i

New Jersey Institute of Technology

School of Management

Demand Forecast & Network Design

Distribution Logistics - MGMT 625

by

Anjaneya Ravi Teja Golla

Davide Lispi

Under the guidance of

Prof. Pius Egbelu

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ABSTRACT

Increasing demand and capacity constraints have become the keys concerns for the

cosmetic company which gave us the opportunity to work on developing the optimal network

design in order to satisfy the growing demand of one of their most competitive cosmetic product

having a global market.

In this paper we analyzed the global demand trends and stages in order to forecast the

maturity demand of the particular product according to the company’s previous global sales data.

We studied the different forecasting models in order to figure out which fits better with the

demand data characteristics, such as level, trend and seasonality. We identified and applied the

Holt’s model, which gave us the forecasted demand level for the maturity stage.

The forecasted demand has been used as the input in developing the network design

model, which aimed to meet the growing demand and the production capacity. The main

objective is to provide a solution regarding whether and where to open new manufacturing

plant(s) from the potential locations identified by the cosmetic company.

The objective of the company is to define the optimum distribution network in order to

satisfy the regional demand with the minimum cost. The main objective of the paper is to use the

demand data to forecast the expected demand level of the product maturity stage, and utilize

those results as input for the network design process in order to define the optimal distribution

network at the minimum cost.

As per the agreements, we are not supposed to give out the name of the company, the

product type and brand. All the used data has been modified as per the original data by the

company, in accordance to the privacy policy.

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Contents

1. DESCRIPTION OF THE PROBLEM ........................................................................................ 1

2. ELEMENT OF THE PROBLEM ............................................................................................... 2

3. PRESENTATION OF THE DEMAND DATA ......................................................................... 3

4. DESCRIPTION OF THE TOOLS .............................................................................................. 5

4.1 Forecasting model ................................................................................................................. 5

4.1.1 Trend-corrected exponential smoothing (Holt’s model) ................................................ 9

4.1.2 Forecasting Error Measurements ................................................................................. 10

4.2 Network design ................................................................................................................... 12

4.2.1 Facilities - drivers of supply chain performance.......................................................... 12

4.2.2 Role in the supply chain ............................................................................................... 12

4.2.3 Role in the competitive strategy .................................................................................. 13

4.2.4 Components of facilities decisions .............................................................................. 13

4.2.5 Facility-Related Metrics............................................................................................... 15

4.2.6 Overall trade-off: responsiveness versus efficiency .................................................... 16

4.2.7 Factors influencing distribution network design.......................................................... 17

4.2.8 The role of network design in the supply chain ........................................................... 18

4.2.9 Factors influencing network design decisions ............................................................. 20

4.2.10 Capacitated Plant Location Model ................................................................................. 23

5. APPLICATION OF THE TOOLS & ANALYSIS OF RESULTS .......................................... 25

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5.1 Forecasts ............................................................................................................................. 25

5.1.1 Aggregate forecasted data ............................................................................................ 25

5.1.2 Europe .......................................................................................................................... 31

5.1.3 America ........................................................................................................................ 32

5.1.4 Africa ........................................................................................................................... 33

5.1.5 Asia pacific .................................................................................................................. 34

5.1.6 Middle East .................................................................................................................. 35

5.2 Application of the Network Design tool ............................................................................. 36

5.2.1 Network model when all the locations are opened ...................................................... 37

5.2.2 Network Model - Capitalized Plant location Network model ..................................... 38

6. CONCLUSIONS....................................................................................................................... 39

7. FUTURE WORK ...................................................................................................................... 39

8. REFERENCES ......................................................................................................................... 41

List of Tables:

table 1: Aggregate Demand ............................................................................................................ 3

Table 2: Quarterly Regional Demand Data .................................................................................... 4

Table 3: Aggregate Demand Forecast – Model 1 ......................................................................... 26

Table 4: Regional Demand Forecast – Model 1 ........................................................................... 28

Table 5: Aggregate Demand Forecast – Model 2 (Growing Stage) ............................................. 30

Table 6: Europe Demand Forecast – Model 2 .............................................................................. 31

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Table 7: America Demand Forecast – Model 2 ............................................................................ 32

Table 8: Africa Demand Forecast – Model 2................................................................................ 33

Table 9: Asia Demand Forecast – Model 2 .................................................................................. 34

Table 10: Middle East Demand Forecast – Model 2 .................................................................... 35

Table 11: Network Design Data ................................................................................................... 36

Table 12: Network Model – All Locations Opened...................................................................... 37

Table 13: Network Design – Capitalized Plant Locations ............................................................ 38

List of Figures:

Figure 1: Graph Illustrating Product Life Cycle ............................................................................. 1

Figure 2: Aggregate Demand .......................................................................................................... 3

Figure 3: Quarterly Regional Demand Data Graph ........................................................................ 4

Figure 4: Costs Vs. Number Of Facilities .................................................................................... 16

Figure 5: Facility Costs Vs. Number Of Facilities ....................................................................... 18

Figure 6: Graph Of Aggregate Demand Forecast – Model 1........................................................ 27

Figure 7: Graph Illustrating The Year-Wise Product Life Cycle ................................................. 29

Figure 8: Aggregate Demand Forecast – Model 2 (Growing Stage) ............................................ 30

Figure 9: Europe Demand Forecast – Model 2 ............................................................................. 32

Figure 10: Africa Demand Forecast – Model 2 ............................................................................ 33

Figure 11: Asia Demand Forecast – Model 2 ............................................................................... 34

Figure 12: Middle East Demand Forecast – Model 2 ................................................................... 35

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1. DESCRIPTION OF THE PROBLEM

The main objective of the company is to study the evolution of the demand related to the

cosmetic products in order to understand if their actual production capacity can satisfy the future

demand. In particular, the company collected regional quarterly demand data from 2009 to 2014.

According to those data, the demand shows a strong increasing trend since the beginning of 2012

without seasonality. This is the reason why the company considers the product in its growing

phase. Moreover, the company is actually serving all the markets thanks to three plants located in

France, America and India. The CEO of the company is convinced that the available production

demand is not enough to completely satisfy the

future demand. In fact, the responsible of

marketing predicted that the product demand

will reach its maturity stage at the end of 2017

according to its marketing effort. Thus, the first

objective of this study is to identify the best

forecasting model to estimate the regional

demand for the next three years.

The second purpose of the analysis is to set up a better distribution network that allows

the company to minimize the total costs and satisfy the forecasted demand. To do so, the

company wants to increase its total production capacity by setting up new facilities. Thus, they

have to figure out which are the best locations considering those ones the company has already

identified as potential sites. In particular, there are four alternatives that are Germany, South

Africa, Dubai and Japan. In order to solve the problem, the company has figured out the potential

Figure 1: Graph illustrating Product Life Cycle

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costs dealing with production, transportation and fixed costs for each location. They can be used

to set up a network design optimization model.

Considering the outcomes of the forecasted demand and utilizing them as the input for

the network design, the major objective of the project is to define the optimum distribution

network. In particular, the cosmetic company wants to satisfy the expected demand for the

product in the maturity stage by defining the optimal network, which has the minimum total cost.

2. ELEMENT OF THE PROBLEM

The critical key element of the problem is the demand data. This is essential to complete

the analysis regarding future forecasts. The data comes directly from the company’s resources

and sales department located in the different regions in which they operate. They have been

collected from the company’s accounting and sales departments from the launch of the product

and during the previous years of activity. As previously said, the demand is quarterly.

All the data needed to set up the network design problem come from the company’s

actual cost structure and estimations. The first item is represented by production costs. The

company’s finance department estimates the production costs for the potential locations based

upon its actual production costs from its existing plants. Moreover, for each potential region the

department takes into account the raw materials costs, components costs, labor cost, energy, tax

and other overhead costs accordingly. The second element of the network design problem deals

with transportation costs. The company estimates them based on the average quotations from its

main logistic partners that operate all over the world. Furthermore, fixed costs represent an

important item that has to be included in the formulation of the model. Costs regarding actual

locations come from the finance department, while fees dealing with potential location have been

estimated from the company taking into account they actual fixed costs and regional influences.

