost as a single product, thus we have an extremely
high GMROI of 3.64 (Table 4.1).
As mentioned in the previous chapter, the overall GMROI model inherently
causes the product to lose the link between the margin dollars and average inven-
tory cost due to the fact that the objective function is a summation of margin over
summation of cost as opposed to the sum of individual margin over individual
cost (individual GMROI model). Therefore, in situations where the constraints
allow for very small changes in cost reduction, the overall GMROI model will
provide a better solution (in terms of GMROI, margin dollars, and turnover).
However, having large inventory investment reductions in the constraint will give
a false sense of high GMROI and impractical product selections in the optimal
solution.
When maximizing the GMROI ratio, we need to be careful of the inventory
investment capital constraint (Equation 3.2.2). As mentioned in Chapter 3, the
behavior of the inventory capital constraint (Equation 3.2.2) will inherently affect
the optimal solution given from the output depending if the constraint is modeled
to be ≤ or ≥. Table 4.5 shows what happens when we solve the overall GMROI
model with a less than or equal investment capital constraint. In scenario 7,
45
GMROI is at 4 with a less than or equal to 10% reduced capital, however, this
is unrealistic since we are only spending 7.6 million dollars and our gross margin
dollar for the portfolio is now less than half of the original baseline. This is due
to the fact that when maximizing the GMROI ratio, the sum of product costs
(cimi) is non-binding and will always be reduced at the lowest level in order to
maximize the GMROI ratio. Therefore, you will see unreasonable products being
selected, resulting in high GMROI metric, but an extremely low margin dollar
and low investment capital product portfolio.
Table 4.5: Overall GMROI model with ≤ constraint
46
Chapter 5
Discussion and Conclusion
In this thesis, we explored the feasibility of using GMROI as a performance metric
in product rationalization decisions. We developed two different approaches to
achieve a better product portfolio: (1) Overall GMROI model and (2) Individual
GMROI model. In addition, we also showed two mathematical methods to solve
the Overall GMROI model: (1) linearized GMROI with auxiliary variables and
(2) Dinkelbach’s Algorithm. We then compared the solutions under different sce-
narios between the two models and found that maximizing the overall GMROI
of the product portfolio has its own limits. For example, under the first 3 scenar-
ios, the overall GMROI’s optimal solutions can be considered logical and made
business sense. However, the flaw of GMROI will always remain. GMROI does
not truly differentiate between high margin/lower turnover and low margin/high
turnover products.
As seen in Table 4.4, when we reduced the available inventory investment
down to 60%, the overall GMROI model maximizes the GMROI metric by taking
in a few high margin products but at the same time keeping the worst gross
margin products in the product portfolio. The overall GMROI model may work
well under certain scenarios and conditions set by the constraints. Ultimately,
the individual GMROI model provides a more consistent optimal solution under
47
different scenarios of reduced inventory investment capital.
5.1 Redistribution and Sales Margin Model
As mentioned earlier, one of the mathematical programming approaches pro-
posed was to formulate a two-stage stochastic model that looks into both the cur-
rent impact and the aftermath of eliminating underperforming products. While
there are multiple ways of optimizing the product rationalization problem, we also
need to be careful about the correlation of product demands. The research done
in this thesis does not take into account the correlation factor between products.
For example, consumers who buy item A also tend to buy item B. If the decision
is to eliminate item A, we must consider the possible sales impact it can have on
item B. If two items go hand in hand (complementary), we need to make sure
that we are eliminating both rather than just one.
Furthermore, if the company chooses to eliminate item A, which shares similar
product characteristics with item C and item D, then perhaps the consumer would
see item C or item D as a substitute and make a purchase. Thus we would have
a redistribution of sales from an eliminated product, back into the remaining
product within the product portfolio. We give a general model in the following
formulation:
Index:Notation Meaningi, j index for products
48
Parameters:Notation Meaning
aij Margin factor increase for product j from dropping product i, i 6= jeij Units sold factor increase for product j from dropping product i, i 6= jmj Gross Margin in dollars for product jcj Average Inventory Investment in dollars for product jsj Expected Units Sold (Last 52 weeks) of product jgj Average Inventory (Units) of product jIC Investment Capitalb Inventory TurnoverN Desired product count in new product portfolio
Variables:Notation Meaning
xj Decision to invest in product j
Redistribution of Sales Margin model:
Max :∑j
mjxj +∑ij
aij(1− xi)mj (5.1.1)
s.t.∑j
xjcj ≤ IC (5.1.2)
(∑j
xjsj +∑ij
eij(1− xi)sj
)− b∑j
xjgj ≥ 0 (5.1.3)
∑j
xj ≥ N (5.1.4)
xj, xj ∈ {0, 1} (5.1.5)
The objective function (Equation 5.1.1) includes the current gross margin
(mj) and the margin factor increase (aij) if a correlated product was selected to
be pruned. This formulation is more realistic since it includes both the current
and future impacts of eliminating products from the portfolio. The index sets of i
and j are both the same amount based on the number of products in the portfolio,
49
and the correlation factor aij represents how much margin sales is redistributed
back into product j if product i is dropped and considered a substitute for product
j. A product’s correlation factor to itself will be 0, otherwise this will create an
error where the kept product’s gross margin sale is doubled.
5.2 Limitations and Extensions of Future Re-
search
There are multiple approaches to solving the product rationalization prob-
lem with mathematical programming. Multi-criteria optimization could be one
approach since product rationalization will affect the product portfolio’s gross
margin dollars and inventory turnover. The scenario examples shown in this the-
sis assumes that management knows the exact amount of products to drop from
the portfolio. However, this typically should not be the case and we must allow
for the solver to find the optimal amount of products to prune.
While most of the emphasis was placed on saving inventory investment, we
could easily switch to placing emphasis on the inventory turnover. If management
believes that they can increase their sales margin through other means, then there
will be more incentive to prune slow moving products. In addition, management
may already have a given investment capital allowance and the problem will shift
to which products to keep, or perhaps keep all the products but not service all
sales or a combination of both. The optimization model will incorporate both
binary and continuous decision variables, where binary decision represents which
products to keep and eliminate, and the continuous decision variables represents
how many of the kept products are serviced. Management will then have a fill
rate objective for certain products that are kept. If management does not know
their optimal fill rate, then the inventory fill rate can also be considered as a
50
continuous decision variable. Therefore, the model will have both binary and
continuous decision variables. This all depends on the goals and objectives the
management is trying to achieve.
The redistribution of sales margin model maximizes the margin dollars of
retained products in the portfolio. However, in some cases, the company may
also face customer (retailer) constraints where certain products are correlated
differently. For example, in order to sell product A to a customer, we must also
offer product B. Therefore, the model must also include constraints where if a
product is kept, it must also keep another product due to the customer’s demand.
Otherwise, if the solution is to eliminate product B because of low margin, the
company faces the consequence of also losing margin dollars from product A (high
margin) because of the customer demand.
The largest challenge in applying mathematical programming is the need for
accurate and high quality data for the parameters. The conditions of the prod-
uct portfolio must also be under the optimal inventory policy of the company.
Otherwise, the optimal solutions from the optimization models will not be ac-
curate and eliminating the suggested products from the portfolio will have dire
consequences. Therefore, product rationalization requires management to clearly
define the goals they want to achieve and strictly place a threshold on products