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3. PRESENTATION OF THE DEMAND DATA

In this section we present the demand data. The company provided us the demand data

coming from the sales department. All data regarding demand are reported in the following

tables. The first table describes the aggregate demand, while the following tables shows the

quarterly demand for each region. The information reported in the tables is plotted on graphs to

show the patter of the demand and the shape of its curve.

Table 1: Aggregate Demand

Here we have the demand data referred to each different region and

divided quarterly. We noticed that the patterns of the demand referred to each region have the

same shape of the aggregate demand, thus they can be analyzed using the same model. The

following graph describes the pattern of the demand of each region:

AGGREGATE DEMAND

YEAR QUARTER DEMAND

2009 I 15000

II 15000

III 16000

IV 17000

2010 I 18000

II 20000

III 21000

IV 21000

2011 I 20500

II 20000

III 20000

IV 19000

2012 I 20000

II 22000

III 27000

IV 30000

2013 I 32100

II 37000

III 41000

IV 38200

2014 I 43300

II 51000

III 55800

IV 60000

0

10000

20000

30000

40000

50000

60000

70000

0 5 10 15 20 25 30

Dem

and

Quarters

AGGREGATE DEMAND

Figure 2: Aggregate Demand

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Table 2: Quarterly Regional Demand Data

EUROPE AMERICA AFRICA ASIA PACIFIC MIDDLE EAST

YEAR QUARTER DEMAND DEMAND DEMAND DEMAND DEMAND

2009 I 8970 3000 105 2625 300

II 8805 3075 105 2685 330

III 9312 3248 112 2944 384

IV 9758 3434 136 3230 442

2010 I 10188 3672 144 3492 504

II 11419 4285 164 4018 615

III 11466 4481 191 4160 701

IV 11256 4896 195 3950 703

2011 I 11644 4797 200 3101 758

II 10720 4760 188 3520 813

III 9707 5120 191 4115 867

IV 9538 4389 200 3953 921

2012 I 10220 4400 260 4060 1060

II 11662 4860 311 4714 1244

III 13600 5785 383 6287 1745

IV 13852 6486 419 7260 1983

2013 I 14712 6856 451 7793 2288

II 17364 7827 549 9114 2852

III 18544 8532 607 9870 3447

IV 16176 7665 657 10295 2466

2014 I 16759 8703 711 13000 4027

II 18910 10281 697 16660 4445

III 19272 10856 764 19902 5206

IV 20139 11163 820 22318 5561

As the graphs show that both aggregate demand and region demand have a strong

increasing trend. Moreover, they do not show any visible seasonality.

0

5000

10000

15000

20000

25000

0 5 10 15 20 25 30

Dem

and

Quarters

EUROPE

AMERICA

AFRICA

ASIA PACIFIC

MIDDLE EAST

Figure 3: Quarterly Regional Demand Data Graph

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4. DESCRIPTION OF THE TOOLS

4.1 Forecasting model

Demand forecast is the bedrock and the base of all supply chain planning. Since the

company uses a push process for the supply chain, activities have to be performed in anticipation

of customer demand. Thus, managers have to plan the level of activity in advance. Moreover,

forecasting is difficult when the demand for finished product is unpredictable.

There are four different types of forecasting methods:

- Qualitative: Qualitative forecasting methods are subjective and rely on human judgment.

They are most appropriate when little historical data are available or when experts have

market intelligence that may affect the forecast.

- Time series: Time-series forecasting methods use historical demand to make the forecast.

They are based on the assumption that past demand history is a good indicator of future

demand. They are appropriate when the basic demand pattern does not vary significantly

from one year to the next.

- Causal: Causal forecasting methods assume that the demand forecast is highly correlated

with certain factors in the environment.

- Simulation: Simulation forecasting methods imitate the consumer choice that give rise to

the demand to arrive at forecast. They can combine causal methods and time-series.

The analysis performed in this paper deals with time-series methods, which are most

appropriate when future demand is related to historical demand, grow patterns and any seasonal

patterns. An observed demand can be broken down into two different components which are

systematic component and random component.

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𝑂𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝐷𝑒𝑚𝑎𝑛𝑑 = 𝑠𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 + 𝑟𝑎𝑛𝑑𝑜𝑚 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡

The systematic component measures the expected value of the demand and consist of

level, the current deseasonalized demand; trend, the rate of growth or decline of the demand; and

seasonality, the predictable seasonal fluctuations in demand. The random component is that part

of demand that deviates from the systematic part. Random component cannot be forecasted but a

company can predict the random component’s size and variability, which provide a measure of

forecast error.

The goal of any forecasting method is to predict the systematic component of the demand

and estimate the random component. The equation for calculating systematic component may

take a variety of forms:

𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑐𝑎𝑡𝑖𝑣𝑒: 𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 = 𝑙𝑒𝑣𝑒𝑙 𝑥 𝑡𝑟𝑒𝑛𝑑 𝑥 𝑠𝑒𝑎𝑠𝑜𝑛𝑎𝑙 𝑓𝑎𝑐𝑡𝑜𝑟

𝐴𝑑𝑑𝑖𝑡𝑖𝑣𝑒: 𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 = 𝑙𝑒𝑣𝑒𝑙 + 𝑡𝑟𝑒𝑛𝑑 + 𝑠𝑒𝑎𝑠𝑜𝑛𝑎𝑙 𝑓𝑎𝑐𝑡𝑜𝑟

𝑀𝑖𝑥𝑒𝑑: 𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 = (𝑙𝑒𝑣𝑒𝑙 + 𝑡𝑟𝑒𝑛𝑑) 𝑥 𝑠𝑒𝑎𝑠𝑜𝑛𝑎𝑙 𝑓𝑎𝑐𝑡𝑜𝑟

Companies may develop two different kind of forecasting methods, which are called

static and adaptive. A static method assumes that the estimates of level, trend and seasonality

within the systematic component do not vary as new demand is observed. On the other hand, in

adaptive forecasting methods the estimates of level, trend and seasonality are updated after each

demand observation. The main advantage of adaptive forecasting methods is that estimates

incorporate all new data that are observed. Thus, since the problem discussed this report takes

into account a sufficient amount of historical data and adaptive forecasting methods provide a

more reliable forecast; it has been chosen to select an adaptive forecasting method to perform

demand forecasts.

The adaptive forecasting framework includes four main steps which are described as follows:

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Initialize: Compute the initial estimation of level(𝐿0), trend(𝑇0), and seasonal factors (𝑆1 … 𝑆𝑝)

from the given data. This process is done exactly as in the static forecasting methods.

The first step to estimate level and trend is to “deseasonalize” the demand.

𝐷𝑒𝑠𝑒𝑎𝑠𝑜𝑛𝑎𝑙𝑖𝑧𝑒𝑑 𝑑𝑒𝑚𝑎𝑛𝑑 (�̅�𝑡) represents the demand that would have been observed in

absence of seasonal fluctuations. The 𝑝𝑒𝑟𝑖𝑜𝑑𝑖𝑐𝑖𝑡𝑦 (𝑝) is the number of periods after which the

seasonal cycle repeats.

�̅�𝑡 =

[𝐷𝑡−(

𝑝2

)+ 𝐷

𝑡+(𝑝2

)+ ∑ 2𝐷𝑖

𝑡−1+(𝑝2

)

𝑖=𝑡+1−(𝑝2

)]

2𝑝⁄

𝐹𝑜𝑟 𝑝 𝑒𝑣𝑒𝑛

�̅�𝑡 =

[∑ 𝐷𝑖

𝑡+[𝑝−1

2]

𝑖=𝑡−[𝑝−1

2]

]

𝑝⁄

𝐹𝑜𝑟 𝑝 𝑜𝑑𝑑

The following equation is the linear relationship between the 𝐷𝑒𝑠𝑒𝑎𝑠𝑜𝑛𝑎𝑙𝑖𝑧𝑒𝑑 𝑑𝑒𝑚𝑎𝑛𝑑 (�̅�𝑡)

and the time 𝑡 based on the change in demand over time:

�̅�𝑡 = 𝐿 + 𝑇 ∙ 𝑡

Where 𝐿 is the level, or deseasonalized demand at period O, and 𝑇 is the trend, or the rate of

growth of deseasonalized demand. The values of 𝐿 and 𝑇 can be estimated using linear

regression with deseasonalized demand.

The 𝑠𝑒𝑎𝑠𝑜𝑛𝑎𝑙 𝑓𝑎𝑐𝑡𝑜𝑟 (𝑆�̅�) of period t is the ratio of actual demand 𝐷𝑡 to deseasonalized

demand:

(𝑆�̅�) =𝐷𝑡

�̅�𝑡

Given 𝑟 seasonal cycles in the data, seasonal factors can be obtained ad follows:

𝑆𝑖 =∑ 𝑆�̅�𝑝+1

𝑟−1𝑗=0

𝑟

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Forecast: Given the estimates in Period 𝑡, forecast the demand in Period 𝑡 + 1 according to the

chosen forecasting method.

Estimate error: Record the actual demand 𝐷𝑡+1 for Period 𝑡 + 1 and compute the error 𝐸𝑡+1 as

the difference between the forecast and the actual demand:

𝐸𝑡+1 = 𝐹𝑡+1 − 𝐷𝑡+1

Modify estimates: Modify the estimates of level, trend and seasonal factor according to the

chosen forecasting method.

There are various adaptive forecasting methods. Each of them has different

characteristics. Thus, the method that is most appropriate depends on the characteristic of the

demand and the composition of its systematic component. The different models are:

Moving Average: This method is used when the demand has no observable trend or seasonality.

Simple Exponential Smoothing: This method is appropriate when demand has no observable

trend or seasonality.

Simple Exponential smoothing: This model is appropriate when demand has no observable

trend or seasonality.

Trend-Corrected Exponential Smoothing (HOLT’s Model): This model is appropriate when

the demand is assumed to have a level and an observable trend.

Trend and Seasonality-Corrected Exponential Smoothing (WINTER’s Model): This model

is appropriate when the systematic component of demand has a level, a trend, and a seasonal

factor.

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The demand data regarding the cosmetic product analyzed in this paper shows a strong

increasing trend, but it does not have an observable seasonal factor. Thus, according to the

description of the different adaptive forecasting methods, the most appropriate model which can

be implemented to forecast the future demand is Holt’s model.

4.1.1 Trend-corrected exponential smoothing (Holt’s model)

Holt’s model aims at forecasting the systematic component of the demand taking into

account the level and the trend:

𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 = 𝑙𝑒𝑣𝑒𝑙 + 𝑡𝑟𝑒𝑛𝑑

The initial estimate of level and trend can be obtained by running a linear regression between

Demand 𝐷𝑡 and Period 𝑡.

𝐷𝑡 = 𝑎𝑡 + 𝑏

Where 𝑎 = 𝑇0 (trend at Period 𝑡 = 0) and 𝑏 = 𝐿0 (level at Period 𝑡 = 0). In this case, running a

linear regression between demand and time periods is appropriate because it has been assumed

that demand has a strong trend but no seasonality.

Given the estimated of level 𝐿𝑡 and trend 𝑇𝑡 in Period 𝑡, the forecast of future period is

expressed as follows:

𝐹𝑡+1 = 𝐿𝑡 + 𝑇𝑡 and 𝐹𝑡+𝑛 = 𝐿𝑡 + 𝑛𝑇𝑡

After observing demand for Period 𝑡, the estimates of level 𝐿𝑡 and trend 𝑇𝑡 have to be

revised as follows:

𝐿𝑡+1 = 𝛼𝐷𝑡+1 + (1 − 𝛼)(𝐿𝑡 + 𝑇𝑡)

𝑇𝑡+1 = 𝛽(𝑇𝑡+1 − 𝐿𝑡) + (1 − 𝛽)𝑇𝑡

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Where α is a smoothing constant for the level (0 < α < 1), and β is a smoothing constant

for the trend (0 < β < 1). Those smoothing constant have to been chosen taking into account that

is not a good idea to use smoothing constants much larger than 0.2 for extended periods of time.

A larger smoothing constant may be justified for a short period of time when demand is in

transaction. However, it should be avoided for extended periods of time. In general, it is best to

pick smoothing constant that minimize the error term that a manager is most confortable with.

Observe that in each of the two updates, the revised estimate is a weighted average of the

observed value and the old estimate.

4.1.2 Forecasting Error Measurements

As mentioned before, every instance of demand has a random component. A good

forecasting method should capture the systematic component of demand but not the random

component. The random component manifest itself in the form of forecasting error. Forecast

errors must be analyzed in order to understand whether the forecasting method is predicting the

systematic component of the demand accurately or if the demand has fundamentally changed and

the chosen model is no longer appropriate.

The 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟 𝐸𝑡 is defined as follows:

𝐸𝑡 = 𝐹𝑡 − 𝐷𝑡

There are different indicators that can be used to measure forecast errors. They are:

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Mean Square Error (MSE)

𝑀𝑆𝐸 =1

𝑛∑ 𝐸2

𝑛

𝑖=1

The MSE can be related to the variance of the forecasting error. Here, the random component of

demand has a mean of zero and a variance of MSE. The MSE penalized large errors much more

that small errors because all errors are squared. In the process of selecting the best smoothing

constants, in absence of a preference among error terms, it is best to pick smoothing constant that

minimize MSE.

Mean Absolute Deviation (MAD)

𝑀𝐴𝐷 =1

𝑛∑|𝐸𝑡|

𝑛

𝑖=1

=1

𝑛∑ 𝐴𝑡

𝑛

𝑖=1

The MAD can be used to estimate the standard deviation of the random component assuming

that the random component is normally distributed.

𝜎 = 1.25 𝑀𝐴𝐷

The MAD is a better measure of error compared with MSE if the forecast error does not have a

symmetric distribution.

Mean Absolute Percentage Error (MAPE)

𝑀𝐴𝑃𝐸 =1

𝑛∑ |

𝐸𝑡

𝐷𝑡| 100

𝑛

𝑖=1

The MAPE is a good measure of forecast error when the underlying forecast has a significant

seasonality and demand varies considerably from one period to another.

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Bias

𝑏𝑖𝑎𝑠𝑡 = ∑ 𝐸𝑡

𝑛

𝑖=1

This is a method to track and control forecast errors. The bias will fluctuate around zero if the

error is truly random and there are no biases.

Tracking Signal (TS)

𝑇𝑆𝑡 =𝑏𝑖𝑎𝑠𝑡

𝑀𝐴𝐷𝑡

The Tracking Signal is an indicator that shows whether the forecast has any visible bias. If the

TS is outside the range of ± 6, this is the signal that the forecast is biased and is either under-

forecasting (TS < -6) or over-forecasting (TS > +6). This may happen because the forecasting

method is flawed or the underlying pattern has shifted.

4.2 Network design

4.2.1 Facilities - drivers of supply chain performance

We discuss the role that facilities play in the supply chain as well as critical facility-

related decisions that supply chain managers need to make.

4.2.2 Role in the supply chain

If we think of inventory as what is being passed along the supply chain and transportation

as how it is passed along, then facilities are the where of the supply chain. They are the locations

to or from which the inventory is transported. Within a facility, inventory is either transformed

into another state (manufacturing) or it is stored (warehousing).

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4.2.3 Role in the competitive strategy

Facilities are a key driver of supply chain performance in terms of responsiveness and

efficiency. For example, companies can gain economies of scale when a product is manufactured

or stored in only one location; this centralization increases efficiency. The cost reduction,

however, comes at the expense of responsiveness, as many of a company's customers may be

located far from the production facility. The opposite is also true. Locating facilities close to

customers increases the number of facilities needed and consequently reduces efficiency. If the

customer demands and is willing to pay for the responsiveness that having numerous facilities

adds, however, then this facilities decision helps meet the company's competitive strategy goals.

4.2.4 Components of facilities decisions

Decisions regarding facilities are a crucial part of supply chain design. We now identify

components of facilities decisions that companies must analyze.

Role

For production facilities, firms must decide whether they will be flexible, dedicated, or a

combination of the two. Flexible capacity can be used for many types of products but is often

less efficient, whereas dedicated capacity can be used for only a limited number of products but

is more efficient. Firms must also decide whether to design a facility with a product focus or a

functional focus. A product-focused facility performs many different functions (e.g., fabrication

and assembly) in producing a single type of product. A functional-focused facility performs few

functions (e.g., only fabrication or only assembly) on many types of products. A product focus

tends to result in more expertise about a particular type of product at the expense of the

14

functional expertise that comes from a functional methodology. For warehouses and DCs, firms

must decide whether they will be primarily cross docking facilities or storage facilities. At cross-

docking facilities, inbound trucks from suppliers are unloaded; the product is broken into smaller

lots, and is quickly loaded onto store-bound trucks. Each store-bound truck carries a variety of

products, some from each inbound truck. For storage facilities, firms must decide on the products

to be stored at each facility.