to distinguish between good and bad products.
51
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54
Appendices
55
.1 Appendix A: Overall GMROI Model Opti-
mal Solution
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Product 1 2 3 4 5 6 Sty010_Clr036 1 1 1 1 1 1 Sty082_Clr017 0 0 0 0 1 1
Sty003_Clr003 0 1 1 1 1 1 Sty010_Clr037 1 1 1 1 1 1 Sty084_Clr050 0 0 0 0 0 1
Sty003_Clr004 1 1 1 1 1 1 Sty011_Clr003 0 0 0 0 0 0 Sty102_Clr050 0 0 0 0 0 0
Sty003_Clr005 0 0 0 0 0 1 Sty011_Clr004 0 0 0 0 0 0 Sty155_Clr050 0 0 0 0 1 1
Sty003_Clr006 1 1 1 1 1 1 Sty011_Clr006 0 1 1 1 1 1 Sty158_Clr050 0 0 0 0 1 1
Sty003_Clr007 1 1 1 1 1 1 Sty011_Clr007 1 1 1 0 0 0 Sty159_Clr004 0 0 0 0 0 0
Sty003_Clr008 1 1 1 1 1 1 Sty011_Clr008 0 0 0 0 0 0 Sty159_Clr008 0 0 0 0 0 0
Sty003_Clr009 1 1 1 1 1 1 Sty011_Clr009 0 0 0 0 0 0 Sty159_Clr017 0 0 0 0 0 1
Sty003_Clr010 0 1 1 1 1 1 Sty011_Clr010 0 0 0 1 1 1 Sty160_Clr004 0 0 0 0 0 0
Sty003_Clr011 1 1 1 1 1 1 Sty011_Clr011 1 1 1 1 1 1 Sty160_Clr008 0 0 0 0 0 0
Sty003_Clr012 0 1 1 1 1 1 Sty011_Clr012 0 0 0 0 0 0 Sty160_Clr017 1 1 1 1 1 1
Sty003_Clr013 1 1 1 1 1 1 Sty011_Clr014 1 1 1 0 0 0 Sty161_Clr004 0 1 1 1 1 1
Sty003_Clr014 1 1 1 1 1 1 Sty011_Clr015 1 1 1 1 0 0 Sty161_Clr008 0 0 0 0 0 1
Sty003_Clr015 1 1 1 1 1 1 Sty011_Clr017 1 1 1 0 0 0 Sty161_Clr017 0 0 0 0 0 0
Sty003_Clr017 1 1 1 1 1 1 Sty011_Clr030 0 0 0 0 0 0 Sty166_Clr004 1 1 1 1 1 1
Sty003_Clr018 1 1 1 1 1 1 Sty011_Clr032 0 0 0 0 0 0 Sty166_Clr006 0 1 1 1 0 0
Sty009_Clr003 1 1 1 1 1 1 Sty011_Clr034 0 0 0 0 0 0 Sty166_Clr007 1 1 1 1 1 0
Sty009_Clr004 1 1 1 1 1 1 Sty011_Clr036 1 1 1 1 0 0 Sty166_Clr009 0 0 0 0 0 0
Sty009_Clr006 1 1 1 1 1 1 Sty011_Clr037 0 0 0 0 0 0 Sty166_Clr011 1 1 1 1 1 1
Sty009_Clr007 1 1 1 1 1 1 Sty012_Clr003 1 1 1 1 1 1 Sty166_Clr014 1 1 1 1 1 1
Sty009_Clr008 1 1 1 1 1 1 Sty012_Clr004 1 1 1 1 1 1 Sty166_Clr015 1 1 1 1 1 0
Sty009_Clr009 1 1 1 1 1 1 Sty012_Clr006 1 1 1 1 1 1 Sty166_Clr017 1 1 1 1 1 0
Sty009_Clr010 1 1 1 1 1 1 Sty012_Clr007 1 1 1 1 1 1 Sty166_Clr032 0 0 0 0 0 0
Sty009_Clr011 1 1 1 1 1 1 Sty012_Clr008 1 1 1 1 1 1 Sty166_Clr036 1 1 1 0 0 0
Sty009_Clr014 1 1 1 1 1 1 Sty012_Clr009 1 1 1 1 1 1 Sty166_Clr041 1 0 0 0 0 0
Sty009_Clr015 1 1 1 1 1 1 Sty012_Clr010 1 1 1 1 1 1 Sty166_Clr053 1 1 1 1 1 1
Sty009_Clr017 1 1 1 1 1 1 Sty012_Clr011 1 1 1 1 1 1 Sty166_Clr054 1 1 1 1 0 0
Sty009_Clr030 0 0 0 1 1 1 Sty012_Clr014 1 1 1 1 1 1 Sty166_Clr055 1 1 1 1 1 0
Sty009_Clr032 0 0 1 1 1 1 Sty012_Clr015 1 1 1 1 1 1 Sty166_Clr056 1 1 1 1 0 0
Sty010_Clr003 1 1 1 1 1 1 Sty012_Clr017 1 1 1 1 1 1 Sty167_Clr004 0 0 0 0 0 0
Sty010_Clr004 1 1 1 1 1 1 Sty012_Clr018 1 1 1 1 1 1 Sty167_Clr007 0 0 0 0 0 0
Sty010_Clr006 1 1 1 1 1 1 Sty012_Clr030 1 1 1 1 1 1 Sty167_Clr011 0 0 0 0 0 0
Sty010_Clr007 1 1 1 1 1 1 Sty012_Clr036 0 0 0 1 1 1 Sty167_Clr014 0 0 0 0 0 0
Sty010_Clr008 1 1 1 1 1 1 Sty012_Clr038 0 1 1 1 1 1 Sty167_Clr015 0 0 0 0 0 0
Sty010_Clr009 1 1 1 1 1 1 Sty012_Clr040 0 0 0 0 0 0 Sty167_Clr017 1 0 0 0 0 0
Sty010_Clr010 1 1 1 1 1 1 Sty012_Clr041 0 0 1 1 1 1 Sty167_Clr053 0 0 0 0 0 0
Sty010_Clr011 1 1 1 1 1 1 Sty012_Clr042 0 1 1 1 1 1 Sty167_Clr054 0 0 0 0 0 0
Sty010_Clr012 0 0 0 1 1 1 Sty012_Clr044 0 0 0 0 0 0 Sty167_Clr055 1 0 0 0 0 0
Sty010_Clr014 1 1 1 1 1 1 Sty012_Clr045 0 0 0 0 0 0 Sty167_Clr056 0 0 0 0 0 0
Sty010_Clr015 1 1 1 1 1 1 Sty012_Clr046 0 1 1 1 1 1 Sty168_Clr004 0 0 0 0 0 1
Sty010_Clr017 1 1 1 1 1 1 Sty012_Clr047 0 1 1 1 1 1 Sty168_Clr006 0 0 0 0 0 1
Sty010_Clr018 1 1 1 1 1 1 Sty012_Clr048 0 0 0 0 0 1 Sty168_Clr007 0 0 0 0 0 0
Sty010_Clr030 1 1 1 1 1 1 Sty012_Clr049 0 0 0 1 1 1 Sty168_Clr011 0 0 0 0 0 1
Sty010_Clr032 1 1 1 1 1 1 Sty024_Clr050 1 1 0 0 0 0 Sty168_Clr014 0 0 0 0 0 1
Sty010_Clr034 1 1 1 1 1 1 Sty028_Clr050 0 0 0 0 0 1 Sty168_Clr015 0 0 0 0 0 0
Sty010_Clr035 1 1 1 1 1 1 Sty055_Clr050 0 0 0 0 1 1 Sty168_Clr017 0 0 0 0 0 0
Solution (xi) for each scenario
56
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Sty168_Clr032 0 0 0 0 0 1 Sty171_Clr015 0 0 0 0 0 0 Sty178_Clr015 1 0 0 0 0 0
Sty168_Clr053 0 0 0 0 0 1 Sty171_Clr017 0 0 0 0 0 0 Sty178_Clr017 1 0 0 0 0 0
Sty168_Clr054 0 0 0 0 0 0 Sty173_Clr014 1 1 1 1 1 0 Sty179_Clr030 1 1 1 1 1 0
Sty168_Clr055 0 0 0 0 0 1 Sty173_Clr017 1 1 1 0 0 0 Sty179_Clr032 1 1 1 1 1 1
Sty168_Clr056 0 0 0 0 0 1 Sty173_Clr018 1 1 1 1 1 1 Sty179_Clr080 1 1 1 1 1 1
Sty169_Clr004 1 1 1 1 0 0 Sty173_Clr058 1 1 1 1 1 1 Sty180_Clr017 1 1 1 1 0 0
Sty169_Clr007 0 1 1 0 0 0 Sty173_Clr059 1 1 1 1 1 1 Sty180_Clr018 1 1 1 1 1 1
Sty169_Clr011 0 0 1 1 0 0 Sty173_Clr060 1 1 1 1 1 1 Sty180_Clr038 1 1 1 1 1 1
Sty169_Clr017 1 1 1 1 0 0 Sty174_Clr003 1 1 1 1 1 1 Sty180_Clr045 1 0 0 0 0 0
Sty169_Clr053 1 1 1 1 1 1 Sty174_Clr007 1 1 1 1 1 1 Sty180_Clr046 1 1 1 1 1 1
Sty170_Clr003 1 1 1 1 0 0 Sty174_Clr012 1 1 1 1 1 0 Sty180_Clr053 1 1 1 1 1 1
Sty170_Clr004 1 1 1 1 0 0 Sty174_Clr034 1 1 1 1 1 1 Sty180_Clr058 1 1 1 1 1 1
Sty170_Clr006 1 0 0 0 0 0 Sty174_Clr037 1 1 1 1 1 1 Sty180_Clr059 1 1 1 1 1 1
Sty170_Clr007 1 1 1 1 1 1 Sty174_Clr047 1 1 1 1 1 1 Sty180_Clr061 1 1 1 1 1 1
Sty170_Clr008 1 0 0 0 0 0 Sty174_Clr048 1 1 1 1 1 1 Sty180_Clr064 0 0 0 0 0 0
Sty170_Clr009 1 0 0 0 0 0 Sty174_Clr049 1 1 1 1 1 1 Sty180_Clr076 1 1 1 1 1 1
Sty170_Clr010 1 1 1 0 0 0 Sty174_Clr063 1 1 1 1 1 1 Sty180_Clr081 1 1 1 1 0 0
Sty170_Clr011 1 1 1 1 0 0 Sty175_Clr004 1 1 1 1 1 1 Sty180_Clr082 1 1 1 1 1 1
Sty170_Clr012 1 1 1 1 1 0 Sty175_Clr006 1 1 1 1 1 1 Sty180_Clr088 1 1 1 1 1 1
Sty170_Clr014 1 1 1 1 0 0 Sty175_Clr008 1 1 1 1 1 1 Sty181_Clr003 1 1 1 1 1 1
Sty170_Clr015 1 1 1 1 0 0 Sty175_Clr009 1 1 1 1 1 1 Sty181_Clr005 1 1 1 1 1 1
Sty170_Clr017 1 0 0 0 0 0 Sty175_Clr010 1 1 1 1 0 0 Sty181_Clr007 1 1 1 1 1 1
Sty170_Clr018 1 1 1 1 1 1 Sty175_Clr011 1 1 1 1 1 1 Sty181_Clr012 1 1 1 1 1 1
Sty170_Clr032 0 0 0 0 0 0 Sty175_Clr015 1 1 1 1 1 0 Sty181_Clr034 1 1 1 1 1 1
Sty170_Clr034 1 1 1 1 1 1 Sty175_Clr035 1 1 1 1 1 0 Sty181_Clr037 1 1 1 1 1 1
Sty170_Clr035 1 1 1 1 1 1 Sty175_Clr036 1 1 1 1 1 0 Sty181_Clr040 1 1 1 1 1 1
Sty170_Clr036 1 1 1 1 1 1 Sty175_Clr041 1 1 1 1 1 1 Sty181_Clr044 1 1 1 0 0 0
Sty170_Clr037 1 1 1 0 0 0 Sty175_Clr042 1 1 1 1 1 1 Sty181_Clr047 1 1 1 1 1 1
Sty170_Clr041 1 1 1 1 1 1 Sty177_Clr003 1 1 1 1 1 1 Sty181_Clr048 1 1 1 1 1 1
Sty170_Clr046 1 1 1 0 0 0 Sty177_Clr004 1 1 1 1 1 1 Sty181_Clr049 1 1 1 1 1 1
Sty170_Clr057 0 0 0 0 0 0 Sty177_Clr006 1 1 1 0 0 0 Sty181_Clr055 1 1 1 1 1 1
Sty170_Clr058 1 1 1 1 1 0 Sty177_Clr007 1 1 1 1 1 1 Sty181_Clr062 1 1 1 1 1 1
Sty170_Clr059 1 1 0 0 0 0 Sty177_Clr008 1 1 1 1 1 1 Sty181_Clr063 1 1 1 1 1 1
Sty170_Clr060 1 1 1 1 0 0 Sty177_Clr009 1 1 0 0 0 0 Sty181_Clr075 1 1 1 1 1 1
Sty170_Clr061 1 1 1 0 0 0 Sty177_Clr011 1 1 1 1 1 1 Sty182_Clr004 1 1 1 1 1 1
Sty170_Clr062 1 1 1 1 0 0 Sty177_Clr014 1 1 1 1 0 0 Sty182_Clr006 1 1 1 1 1 1
Sty170_Clr063 1 1 1 1 1 1 Sty177_Clr015 1 1 1 0 0 0 Sty182_Clr008 1 1 1 1 1 1
Sty171_Clr003 0 0 0 0 0 0 Sty177_Clr017 1 1 1 1 0 0 Sty182_Clr009 1 1 1 1 1 1
Sty171_Clr004 0 0 0 0 0 0 Sty178_Clr003 1 0 0 0 0 0 Sty182_Clr010 1 1 1 1 1 1
Sty171_Clr006 0 0 0 0 0 0 Sty178_Clr004 1 1 0 0 0 0 Sty182_Clr011 1 1 1 1 1 1
Sty171_Clr007 0 0 0 0 0 0 Sty178_Clr006 1 0 0 0 0 0 Sty182_Clr013 1 1 1 1 1 1
Sty171_Clr008 0 0 0 0 0 0 Sty178_Clr007 1 0 0 0 0 0 Sty182_Clr014 1 1 1 1 1 1
Sty171_Clr009 0 0 0 0 0 0 Sty178_Clr008 1 1 1 1 0 0 Sty182_Clr015 1 1 1 1 1 1
Sty171_Clr011 0 0 0 0 0 0 Sty178_Clr009 0 0 0 0 0 0 Sty182_Clr032 1 1 1 1 1 1
Sty171_Clr012 0 0 0 0 0 0 Sty178_Clr011 1 1 0 0 0 0 Sty182_Clr035 1 1 1 1 1 0
Sty171_Clr014 0 0 0 0 0 0 Sty178_Clr014 1 0 0 0 0 0 Sty182_Clr036 1 1 1 1 1 1
57
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Sty182_Clr041 1 1 1 1 1 1 Sty189_Clr063 1 1 1 1 1 1 Sty198_Clr037 1 1 1 1 1 1
Sty182_Clr042 1 1 1 1 1 1 Sty190_Clr003 1 1 1 1 1 1 Sty198_Clr040 1 1 1 1 1 0
Sty182_Clr043 1 1 1 1 1 1 Sty190_Clr007 1 1 1 1 1 1 Sty198_Clr044 1 1 1 0 0 0
Sty182_Clr060 1 1 1 1 1 1 Sty190_Clr034 1 1 1 1 1 1 Sty198_Clr048 1 1 1 1 1 1
Sty182_Clr073 1 1 1 1 1 1 Sty190_Clr044 1 1 1 1 1 1 Sty199_Clr004 1 1 1 1 1 0
Sty183_Clr007 1 1 1 1 1 1 Sty191_Clr004 1 1 1 1 1 1 Sty199_Clr006 1 1 1 1 1 0
Sty183_Clr009 1 1 1 1 1 1 Sty191_Clr006 1 1 1 1 1 1 Sty199_Clr008 1 1 1 1 1 1
Sty183_Clr012 1 1 1 1 1 1 Sty191_Clr008 1 1 1 1 1 1 Sty199_Clr009 1 1 1 1 1 1
Sty183_Clr017 1 1 1 1 1 1 Sty191_Clr010 1 1 1 1 1 1 Sty199_Clr010 1 1 1 1 0 0
Sty183_Clr018 1 1 1 1 1 1 Sty191_Clr011 1 1 1 1 1 1 Sty199_Clr011 1 1 1 1 1 1
Sty183_Clr037 1 1 1 1 1 1 Sty191_Clr014 1 1 1 1 1 1 Sty199_Clr015 1 1 1 1 1 0
Sty183_Clr045 0 0 0 0 0 0 Sty191_Clr015 1 1 1 1 1 1 Sty199_Clr035 1 1 1 0 0 0
Sty183_Clr046 0 0 0 0 0 0 Sty191_Clr035 1 1 1 1 1 1 Sty199_Clr036 1 1 1 1 1 1
Sty183_Clr058 1 1 1 1 1 1 Sty191_Clr041 1 1 1 1 1 1 Sty199_Clr041 1 1 1 1 1 1
Sty183_Clr059 1 1 1 1 1 1 Sty192_Clr030 1 1 1 1 1 1 Sty199_Clr042 1 1 1 1 1 1
Sty183_Clr060 1 1 1 1 1 0 Sty197_Clr005 1 1 1 1 1 1 Sty201_Clr032 1 1 1 1 1 1
Sty183_Clr063 1 1 1 1 1 1 Sty197_Clr012 1 1 1 1 1 1 Sty203_Clr009 1 1 1 1 0 0
Sty184_Clr003 1 1 1 1 1 1 Sty197_Clr013 1 1 1 1 1 1 Sty203_Clr012 1 1 1 1 1 0
Sty184_Clr034 1 1 1 1 1 1 Sty197_Clr014 1 1 1 1 0 0 Sty203_Clr014 1 1 1 0 0 0
Sty184_Clr044 1 1 1 1 1 1 Sty197_Clr017 1 1 0 0 0 0 Sty203_Clr017 1 1 0 0 0 0
Sty184_Clr048 1 1 1 1 1 1 Sty197_Clr018 1 1 1 1 1 1 Sty203_Clr058 1 1 1 1 0 0
Sty184_Clr049 1 1 1 1 1 1 Sty197_Clr030 1 1 1 1 1 0 Sty203_Clr059 1 1 1 0 0 0
Sty185_Clr004 1 1 1 1 1 1 Sty197_Clr038 1 1 1 1 1 0 Sty203_Clr060 1 1 1 0 0 0
Sty185_Clr006 1 1 1 1 1 1 Sty197_Clr046 1 1 1 1 1 1 Sty204_Clr003 1 1 1 1 1 0
Sty185_Clr008 1 1 1 1 1 1 Sty197_Clr047 1 1 1 1 1 1 Sty204_Clr007 1 1 1 1 0 0
Sty185_Clr010 1 1 1 1 1 1 Sty197_Clr049 1 1 1 1 1 1 Sty204_Clr034 1 1 1 1 1 0
Sty185_Clr011 1 1 1 1 1 1 Sty197_Clr053 1 1 1 1 1 1 Sty204_Clr037 1 1 1 1 0 0
Sty185_Clr014 1 1 1 1 1 1 Sty197_Clr057 1 1 1 1 1 1 Sty204_Clr063 1 1 1 1 0 0
Sty185_Clr015 1 1 1 1 1 1 Sty197_Clr058 1 1 1 1 1 0 Sty205_Clr004 1 1 1 0 0 0
Sty185_Clr035 1 1 1 1 1 1 Sty197_Clr059 1 1 1 1 0 0 Sty205_Clr006 1 1 1 1 0 0
Sty185_Clr036 1 1 1 1 1 1 Sty197_Clr060 1 1 1 1 1 0 Sty205_Clr008 1 1 1 1 0 0
Sty185_Clr041 0 1 1 1 1 1 Sty197_Clr061 1 1 1 1 1 1 Sty205_Clr010 1 0 0 0 0 0
Sty185_Clr042 1 1 1 1 1 1 Sty197_Clr063 1 1 1 1 1 1 Sty205_Clr011 1 1 1 1 0 0
Sty187_Clr030 1 1 1 1 0 0 Sty197_Clr076 1 1 1 1 1 1 Sty205_Clr015 1 1 1 0 0 0
Sty188_Clr030 1 1 1 1 1 1 Sty197_Clr080 1 1 1 1 1 1 Sty205_Clr035 1 1 0 0 0 0
Sty188_Clr080 1 1 1 1 1 1 Sty197_Clr081 1 1 1 1 1 0 Sty205_Clr036 1 0 0 0 0 0
Sty189_Clr009 1 1 1 1 1 1 Sty197_Clr088 1 1 1 1 1 1 Sty205_Clr041 1 1 1 0 0 0
Sty189_Clr012 1 1 1 1 1 1 Sty197_Clr089 1 0 0 0 0 0 Sty206_Clr007 0 1 1 1 1 1
Sty189_Clr017 1 1 1 1 1 1 Sty197_Clr091 1 1 1 1 0 0 Sty206_Clr008 1 1 1 1 1 0
Sty189_Clr036 1 1 1 1 1 1 Sty197_Clr092 1 1 0 0 0 0 Sty206_Clr009 0 0 0 1 1 1
Sty189_Clr037 1 1 1 1 1 1 Sty197_Clr093 1 1 1 1 0 0 Sty206_Clr014 1 1 1 1 0 0
Sty189_Clr042 1 1 1 1 1 1 Sty197_Clr095 1 1 1 1 1 1 Sty206_Clr017 1 1 0 0 0 0
Sty189_Clr045 0 0 0 0 0 0 Sty197_Clr096 0 0 0 0 0 1 Sty207_Clr003 1 1 1 1 1 1
Sty189_Clr058 1 1 1 1 1 1 Sty198_Clr003 1 1 1 1 1 1 Sty208_Clr004 1 1 1 1 0 0
Sty189_Clr059 1 1 1 1 1 1 Sty198_Clr007 1 1 1 1 1 1 Sty208_Clr006 1 1 1 1 1 1
Sty189_Clr060 1 1 1 1 1 1 Sty198_Clr034 1 1 1 1 1 1 Sty208_Clr010 0 0 0 0 0 0
58
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Sty208_Clr011 1 1 1 1 0 0 Sty223_Clr008 1 1 1 1 1 1 Sty225_Clr093 0 0 0 0 0 0
Sty208_Clr015 1 1 1 1 0 0 Sty223_Clr010 0 1 1 1 1 1 Sty225_Clr095 0 0 0 1 1 1
Sty209_Clr030 1 0 0 0 0 0 Sty223_Clr011 1 1 1 1 1 1 Sty227_Clr007 1 1 1 1 1 1
Sty216_Clr014 1 1 1 1 1 1 Sty223_Clr014 1 1 1 1 1 1 Sty227_Clr009 0 0 0 0 0 1
Sty216_Clr017 1 1 1 1 0 0 Sty223_Clr015 1 1 1 1 1 1 Sty227_Clr014 1 1 1 1 1 0
Sty216_Clr018 1 1 1 1 1 1 Sty223_Clr035 0 1 1 1 1 1 Sty227_Clr017 1 0 0 0 0 0
Sty216_Clr058 1 1 1 1 1 1 Sty223_Clr036 0 1 1 1 1 1 Sty228_Clr003 1 1 1 1 1 1
Sty216_Clr059 0 1 1 1 1 1 Sty223_Clr041 0 1 1 1 1 1 Sty228_Clr012 0 1 1 1 1 1
Sty216_Clr060 0 1 1 1 1 1 Sty224_Clr080 1 1 1 1 1 1 Sty228_Clr037 0 1 1 1 1 1
Sty217_Clr003 1 1 1 1 1 1 Sty225_Clr003 1 1 1 1 1 1 Sty228_Clr063 1 1 1 1 1 1
Sty217_Clr007 1 1 1 1 1 1 Sty225_Clr004 1 1 1 1 1 1 Sty229_Clr004 1 1 1 1 1 1
Sty217_Clr012 1 1 1 1 1 1 Sty225_Clr006 0 1 1 1 1 1 Sty229_Clr006 0 0 0 0 0 0
Sty217_Clr034 0 1 1 1 1 1 Sty225_Clr007 1 1 1 1 1 1 Sty229_Clr008 1 0 0 0 0 0
Sty217_Clr037 1 1 1 1 1 1 Sty225_Clr008 1 1 1 1 1 1 Sty229_Clr010 0 0 0 0 0 1
Sty217_Clr047 0 1 1 1 1 1 Sty225_Clr009 0 0 1 1 1 1 Sty229_Clr011 1 1 1 1 1 1
Sty217_Clr048 0 0 1 1 1 1 Sty225_Clr010 1 1 1 1 0 0 Sty229_Clr015 1 1 1 1 0 0
Sty217_Clr049 0 0 1 1 1 1 Sty225_Clr011 1 1 1 1 1 1 Sty229_Clr035 1 1 1 0 0 0
Sty217_Clr063 1 1 1 1 1 1 Sty225_Clr012 1 1 1 1 1 1 Sty229_Clr036 0 0 0 0 0 1
Sty218_Clr004 1 1 1 1 1 1 Sty225_Clr013 0 1 1 1 1 1 Sty235_Clr003 0 1 1 1 1 1
Sty218_Clr006 1 1 1 1 1 1 Sty225_Clr014 1 1 1 1 1 1 Sty235_Clr004 1 1 1 1 1 1
Sty218_Clr008 1 1 1 1 1 1 Sty225_Clr015 1 1 1 1 1 1 Sty235_Clr006 1 1 1 1 1 1
Sty218_Clr009 1 1 1 1 1 1 Sty225_Clr017 1 1 1 1 0 0 Sty235_Clr007 0 1 1 1 1 1
Sty218_Clr010 1 1 1 1 1 1 Sty225_Clr018 1 1 1 1 1 1 Sty235_Clr008 1 1 1 1 1 1
Sty218_Clr011 1 1 1 1 1 1 Sty225_Clr030 0 0 0 0 0 0 Sty235_Clr009 1 1 1 1 1 1
Sty218_Clr015 1 1 1 1 1 1 Sty225_Clr034 0 1 1 1 1 1 Sty235_Clr011 1 1 1 1 1 1
Sty218_Clr035 1 1 1 1 1 1 Sty225_Clr035 1 1 1 1 1 1 Sty235_Clr012 0 0 1 1 1 1
Sty218_Clr036 1 1 1 1 1 1 Sty225_Clr036 1 1 1 1 1 1 Sty235_Clr014 1 1 1 1 1 1
Sty218_Clr041 1 1 1 1 1 1 Sty225_Clr037 1 1 1 1 1 1 Sty235_Clr015 1 1 1 1 1 1
Sty220_Clr030 1 1 1 1 1 1 Sty225_Clr038 1 0 0 0 0 0 Sty235_Clr017 1 1 1 1 1 1
Sty220_Clr032 1 1 1 1 1 1 Sty225_Clr041 1 1 1 1 1 1 Sty235_Clr041 1 1 1 1 0 0
Sty220_Clr080 1 1 1 1 1 1 Sty225_Clr053 1 1 1 1 1 1 Sty236_Clr004 1 1 1 0 0 0
Sty221_Clr009 0 0 0 1 1 1 Sty225_Clr054 0 0 0 0 0 0 Sty236_Clr008 0 0 0 0 0 1
Sty221_Clr013 1 1 1 1 1 1 Sty225_Clr056 0 0 0 0 0 0 Sty236_Clr010 0 0 0 1 1 1
Sty221_Clr017 1 1 1 1 1 1 Sty225_Clr057 0 0 0 1 1 1 Sty236_Clr012 0 0 0 1 1 1
Sty221_Clr058 0 1 1 1 1 1 Sty225_Clr058 1 1 1 1 1 1 Sty236_Clr014 0 0 0 0 0 0
Sty221_Clr059 0 0 0 0 1 1 Sty225_Clr059 0 0 1 1 1 1 Sty236_Clr017 1 0 0 0 0 0
Sty221_Clr060 0 0 1 1 1 1 Sty225_Clr060 1 1 1 1 1 1 Sty237_Clr003 1 1 1 1 1 1
Sty222_Clr003 1 1 1 1 1 1 Sty225_Clr061 0 0 0 1 1 1 Sty237_Clr004 1 1 1 1 1 0
Sty222_Clr007 1 1 1 1 1 1 Sty225_Clr063 1 1 1 1 1 1 Sty237_Clr006 1 1 1 1 0 0
Sty222_Clr012 1 1 1 1 1 1 Sty225_Clr076 0 1 1 1 1 1 Sty237_Clr007 1 1 1 1 1 1
Sty222_Clr034 0 0 0 1 1 1 Sty225_Clr080 1 1 1 1 1 1 Sty237_Clr008 1 1 1 1 1 1
Sty222_Clr037 0 1 1 1 1 1 Sty225_Clr081 1 1 1 1 1 1 Sty237_Clr009 1 1 1 0 0 0
Sty222_Clr044 0 0 0 0 0 0 Sty225_Clr088 0 1 1 1 1 1 Sty237_Clr010 1 1 1 1 1 1
Sty222_Clr063 1 1 1 1 1 1 Sty225_Clr089 0 0 0 0 0 0 Sty237_Clr011 1 1 1 1 1 0
Sty223_Clr004 1 1 1 1 1 1 Sty225_Clr091 0 0 0 0 0 0 Sty237_Clr012 1 1 1 1 1 1
Sty223_Clr006 0 1 1 1 1 1 Sty225_Clr092 0 0 0 0 0 0 Sty237_Clr014 1 1 1 1 1 0
59
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Sty237_Clr015 1 1 1 1 1 0 Sty239_Clr007 1 1 1 1 1 1 Sty285_Clr008 0 0 0 0 0 0
Sty237_Clr017 1 1 1 1 0 0 Sty239_Clr008 1 1 1 1 1 1 Sty285_Clr009 0 0 0 0 0 0
Sty237_Clr034 1 1 1 1 1 1 Sty239_Clr009 1 1 1 1 1 0 Sty285_Clr011 1 0 0 0 0 0
Sty237_Clr035 1 1 1 1 0 0 Sty239_Clr011 1 1 1 1 1 0 Sty285_Clr014 0 0 0 0 0 0
Sty237_Clr036 1 1 1 1 1 1 Sty239_Clr014 1 1 1 1 1 1 Sty285_Clr017 0 0 0 0 0 0
Sty237_Clr037 1 1 1 1 1 1 Sty239_Clr015 1 1 1 1 1 0 Sty285_Clr043 0 0 0 0 0 0
Sty237_Clr041 1 1 1 1 0 0 Sty239_Clr017 1 1 1 1 1 1 Sty285_Clr059 0 0 0 0 0 0
Sty237_Clr054 1 0 0 0 0 0 Sty239_Clr035 1 1 1 1 1 0 Sty286_Clr003 1 0 0 0 0 0
Sty237_Clr056 0 0 0 0 0 0 Sty239_Clr054 1 0 0 0 0 0 Sty286_Clr004 1 1 1 0 0 0
Sty237_Clr058 1 1 1 1 1 0 Sty239_Clr056 0 0 0 0 0 0 Sty286_Clr006 0 0 0 0 0 0
Sty237_Clr059 1 1 1 1 1 1 Sty243_Clr005 0 0 0 1 1 1 Sty286_Clr008 1 0 0 0 0 0
Sty237_Clr060 1 1 1 1 1 1 Sty245_Clr010 0 0 0 1 1 1 Sty286_Clr011 1 1 1 0 0 0
Sty237_Clr063 1 1 1 1 1 1 Sty245_Clr013 1 1 1 1 1 1 Sty286_Clr014 0 0 0 0 0 0
Sty238_Clr003 1 1 1 1 1 1 Sty245_Clr014 0 1 1 1 1 1 Sty286_Clr015 1 0 0 0 0 0
Sty238_Clr004 1 1 1 1 1 1 Sty245_Clr015 0 0 0 0 0 0 Sty286_Clr017 0 0 0 0 0 0
Sty238_Clr006 1 1 1 1 1 1 Sty245_Clr017 1 0 0 0 0 0 Sty286_Clr043 0 0 0 0 0 0
Sty238_Clr007 1 1 1 1 1 1 Sty245_Clr018 0 0 0 1 1 1 Sty286_Clr059 0 0 0 0 0 0
Sty238_Clr008 1 1 1 1 1 1 Sty245_Clr053 1 1 1 1 1 1 Sty291_Clr004 0 1 1 1 1 1
Sty238_Clr009 1 1 1 1 1 1 Sty245_Clr059 0 0 0 0 1 1 Sty291_Clr006 0 0 0 0 0 0
Sty238_Clr010 1 1 1 1 1 1 Sty245_Clr072 0 0 0 0 1 1 Sty291_Clr008 0 0 0 0 0 0
Sty238_Clr011 1 1 1 1 1 1 Sty245_Clr075 0 0 1 1 1 1 Sty291_Clr009 0 0 0 0 0 0
Sty238_Clr012 0 1 1 1 1 1 Sty245_Clr076 0 0 0 1 1 1 Sty291_Clr011 1 0 0 0 0 0
Sty238_Clr014 1 1 1 1 1 1 Sty245_Clr080 0 0 0 1 1 1 Sty291_Clr014 0 0 0 0 0 0
Sty238_Clr015 1 1 1 1 1 1 Sty245_Clr082 0 1 1 1 1 1 Sty291_Clr015 0 0 0 0 0 0
Sty238_Clr017 1 1 1 1 1 1 Sty245_Clr095 0 0 0 0 0 1 Sty291_Clr017 0 0 0 0 0 0
Sty238_Clr018 0 0 0 0 0 0 Sty245_Clr096 0 0 0 0 1 1 Sty309_Clr011 0 0 0 0 0 1
Sty238_Clr034 1 1 1 1 1 1 Sty246_Clr005 0 1 1 1 1 1 Sty309_Clr013 0 0 0 0 0 1
Sty238_Clr035 1 1 1 1 1 0 Sty246_Clr007 0 0 0 1 1 1 Sty309_Clr029 0 0 0 0 0 0
Sty238_Clr036 0 1 1 1 1 1 Sty246_Clr012 1 1 1 1 1 1 Sty310_Clr008 0 0 0 0 0 0
Sty238_Clr037 1 1 1 1 1 1 Sty247_Clr004 1 1 1 1 1 1 Sty310_Clr012 0 0 0 0 0 0
Sty238_Clr041 1 1 1 1 1 1 Sty247_Clr008 0 1 1 1 1 1 Sty311_Clr004 0 0 0 0 1 1
Sty238_Clr053 0 0 0 0 0 1 Sty247_Clr011 0 0 0 0 0 0 Sty311_Clr011 0 0 0 0 0 0
Sty238_Clr054 1 1 1 0 0 0 Sty252_Clr004 1 1 1 1 1 1 Sty311_Clr014 0 0 0 0 0 1
Sty238_Clr056 1 1 1 0 0 0 Sty252_Clr005 0 0 0 1 1 1 Sty311_Clr015 0 0 0 0 0 0
Sty238_Clr058 1 1 1 1 1 1 Sty252_Clr008 0 1 1 1 1 1 Sty311_Clr030 0 0 0 0 0 0
Sty238_Clr059 1 1 1 1 1 1 Sty252_Clr010 0 1 1 1 1 1 Sty312_Clr004 0 0 0 0 0 1
Sty238_Clr060 1 1 1 1 1 1 Sty252_Clr012 1 1 1 1 1 1 Sty313_Clr004 0 0 0 0 0 0
Sty238_Clr063 1 1 1 1 1 1 Sty252_Clr013 1 1 1 1 1 1 Sty313_Clr008 1 1 1 1 1 1
Sty238_Clr081 0 0 0 0 0 0 Sty252_Clr014 1 1 1 1 1 1 Sty314_Clr004 0 0 0 0 0 0
Sty238_Clr089 0 0 0 0 0 1 Sty252_Clr017 1 1 1 1 1 1 Sty314_Clr008 1 0 0 0 0 0