Location

Deciding where a company will locate its facilities constitutes a large part of the design

of a supply chain. A basic trade-off here is whether to centralize in order to gain economies of

scale or to decentralize to become more responsive by being closer to the customer. Companies

must also consider a host of issues related to the various characteristics of the local area in which

the facility is situated. These include macroeconomic factors, quality of workers, cost of

workers, cost of facility, availability of infrastructure, proximity to customers, the location of

that firm's other facilities, tax effects, and other strategic factors.

Capacity

Companies must also determine a facility's capacity to perform its intended function or

functions. A large amount of excess capacity allows the facility to be very flexible and to

respond to wide swings in the demands placed on it. Excess capacity, however, costs money and

therefore can decrease efficiency. A facility with little excess capacity will likely be more

efficient per unit of product it produces than one with a lot of unused capacity. The high-

utilization facility, however, will have difficulty responding to demand fluctuations. Therefore, a

company must make a trade-off to determine the right amount of capacity to have at each of its

facilities.

15

4.2.5 Facility-Related Metrics

A manager should track the following facility-related metrics that influence supply chain

performance.

• Capacity measures the maximum amount a facility can process.

• Utilization measures the fraction of capacity that is currently being used in the facility.

Utilization affects both the unit cost of processing and the associated delays. Unit costs tend to

decline and delays increase with increasing utilization.

• Theoretical flow/cycle time of production measures the time required to process a unit if there

are absolutely no delays at any stage.

• Actual average flow/cycle time measures the average actual time taken for all units processed

over a specified duration such as a week or month. The actual flow/cycle time includes the

theoretical time and any delays.

• Flow time efficiency is the ratio of the theoretical flow time to the actual average flow time.

• Product variety measures the number of products/product families processed in a facility.

Processing costs and flow times are likely to increase with product variety.

• Volume contribution of top 20 percent SKUs and customers measures the fraction of total

volume processed by a facility that comes from the top 20 percent SKUs or customers. An 80/20

outcome in which the top 20 percent contribute 80 percent of volume indicates likely benefits

from focusing the facility where separate processes are used to process the top 20 percent and the

remaining 80 percent.

16

• Processing/setup/down/idle time measure the fraction of time that the facility was processing

units, being set up to process units, unavailable because it was down, or idle because it had no

units to process.

• Average production batch size measures the average amount produced in each production

batch. Large batch sizes will decrease production cost but increase inventories in the supply

chain.

• Production service level measures the fraction of production orders completed on time and in

full.

4.2.6 Overall trade-off: responsiveness versus efficiency

The fundamental trade-off that managers face when making facilities decisions is

between the cost of the number, location, and type of facilities (efficiency) and the level of

responsiveness that these facilities provide the company's customers. Increasing the number of

facilities increases facility and

inventory costs but decreases

transportation costs and reduces

response time. Increasing the

flexibility of a facility increases

facility costs but decreases inventory

costs and response time.

Figure 4: Costs vs. Number of Facilities

17

4.2.7 Factors influencing distribution network design

At the highest level, performance of a distribution network should be evaluated along two

dimensions:

1. Customer needs that are met

2. Cost of meeting customer needs

Thus, a firm must evaluate the impact on customer service and cost as it compares

different distribution network options. The customer needs that are met influence the company's

revenues, which along with cost decide the profitability of the delivery network.

Although customer service consists of many components, we focus on those measures

that are influenced by the structure of the distribution network. These include: Response time,

Product variety, Product availability, Customer experience, Time to market, Order visibility, and

Returnability.

Response time is the amount of time it takes for a customer to receive an order. Product

variety is the number of different products/configurations that are offered by the distribution

network. Product availability is the probability of having a product in stock when a customer

order arrives. Customer experience includes the ease with which customers can place and receive

orders as well as the extent to which this experience is customized. It also includes purely

experiential aspects, such as the possibility of getting a cup of coffee and the value that the sales

staff provides. Time to market is the time it takes to bring a new product to the market. Order

visibility is the ability of customers to track their orders from placement to delivery.

Returnability is the ease with which a customer can return unsatisfactory merchandise and the

ability of the network to handle such returns. It may seem at first that a customer always wants

18

the highest level of performance along all these dimensions. In practice, however, this is not the

case.

Firms that target customers who can tolerate a long response time require only a few

locations that may be far from the customer. These companies can focus on increasing the

capacity of each location. In contrast, firms that target customers who value short response times

need to locate facilities close to them. These firms must have

many facilities, each with a low capacity. Thus, a decrease in

the response time customers’ desire increases the number of

facilities required in the network, as shown in the figure on

the right.

4.2.8 The role of network design in the supply chain

Supply chain network design decisions include the assignment of facility role, location of

manufacturing, storage, or transportation-related facilities, and the allocation of capacity and

markets to each facility. Supply chain network design decisions are classified as follows.

1. Facility role: What role should each facility play? What processes are performed at each

facility?

2. Facility location: Where should facilities be located?

3. Capacity allocation: How much capacity should be allocated to each facility?

4. Market and supply allocation: What markets should each facility serve? Which supply sources

should feed each facility?

Figure 5: Facility Costs vs. Number of

Facilities

19

Network design decisions have a significant impact on performance because they

determine the supply chain configuration and set constraints within which the other supply chain

drivers can be used either to decrease supply chain cost or to increase responsiveness. All

network design decisions affect each other and must be made taking this fact into consideration.

Decisions concerning the role of each facility are significant because they determine the amount

of flexibility the supply chain has in changing the way it meets demand.

Facility location decisions have a long-term impact on a supply chain's performance

because it is very expensive to shut down a facility or move it to a different location. A good

location decision can help a supply chain be responsive while keeping its costs low. In contrast, a

poorly located facility makes it very difficult for a supply chain to perform close to the efficient

frontier.

Capacity allocation decisions also have a significant impact on supply chain performance.

Whereas capacity allocation can be altered more easily than location, capacity decisions do tend

to stay in place for several years. Allocating too much capacity to a location results in poor

utilization, and as a result, higher costs. Allocating too little capacity results in poor

responsiveness if demand is not satisfied, or high cost if demand is filled from a distant facility.

The allocation of supply sources and markets to facilities has a significant impact on

performance because it affects total production, inventory, and transportation costs incurred by

the supply chain to satisfy customer demand. This decision should be reconsidered on a regular

basis so that the allocation can be changed as market conditions or plant capacities change. Of

course, the allocation of markets and supply sources can only be changed if the facilities are

flexible enough to serve different markets and receive supply from different sources.

20

Network design decisions must be revisited as a firm grows or when two companies

merge. Because of the redundancies and differences in markets served by either of the two

separate firms, consolidating some facilities and changing the location and role of others can

often help reduce cost and improve responsiveness.

We focus on developing a framework as well as methodologies that can be used for

network design in a supply chain. In the next section, we identify various factors that influence

network design decisions.

4.2.9 Factors influencing network design decisions

In this section we examine a wide variety of factors that influence network design

decisions in supply chains.

Strategic factors

A firm's competitive strategy has a significant impact on network design decisions within

the supply chain. Firms that focus on cost leadership tends to find the lowest-cost location for

their manufacturing facilities, even if that means locating very far from the markets they serve.

Firms that focus on responsiveness tend to locate facilities closer to the market and may select a

high-cost location if this choice allows the firm to react quickly to changing market needs.

Global supply chain networks can best support their strategic objectives with facilities in

different countries playing different roles. It is important for a firm to identify the mission or

strategic role of each facility when designing its global network. Kasra Ferdows (1997) suggests

the following classification of possible strategic roles for various facilities in a global supply

chain network.

21

1. Offshore facility: low-cost facility for export production. An offshore facility serves the role

of being a low-cost supply source for markets located outside the country where the facility is

located. The location selected for an offshore facility should have low labor and other costs to

facilitate low-cost production.