Sty238_Clr091 0 0 0 0 0 1 Sty252_Clr075 1 1 1 1 1 1 Sty314_Clr011 0 0 0 0 0 0
Sty238_Clr092 0 0 0 0 0 0 Sty252_Clr076 0 1 1 1 1 1 Sty315_Clr008 0 0 0 0 0 0
Sty238_Clr093 0 0 0 0 0 1 Sty285_Clr003 0 0 0 0 0 0 Sty315_Clr015 0 0 0 0 0 0
Sty239_Clr003 1 1 1 1 1 1 Sty285_Clr004 0 0 0 0 0 0 Sty315_Clr029 0 0 0 0 0 1
Sty239_Clr004 1 1 1 1 1 0 Sty285_Clr006 1 0 0 0 0 0 Sty315_Clr030 0 0 0 0 0 0
Sty239_Clr006 1 1 1 1 1 0 Sty285_Clr007 0 0 0 0 0 0 Sty315_Clr061 0 0 0 0 0 0
60
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Sty315_Clr073 0 0 0 0 0 0 Sty338_Clr014 0 0 0 0 0 0 Sty345_Clr017 0 0 0 0 0 0
Sty316_Clr011 0 0 0 0 0 0 Sty338_Clr015 0 0 0 0 0 0 Sty345_Clr053 0 0 0 0 0 0
Sty318_Clr008 1 1 1 1 0 0 Sty338_Clr029 0 0 0 0 0 0 Sty346_Clr004 0 0 0 0 0 0
Sty319_Clr008 1 0 0 0 0 0 Sty338_Clr030 0 0 0 0 0 0 Sty346_Clr008 1 1 1 0 0 0
Sty320_Clr008 0 0 0 0 0 0 Sty338_Clr076 0 0 0 0 1 1 Sty346_Clr011 1 0 0 0 0 0
Sty320_Clr053 1 0 0 0 0 0 Sty339_Clr008 0 0 0 0 1 1 Sty346_Clr015 0 0 0 0 0 0
Sty320_Clr076 0 0 0 0 0 0 Sty341_Clr008 0 0 0 0 0 0 Sty346_Clr017 0 0 0 0 0 0
Sty321_Clr008 0 0 0 0 0 0 Sty341_Clr011 0 0 0 0 0 0 Sty346_Clr029 0 0 0 0 0 0
Sty322_Clr008 0 0 0 0 0 0 Sty341_Clr012 0 0 0 0 0 0 Sty347_Clr004 1 0 0 0 0 0
Sty322_Clr011 0 0 0 0 0 0 Sty341_Clr017 0 0 0 0 0 0 Sty347_Clr008 0 0 0 0 0 0
Sty323_Clr008 0 0 0 0 0 0 Sty342_Clr004 0 0 0 0 0 0 Sty347_Clr011 0 0 0 0 0 0
Sty323_Clr014 0 0 0 0 0 0 Sty342_Clr007 0 0 0 0 1 1 Sty347_Clr012 1 0 0 0 0 0
Sty323_Clr015 0 0 0 0 0 0 Sty342_Clr008 1 0 0 0 0 0 Sty347_Clr017 1 0 0 0 0 0
Sty323_Clr029 0 0 0 0 0 1 Sty342_Clr011 1 0 0 0 0 0 Sty348_Clr008 0 0 0 0 0 1
Sty323_Clr030 0 0 0 0 0 0 Sty342_Clr012 0 0 0 0 0 0 Sty349_Clr004 1 0 0 0 0 0
Sty325_Clr017 0 0 0 0 0 0 Sty342_Clr013 0 0 0 0 0 0 Sty349_Clr007 0 0 0 0 0 0
Sty325_Clr053 0 0 0 0 0 0 Sty342_Clr014 1 0 0 0 0 0 Sty349_Clr008 1 0 0 0 0 0
Sty326_Clr008 1 1 1 0 0 0 Sty342_Clr015 0 0 0 0 0 0 Sty349_Clr011 1 0 0 0 0 0
Sty327_Clr004 0 0 0 0 0 0 Sty342_Clr017 0 0 0 0 0 0 Sty349_Clr013 0 0 0 0 0 0
Sty327_Clr008 0 0 0 0 0 0 Sty342_Clr030 1 0 0 0 0 0 Sty349_Clr014 0 0 0 0 0 0
Sty327_Clr011 0 0 0 0 0 0 Sty342_Clr034 0 0 0 0 0 0 Sty349_Clr015 1 0 0 0 0 0
Sty327_Clr042 0 0 0 0 0 1 Sty342_Clr036 0 0 0 0 0 0 Sty349_Clr029 0 0 0 0 0 0
Sty329_Clr006 0 0 0 0 0 0 Sty342_Clr053 0 0 0 0 0 0 Sty349_Clr034 0 0 0 0 0 0
Sty329_Clr008 0 0 0 0 1 1 Sty342_Clr055 0 0 0 0 0 0 Sty349_Clr036 0 0 0 0 0 0
Sty329_Clr015 0 0 0 0 0 0 Sty342_Clr073 0 0 0 0 0 0 Sty349_Clr042 0 0 0 0 0 0
Sty329_Clr030 0 0 0 0 0 0 Sty342_Clr082 0 0 0 0 0 0 Sty349_Clr045 0 0 0 0 0 0
Sty329_Clr046 0 0 0 0 0 0 Sty342_Clr084 0 0 0 0 0 0 Sty349_Clr053 0 0 0 0 0 0
Sty329_Clr059 0 0 0 0 0 0 Sty343_Clr004 1 1 1 1 0 0 Sty349_Clr055 0 0 0 0 0 0
Sty329_Clr061 0 0 0 0 0 0 Sty343_Clr007 0 0 0 0 0 0 Sty349_Clr059 0 0 0 0 0 0
Sty330_Clr014 1 0 0 0 0 0 Sty343_Clr008 1 1 1 1 0 0 Sty349_Clr060 0 0 0 0 0 0
Sty330_Clr047 0 0 0 0 0 0 Sty343_Clr011 1 1 1 1 0 0 Sty349_Clr061 0 0 0 0 0 0
Sty331_Clr008 0 0 0 0 0 0 Sty343_Clr012 0 0 0 0 0 0 Sty349_Clr063 0 0 0 0 0 0
Sty331_Clr073 0 0 0 0 0 0 Sty343_Clr013 0 0 0 0 0 0 Sty349_Clr073 0 0 0 0 0 0
Sty332_Clr004 0 0 0 0 0 0 Sty343_Clr014 1 1 0 0 0 0 Sty349_Clr082 0 0 0 0 0 0
Sty332_Clr008 1 0 0 0 0 0 Sty343_Clr015 1 1 1 1 0 0 Sty349_Clr084 0 0 0 0 0 0
Sty332_Clr011 1 0 0 0 0 0 Sty343_Clr017 0 0 0 0 0 0 Sty349_Clr165 0 0 0 0 0 0
Sty333_Clr008 1 0 0 0 0 0 Sty343_Clr029 0 0 0 0 0 0 Sty349_Clr166 0 0 0 0 0 0
Sty335_Clr011 1 0 0 0 0 0 Sty343_Clr030 0 0 0 0 0 0 Sty350_Clr011 1 0 0 0 0 0
Sty336_Clr012 0 0 0 0 0 0 Sty343_Clr036 0 0 0 0 0 0 Sty351_Clr073 0 0 0 0 0 0
Sty336_Clr017 0 0 0 0 0 0 Sty343_Clr055 0 0 0 0 0 1 Sty352_Clr004 1 0 0 0 0 0
Sty338_Clr004 0 0 0 0 1 1 Sty343_Clr063 0 0 0 0 0 1 Sty353_Clr008 0 0 0 0 0 0
Sty338_Clr007 0 0 0 0 0 0 Sty343_Clr082 0 0 0 0 0 0 Sty354_Clr009 1 1 1 1 1 1
Sty338_Clr008 0 0 0 0 0 0 Sty343_Clr084 0 0 0 0 0 0 Sty354_Clr014 1 1 1 1 1 1
Sty338_Clr011 0 0 0 0 0 0 Sty345_Clr007 0 0 0 0 0 0 Sty354_Clr017 1 1 1 1 1 1
Sty338_Clr012 0 0 0 0 0 0 Sty345_Clr008 0 0 0 0 0 0 Sty354_Clr018 0 1 1 1 1 1
Sty338_Clr013 0 0 1 1 0 0 Sty345_Clr012 0 0 1 0 0 0 Sty354_Clr032 0 0 0 1 1 1
61
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Sty354_Clr059 1 1 1 1 1 1 Sty398_Clr014 1 1 1 1 0 0 Sty404_Clr035 1 0 0 0 0 0
Sty354_Clr088 1 1 1 1 1 1 Sty398_Clr017 1 1 1 0 0 0 Sty405_Clr030 1 1 1 1 1 1
Sty355_Clr003 1 1 1 1 1 1 Sty398_Clr018 1 0 0 0 0 0 Sty406_Clr003 1 1 1 1 1 1
Sty355_Clr007 1 1 1 1 1 1 Sty398_Clr056 0 0 0 0 0 0 Sty406_Clr004 1 1 1 1 1 1
Sty356_Clr004 1 1 1 1 1 1 Sty398_Clr059 0 0 0 0 0 1 Sty406_Clr006 1 1 1 1 1 1
Sty356_Clr006 1 1 1 1 1 1 Sty399_Clr003 1 1 1 1 1 0 Sty406_Clr007 1 1 1 1 1 1
Sty356_Clr008 1 1 1 1 1 1 Sty399_Clr005 1 0 0 0 0 0 Sty406_Clr008 1 1 1 1 1 1
Sty356_Clr010 1 1 1 1 0 0 Sty399_Clr007 1 1 1 1 1 1 Sty406_Clr009 1 1 1 1 1 1
Sty356_Clr011 1 1 1 1 1 1 Sty399_Clr012 1 0 0 0 0 0 Sty406_Clr010 0 0 0 0 0 0
Sty356_Clr015 1 1 1 1 1 0 Sty399_Clr048 1 0 0 0 0 0 Sty406_Clr011 1 1 1 1 1 1
Sty356_Clr042 1 1 1 1 1 1 Sty400_Clr004 1 1 1 1 0 0 Sty406_Clr014 1 1 1 1 1 1
Sty358_Clr007 1 1 1 1 1 1 Sty400_Clr006 1 1 1 1 1 0 Sty406_Clr015 1 1 1 1 1 1
Sty358_Clr009 1 1 1 1 1 1 Sty400_Clr008 1 1 1 1 1 1 Sty406_Clr017 1 1 1 1 1 1
Sty358_Clr014 1 1 1 1 1 0 Sty400_Clr009 1 1 1 1 1 1 Sty407_Clr014 1 1 1 1 1 1
Sty358_Clr017 1 1 1 1 1 1 Sty400_Clr010 1 0 0 0 0 0 Sty407_Clr017 1 1 1 1 1 1
Sty358_Clr018 0 1 1 1 1 1 Sty400_Clr011 1 1 1 1 1 0 Sty407_Clr059 0 0 0 0 0 0
Sty358_Clr032 0 0 0 1 1 1 Sty400_Clr015 1 1 1 0 0 0 Sty408_Clr003 1 1 1 1 1 1
Sty358_Clr059 1 1 1 1 1 1 Sty400_Clr035 0 0 0 0 0 0 Sty408_Clr005 0 0 0 0 0 0
Sty358_Clr088 1 1 1 1 1 1 Sty400_Clr036 1 0 0 0 0 0 Sty408_Clr007 1 1 1 1 1 1
Sty359_Clr003 1 1 1 1 1 1 Sty400_Clr041 0 0 0 0 1 1 Sty408_Clr012 0 1 1 1 1 1
Sty359_Clr005 0 0 0 1 1 1 Sty400_Clr060 1 0 0 0 0 0 Sty409_Clr004 1 1 1 1 1 1
Sty359_Clr044 0 1 1 1 1 1 Sty401_Clr030 0 0 0 0 0 0 Sty409_Clr006 1 1 1 1 1 1
Sty359_Clr047 0 0 0 1 1 1 Sty402_Clr007 1 1 1 1 1 1 Sty409_Clr008 1 1 1 1 1 1
Sty360_Clr004 1 1 1 1 1 1 Sty402_Clr012 1 1 1 1 1 1 Sty409_Clr009 0 1 1 1 1 1
Sty360_Clr006 1 1 1 1 1 1 Sty402_Clr014 1 1 1 1 1 0 Sty409_Clr010 1 0 0 0 0 0
Sty360_Clr008 1 1 1 1 1 1 Sty402_Clr017 1 1 1 1 1 1 Sty409_Clr011 1 1 1 1 1 1
Sty360_Clr010 0 0 0 0 0 0 Sty402_Clr018 0 1 1 1 1 1 Sty409_Clr015 1 1 1 1 1 1
Sty360_Clr011 1 1 1 1 1 0 Sty402_Clr034 1 1 1 0 0 0 Sty409_Clr036 0 0 0 0 0 1
Sty360_Clr015 1 1 1 1 1 1 Sty402_Clr036 1 1 1 1 1 1 Sty409_Clr041 0 0 0 0 1 1
Sty360_Clr042 1 1 1 1 1 1 Sty402_Clr037 1 0 0 0 0 0 Sty409_Clr060 0 0 0 0 1 1
Sty361_Clr030 0 0 0 1 1 1 Sty402_Clr041 1 1 1 1 1 1 Sty410_Clr030 0 0 0 0 1 1
Sty362_Clr003 1 1 1 1 1 1 Sty402_Clr045 1 0 0 0 0 0 Sty411_Clr003 1 1 1 1 1 1
Sty362_Clr007 1 1 1 1 1 1 Sty402_Clr054 0 0 0 0 0 0 Sty411_Clr007 0 0 0 0 1 1
Sty362_Clr009 1 1 1 1 1 1 Sty402_Clr056 0 0 0 0 0 0 Sty411_Clr008 1 1 1 1 1 1
Sty362_Clr015 1 1 1 1 1 1 Sty402_Clr058 1 1 1 1 0 0 Sty411_Clr009 0 1 1 1 1 1
Sty362_Clr017 1 1 1 1 1 1 Sty402_Clr059 1 1 1 1 1 1 Sty411_Clr017 0 1 1 1 1 1
Sty362_Clr042 1 1 1 1 1 1 Sty402_Clr060 1 1 1 1 1 0 Sty412_Clr004 1 1 1 1 1 1
Sty362_Clr059 1 1 1 1 1 1 Sty402_Clr063 1 1 1 1 1 1 Sty412_Clr006 0 1 1 1 1 1
Sty362_Clr088 1 1 1 1 1 0 Sty403_Clr003 1 1 1 1 1 1 Sty412_Clr011 1 1 1 1 1 1
Sty363_Clr004 1 1 1 1 1 1 Sty404_Clr004 1 1 1 1 1 1 Sty412_Clr014 0 1 1 1 1 1
Sty363_Clr006 1 1 1 1 1 1 Sty404_Clr006 1 1 1 1 1 1 Sty412_Clr015 0 1 1 1 1 1
Sty363_Clr008 1 1 1 1 1 1 Sty404_Clr008 1 1 1 1 1 1 Sty413_Clr003 1 1 1 1 1 1
Sty363_Clr010 0 0 0 1 1 1 Sty404_Clr009 1 1 1 1 1 1 Sty413_Clr007 1 1 1 1 1 1
Sty363_Clr011 1 1 1 1 1 1 Sty404_Clr010 1 0 0 0 0 0 Sty413_Clr008 1 1 1 1 1 1
Sty363_Clr014 1 1 1 1 1 1 Sty404_Clr011 1 1 1 1 1 0 Sty413_Clr009 1 1 1 1 1 1
Sty365_Clr003 0 0 0 0 1 1 Sty404_Clr015 1 1 1 1 0 0 Sty413_Clr012 1 1 1 1 1 1
62
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Sty413_Clr017 1 1 1 1 1 1 Sty430_Clr018 1 1 0 0 0 0 Sty494_Clr017 0 0 0 0 1 1
Sty413_Clr059 0 0 0 0 1 1 Sty430_Clr030 0 0 0 0 1 1 Sty494_Clr050 0 0 0 1 1 1
Sty413_Clr060 0 0 0 0 1 1 Sty430_Clr038 0 0 0 0 1 1 Sty495_Clr050 0 0 0 0 1 1
Sty414_Clr004 1 1 1 1 1 1 Sty430_Clr053 1 1 1 1 1 1 Sty496_Clr017 0 0 0 0 1 1
Sty414_Clr006 1 1 1 1 1 1 Sty430_Clr055 0 0 0 0 0 1 Sty496_Clr050 0 0 0 0 1 1
Sty414_Clr010 1 0 0 0 0 0 Sty430_Clr057 0 0 1 0 0 0 Sty497_Clr050 0 0 0 0 1 1
Sty414_Clr011 1 1 1 1 1 1 Sty430_Clr059 0 0 0 1 1 1 Sty498_Clr050 0 0 0 0 1 1
Sty414_Clr014 1 1 1 1 1 1 Sty430_Clr072 0 0 0 0 0 0 Sty499_Clr050 0 0 0 0 1 1
Sty414_Clr015 1 1 1 1 1 1 Sty430_Clr075 0 1 1 1 1 1 Sty500_Clr050 0 0 0 0 1 1
Sty415_Clr003 1 1 1 1 1 1 Sty430_Clr076 0 0 0 0 0 0 Sty501_Clr050 0 0 0 0 1 1
Sty415_Clr004 1 1 1 1 1 1 Sty430_Clr080 0 0 0 1 1 1 Sty502_Clr050 0 0 0 0 1 1
Sty415_Clr006 1 1 1 1 1 1 Sty430_Clr082 0 1 1 1 1 1 Sty503_Clr017 0 0 0 0 1 1
Sty415_Clr007 1 1 1 1 1 1 Sty430_Clr095 0 0 0 0 0 1 Sty503_Clr050 0 0 0 0 0 1
Sty415_Clr008 1 1 1 1 1 1 Sty430_Clr096 0 0 0 0 0 0 Sty504_Clr017 0 0 0 0 1 1