2. Source facility: low-cost facility for global production. A source facility also has low cost as

its primary objective, but its strategic role is broader than that of an offshore facility. A source

facility is often a primary source of product for the entire global network. Source facilities tend

to be located in places where production costs are relatively low, infrastructure is well

developed, and a skilled workforce is available. Good offshore facilities migrate over time into

source facilities.

3. Server facility: regional production facility. A server facility's objective is to supply the

market where it is located. A server facility is built because of tax incentives, local content

requirement, tariff barriers, or high logistics cost to supply the region from elsewhere.

4. Contributor facility: regional production facility with development skills. A contributor

facility serves the market where it is located but also assumes responsibility for product

customization, process improvements, product modifications, or product development. Most

well-managed server facilities become contributor facilities over time.

5. Outpost facility: regional production facility built to gain local skills. An outpost facility is

located primarily to obtain access to knowledge or skills that may exist within a certain region.

Given its location, it also plays the role of a server facility. The primary objective remains one of

being a source of knowledge and skills for the entire network.

22

6. Lead facility: facility that leads in development and process technologies. A lead facility

creates new products, processes, and technologies for the entire network. Lead facilities are

located in areas with good access to a skilled workforce and technological resources.

Technological factors

Characteristics of available production technologies have a significant impact on network

design decisions. If production technology displays significant economies of scale, a few high-

capacity locations are most effective. This is the case in the manufacture of computer chips, for

which factories require a very large investment. As a result, most semiconductor companies

build few high-capacity facilities. In contrast, if facilities have lower fixed costs, many local

facilities are preferred because this helps lower transportation costs. Flexibility of the production

technology affects the degree of consolidation that can be achieved in the network. If the

production technology is very inflexible and product requirements vary from one country to

another, a firm has to set up local facilities to serve the market in each country. Conversely, if the

technology is flexible, it becomes easier to consolidate manufacturing in a few large facilities.

Macroeconomic factors

Macroeconomic factors include taxes, tariffs, exchange rates, and other economic factors

that are not internal to an individual firm. As global trade has increased, macroeconomic factors

have had a significant influence on the success or failure of supply chain networks. Thus, it is

imperative that firms take these factors into account when making network design decisions.

Tariffs and Tax Incentives

Tariffs refer to any duties that must be paid when products and/or equipment are moved

across international, state, or city boundaries. Tariffs have a strong influence on location

decisions within a supply chain. If a country has very high tariffs, companies either do not serve

23

the local market or set up manufacturing plants within the country to save on duties. High tariffs

lead to more production locations within a supply chain network, with each location having a

lower allocated capacity. For global firms, a decrease in tariffs has led to a decrease in the

number of manufacturing facilities and an increase in the capacity of each facility built. Tax

incentives are a reduction in tariffs or taxes that countries, states, and cities often provide to

encourage firms to locate their facilities in specific areas.

4.2.10 Capacitated Plant Location Model

For this particular case of the problem, we will be using the Capacitated Plant Location

Model, which best fits and provides optimal solution for the problem statement. The capacitated

plant location network optimization model requires the following inputs:

𝑛 = number of potential plant locations/capacity (each level of capacity will count as a separate

location)

𝑚 = number of markets or demand points

𝐷𝑗 = annual demand from market j

𝐾𝑖 = potential capacity of plant i

𝑓𝑖 = annualized fixed cost of keeping factory i open

𝑐𝑖𝑗 = cost of producing and shipping one unit from factory i to market j (cost includes

production, inventory, transportation, and tariffs)

The supply chain team's goal is to decide on a network design that maximizes profits

after taxes. For the sake of simplicity, however, we assume that all demand must be met and

taxes on earnings are ignored. The model thus focuses on minimizing the cost of meeting global

demand. It can, however, be modified to include profits and taxes. Define the following decision

variables:

24

𝑦𝑖 = 1 if plant i is open, 0 otherwise

𝑥𝑖𝑗= quantity shipped from plant i to market j

The problem is then formulated as the following integer program:

Minimum of

∑ 𝑓𝑖𝑦𝑖

𝑛

𝑖=1

+ ∑ ∑ 𝑐𝑖𝑗𝑥𝑖𝑗

𝑚

𝑗=1

𝑛

𝑖=1

Subject to

∑ 𝑥𝑖𝑗

𝑛

𝑖=1

= 𝐷𝑗 𝑓𝑜𝑟 𝑗 = 1, … . , 𝑚

∑ 𝑥𝑖𝑗

𝑚

𝑗=1

≤ 𝐾𝑖𝑦𝑖 𝑓𝑜𝑟 𝑖 = 1, … . . , 𝑛

𝑦𝑖 ∈ {0,1} 𝑓𝑜𝑟 𝑖 = 1, . . , 𝑛, 𝑥𝑖𝑗 ≥ 0

The objective function minimizes the total cost (fixed+ variable) of setting up and

operating the network. The constraint in Equation 1 requires that the demand at each regional

market be satisfied. The constraint in Equation 2 states that no plant can supply more than its

capacity. (Clearly, the capacity is 0 if the plant is closed and Ki if it is open. The product of

terms, KJii, captures this effect.) The constraint in Equation 3 enforces that each plant is either

open (yi = 1) or closed (Yi = 0). The solution identifies the plants that are to be kept open, their

capacity, and the allocation of regional demand to these plants.

25

5. APPLICATION OF THE TOOLS & ANALYSIS OF RESULTS

In this section we are going to describe the application of the tools for the forecasting process

and for the solution of the network design phase. Then, we are going to comment all the results.

5.1 Forecasts

The forecasted data have been obtained according to Holt’s model. As previously said,

this is the chosen method because the demand does not show an observable seasonality and a

recognizable periodicity. In addition to that, we decided to implement the forecasting process

utilizing Holt’s model for both the aggregate demand and each region demand separately. We

defined an appropriate model for each set of available data. Holt’s model can be properly applied

to all of them because the show the same pattern with a strong trend and no seasonality.

Moreover, we decided to firstly present the forecasted data for the aggregate demand and then

report the forecasting results for each different region. Before running the model, we analyzed

the shape of the demand and noticed that it shows a relevant change between the end of 2011 and

the beginning of 2012. Thus, we expected a bias in that period.

5.1.1 Aggregate forecasted data

The first step to implement Holt’s model is to define the initial Level (𝐿0) and Trend (𝑇0)

by running linear regression trough Microsoft Excel. We obtained 𝐿0 = 6887.64 and 𝑇0 =

1721.83. Then we defined the smoothing constants to use for the implementation of the Holt’s

model, which are 𝛼 = 0.2 and 𝛽 = 0.3. Those constants have been chosen according to the

theory of forecast and qualitative evaluations of this specific problem. In particular, we run the

Microsoft Excel solver in order to minimize the MSE. Since the result gave us high values for

the smoothing constants, we decided to qualitatively adapt them to the specific problem. We

considered that it is preferable not to use high values for long periods of time.

26

In the following table we reported the forecasting data regarding the aggregate demand:

Table 3: Aggregate Demand Forecast – Model 1

Quarter Period DEMAND L T F E |At| bias MSE MAD MAPE TS

2009 I 1 15000 9888 2105 8609 -6391 6391 -6391 40838874 6391 42.60 -1.00

II 2 15000 12594 2286 11993 -3007 3007 -9398 24940953 4699 31.33 -2.00

III 3 16000 15104 2353 14880 -1120 1120 -10518 17045466 3506 23.22 -3.00

IV 4 17000 17365 2325 17457 457 457 -10061 12836280 2744 18.08 -3.67

2010 I 5 18000 19353 2224 19691 1691 1691 -8370 10840899 2533 16.35 -3.30

II 6 20501 21362 2159 21577 1076 1076 -7294 9226973 2290 14.50 -3.18

III 7 20999 23017 2008 23521 2522 2522 -4772 8817557 2323 14.14 -2.05

IV 8 21000 24220 1767 25025 4025 4025 -747 9740278 2536 14.77 -0.29

2011 I 9 20500 24889 1437 25987 5487 5487 4739 12002692 2864 16.10 1.65

II 10 20001 25062 1058 26327 6326 6326 11065 14803858 3210 17.65 3.45

III 11 20000 24896 691 26119 6119 6119 17185 16862415 3475 18.83 4.95

IV 12 19001 24269 296 25586 6585 6585 23770 19071103 3734 20.15 6.37

2012 I 13 20000 23652 22 24565 4565 4565 28335 19207046 3798 20.36 7.46

II 14 22791 23497 -31 23674 883 883 29217 17890764 3589 19.18 8.14

III 15 27800 24333 229 23466 -4334 4334 24883 17950333 3639 18.94 6.84

IV 16 30000 25649 555 24562 -5438 5438 19445 18676978 3752 18.89 5.18

2013 I 17 32100 27384 909 26204 -5896 5896 13549 19622940 3878 18.86 3.49

II 18 37706 30175 1474 28292 -9414 9414 4136 23455907 4185 19.20 0.99

III 19 41000 33519 2035 31649 -9351 9351 -5216 26823763 4457 19.39 -1.17

IV 20 37259 35895 2137 35554 -1705 1705 -6921 25627962 4320 18.65 -1.60

2014 I 21 43200 39066 2447 38032 -5168 5168 -12089 25679449 4360 18.33 -2.77

II 22 50993 43409 3016 41513 -9480 9480 -21569 28597493 4593 18.34 -4.70

III 23 56000 48340 3590 46425 -9575 9575 -31144 31340467 4809 18.29 -6.48

IV 24 60001 53544 4075 51930 -8071 8071 -39215 32748639 4945 18.08 -7.93

2015 I 25 - - - 56005 - - - - - - -

II 26 - - - 60080 - - - - - - -

III 27 - - - 64154 - - - - - - -

IV 28 - - - 68229 - - - - - - -

2016 I 29 - - - 72304 - - - - - - -

II 30 - - - 76379 - - - - - - -

III 31 - - - 80453 - - - - - - -

IV 32 - - - 84528 - - - - - - -

2017 I 33 - - - 88603 - - - - - - -

II 34 - - - 92678 - - - - - - -

III 35 - - - 96752 - - - - - - -

IV 36 - - - 100827 - - - - - - -

27

Figure 6: Graph of Aggregate Demand Forecast – Model 1

Values dealing with Level 𝐿𝑡, Trend 𝑇𝑡, Forecast 𝐹𝑡, Forecasting Error 𝐸𝑡, 𝑏𝑖𝑎𝑠𝑡, 𝑀𝐴𝐷𝑡,

𝑀𝐴𝑃𝐸𝑡, 𝑀𝑆𝐸𝑡 and 𝑇𝑆𝑡 have been calculated according to the formulas presented in the previous

chapter named “Description of the tool”. Moreover, they have been applied to the forecasting

process for each individual region.

Before introducing the forecasting results for the regional demand, some comments

should be stated regarding the forecasted aggregate demand data. In particular, 𝑇𝑆𝑡 values show

that there is a visible bias affecting the forecasts for the periods between the end of 2011 and the

beginning of 2012, as previously anticipated by our initial analysis, and at the end of 2014. This

means that there are some reasons that changed the shape of the demand. Thus the forecasting

method should be adapted to the new shape of the demand. However, before introducing a new

model we would like to present the regional forecasting outcomes and comment them. Table 4

reports the forecasted data obtained by running the specific model for each region and the

corresponding 𝑇𝑆𝑡 values.

0

20000

40000

60000

80000

100000

120000

0 5 10 15 20 25 30 35 40

DEM

AN

D

Quarters

DEMAND

FORECAST

28

Table 4: Regional Demand Forecast – Model 1

EUROPE AMERICA AFRICA ASIA PACIFIC MIDDLE EAST

Lo 7143.35 1809.58 -44.41 -1230.46 -790.42

To 475.18 330.47 32.09 675.32 208.77

Quarter Period F TS F TS F TS F TS F TS

2009 I 1 7618.53 -1.00 2140.05 -1.00 -12.32 -1.00 -555.14 -1.00 -581.65 -1.00

II 2 8445.08 -2.00 2702.71 -2.00 50.27 -2.00 1360.44 -2.00 -143.65 -2.00

III 3 9094.93 -3.00 3193.89 -3.00 103.62 -3.00 2838.55 -3.00 241.17 -3.00

IV 4 9729.22 -4.00 3625.23 -2.96 148.21 -3.49 3960.42 -2.91 568.40 -3.38

2010 I 5 10327.59 -4.33 3994.11 -2.15 187.95 -2.63 4765.80 -1.97 834.20 -2.66

II 6 10883.91 -5.36 4314.27 -2.44 218.70 -1.43 5293.51 -1.01 1039.42 -1.56

III 7 11607.26 -5.58 4690.95 -1.83 244.02 -0.34 5705.92 0.16 1200.34 -0.29

IV 8 12186.88 -2.77 5016.79 -1.53 266.50 1.06 5898.07 1.52 1316.31 1.14

2011 I 9 12552.71 -0.73 5352.01 0.47 280.99 2.46 5794.25 3.11 1372.69 2.43

II 10 12868.46 2.63 5561.54 2.68 288.72 3.96 5224.48 4.16 1391.91 3.61

III 11 12807.35 5.44 5665.65 4.03 286.46 5.27 4797.94 4.84 1383.55 4.66

IV 12 12369.84 7.29 5782.75 6.34 279.53 6.39 4616.40 5.54 1356.67 5.62

2012 I 13 11816.12 8.47 5632.66 8.00 271.01 7.01 4381.01 6.13 1319.83 6.40

II 14 11413.78 8.72 5428.51 9.04 275.54 6.62 4219.45 6.03 1302.57 6.96

III 15 11395.20 6.14 5317.39 8.19 291.48 4.87 4347.07 4.37 1322.04 5.97

IV 16 11900.22 4.19 5446.22 5.80 324.13 3.20 5082.89 2.62 1463.20 4.68

2013 I 17 12471.75 2.16 5762.28 3.59 363.14 1.76 6085.81 1.37 1654.91 3.12

II 18 13235.39 -1.05 6165.68 0.66 406.02 -0.44 7101.40 -0.07 1907.27 0.93

III 19 14624.41 -3.53 6798.90 -1.88 468.51 -2.33 8389.75 -1.10 2278.64 -1.44

IV 20 16206.81 -3.69 7567.79 -2.11 538.40 -3.85 9651.61 -1.60 2764.83 -0.87

2014 I 21 16997.27 -3.68 8016.30 -3.13 611.44 -5.10 10720.32 -3.14 2939.66 -2.89

II 22 17731.95 -4.55 8630.78 -5.25 686.64 -5.45 12485.09 -5.56 3456.96 -4.59

III 23 18820.58 -5.03 9553.49 -6.83 744.62 -5.90 15194.17 -7.88 4013.69 -6.44

IV 24 19790.96 -5.45 10497.82 -7.77 805.57 -6.32 18486.83 -9.63 4682.81 -7.80

2015 I 25 20691.95 - 11228.22 - 863.50 - 20711.95 - 5166.15 -

II 26 21592.93 - 11958.61 - 921.44 - 22937.06 - 5649.50 -

III 27 22493.91 - 12689.01 - 979.38 - 25162.18 - 6132.85 -

IV 28 23394.90 - 13419.41 - 1037.32 - 27387.30 - 6616.19 -

2016 I 29 24295.88 - 14149.80 - 1095.26 - 29612.41 - 7099.54 -

II 30 25196.86 - 14880.20 - 1153.19 - 31837.53 - 7582.89 -

III 31 26097.85 - 15610.60 - 1211.13 - 34062.65 - 8066.24 -

IV 32 26998.83 - 16340.99 - 1269.07 - 36287.77 - 8549.58 -

2017 I 33 27899.81 - 17071.39 - 1327.01 - 38512.88 - 9032.93 -

II 34 28800.80 - 17801.78 - 1384.94 - 40738.00 - 9516.28 -

III 35 29701.78 - 18532.18 - 1442.88 - 42963.12 - 9999.63 -

IV 36 30602.76 - 19262.58 - 1500.82 - 45188.23 - 10482.97 -

29

The previous table shows the forecasting results for the regional demand. Since the

regional demand patterns are similar to the aggregate one, the outcomes of Holt’s model are

consistent with those ones obtained for the aggregate demand. In particular, 𝑇𝑆𝑡 confirms the

bias affecting the demand from the end of 2011 and the beginning of 2012, and at the end of

2014. The main reason dealing with the

bias could be the transition of the

demand from the introduction phase of

the product from 2009 to 2011 to the

growing stage from 2012. In fact,

analyzing the shape of the demand and

each of the regional demand, we can

notice a different trend from the

beginning of 2012. This means that the

demand changed in that period. Moreover, the measures of error noticed this. Thus, the previous

model should be modified and adapted to better fit that situation.