Sty415_Clr009 1 1 1 1 1 1 Sty458_Clr017 1 1 1 1 1 1 Sty504_Clr050 0 0 0 0 1 1
Sty415_Clr011 1 1 1 1 1 1 Sty459_Clr005 0 1 1 1 1 1 Sty505_Clr017 0 0 0 0 1 1
Sty415_Clr014 1 1 1 1 1 1 Sty459_Clr007 0 1 1 1 1 1 Sty505_Clr050 0 0 0 0 1 1
Sty415_Clr015 1 1 1 1 1 1 Sty459_Clr012 0 1 1 1 1 1 Sty508_Clr017 0 0 0 0 1 1
Sty415_Clr017 1 1 1 1 1 1 Sty460_Clr008 0 0 0 1 1 1 Sty508_Clr050 0 0 0 0 0 1
Sty417_Clr003 1 1 1 1 1 1 Sty460_Clr011 0 0 0 1 1 1 Sty509_Clr017 0 0 0 0 1 1
Sty417_Clr004 1 1 1 1 1 1 Sty461_Clr017 1 1 1 1 1 1 Sty510_Clr017 0 0 0 0 1 1
Sty417_Clr006 1 1 1 1 1 1 Sty462_Clr005 0 1 1 1 1 1 Sty511_Clr017 0 0 0 0 1 1
Sty417_Clr007 0 0 0 0 1 1 Sty462_Clr007 0 1 1 1 1 1 Sty511_Clr050 0 0 0 0 1 1
Sty417_Clr008 1 1 1 1 1 1 Sty462_Clr012 0 1 1 1 1 1 Sty513_Clr017 0 0 0 0 0 0
Sty417_Clr009 0 1 1 1 1 1 Sty463_Clr008 0 0 0 1 1 1 Sty513_Clr050 1 0 0 0 0 0
Sty417_Clr011 1 1 1 1 1 1 Sty472_Clr004 1 1 1 1 1 1 Sty514_Clr017 0 1 1 1 1 1
Sty417_Clr014 1 1 1 1 1 1 Sty472_Clr008 1 1 1 1 1 1 Sty514_Clr050 1 1 1 1 1 1
Sty417_Clr015 1 1 1 1 1 1 Sty472_Clr010 1 1 1 1 1 1 Sty515_Clr017 0 0 0 0 0 0
Sty417_Clr017 0 1 1 1 1 1 Sty472_Clr012 1 1 1 1 1 1 Sty515_Clr050 0 0 0 0 0 0
Sty421_Clr004 1 1 1 1 1 1 Sty472_Clr014 1 1 1 1 1 1 Sty522_Clr017 0 0 0 0 1 1
Sty421_Clr008 0 0 0 0 0 1 Sty472_Clr017 1 1 1 1 1 1 Sty522_Clr050 0 0 0 0 1 1
Sty421_Clr010 1 1 1 1 0 0 Sty472_Clr018 1 1 1 1 1 1 Sty525_Clr017 0 0 0 0 1 1
Sty421_Clr012 1 1 1 1 0 0 Sty472_Clr059 1 1 1 1 1 1 Sty525_Clr050 0 0 0 0 0 0
Sty421_Clr014 1 1 1 0 0 0 Sty473_Clr004 1 1 1 1 1 1 Sty526_Clr017 0 0 0 0 0 1
Sty421_Clr017 1 1 1 1 0 0 Sty473_Clr008 1 1 1 1 1 1 Sty526_Clr050 1 1 1 1 1 1
Sty430_Clr004 1 1 1 1 1 1 Sty473_Clr010 1 1 1 1 1 1 Sty527_Clr017 0 0 0 0 1 1
Sty430_Clr005 0 0 0 0 0 0 Sty473_Clr012 1 1 1 1 1 1 Sty527_Clr050 1 1 1 1 1 1
Sty430_Clr007 0 0 0 0 1 1 Sty473_Clr014 0 1 1 1 1 1 Sty528_Clr050 0 0 0 0 0 1
Sty430_Clr008 0 1 1 1 0 0 Sty473_Clr017 1 1 1 1 1 1 Sty529_Clr017 0 0 0 0 1 1
Sty430_Clr010 1 1 1 1 1 1 Sty473_Clr018 0 1 1 1 1 1 Sty529_Clr050 0 0 0 0 0 1
Sty430_Clr011 0 0 0 0 0 0 Sty473_Clr059 1 1 1 1 1 1 Sty530_Clr017 0 0 0 0 0 0
Sty430_Clr012 0 0 0 0 0 0 Sty486_Clr017 0 0 0 0 0 1 Sty530_Clr050 0 0 0 0 0 1
Sty430_Clr013 1 1 1 1 1 1 Sty486_Clr050 0 0 0 0 0 0 Sty532_Clr017 0 0 0 0 1 1
Sty430_Clr014 1 1 1 1 1 1 Sty492_Clr017 0 0 0 0 1 1 Sty532_Clr050 0 0 0 0 0 1
Sty430_Clr015 0 0 0 1 1 1 Sty493_Clr017 0 0 0 0 1 1 Sty533_Clr017 0 0 0 0 1 1
Sty430_Clr017 1 0 0 0 0 0 Sty493_Clr050 0 0 0 1 1 1 Sty533_Clr050 0 0 0 0 1 1
63
Product 1 2 3 4 5 6
Sty534_Clr050 0 0 0 1 1 1
Sty535_Clr017 0 0 0 0 1 1
Sty535_Clr050 0 0 0 0 1 1
Sty536_Clr017 0 0 0 0 0 0
Sty536_Clr050 0 0 0 0 0 0
Sty537_Clr017 0 0 0 0 1 1
Sty537_Clr050 0 0 0 0 0 1
Sty538_Clr017 0 0 0 0 0 1
Sty538_Clr050 0 0 0 0 1 1
Sty541_Clr017 0 0 0 0 0 1
Sty541_Clr050 0 0 0 0 0 0
Sty544_Clr017 0 0 0 0 0 0
Sty544_Clr050 1 1 0 0 0 0
Sty546_Clr017 0 0 0 1 1 1
Sty546_Clr050 0 0 0 0 1 1
Sty547_Clr017 0 0 0 0 1 1
Sty547_Clr050 0 0 0 0 1 1
64
.2 Appendix B: Individual GMROI Model Op-
timal Solution
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Product 1 2 3 4 5 6 Sty010_Clr036 1 1 1 1 1 1 Sty082_Clr017 0 0 0 0 0 0
Sty003_Clr003 1 1 1 1 1 1 Sty010_Clr037 1 1 1 1 1 1 Sty084_Clr050 0 0 0 0 0 0
Sty003_Clr004 1 1 1 1 1 1 Sty011_Clr003 0 0 0 0 0 0 Sty102_Clr050 0 0 0 0 0 0
Sty003_Clr005 0 0 0 0 0 0 Sty011_Clr004 0 0 0 0 0 0 Sty155_Clr050 0 0 0 0 0 0
Sty003_Clr006 1 1 1 1 1 1 Sty011_Clr006 0 1 1 1 1 1 Sty158_Clr050 0 0 0 0 0 0
Sty003_Clr007 1 1 1 1 1 1 Sty011_Clr007 1 0 0 0 0 0 Sty159_Clr004 0 0 0 0 0 0
Sty003_Clr008 1 1 1 1 1 1 Sty011_Clr008 0 0 0 0 0 0 Sty159_Clr008 0 0 0 0 0 0
Sty003_Clr009 1 1 1 1 1 1 Sty011_Clr009 0 0 0 0 0 0 Sty159_Clr017 0 0 0 0 0 0
Sty003_Clr010 1 1 1 1 1 1 Sty011_Clr010 0 1 1 1 1 1 Sty160_Clr004 0 0 0 0 0 0
Sty003_Clr011 1 1 1 1 1 1 Sty011_Clr011 0 1 1 1 1 1 Sty160_Clr008 0 0 0 0 0 0
Sty003_Clr012 1 1 1 1 1 1 Sty011_Clr012 0 0 0 0 0 0 Sty160_Clr017 1 1 1 1 1 1
Sty003_Clr013 1 1 1 1 1 1 Sty011_Clr014 1 0 0 0 0 0 Sty161_Clr004 0 1 1 1 1 1
Sty003_Clr014 1 1 1 1 1 1 Sty011_Clr015 1 1 1 1 1 1 Sty161_Clr008 0 0 0 0 0 0
Sty003_Clr015 1 1 1 1 1 1 Sty011_Clr017 1 0 0 0 0 0 Sty161_Clr017 0 0 0 0 0 0
Sty003_Clr017 1 1 1 1 1 1 Sty011_Clr030 0 0 0 0 0 0 Sty166_Clr004 1 1 1 1 1 1
Sty003_Clr018 1 1 1 1 1 1 Sty011_Clr032 0 0 0 0 0 0 Sty166_Clr006 0 1 1 1 1 1
Sty009_Clr003 1 1 1 1 1 1 Sty011_Clr034 0 0 0 0 0 0 Sty166_Clr007 1 1 1 1 1 1
Sty009_Clr004 1 1 1 1 1 1 Sty011_Clr036 0 0 0 0 0 0 Sty166_Clr009 0 0 0 0 0 0
Sty009_Clr006 1 1 1 1 1 1 Sty011_Clr037 0 0 0 0 0 0 Sty166_Clr011 1 1 1 1 1 1
Sty009_Clr007 1 1 1 1 1 1 Sty012_Clr003 1 1 1 1 1 1 Sty166_Clr014 1 1 1 1 1 1
Sty009_Clr008 1 1 1 1 1 1 Sty012_Clr004 1 1 1 1 1 1 Sty166_Clr015 1 1 1 1 1 1
Sty009_Clr009 1 1 1 1 1 1 Sty012_Clr006 1 1 1 1 1 1 Sty166_Clr017 1 1 1 1 1 1
Sty009_Clr010 1 1 1 1 1 1 Sty012_Clr007 1 1 1 1 1 1 Sty166_Clr032 0 0 0 0 0 0
Sty009_Clr011 1 1 1 1 1 1 Sty012_Clr008 1 1 1 1 1 1 Sty166_Clr036 0 0 0 0 0 0
Sty009_Clr014 1 1 1 1 1 1 Sty012_Clr009 1 1 1 1 1 1 Sty166_Clr041 0 0 0 0 0 0
Sty009_Clr015 1 1 1 1 1 1 Sty012_Clr010 1 1 1 1 1 1 Sty166_Clr053 0 1 1 1 1 1
Sty009_Clr017 1 1 1 1 1 1 Sty012_Clr011 1 1 1 1 1 1 Sty166_Clr054 1 1 1 1 1 1
Sty009_Clr030 1 1 1 1 1 1 Sty012_Clr014 1 1 1 1 1 1 Sty166_Clr055 1 1 1 1 1 1
Sty009_Clr032 0 1 1 1 1 1 Sty012_Clr015 1 1 1 1 1 1 Sty166_Clr056 1 1 1 1 1 1
Sty010_Clr003 1 1 1 1 1 1 Sty012_Clr017 1 1 1 1 1 1 Sty167_Clr004 0 0 0 0 0 0
Sty010_Clr004 1 1 1 1 1 1 Sty012_Clr018 1 1 1 1 1 1 Sty167_Clr007 0 0 0 0 0 0
Sty010_Clr006 1 1 1 1 1 1 Sty012_Clr030 0 1 1 1 1 1 Sty167_Clr011 1 0 0 0 0 0
Sty010_Clr007 1 1 1 1 1 1 Sty012_Clr036 0 1 1 1 1 1 Sty167_Clr014 0 0 0 0 0 0
Sty010_Clr008 1 1 1 1 1 1 Sty012_Clr038 1 1 1 1 1 1 Sty167_Clr015 0 0 0 0 0 0
Sty010_Clr009 1 1 1 1 1 1 Sty012_Clr040 0 0 0 0 0 0 Sty167_Clr017 0 0 0 0 0 0
Sty010_Clr010 1 1 1 1 1 1 Sty012_Clr041 0 1 1 1 1 1 Sty167_Clr053 0 0 0 0 0 0
Sty010_Clr011 1 1 1 1 1 1 Sty012_Clr042 1 1 1 1 1 1 Sty167_Clr054 0 0 0 0 0 0
Sty010_Clr012 0 1 1 1 1 1 Sty012_Clr044 0 0 0 0 0 0 Sty167_Clr055 0 0 0 0 0 0
Sty010_Clr014 1 1 1 1 1 1 Sty012_Clr045 0 0 0 0 0 0 Sty167_Clr056 0 0 0 0 0 0
Sty010_Clr015 1 1 1 1 1 1 Sty012_Clr046 0 1 1 1 1 1 Sty168_Clr004 0 0 0 0 0 0
Sty010_Clr017 1 1 1 1 1 1 Sty012_Clr047 0 1 1 1 1 1 Sty168_Clr006 0 0 0 0 0 0
Sty010_Clr018 1 1 1 1 1 1 Sty012_Clr048 0 0 0 0 0 0 Sty168_Clr007 0 0 0 0 0 0
Sty010_Clr030 1 1 1 1 1 1 Sty012_Clr049 0 1 1 1 1 1 Sty168_Clr011 0 0 0 0 0 0
Sty010_Clr032 1 1 1 1 1 1 Sty024_Clr050 0 0 0 0 0 0 Sty168_Clr014 0 0 0 0 0 0
Sty010_Clr034 1 1 1 1 1 1 Sty028_Clr050 0 0 0 0 0 0 Sty168_Clr015 0 0 0 0 0 0
Sty010_Clr035 1 1 1 1 1 1 Sty055_Clr050 0 0 0 0 0 0 Sty168_Clr017 0 0 0 0 0 0
Solution (xi) for each scenario
65
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Sty168_Clr032 0 0 0 0 0 0 Sty171_Clr015 0 0 0 0 0 0 Sty178_Clr015 1 0 0 0 0 0
Sty168_Clr053 0 0 0 0 0 0 Sty171_Clr017 0 0 0 0 0 0 Sty178_Clr017 1 0 0 0 0 0
Sty168_Clr054 0 0 0 0 0 0 Sty173_Clr014 1 1 1 1 1 1 Sty179_Clr030 1 1 1 1 1 1
Sty168_Clr055 0 0 0 0 0 0 Sty173_Clr017 1 0 0 0 0 0 Sty179_Clr032 1 1 1 1 1 1
Sty168_Clr056 0 0 0 0 0 0 Sty173_Clr018 1 1 1 1 1 1 Sty179_Clr080 1 1 1 1 1 1
Sty169_Clr004 0 1 1 1 1 1 Sty173_Clr058 1 1 1 1 1 1 Sty180_Clr017 1 1 1 1 1 1
Sty169_Clr007 0 0 0 0 0 0 Sty173_Clr059 1 1 1 1 1 1 Sty180_Clr018 1 1 1 1 1 1
Sty169_Clr011 0 1 1 1 1 1 Sty173_Clr060 1 1 1 1 1 1 Sty180_Clr038 0 1 1 1 1 1
Sty169_Clr017 0 1 1 1 1 1 Sty174_Clr003 1 1 1 1 1 1 Sty180_Clr045 0 0 0 0 0 0
Sty169_Clr053 0 1 1 1 1 1 Sty174_Clr007 1 1 1 1 1 1 Sty180_Clr046 1 1 1 1 1 1
Sty170_Clr003 0 0 0 0 0 0 Sty174_Clr012 1 1 1 1 1 1 Sty180_Clr053 1 1 1 1 1 1
Sty170_Clr004 1 1 1 1 1 1 Sty174_Clr034 1 1 1 1 1 1 Sty180_Clr058 1 1 1 1 1 1
Sty170_Clr006 1 0 0 0 0 0 Sty174_Clr037 1 1 1 1 1 1 Sty180_Clr059 1 1 1 1 1 1
Sty170_Clr007 1 1 1 1 1 1 Sty174_Clr047 1 1 1 1 1 1 Sty180_Clr061 1 1 1 1 1 1
Sty170_Clr008 1 0 0 0 0 0 Sty174_Clr048 1 1 1 1 1 1 Sty180_Clr064 1 0 0 0 0 0
Sty170_Clr009 0 0 0 0 0 0 Sty174_Clr049 1 1 1 1 1 1 Sty180_Clr076 1 1 1 1 1 1
Sty170_Clr010 1 0 0 0 0 0 Sty174_Clr063 1 1 1 1 1 1 Sty180_Clr081 1 1 1 1 1 1
Sty170_Clr011 1 1 1 1 1 1 Sty175_Clr004 1 1 1 1 1 1 Sty180_Clr082 1 1 1 1 1 1
Sty170_Clr012 0 1 1 1 1 1 Sty175_Clr006 1 1 1 1 1 1 Sty180_Clr088 1 1 1 1 1 1
Sty170_Clr014 1 1 1 1 1 1 Sty175_Clr008 1 1 1 1 1 1 Sty181_Clr003 1 1 1 1 1 1
Sty170_Clr015 1 1 1 1 1 1 Sty175_Clr009 1 1 1 1 1 1 Sty181_Clr005 1 1 1 1 1 1
Sty170_Clr017 1 0 0 0 0 0 Sty175_Clr010 1 1 1 1 1 1 Sty181_Clr007 1 1 1 1 1 1
Sty170_Clr018 0 1 1 1 1 1 Sty175_Clr011 1 1 1 1 1 1 Sty181_Clr012 1 1 1 1 1 1
Sty170_Clr032 0 0 0 0 0 0 Sty175_Clr015 1 1 1 1 1 1 Sty181_Clr034 1 1 1 1 1 1
Sty170_Clr034 1 1 1 1 1 1 Sty175_Clr035 1 1 1 1 1 1 Sty181_Clr037 1 1 1 1 1 1
Sty170_Clr035 0 1 1 1 1 1 Sty175_Clr036 1 1 1 1 1 1 Sty181_Clr040 1 1 1 1 1 1
Sty170_Clr036 1 1 1 1 1 1 Sty175_Clr041 1 1 1 1 1 1 Sty181_Clr044 0 0 0 0 0 0
Sty170_Clr037 1 0 0 0 0 0 Sty175_Clr042 1 1 1 1 1 1 Sty181_Clr047 1 1 1 1 1 1
Sty170_Clr041 0 1 1 1 1 1 Sty177_Clr003 1 1 1 1 1 1 Sty181_Clr048 1 1 1 1 1 1
Sty170_Clr046 0 0 0 0 0 0 Sty177_Clr004 1 1 1 1 1 1 Sty181_Clr049 1 1 1 1 1 1
Sty170_Clr057 0 0 0 0 0 0 Sty177_Clr006 0 0 0 0 0 0 Sty181_Clr055 1 1 1 1 1 1
Sty170_Clr058 1 1 1 1 1 1 Sty177_Clr007 1 1 1 1 1 1 Sty181_Clr062 1 1 1 1 1 1
Sty170_Clr059 1 0 0 0 0 0 Sty177_Clr008 1 1 1 1 1 1 Sty181_Clr063 1 1 1 1 1 1
Sty170_Clr060 1 1 1 1 1 1 Sty177_Clr009 0 0 0 0 0 0 Sty181_Clr075 1 1 1 1 1 1
Sty170_Clr061 0 0 0 0 0 0 Sty177_Clr011 1 1 1 1 1 1 Sty182_Clr004 1 1 1 1 1 1
Sty170_Clr062 1 1 1 0 0 0 Sty177_Clr014 0 0 0 1 1 1 Sty182_Clr006 1 1 1 1 1 1
Sty170_Clr063 1 1 1 1 1 1 Sty177_Clr015 1 0 0 0 0 0 Sty182_Clr008 1 1 1 1 1 1
Sty171_Clr003 0 0 0 0 0 0 Sty177_Clr017 1 1 1 1 1 1 Sty182_Clr009 1 1 1 1 1 1
Sty171_Clr004 0 0 0 0 0 0 Sty178_Clr003 0 0 0 0 0 0 Sty182_Clr010 1 1 1 1 1 1
Sty171_Clr006 0 0 0 0 0 0 Sty178_Clr004 1 0 0 0 0 0 Sty182_Clr011 1 1 1 1 1 1
Sty171_Clr007 0 0 0 0 0 0 Sty178_Clr006 0 0 0 0 0 0 Sty182_Clr013 1 1 1 1 1 1
Sty171_Clr008 0 0 0 0 0 0 Sty178_Clr007 0 0 0 0 0 0 Sty182_Clr014 1 1 1 1 1 1
Sty171_Clr009 0 0 0 0 0 0 Sty178_Clr008 1 1 1 1 1 1 Sty182_Clr015 1 1 1 1 1 1
Sty171_Clr011 0 0 0 0 0 0 Sty178_Clr009 0 0 0 0 0 0 Sty182_Clr032 1 1 1 1 1 1
Sty171_Clr012 0 0 0 0 0 0 Sty178_Clr011 1 0 0 0 0 0 Sty182_Clr035 1 1 1 1 1 1
Sty171_Clr014 0 0 0 0 0 0 Sty178_Clr014 0 0 0 0 0 0 Sty182_Clr036 1 1 1 1 1 1
66
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Sty182_Clr041 1 1 1 1 1 1 Sty189_Clr063 1 1 1 1 1 1 Sty198_Clr037 1 1 1 1 1 1
Sty182_Clr042 1 1 1 1 1 1 Sty190_Clr003 1 1 1 1 1 1 Sty198_Clr040 1 1 1 1 1 1
Sty182_Clr043 1 1 1 1 1 1 Sty190_Clr007 1 1 1 1 1 1 Sty198_Clr044 1 0 0 0 0 0
Sty182_Clr060 1 1 1 1 1 1 Sty190_Clr034 1 1 1 1 1 1 Sty198_Clr048 1 1 1 1 1 1
Sty182_Clr073 1 1 1 1 1 1 Sty190_Clr044 1 1 1 1 1 1 Sty199_Clr004 1 1 1 1 1 1
Sty183_Clr007 1 1 1 1 1 1 Sty191_Clr004 1 1 1 1 1 1 Sty199_Clr006 1 1 1 1 1 1
Sty183_Clr009 1 1 1 1 1 1 Sty191_Clr006 1 1 1 1 1 1 Sty199_Clr008 1 1 1 1 1 1
Sty183_Clr012 1 1 1 1 1 1 Sty191_Clr008 1 1 1 1 1 1 Sty199_Clr009 1 1 1 1 1 1
Sty183_Clr017 1 1 1 1 1 1 Sty191_Clr010 1 1 1 1 1 1 Sty199_Clr010 1 1 1 1 1 1
Sty183_Clr018 1 1 1 1 1 1 Sty191_Clr011 1 1 1 1 1 1 Sty199_Clr011 1 1 1 1 1 1
Sty183_Clr037 1 1 1 1 1 1 Sty191_Clr014 1 1 1 1 1 1 Sty199_Clr015 1 1 1 1 1 1
Sty183_Clr045 0 0 0 0 0 0 Sty191_Clr015 1 1 1 1 1 1 Sty199_Clr035 1 0 0 0 0 0
Sty183_Clr046 0 0 0 0 0 0 Sty191_Clr035 1 1 1 1 1 1 Sty199_Clr036 1 1 1 1 1 1
Sty183_Clr058 1 1 1 1 1 1 Sty191_Clr041 1 1 1 1 1 1 Sty199_Clr041 1 1 1 1 1 1
Sty183_Clr059 1 1 1 1 1 1 Sty192_Clr030 1 1 1 1 1 1 Sty199_Clr042 1 1 1 1 1 1
Sty183_Clr060 1 1 1 1 1 1 Sty197_Clr005 1 1 1 1 1 1 Sty201_Clr032 1 1 1 1 1 1
Sty183_Clr063 1 1 1 1 1 1 Sty197_Clr012 1 1 1 1 1 1 Sty203_Clr009 1 0 0 0 0 0
Sty184_Clr003 1 1 1 1 1 1 Sty197_Clr013 1 1 1 1 1 1 Sty203_Clr012 1 1 1 1 1 1
Sty184_Clr034 1 1 1 1 1 1 Sty197_Clr014 1 1 1 1 1 1 Sty203_Clr014 1 1 1 0 0 0
Sty184_Clr044 1 1 1 1 1 1 Sty197_Clr017 1 0 0 0 0 0 Sty203_Clr017 1 1 0 0 0 0
Sty184_Clr048 1 1 1 1 1 1 Sty197_Clr018 1 1 1 1 1 1 Sty203_Clr058 1 1 1 0 0 0
Sty184_Clr049 1 1 1 1 1 1 Sty197_Clr030 1 1 1 1 1 1 Sty203_Clr059 1 0 0 0 0 0
Sty185_Clr004 1 1 1 1 1 1 Sty197_Clr038 1 1 1 1 1 1 Sty203_Clr060 1 0 0 0 0 0
Sty185_Clr006 1 1 1 1 1 1 Sty197_Clr046 1 1 1 1 1 1 Sty204_Clr003 1 1 1 1 1 1
Sty185_Clr008 1 1 1 1 1 1 Sty197_Clr047 1 1 1 1 1 1 Sty204_Clr007 1 1 1 1 1 1
Sty185_Clr010 1 1 1 1 1 1 Sty197_Clr049 1 1 1 1 1 1 Sty204_Clr034 1 1 1 1 1 1
Sty185_Clr011 1 1 1 1 1 1 Sty197_Clr053 1 1 1 1 1 1 Sty204_Clr037 1 1 1 1 1 1
Sty185_Clr014 1 1 1 1 1 1 Sty197_Clr057 1 1 1 1 1 1 Sty204_Clr063 1 1 1 1 1 1
Sty185_Clr015 1 1 1 1 1 1 Sty197_Clr058 1 1 1 1 1 1 Sty205_Clr004 1 1 0 0 0 0
Sty185_Clr035 1 1 1 1 1 1 Sty197_Clr059 1 1 1 1 1 1 Sty205_Clr006 1 0 1 0 0 0
Sty185_Clr036 1 1 1 1 1 1 Sty197_Clr060 1 1 1 1 1 1 Sty205_Clr008 1 1 1 1 1 1
Sty185_Clr041 1 1 1 1 1 1 Sty197_Clr061 1 1 1 1 1 1 Sty205_Clr010 1 0 0 0 0 0
Sty185_Clr042 1 1 1 1 1 1 Sty197_Clr063 1 1 1 1 1 1 Sty205_Clr011 1 1 1 1 1 1
Sty187_Clr030 1 1 1 1 1 1 Sty197_Clr076 1 1 1 1 1 1 Sty205_Clr015 1 0 0 0 0 0
Sty188_Clr030 1 1 1 1 1 1 Sty197_Clr080 1 1 1 1 1 1 Sty205_Clr035 1 0 0 0 0 0
Sty188_Clr080 1 1 1 1 1 1 Sty197_Clr081 1 1 1 1 1 1 Sty205_Clr036 1 0 0 0 0 0
Sty189_Clr009 1 1 1 1 1 1 Sty197_Clr088 1 1 1 1 1 1 Sty205_Clr041 1 0 0 0 0 0
Sty189_Clr012 1 1 1 1 1 1 Sty197_Clr089 1 0 0 0 0 0 Sty206_Clr007 0 1 1 1 1 1
Sty189_Clr017 1 1 1 1 1 1 Sty197_Clr091 1 1 1 1 1 1 Sty206_Clr008 1 1 1 1 1 1
Sty189_Clr036 1 1 1 1 1 1 Sty197_Clr092 1 0 0 0 0 0 Sty206_Clr009 0 1 1 1 1 1
Sty189_Clr037 1 1 1 1 1 1 Sty197_Clr093 1 1 1 1 1 1 Sty206_Clr014 1 1 1 1 1 1
Sty189_Clr042 1 1 1 1 1 1 Sty197_Clr095 1 1 1 1 1 1 Sty206_Clr017 1 0 0 0 0 0
Sty189_Clr045 0 0 0 0 0 0 Sty197_Clr096 0 0 0 0 0 0 Sty207_Clr003 0 1 1 1 1 1
Sty189_Clr058 1 1 1 1 1 1 Sty198_Clr003 1 1 1 1 1 1 Sty208_Clr004 1 1 1 1 1 1
Sty189_Clr059 1 1 1 1 1 1 Sty198_Clr007 1 1 1 1 1 1 Sty208_Clr006 0 1 1 1 1 1
Sty189_Clr060 1 1 1 1 1 1 Sty198_Clr034 1 1 1 1 1 1 Sty208_Clr010 0 0 0 0 0 0
67
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Sty208_Clr011 1 1 1 1 1 1 Sty223_Clr008 1 1 1 1 1 1 Sty225_Clr093 0 0 0 0 0 0
Sty208_Clr015 0 1 1 1 1 1 Sty223_Clr010 1 1 1 1 1 1 Sty225_Clr095 0 1 1 1 1 1
Sty209_Clr030 1 0 0 0 0 0 Sty223_Clr011 1 1 1 1 1 1 Sty227_Clr007 1 1 1 1 1 1
Sty216_Clr014 1 1 1 1 1 1 Sty223_Clr014 1 1 1 1 1 1 Sty227_Clr009 0 0 0 0 0 0
Sty216_Clr017 1 1 1 1 1 1 Sty223_Clr015 1 1 1 1 1 1 Sty227_Clr014 1 1 1 1 1 1
Sty216_Clr018 1 1 1 1 1 1 Sty223_Clr035 0 1 1 1 1 1 Sty227_Clr017 1 0 0 0 0 0
Sty216_Clr058 1 1 1 1 1 1 Sty223_Clr036 1 1 1 1 1 1 Sty228_Clr003 1 1 1 1 1 1
Sty216_Clr059 0 1 1 1 1 1 Sty223_Clr041 1 1 1 1 1 1 Sty228_Clr012 1 1 1 1 1 1
Sty216_Clr060 1 1 1 1 1 1 Sty224_Clr080 0 1 1 1 1 1 Sty228_Clr037 0 1 1 1 1 1
Sty217_Clr003 1 1 1 1 1 1 Sty225_Clr003 1 1 1 1 1 1 Sty228_Clr063 1 1 1 1 1 1
Sty217_Clr007 1 1 1 1 1 1 Sty225_Clr004 1 1 1 1 1 1 Sty229_Clr004 1 1 1 1 1 1
Sty217_Clr012 1 1 1 1 1 1 Sty225_Clr006 0 1 1 1 1 1 Sty229_Clr006 0 0 0 0 0 0
Sty217_Clr034 1 1 1 1 1 1 Sty225_Clr007 1 1 1 1 1 1 Sty229_Clr008 1 0 0 0 0 0
Sty217_Clr037 1 1 1 1 1 1 Sty225_Clr008 1 1 1 1 1 1 Sty229_Clr010 0 0 0 0 0 0
Sty217_Clr047 0 1 1 1 1 1 Sty225_Clr009 0 1 1 1 1 1 Sty229_Clr011 1 1 1 1 1 1
Sty217_Clr048 0 1 1 1 1 1 Sty225_Clr010 0 1 1 1 1 1 Sty229_Clr015 1 1 1 1 1 1
Sty217_Clr049 1 1 1 1 1 1 Sty225_Clr011 1 1 1 1 1 1 Sty229_Clr035 0 0 0 0 0 0
Sty217_Clr063 1 1 1 1 1 1 Sty225_Clr012 1 1 1 1 1 1 Sty229_Clr036 0 0 0 0 0 0
Sty218_Clr004 1 1 1 1 1 1 Sty225_Clr013 1 1 1 1 1 1 Sty235_Clr003 0 1 1 1 1 1
Sty218_Clr006 1 1 1 1 1 1 Sty225_Clr014 1 1 1 1 1 1 Sty235_Clr004 1 1 1 1 1 1
Sty218_Clr008 1 1 1 1 1 1 Sty225_Clr015 1 1 1 1 1 1 Sty235_Clr006 0 1 1 1 1 1
Sty218_Clr009 1 1 1 1 1 1 Sty225_Clr017 1 1 1 1 1 1 Sty235_Clr007 1 1 1 1 1 1
Sty218_Clr010 1 1 1 1 1 1 Sty225_Clr018 1 1 1 1 1 1 Sty235_Clr008 1 1 1 1 1 1
Sty218_Clr011 1 1 1 1 1 1 Sty225_Clr030 0 0 0 0 0 0 Sty235_Clr009 0 1 1 1 1 1
Sty218_Clr015 1 1 1 1 1 1 Sty225_Clr034 1 1 1 1 1 1 Sty235_Clr011 1 1 1 1 1 1
Sty218_Clr035 1 1 1 1 1 1 Sty225_Clr035 1 1 1 1 1 1 Sty235_Clr012 0 1 1 1 1 1
Sty218_Clr036 1 1 1 1 1 1 Sty225_Clr036 1 1 1 1 1 1 Sty235_Clr014 1 1 1 1 1 1
Sty218_Clr041 1 1 1 1 1 1 Sty225_Clr037 1 1 1 1 1 1 Sty235_Clr015 1 1 1 1 1 1
Sty220_Clr030 1 1 1 1 1 1 Sty225_Clr038 0 0 0 0 0 0 Sty235_Clr017 1 1 1 1 1 1
Sty220_Clr032 1 1 1 1 1 1 Sty225_Clr041 1 1 1 1 1 1 Sty235_Clr041 0 1 1 1 1 1
Sty220_Clr080 1 1 1 1 1 1 Sty225_Clr053 1 1 1 1 1 1 Sty236_Clr004 1 0 0 0 0 0
Sty221_Clr009 1 1 1 1 1 1 Sty225_Clr054 0 0 0 0 0 0 Sty236_Clr008 0 0 0 0 0 0
Sty221_Clr013 1 1 1 1 1 1 Sty225_Clr056 0 0 0 0 0 0 Sty236_Clr010 0 1 1 1 1 1
Sty221_Clr017 1 1 1 1 1 1 Sty225_Clr057 0 1 1 1 1 1 Sty236_Clr012 0 1 1 1 1 1
Sty221_Clr058 1 1 1 1 1 1 Sty225_Clr058 1 1 1 1 1 1 Sty236_Clr014 0 0 0 0 0 0
Sty221_Clr059 0 1 1 1 1 1 Sty225_Clr059 0 1 1 1 1 1 Sty236_Clr017 0 0 0 0 0 0
Sty221_Clr060 1 1 1 1 1 1 Sty225_Clr060 1 1 1 1 1 1 Sty237_Clr003 1 1 1 1 1 1
Sty222_Clr003 1 1 1 1 1 1 Sty225_Clr061 0 1 1 1 1 1 Sty237_Clr004 1 1 1 1 1 1
Sty222_Clr007 1 1 1 1 1 1 Sty225_Clr063 1 1 1 1 1 1 Sty237_Clr006 1 1 1 1 1 1
Sty222_Clr012 1 1 1 1 1 1 Sty225_Clr076 0 1 1 1 1 1 Sty237_Clr007 1 1 1 1 1 1
Sty222_Clr034 0 1 1 1 1 1 Sty225_Clr080 1 1 1 1 1 1 Sty237_Clr008 1 1 1 1 1 1
Sty222_Clr037 1 1 1 1 1 1 Sty225_Clr081 1 1 1 1 1 1 Sty237_Clr009 1 0 0 0 0 0
Sty222_Clr044 0 0 0 0 0 0 Sty225_Clr088 0 1 1 1 1 1 Sty237_Clr010 0 1 1 1 1 1
Sty222_Clr063 1 1 1 1 1 1 Sty225_Clr089 0 0 0 0 0 0 Sty237_Clr011 1 1 1 1 1 1
Sty223_Clr004 1 1 1 1 1 1 Sty225_Clr091 0 0 0 0 0 0 Sty237_Clr012 1 1 1 1 1 1
Sty223_Clr006 1 1 1 1 1 1 Sty225_Clr092 0 0 0 0 0 0 Sty237_Clr014 1 1 1 1 1 1
68
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Sty237_Clr015 1 1 1 1 1 1 Sty239_Clr007 1 1 1 1 1 1 Sty285_Clr008 0 0 0 0 0 0
Sty237_Clr017 1 1 1 1 1 1 Sty239_Clr008 1 1 1 1 1 1 Sty285_Clr009 0 0 0 0 0 0
Sty237_Clr034 1 1 1 1 1 1 Sty239_Clr009 1 1 1 1 1 1 Sty285_Clr011 1 0 0 0 0 0
Sty237_Clr035 1 1 1 1 1 1 Sty239_Clr011 1 1 1 1 1 1 Sty285_Clr014 0 0 0 0 0 0