In order to set a better model, we decided to implement Holt’s method by using the

demand data dealing only with the growing stage, namely from the beginning of 2012 to the end

of 2014. Thus, we set up the model for the aggregate data by obtaining new values for Level and

Trend running again the linear regression. We obtained 𝐿0 = 15828.09 and 𝑇0 = 3447.60 for

the aggregate demand model. Moreover, we run again the Microsoft Excel solver to define

smoothing constants that minimize MSE. As a result, the model gave values extremely close to

𝛼 = 0.2 and 𝛽 = 0.2, which can be applied for long periods of time. The following table shows

the aggregate demand data used to run the modified model and the following results:

From 2009 to 2011 From 2012 to 2017 Tim

Figure 7: Graph illustrating the year-wise Product Life Cycle

30

Table 5: Aggregate Demand Forecast – Model 2 (Growing Stage)

Quarter Period DEMAND L T F E |At| bias MSE MAD MAPE TS

2012 I 1 20000 19420.55 3476.57 19275.69 -724.31 724.31 -724.31 524621.63 724.31 3.62 -1.00

II 2 22791 22875.90 3472.33 22897.13 106.13 106.13 -618.18 267942.35 415.22 2.04 -1.49

III 3 27800 26638.58 3530.40 26348.23 -1451.77 1451.77 -2069.95 881172.98 760.73 3.10 -2.72

IV 4 30000 30135.19 3523.64 30168.98 168.98 168.98 -1900.97 668018.63 612.80 2.47 -3.10

2013 I 5 32100 33347.06 3461.29 33658.83 1558.83 1558.83 -342.14 1020403.31 802.00 2.95 -0.43

II 6 37706 36987.88 3497.19 36808.35 -897.65 897.65 -1239.79 984632.42 817.94 2.85 -1.52

III 7 41000 40588.06 3517.79 40485.07 -514.93 514.93 -1754.72 881849.35 774.66 2.62 -2.27

IV 8 37259 42736.48 3243.92 44105.85 6846.85 6846.85 5092.13 6631533.51 1533.68 4.59 3.32

2014 I 9 43200 45424.32 3132.70 45980.39 2780.39 2780.39 7872.52 6753651.19 1672.20 4.80 4.71

II 10 50993 49044.21 3230.14 48557.02 -2435.98 2435.98 5436.54 6671687.92 1748.58 4.80 3.11

III 11 56000 53019.48 3379.17 52274.35 -3725.65 3725.65 1710.89 7327029.86 1928.32 4.96 0.89

IV 12 60001 57119.12 3523.26 56398.65 -3602.35 3602.35 -1891.46 7797855.87 2067.82 5.05 -0.91

2015 I 13 - - - 59921.91 - - - - - - -

II 14 - - - 63445.17 - - - - - - -

III 15 - - - 66968.43 - - - - - - -

IV 16 - - - 70491.69 - - - - - - -

2016 I 17 - - - 74014.95 - - - - - - -

II 18 - - - 77538.21 - - - - - - -

III 19 - - - 81061.47 - - - - - - -

IV 20 - - - 84584.73 - - - - - - -

2017 I 21 - - - 88107.99 - - - - - - -

II 22 - - - 91631.25 - - - - - - -

III 23 - - - 95154.51 - - - - - - -

IV 24 - - - 98677.77 - - - - - - -

0

20000

40000

60000

80000

100000

120000

0 5 10 15 20 25 30

DEM

AN

D

QUARTERS

DEMAND

F

Figure 8: Aggregate Demand Forecast – Model 2 (Growing Stage)

31

As a result, this model uses better smoothing constants and gives better results according

to the measures of error and the evaluation of biases trough 𝑇𝑆𝑡 indicator. Thus, we can predict

that the aggregate demand will be around 98,000 units at the end of 2017, which is the end of

growing stage and the beginning of maturity stage, according to company’s estimations.

The following tables show the regional forecasting results obtained with the adapted

models for each region, which are more precise and does not have a visible bias. Values for

Level, Trend and smoothing constant have been defined for each region according to the data.