Sty237_Clr036 1 1 1 1 1 1 Sty239_Clr014 1 1 1 1 1 1 Sty285_Clr017 0 0 0 0 0 0
Sty237_Clr037 1 1 1 1 1 1 Sty239_Clr015 1 1 1 1 1 1 Sty285_Clr043 0 0 0 0 0 0
Sty237_Clr041 1 1 1 1 1 1 Sty239_Clr017 1 1 1 1 1 1 Sty285_Clr059 0 0 0 0 0 0
Sty237_Clr054 1 0 0 0 0 0 Sty239_Clr035 1 1 1 1 1 1 Sty286_Clr003 1 0 0 0 0 0
Sty237_Clr056 0 0 0 0 0 0 Sty239_Clr054 1 0 0 0 0 0 Sty286_Clr004 0 0 0 0 0 0
Sty237_Clr058 1 1 1 1 1 1 Sty239_Clr056 0 0 0 0 0 0 Sty286_Clr006 1 0 0 0 0 0
Sty237_Clr059 1 1 1 1 1 1 Sty243_Clr005 1 1 1 1 1 1 Sty286_Clr008 1 0 0 0 0 0
Sty237_Clr060 1 1 1 1 1 1 Sty245_Clr010 0 1 1 1 1 1 Sty286_Clr011 1 0 0 0 0 0
Sty237_Clr063 1 1 1 1 1 1 Sty245_Clr013 1 1 1 1 1 1 Sty286_Clr014 0 0 0 0 0 0
Sty238_Clr003 1 1 1 1 1 1 Sty245_Clr014 1 1 1 1 1 1 Sty286_Clr015 1 0 0 0 0 0
Sty238_Clr004 1 1 1 1 1 1 Sty245_Clr015 0 0 0 0 0 0 Sty286_Clr017 0 0 0 0 0 0
Sty238_Clr006 1 1 1 1 1 1 Sty245_Clr017 1 0 0 0 0 0 Sty286_Clr043 0 0 0 0 0 0
Sty238_Clr007 1 1 1 1 1 1 Sty245_Clr018 0 1 1 1 1 1 Sty286_Clr059 1 0 0 0 0 0
Sty238_Clr008 1 1 1 1 1 1 Sty245_Clr053 1 1 1 1 1 1 Sty291_Clr004 0 1 1 1 1 1
Sty238_Clr009 1 1 1 1 1 1 Sty245_Clr059 0 0 0 0 0 0 Sty291_Clr006 0 0 0 0 0 0
Sty238_Clr010 1 1 1 1 1 1 Sty245_Clr072 0 0 0 0 0 0 Sty291_Clr008 0 0 0 0 0 0
Sty238_Clr011 1 1 1 1 1 1 Sty245_Clr075 0 1 1 1 1 1 Sty291_Clr009 0 0 0 0 0 0
Sty238_Clr012 1 1 1 1 1 1 Sty245_Clr076 0 1 1 1 1 1 Sty291_Clr011 0 0 0 0 0 0
Sty238_Clr014 1 1 1 1 1 1 Sty245_Clr080 0 1 1 1 1 1 Sty291_Clr014 0 0 0 0 0 0
Sty238_Clr015 1 1 1 1 1 1 Sty245_Clr082 1 1 1 1 1 1 Sty291_Clr015 0 0 0 0 0 0
Sty238_Clr017 1 1 1 1 1 1 Sty245_Clr095 0 0 0 0 0 0 Sty291_Clr017 0 0 0 0 0 0
Sty238_Clr018 0 0 0 0 0 0 Sty245_Clr096 0 1 1 1 1 1 Sty309_Clr011 0 0 0 0 0 0
Sty238_Clr034 1 1 1 1 1 1 Sty246_Clr005 0 1 1 1 1 1 Sty309_Clr013 0 0 0 0 0 0
Sty238_Clr035 1 1 1 1 1 1 Sty246_Clr007 0 0 0 1 1 1 Sty309_Clr029 0 0 0 0 0 0
Sty238_Clr036 1 1 1 1 1 1 Sty246_Clr012 1 1 1 1 1 1 Sty310_Clr008 0 0 0 0 0 0
Sty238_Clr037 1 1 1 1 1 1 Sty247_Clr004 1 1 1 1 1 1 Sty310_Clr012 0 0 0 0 0 0
Sty238_Clr041 1 1 1 1 1 1 Sty247_Clr008 1 1 1 1 1 1 Sty311_Clr004 0 0 0 0 0 0
Sty238_Clr053 0 0 0 0 0 0 Sty247_Clr011 0 0 0 0 0 0 Sty311_Clr011 0 0 0 0 0 0
Sty238_Clr054 1 0 0 0 0 0 Sty252_Clr004 1 1 1 1 1 1 Sty311_Clr014 0 0 0 0 0 0
Sty238_Clr056 0 0 0 0 0 0 Sty252_Clr005 0 1 1 1 1 1 Sty311_Clr015 0 0 0 0 0 0
Sty238_Clr058 1 1 1 1 1 1 Sty252_Clr008 1 1 1 1 1 1 Sty311_Clr030 0 0 0 0 0 0
Sty238_Clr059 1 1 1 1 1 1 Sty252_Clr010 1 1 1 1 1 1 Sty312_Clr004 0 0 0 0 0 0
Sty238_Clr060 1 1 1 1 1 1 Sty252_Clr012 1 1 1 1 1 1 Sty313_Clr004 0 0 0 0 0 0
Sty238_Clr063 1 1 1 1 1 1 Sty252_Clr013 1 1 1 1 1 1 Sty313_Clr008 1 1 1 1 1 1
Sty238_Clr081 0 0 0 0 0 0 Sty252_Clr014 1 1 1 1 1 1 Sty314_Clr004 0 0 0 0 0 0
Sty238_Clr089 0 0 0 0 0 0 Sty252_Clr017 1 1 1 1 1 1 Sty314_Clr008 0 0 0 0 0 0
Sty238_Clr091 0 0 0 0 0 0 Sty252_Clr075 1 1 1 1 1 1 Sty314_Clr011 0 0 0 0 0 0
Sty238_Clr092 0 0 0 0 0 0 Sty252_Clr076 1 1 1 1 1 1 Sty315_Clr008 0 0 0 0 0 0
Sty238_Clr093 0 0 0 0 0 0 Sty285_Clr003 1 0 0 0 0 0 Sty315_Clr015 0 0 0 0 0 0
Sty239_Clr003 1 1 1 1 1 1 Sty285_Clr004 0 0 0 0 0 0 Sty315_Clr029 0 0 0 0 0 0
Sty239_Clr004 1 1 1 1 1 1 Sty285_Clr006 0 0 0 0 0 0 Sty315_Clr030 0 0 0 0 0 0
Sty239_Clr006 1 1 1 1 1 1 Sty285_Clr007 1 0 0 0 0 0 Sty315_Clr061 0 0 0 0 0 0
69
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Sty315_Clr073 0 0 0 0 0 0 Sty338_Clr014 0 0 0 0 0 0 Sty345_Clr017 0 0 0 0 0 0
Sty316_Clr011 0 0 0 0 0 0 Sty338_Clr015 0 0 0 0 0 0 Sty345_Clr053 0 0 0 0 0 0
Sty318_Clr008 0 0 0 0 0 0 Sty338_Clr029 0 0 0 0 0 0 Sty346_Clr004 0 0 0 0 0 0
Sty319_Clr008 1 0 0 0 0 0 Sty338_Clr030 0 0 0 0 0 0 Sty346_Clr008 1 0 0 0 0 0
Sty320_Clr008 0 0 0 0 0 0 Sty338_Clr076 0 0 0 0 0 0 Sty346_Clr011 1 0 0 0 0 0
Sty320_Clr053 1 0 0 0 0 0 Sty339_Clr008 0 0 0 0 0 0 Sty346_Clr015 0 0 0 0 0 0
Sty320_Clr076 0 0 0 0 0 0 Sty341_Clr008 0 0 0 0 0 0 Sty346_Clr017 1 0 0 0 0 0
Sty321_Clr008 0 0 0 0 0 0 Sty341_Clr011 1 0 0 0 0 0 Sty346_Clr029 0 0 0 0 0 0
Sty322_Clr008 0 0 0 0 0 0 Sty341_Clr012 0 0 0 0 0 0 Sty347_Clr004 1 0 0 0 0 0
Sty322_Clr011 1 0 0 0 0 0 Sty341_Clr017 0 0 0 0 0 0 Sty347_Clr008 0 0 0 0 0 0
Sty323_Clr008 0 0 0 0 0 0 Sty342_Clr004 0 0 0 0 0 0 Sty347_Clr011 0 0 0 0 0 0
Sty323_Clr014 0 0 0 0 0 0 Sty342_Clr007 0 0 0 0 0 0 Sty347_Clr012 1 0 0 0 0 0
Sty323_Clr015 0 0 0 0 0 0 Sty342_Clr008 0 0 0 0 0 0 Sty347_Clr017 1 0 0 0 0 0
Sty323_Clr029 0 0 0 0 0 0 Sty342_Clr011 1 0 0 0 0 0 Sty348_Clr008 0 0 0 0 0 0
Sty323_Clr030 0 0 0 0 0 0 Sty342_Clr012 0 0 0 0 0 0 Sty349_Clr004 1 0 0 0 0 0
Sty325_Clr017 0 0 0 0 0 0 Sty342_Clr013 0 0 0 0 0 0 Sty349_Clr007 0 0 0 0 0 0
Sty325_Clr053 0 0 0 0 0 0 Sty342_Clr014 0 0 0 0 0 0 Sty349_Clr008 1 0 0 0 0 0
Sty326_Clr008 1 0 0 0 0 0 Sty342_Clr015 0 0 0 0 0 0 Sty349_Clr011 1 0 0 0 0 0
Sty327_Clr004 0 0 0 0 0 0 Sty342_Clr017 0 0 0 0 0 0 Sty349_Clr013 1 0 0 0 0 0
Sty327_Clr008 0 0 0 0 0 0 Sty342_Clr030 0 0 0 0 0 0 Sty349_Clr014 1 0 0 0 0 0
Sty327_Clr011 0 0 0 0 0 0 Sty342_Clr034 0 0 0 0 0 0 Sty349_Clr015 1 0 0 0 0 0
Sty327_Clr042 0 0 0 0 0 0 Sty342_Clr036 0 0 0 0 0 0 Sty349_Clr029 0 0 0 0 0 0
Sty329_Clr006 0 0 0 0 0 0 Sty342_Clr053 1 0 0 0 0 0 Sty349_Clr034 1 0 0 0 0 0
Sty329_Clr008 0 0 0 0 0 0 Sty342_Clr055 0 0 0 0 0 0 Sty349_Clr036 0 0 0 0 0 0
Sty329_Clr015 0 0 0 0 0 0 Sty342_Clr073 0 0 0 0 0 0 Sty349_Clr042 1 0 0 0 0 0
Sty329_Clr030 0 0 0 0 0 0 Sty342_Clr082 0 0 0 0 0 0 Sty349_Clr045 0 0 0 0 0 0
Sty329_Clr046 1 0 0 0 0 0 Sty342_Clr084 0 0 0 0 0 0 Sty349_Clr053 0 0 0 0 0 0
Sty329_Clr059 0 0 0 0 0 0 Sty343_Clr004 1 0 0 0 0 0 Sty349_Clr055 1 0 0 0 0 0
Sty329_Clr061 0 0 0 0 0 0 Sty343_Clr007 0 0 0 0 0 0 Sty349_Clr059 0 0 0 0 0 0
Sty330_Clr014 1 0 0 0 0 0 Sty343_Clr008 1 1 1 1 1 1 Sty349_Clr060 0 0 0 0 0 0
Sty330_Clr047 1 0 0 0 0 0 Sty343_Clr011 1 1 1 1 1 1 Sty349_Clr061 1 0 0 0 0 0
Sty331_Clr008 0 0 0 0 0 0 Sty343_Clr012 0 0 0 0 0 0 Sty349_Clr063 0 0 0 0 0 0
Sty331_Clr073 0 0 0 0 0 0 Sty343_Clr013 0 0 0 0 0 0 Sty349_Clr073 0 0 0 0 0 0
Sty332_Clr004 0 0 0 0 0 0 Sty343_Clr014 1 0 0 0 0 0 Sty349_Clr082 1 0 0 0 0 0
Sty332_Clr008 1 0 0 0 0 0 Sty343_Clr015 1 1 1 1 1 1 Sty349_Clr084 0 0 0 0 0 0
Sty332_Clr011 1 0 0 0 0 0 Sty343_Clr017 0 0 0 0 0 0 Sty349_Clr165 0 0 0 0 0 0
Sty333_Clr008 1 0 0 0 0 0 Sty343_Clr029 0 0 0 0 0 0 Sty349_Clr166 0 0 0 0 0 0
Sty335_Clr011 1 0 0 0 0 0 Sty343_Clr030 0 0 0 0 0 0 Sty350_Clr011 1 0 0 0 0 0
Sty336_Clr012 0 0 0 0 0 0 Sty343_Clr036 0 0 0 0 0 0 Sty351_Clr073 0 0 0 0 0 0
Sty336_Clr017 0 0 0 0 0 0 Sty343_Clr055 0 0 0 0 0 0 Sty352_Clr004 0 0 0 0 0 0
Sty338_Clr004 0 0 0 0 0 0 Sty343_Clr063 0 0 0 0 0 0 Sty353_Clr008 0 0 0 0 0 0
Sty338_Clr007 0 0 0 0 0 0 Sty343_Clr082 0 0 0 0 0 0 Sty354_Clr009 1 1 1 1 1 1
Sty338_Clr008 0 0 0 0 0 0 Sty343_Clr084 0 0 0 0 0 0 Sty354_Clr014 1 1 1 1 1 1
Sty338_Clr011 0 0 0 0 0 0 Sty345_Clr007 0 0 0 0 0 0 Sty354_Clr017 1 1 1 1 1 1
Sty338_Clr012 0 0 0 0 0 0 Sty345_Clr008 0 0 0 0 0 0 Sty354_Clr018 1 1 1 1 1 1
Sty338_Clr013 0 1 1 1 1 1 Sty345_Clr012 0 0 0 0 0 0 Sty354_Clr032 0 1 1 1 1 1
70
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Sty354_Clr059 1 1 1 1 1 1 Sty398_Clr014 1 0 0 0 0 0 Sty404_Clr035 1 0 0 0 0 0
Sty354_Clr088 1 1 1 1 1 1 Sty398_Clr017 1 0 0 0 0 0 Sty405_Clr030 1 1 1 1 1 1
Sty355_Clr003 1 1 1 1 1 1 Sty398_Clr018 0 0 0 0 0 0 Sty406_Clr003 1 1 1 1 1 1
Sty355_Clr007 1 1 1 1 1 1 Sty398_Clr056 0 0 0 0 0 0 Sty406_Clr004 1 1 1 1 1 1
Sty356_Clr004 1 1 1 1 1 1 Sty398_Clr059 0 0 0 0 0 0 Sty406_Clr006 1 1 1 1 1 1
Sty356_Clr006 1 1 1 1 1 1 Sty399_Clr003 1 1 1 1 1 1 Sty406_Clr007 1 1 1 1 1 1
Sty356_Clr008 1 1 1 1 1 1 Sty399_Clr005 1 0 0 0 0 0 Sty406_Clr008 1 1 1 1 1 1
Sty356_Clr010 1 1 1 1 1 1 Sty399_Clr007 0 1 1 1 1 1 Sty406_Clr009 1 1 1 1 1 1
Sty356_Clr011 1 1 1 1 1 1 Sty399_Clr012 0 0 0 0 0 0 Sty406_Clr010 1 0 0 0 0 0
Sty356_Clr015 1 1 1 1 1 1 Sty399_Clr048 1 0 0 0 0 0 Sty406_Clr011 1 1 1 1 1 1
Sty356_Clr042 1 1 1 1 1 1 Sty400_Clr004 1 1 1 1 1 1 Sty406_Clr014 1 1 1 1 1 1
Sty358_Clr007 1 1 1 1 1 1 Sty400_Clr006 1 1 1 1 1 1 Sty406_Clr015 1 1 1 1 1 1
Sty358_Clr009 1 1 1 1 1 1 Sty400_Clr008 1 1 1 1 1 1 Sty406_Clr017 1 1 1 1 1 1
Sty358_Clr014 1 1 1 1 1 1 Sty400_Clr009 1 1 1 1 1 1 Sty407_Clr014 1 1 1 1 1 1
Sty358_Clr017 1 1 1 1 1 1 Sty400_Clr010 1 0 0 0 0 0 Sty407_Clr017 1 1 1 1 1 1
Sty358_Clr018 1 1 1 1 1 1 Sty400_Clr011 1 1 1 1 1 1 Sty407_Clr059 0 0 0 0 0 0
Sty358_Clr032 0 1 1 1 1 1 Sty400_Clr015 1 0 0 0 0 0 Sty408_Clr003 1 1 1 1 1 1
Sty358_Clr059 0 1 1 1 1 1 Sty400_Clr035 0 0 0 0 0 0 Sty408_Clr005 0 0 0 0 0 0
Sty358_Clr088 1 1 1 1 1 1 Sty400_Clr036 0 0 0 0 0 0 Sty408_Clr007 1 1 1 1 1 1
Sty359_Clr003 1 1 1 1 1 1 Sty400_Clr041 0 0 0 0 0 0 Sty408_Clr012 0 1 1 1 1 1
Sty359_Clr005 1 1 1 1 1 1 Sty400_Clr060 0 0 0 0 0 0 Sty409_Clr004 1 1 1 1 1 1
Sty359_Clr044 1 1 1 1 1 1 Sty401_Clr030 0 0 0 0 0 0 Sty409_Clr006 1 1 1 1 1 1
Sty359_Clr047 1 1 1 1 1 1 Sty402_Clr007 1 1 1 1 1 1 Sty409_Clr008 1 1 1 1 1 1
Sty360_Clr004 1 1 1 1 1 1 Sty402_Clr012 1 1 1 1 1 1 Sty409_Clr009 0 1 1 1 1 1
Sty360_Clr006 1 1 1 1 1 1 Sty402_Clr014 1 1 1 1 1 1 Sty409_Clr010 1 0 0 0 0 0
Sty360_Clr008 1 1 1 1 1 1 Sty402_Clr017 1 1 1 1 1 1 Sty409_Clr011 1 1 1 1 1 1
Sty360_Clr010 0 0 0 0 0 0 Sty402_Clr018 0 1 1 1 1 1 Sty409_Clr015 1 1 1 1 1 1
Sty360_Clr011 1 1 1 1 1 1 Sty402_Clr034 0 0 0 0 0 0 Sty409_Clr036 0 0 0 0 0 0
Sty360_Clr015 1 1 1 1 1 1 Sty402_Clr036 1 1 1 1 1 1 Sty409_Clr041 0 1 1 1 1 1
Sty360_Clr042 1 1 1 1 1 1 Sty402_Clr037 0 0 0 0 0 0 Sty409_Clr060 0 0 0 0 0 0
Sty361_Clr030 0 1 1 1 1 1 Sty402_Clr041 1 1 1 1 1 1 Sty410_Clr030 0 0 0 0 0 0
Sty362_Clr003 1 1 1 1 1 1 Sty402_Clr045 1 0 0 0 0 0 Sty411_Clr003 1 1 1 1 1 1
Sty362_Clr007 1 1 1 1 1 1 Sty402_Clr054 0 0 0 0 0 0 Sty411_Clr007 0 0 0 0 0 0
Sty362_Clr009 1 1 1 1 1 1 Sty402_Clr056 1 0 0 0 0 0 Sty411_Clr008 1 1 1 1 1 1
Sty362_Clr015 1 1 1 1 1 1 Sty402_Clr058 1 1 1 1 1 1 Sty411_Clr009 1 1 1 1 1 1
Sty362_Clr017 1 1 1 1 1 1 Sty402_Clr059 0 1 1 1 1 1 Sty411_Clr017 1 1 1 1 1 1
Sty362_Clr042 1 1 1 1 1 1 Sty402_Clr060 0 1 1 1 1 1 Sty412_Clr004 1 1 1 1 1 1
Sty362_Clr059 1 1 1 1 1 1 Sty402_Clr063 1 1 1 1 1 1 Sty412_Clr006 1 1 1 1 1 1
Sty362_Clr088 1 1 1 1 1 1 Sty403_Clr003 1 1 1 1 1 1 Sty412_Clr011 1 1 1 1 1 1
Sty363_Clr004 1 1 1 1 1 1 Sty404_Clr004 1 1 1 1 1 1 Sty412_Clr014 1 1 1 1 1 1
Sty363_Clr006 1 1 1 1 1 1 Sty404_Clr006 1 1 1 1 1 1 Sty412_Clr015 1 1 1 1 1 1
Sty363_Clr008 1 1 1 1 1 1 Sty404_Clr008 1 1 1 1 1 1 Sty413_Clr003 1 1 1 1 1 1
Sty363_Clr010 0 1 1 1 1 1 Sty404_Clr009 1 1 1 1 1 1 Sty413_Clr007 1 1 1 1 1 1
Sty363_Clr011 1 1 1 1 1 1 Sty404_Clr010 1 0 0 0 0 0 Sty413_Clr008 1 1 1 1 1 1
Sty363_Clr014 1 1 1 1 1 1 Sty404_Clr011 1 1 1 1 1 1 Sty413_Clr009 1 1 1 1 1 1
Sty365_Clr003 0 0 0 0 0 0 Sty404_Clr015 1 1 1 1 1 1 Sty413_Clr012 1 1 1 1 1 1
71
Product 1 2 3 4 5 6 Product 1 2 3 4 5 6 Product 1 2 3 4 5 6
Sty413_Clr017 1 1 1 1 1 1 Sty430_Clr018 0 0 0 0 0 0 Sty494_Clr017 0 0 0 0 0 0
Sty413_Clr059 0 0 0 1 1 1 Sty430_Clr030 0 0 0 0 0 0 Sty494_Clr050 0 1 1 1 1 1
Sty413_Clr060 0 1 1 1 1 1 Sty430_Clr038 0 0 0 0 0 0 Sty495_Clr050 0 0 0 0 0 0
Sty414_Clr004 1 1 1 1 1 1 Sty430_Clr053 1 1 1 1 1 1 Sty496_Clr017 0 0 0 0 0 0
Sty414_Clr006 1 1 1 1 1 1 Sty430_Clr055 0 0 0 0 0 0 Sty496_Clr050 0 0 0 0 0 0
Sty414_Clr010 1 0 0 0 0 0 Sty430_Clr057 0 0 0 0 0 0 Sty497_Clr050 0 0 0 0 0 0
Sty414_Clr011 1 1 1 1 1 1 Sty430_Clr059 0 1 1 1 1 1 Sty498_Clr050 0 0 0 0 0 0
Sty414_Clr014 1 1 1 1 1 1 Sty430_Clr072 0 0 0 0 0 0 Sty499_Clr050 0 0 0 0 0 0
Sty414_Clr015 1 1 1 1 1 1 Sty430_Clr075 0 1 1 1 1 1 Sty500_Clr050 0 0 0 0 0 0
Sty415_Clr003 1 1 1 1 1 1 Sty430_Clr076 0 0 0 0 0 0 Sty501_Clr050 0 1 1 1 1 1
Sty415_Clr004 1 1 1 1 1 1 Sty430_Clr080 0 1 1 1 1 1 Sty502_Clr050 0 0 0 0 0 0
Sty415_Clr006 1 1 1 1 1 1 Sty430_Clr082 0 1 1 1 1 1 Sty503_Clr017 0 0 0 0 0 0
Sty415_Clr007 1 1 1 1 1 1 Sty430_Clr095 0 0 0 0 0 0 Sty503_Clr050 0 0 0 0 0 0
Sty415_Clr008 1 1 1 1 1 1 Sty430_Clr096 0 0 0 0 0 0 Sty504_Clr017 0 0 0 0 0 0
Sty415_Clr009 1 1 1 1 1 1 Sty458_Clr017 1 1 1 1 1 1 Sty504_Clr050 0 0 0 0 0 0
Sty415_Clr011 1 1 1 1 1 1 Sty459_Clr005 1 1 1 1 1 1 Sty505_Clr017 0 0 0 0 0 0
Sty415_Clr014 1 1 1 1 1 1 Sty459_Clr007 1 1 1 1 1 1 Sty505_Clr050 0 0 0 0 0 0
Sty415_Clr015 1 1 1 1 1 1 Sty459_Clr012 1 1 1 1 1 1 Sty508_Clr017 0 0 0 0 0 0
Sty415_Clr017 1 1 1 1 1 1 Sty460_Clr008 0 1 1 1 1 1 Sty508_Clr050 0 0 0 0 0 0
Sty417_Clr003 1 1 1 1 1 1 Sty460_Clr011 1 1 1 1 1 1 Sty509_Clr017 0 0 0 0 0 0
Sty417_Clr004 1 1 1 1 1 1 Sty461_Clr017 1 1 1 1 1 1 Sty510_Clr017 0 0 0 0 0 0
Sty417_Clr006 1 1 1 1 1 1 Sty462_Clr005 1 1 1 1 1 1 Sty511_Clr017 0 0 0 0 0 0
Sty417_Clr007 0 0 0 0 0 0 Sty462_Clr007 1 1 1 1 1 1 Sty511_Clr050 0 0 0 0 0 0
Sty417_Clr008 1 1 1 1 1 1 Sty462_Clr012 1 1 1 1 1 1 Sty513_Clr017 0 0 0 0 0 0
Sty417_Clr009 1 1 1 1 1 1 Sty463_Clr008 1 1 1 1 1 1 Sty513_Clr050 0 0 0 0 0 0
Sty417_Clr011 1 1 1 1 1 1 Sty472_Clr004 1 1 1 1 1 1 Sty514_Clr017 0 1 1 1 1 1
Sty417_Clr014 1 1 1 1 1 1 Sty472_Clr008 1 1 1 1 1 1 Sty514_Clr050 1 1 1 1 1 1
Sty417_Clr015 0 1 1 1 1 1 Sty472_Clr010 1 1 1 1 1 1 Sty515_Clr017 0 0 0 0 0 0
Sty417_Clr017 1 1 1 1 1 1 Sty472_Clr012 1 1 1 1 1 1 Sty515_Clr050 0 0 0 0 0 0
Sty421_Clr004 1 1 1 1 1 1 Sty472_Clr014 1 1 1 1 1 1 Sty522_Clr017 0 0 0 0 0 0
Sty421_Clr008 0 0 0 0 0 0 Sty472_Clr017 1 1 1 1 1 1 Sty522_Clr050 0 0 0 0 0 0
Sty421_Clr010 0 0 0 1 1 1 Sty472_Clr018 1 1 1 1 1 1 Sty525_Clr017 0 0 0 0 0 0
Sty421_Clr012 0 1 1 1 1 1 Sty472_Clr059 1 1 1 1 1 1 Sty525_Clr050 0 0 0 0 0 0
Sty421_Clr014 0 0 0 0 0 0 Sty473_Clr004 1 1 1 1 1 1 Sty526_Clr017 0 0 0 0 0 0
Sty421_Clr017 0 0 1 1 1 1 Sty473_Clr008 1 1 1 1 1 1 Sty526_Clr050 1 1 1 1 1 1
Sty430_Clr004 1 1 1 1 1 1 Sty473_Clr010 1 1 1 1 1 1 Sty527_Clr017 0 1 1 1 1 1
Sty430_Clr005 0 0 0 0 0 0 Sty473_Clr012 1 1 1 1 1 1 Sty527_Clr050 1 1 1 1 1 1
Sty430_Clr007 0 1 1 1 1 1 Sty473_Clr014 0 1 1 1 1 1 Sty528_Clr050 0 0 0 0 0 0
Sty430_Clr008 0 1 1 1 1 1 Sty473_Clr017 1 1 1 1 1 1 Sty529_Clr017 0 0 0 0 0 0
Sty430_Clr010 0 1 1 1 1 1 Sty473_Clr018 1 1 1 1 1 1 Sty529_Clr050 0 0 0 0 0 0
Sty430_Clr011 0 0 0 0 0 0 Sty473_Clr059 1 1 1 1 1 1 Sty530_Clr017 0 0 0 0 0 0
Sty430_Clr012 0 0 0 0 0 0 Sty486_Clr017 0 0 0 0 0 0 Sty530_Clr050 0 0 0 0 0 0
Sty430_Clr013 0 1 1 1 1 1 Sty486_Clr050 0 0 0 0 0 0 Sty532_Clr017 0 0 0 0 0 0
Sty430_Clr014 0 1 1 1 1 1 Sty492_Clr017 0 0 0 0 0 0 Sty532_Clr050 0 0 0 0 0 0
Sty430_Clr015 0 1 1 1 1 1 Sty493_Clr017 0 0 0 0 0 0 Sty533_Clr017 0 0 0 0 0 0
Sty430_Clr017 0 0 0 0 0 0 Sty493_Clr050 0 1 1 1 1 1 Sty533_Clr050 0 1 1 1 1 1
72
Product 1 2 3 4 5 6
Sty534_Clr050 0 1 1 1 1 1
Sty535_Clr017 0 0 0 0 0 0
Sty535_Clr050 0 0 0 0 0 0
Sty536_Clr017 0 0 0 0 0 0
Sty536_Clr050 0 0 0 0 0 0
Sty537_Clr017 0 0 0 0 0 0
Sty537_Clr050 0 0 0 0 0 0
Sty538_Clr017 0 0 0 0 0 0
Sty538_Clr050 0 0 0 0 0 0
Sty541_Clr017 0 0 0 0 0 0
Sty541_Clr050 0 0 0 0 0 0
Sty544_Clr017 0 0 0 0 0 0
Sty544_Clr050 1 0 0 0 0 0
Sty546_Clr017 0 1 1 1 1 1
Sty546_Clr050 0 0 0 0 0 0
Sty547_Clr017 0 0 0 0 0 0
Sty547_Clr050 0 0 0 0 0 0
73
.3 Appendix C: Overall GMROI LINGO Code
!GMROI Model solved using Dinkelbach Algorithm;
Model:
Sets:
SKU/1..1120/: MARGIN, COST, UNITS_SOLD, AVG_INVENTORY, X; !x(i) = decision
SKUs;
Endsets
Data:
MARGIN, COST, UNITS_SOLD, AVG_INVENTORY =
@OLE('C:\Users\Jackson\Dropbox\Northeastern University\OR Masters
Thesis\Models\Data_3.07.2013.xlsx', 'MARGIN', 'COST', 'UNITS_SOLD',
'AVG_INVENTORY');
q = 0; !Initial parameter for q;
tol = .01; !Optimality Tolreance;
continue = 1;
OldStandardGM = 72433436.29; !Old Standard Gross Margin of Product Portfolio; OldInvestmentCap = 33494976.74; !Old Investment Capital of Product Portfolio; NewSKUCount = 672; !Parameter to choose how many to drop in the product
portfolio;
Turns = 4.51; !Inventory Turnover RHS paramter;
Enddata
Submodel Z:
InvestmentCAP = .90*OldInvestmentCap; !Investment Capital RHS parameter;
Check = @SUM(SKU:X);
[OBJ] MAX=@SUM(SKU:(MARGIN*X)) - q*@SUM(SKU:(COST*X));
@SUM(SKU: X*COST) >= InvestmentCAP; !New Product Portfolio must be greater
than certain amount of InvestmetCAP;
@SUM(SKU: X*UNITS_SOLD) - Turns*@SUM(SKU: X*AVG_INVENTORY) >= 0; !Inventory
Turnover constraint (Linearized);
@SUM(SKU: X) <= NewSKUCount; !New SKU count in product portfolio;
@FOR(SKU: @BIN(X)); !Binary only for all X(i);
ENDSUBMODEL
!Dinkelbach Algorithm;
Calc:
!Create loop;
@while ( continue #EQ# 1 :
!Solve until optimal q reached;
@Solve(Z); !Solve the model Z;
@IFC( OBJ #LT# tol : !If Objective value of Z is less than
optimality tolerance, then stop the model;
continue = 0;
@OLE('C:\Users\Jackson\Dropbox\Northeastern University\OR Masters Thesis\Models\Data_3.07.2013.xlsx', 'SOLUTIONS', 'Q') = X, q;
@ELSE !Otherwise, update parameter q and solve again;
q = @SUM(SKU:(MARGIN*X))/@SUM(SKU:(COST*X));
);
);
Endcalc
End
74
.4 Appendix D: Individual GMROI LINGO Code
!Product portfolio optimization model;
Model:
Sets:
SKU/1..1120/: MARGIN, COST, UNITS_SOLD, AVG_INVENTORY, X; !x(i) = decision
SKUs;
Endsets
OldStandardGM = 72433436.29; !Old Standard Gross Margin of Product Portfolio; OldInvestmentCap = 33494976.74 ; !Old Inventory Investment Capital of Prod Portfolio; NewSKUCount = 672; !Parameter to choose how many to drop in the product
portfolio; !20% reduced SKUs = -224;
Turns = 4.51; !Inventory Turnover RHS paramter;
InvestmentCAP = .90*OldInvestmentCap; !Investment Capital RHS parameter;
Check_X = @SUM(SKU:X);
Used = @SUM(SKU: X*COST);
[OBJ] MAX=@SUM(SKU: ((MARGIN/COST)*X));!Maximize Avg. GMROII, select worst
performing SKUs;
@SUM(SKU: X*COST) >= InvestmentCAP; !New Product Portfolio must be greater
than certain amount of InvestmetCAP;
@SUM(SKU: X*UNITS_SOLD) - Turns*@SUM(SKU: X*AVG_INVENTORY) >= 0; !Inventory
Turnover constraint (Linearized);
@SUM(SKU: X) <= NewSKUCount; !New SKU count in product portfolio;
@FOR(SKU: @BIN(X)); !Binary only for all X(i);
Data:
MARGIN, COST, UNITS_SOLD, AVG_INVENTORY =
@OLE('C:\Users\Jackson\Dropbox\Northeastern University\OR Masters
Thesis\Models\Data_3.07.2013.xlsx', 'MARGIN', 'COST', 'UNITS_SOLD',
'AVG_INVENTORY');
!Export solutions into Excel;
@OLE('C:\Users\Jackson\Dropbox\Northeastern University\OR Masters
Thesis\Models\Data_3.07.2013.xlsx', 'AVGSOLUTION')= X;
Enddata
end
75
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