5.1.2 Europe

Table 6: Europe Demand Forecast – Model 2

Quarter Period DEMAND L T F E |At| bias MSE MAD MAPE TS

2012 I 1 10220 11177.86 773.35 11417.32 1197.32 1197.32 1197.32 1433576.41 1197.32 11.72 1.00

II 2 11662 11893.37 761.78 11951.21 289.21 289.21 1486.53 758608.94 743.26 7.10 2.00

III 3 13600 12844.12 799.58 12655.15 -944.85 944.85 541.68 803319.63 810.46 7.05 0.67

IV 4 13852 13685.36 807.91 13643.70 -208.30 208.30 333.38 613337.17 659.92 5.66 0.51

2013 I 5 14712 14537.01 816.66 14493.27 -218.73 218.73 114.64 500238.48 571.68 4.83 0.20

II 6 17364 15755.74 897.07 15353.67 -2010.33 2010.33 -1895.68 1090434.31 811.46 5.95 -2.34

III 7 18544 17031.05 972.72 16652.81 -1891.19 1891.19 -3786.87 1445600.42 965.70 6.56 -3.92

IV 8 16176 17638.21 899.61 18003.77 1827.77 1827.77 -1959.10 1682492.41 1073.46 7.15 -1.83

2014 I 9 16759 18182.06 828.46 18537.82 1778.82 1778.82 -180.28 1847127.99 1151.84 7.54 -0.16

II 10 18910 18990.41 824.44 19010.51 100.51 100.51 -79.76 1663425.51 1046.70 6.84 -0.08

III 11 19272 19706.28 802.72 19814.85 542.85 542.85 463.08 1538994.37 1000.90 6.47 0.46

IV 12 20139 20435.00 787.92 20509.00 370.00 370.00 833.08 1422153.12 948.32 6.08 0.88

2015 I 13 - - - 21296.92 - - - - - - -

II 14 - - - 22084.84 - - - - - - -

III 15 - - - 22872.76 - - - - - - -

IV 16 - - - 23660.69 - - - - - - -

2016 I 17 - - - 24448.61 - - - - - - -

II 18 - - - 25236.53 - - - - - - -

III 19 - - - 26024.45 - - - - - - -

IV 20 - - - 26812.37 - - - - - - -

2017 I 21 - - - 27600.29 - - - - - - -

II 22 - - - 28388.21 - - - - - - -

III 23 - - - 29176.14 - - - - - - -

IV 24 - - - 29964.06 - - - - - - -

L0 10596.08

T0 821.24

32

0

5000

10000

15000

20000

25000

30000

35000

0 5 10 15 20 25 30

DEM

AN

D

QUARTES

DEMAND

F

5.1.3 America

L0 3828.91

T0 608.55 Table 7: America Demand Forecast – Model 2

Quarter Period DEMAND L T F E |At| bias MSE MAD MAPE TS

2012 I 1 4400 4429.97 607.05 4437.46 37.46 37.46 37.46 1403.37 37.46 0.85 1.00

II 2 4860 5001.62 599.97 5037.02 177.02 177.02 214.48 16370.29 107.24 2.25 2.00

III 3 5785 5638.27 607.31 5601.59 -183.41 183.41 31.08 22126.41 132.63 2.55 0.23

IV 4 6486 6293.67 616.93 6245.58 -240.42 240.42 -209.34 31044.92 159.58 2.84 -1.31

2013 I 5 6856 6899.67 614.74 6910.59 54.59 54.59 -154.75 25432.00 138.58 2.43 -1.12

II 6 7827 7576.93 627.25 7514.42 -312.58 312.58 -467.33 37478.11 167.58 2.69 -2.79

III 7 8532 8269.74 640.36 8204.18 -327.82 327.82 -795.15 47476.49 190.47 2.86 -4.17

IV 8 7665 8661.08 590.55 8910.10 1245.10 1245.10 449.95 235326.67 322.30 4.53 1.40

2014 I 9 8703 9141.91 568.61 9251.64 548.64 548.64 998.58 242623.84 347.45 4.73 2.87

II 10 10281 9824.61 591.43 9710.52 -570.48 570.48 428.10 250906.46 369.75 4.81 1.16

III 11 10856 10504.03 609.03 10416.04 -439.96 439.96 -11.86 245693.37 376.13 4.74 -0.03

IV 12 11163 11123.05 611.02 11113.06 -49.94 49.94 -61.80 225426.75 348.95 4.38 -0.18

2015 I 13 - - - 11724.09 - - - - - - -

II 14 - - - 12335.11 - - - - - - -

III 15 - - - 12946.13 - - - - - - -

IV 16 - - - 13557.16 - - - - - - -

2016 I 17 - - - 14168.18 - - - - - - -

II 18 - - - 14779.21 - - - - - - -

III 19 - - - 15390.23 - - - - - - -

IV 20 - - - 16001.25 - - - - - - -

2017 I 21 - - - 16612.28 - - - - - - -

II 22 - - - 17223.30 - - - - - - -

III 23 - - - 17834.33 - - - - - - -

IV 24 - - - 18445.35 - - - - - - -

Figure 9: Europe Demand Forecast – Model 2

33

5.1.4 Africa

L0 221.26

T0 50.95 Table 8: Africa Demand Forecast – Model 2

Quarter Period DEMAND L T F E |At| bias MSE MAD MAPE TS

2012 I 1 260 269.76 50.46 272.21 12.21 12.21 12.21 148.97 12.21 4.69 1.00

II 2 311 318.38 50.09 320.22 9.22 9.22 21.43 117.02 10.71 3.83 2.00

III 3 383 371.38 50.67 368.47 -14.53 14.53 6.90 148.39 11.99 3.82 0.58

IV 4 419 421.44 50.55 422.05 3.05 3.05 9.94 113.62 9.75 3.05 1.02

2013 I 5 451 467.79 49.71 471.99 20.99 20.99 30.93 178.99 12.00 3.37 2.58

II 6 549 523.80 50.97 517.50 -31.50 31.50 -0.57 314.53 15.25 3.76 -0.04

III 7 607 581.22 52.26 574.77 -32.23 32.23 -32.80 417.99 17.67 3.98 -1.86

IV 8 657 638.18 53.20 633.48 -23.52 23.52 -56.32 434.91 18.41 3.93 -3.06

2014 I 9 711 695.30 53.99 691.38 -19.62 19.62 -75.94 429.36 18.54 3.80 -4.10

II 10 697 738.83 51.89 749.29 52.29 52.29 -23.65 659.85 21.92 4.17 -1.08

III 11 764 785.38 50.82 790.73 26.73 26.73 3.07 664.79 22.35 4.11 0.14

IV 12 820 832.96 50.18 836.21 16.21 16.21 19.28 631.28 21.84 3.93 0.88

2015 I 13 - - - 886.38 - - - - - - -

II 14 - - - 936.56 - - - - - - -

III 15 - - - 986.73 - - - - - - -

IV 16 - - - 1036.91 - - - - - - -

2016 I 17 - - - 1087.09 - - - - - - -

II 18 - - - 1137.26 - - - - - - -

III 19 - - - 1187.44 - - - - - - -

IV 20 - - - 1237.62 - - - - - - -

2017 I 21 - - - 1287.79 - - - - - - -

II 22 - - - 1337.97 - - - - - - -

III 23 - - - 1388.14 - - - - - - -

IV 24 - - - 1438.32 - - - - - - -

0

200

400

600

800

1000

1200

1400

1600

0 5 10 15 20 25 30

DEM

AN

D

QUARTERS

DEMAND

F

Figure 10: Africa Demand Forecast – Model 2

34

5.1.5 Asia pacific

L0 777.98

T0 1563.30 Table 9: Asia Demand Forecast – Model 2

Quarter Period DEMAND L T F E |At| bias MSE MAD MAPE TS

2012 I 1 4060 2685.03 1632.05 2341.28 -1718.72 1718.72 -1718.72 2953991.39 1718.72 42.33 -1.00

II 2 4714 4396.46 1647.92 4317.07 -396.93 396.93 -2115.65 1555771.79 1057.82 25.38 -2.00

III 3 6287 6092.90 1657.63 6044.38 -242.62 242.62 -2358.27 1056802.63 786.09 18.20 -3.00

IV 4 7260 7652.43 1638.01 7750.53 490.53 490.53 -1867.73 852757.41 712.20 15.34 -2.62

2013 I 5 7793 8990.95 1578.11 9290.43 1497.43 1497.43 -370.30 1130666.58 869.25 16.12 -0.43

II 6 9114 10278.04 1519.91 10569.06 1455.06 1455.06 1084.75 1295086.36 966.88 16.09 1.12

III 7 9870 11412.36 1442.79 11797.95 1927.95 1927.95 3012.70 1641073.38 1104.18 16.58 2.73

IV 8 10295 12343.12 1340.38 12855.15 2560.15 2560.15 5572.85 2255235.16 1286.17 17.62 4.33

2014 I 9 13000 13546.80 1313.04 13683.50 683.50 683.50 6256.36 2056561.96 1219.21 16.25 5.13

II 10 16660 15219.88 1385.05 14859.85 -1800.15 1800.15 4456.20 2174961.46 1277.30 15.70 3.49

III 11 19902 17264.34 1516.93 16604.93 -3297.07 3297.07 1159.13 2965483.27 1460.92 15.78 0.79

IV 12 22318 19488.62 1658.40 18781.27 -3536.73 3536.73 -2377.60 3760729.88 1633.90 15.79 -1.46

2015 I 13 - - - 20439.67 - - - - - - -

II 14 - - - 22098.07 - - - - - - -

III 15 - - - 23756.48 - - - - - - -

IV 16 - - - 25414.88 - - - - - - -

2016 I 17 - - - 27073.28 - - - - - - -

II 18 - - - 28731.68 - - - - - - -

III 19 - - - 30390.08 - - - - - - -

IV 20 - - - 32048.48 - - - - - - -

2017 I 21 - - - 33706.88 - - - - - - -

II 22 - - - 35365.28 - - - - - - -

III 23 - - - 37023.69 - - - - - - -

IV 24 - - - 38682.09 - - - - - - -

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 5 10 15 20 25 30

DEM

AN

D

QUARTERS

DEMAND

F

Figure 11: Asia Demand Forecast – Model 2

35

5.1.6 Middle East

L0 403.86

T0 403.56 Table 10: Middle East Demand Forecast – Model 2

Quarter Period DEMAND L T F E |At| bias MSE MAD MAPE TS

2012 I 1 1060 857.94 413.66 807.42 -252.58 252.58 -252.58 63795.10 252.58 23.83 -1.00

II 2 1244 1266.08 412.56 1271.60 27.60 27.60 -224.98 32278.46 140.09 13.02 -1.61

III 3 1745 1691.91 415.21 1678.64 -66.36 66.36 -291.34 22986.89 115.51 9.95 -2.52

IV 4 1983 2082.30 410.25 2107.12 124.12 124.12 -167.21 21091.88 117.67 9.03 -1.42

2013 I 5 2288 2451.64 402.07 2492.55 204.55 204.55 37.34 25241.43 135.04 9.01 0.28

II 6 2852 2853.36 402.00 2853.70 1.70 1.70 39.04 21035.01 112.82 7.52 0.35

III 7 3447 3293.69 409.66 3255.36 -191.64 191.64 -152.60 23276.51 124.08 7.24 -1.23

IV 8 2466 3455.88 360.17 3703.35 1237.35 1237.35 1084.75 211747.02 263.24 12.61 4.12

2014 I 9 4027 3858.24 368.61 3816.05 -210.95 210.95 873.80 193163.96 257.43 11.79 3.39

II 10 4445 4270.48 377.33 4226.85 -218.15 218.15 655.65 178606.58 253.50 11.10 2.59

III 11 5206 4759.45 399.66 4647.81 -558.19 558.19 97.46 190694.52 281.20 11.06 0.35

IV 12 5561 5239.49 415.74 5159.11 -401.89 401.89 -304.43 188262.91 291.26 10.75 -1.05

2015 I 13 - - - 5574.85 - - - - - - -

II 14 - - - 5990.58 - - - - - - -

III 15 - - - 6406.32 - - - - - - -

IV 16 - - - 6822.06 - - - - - - -

2016 I 17 - - - 7237.79 - - - - - - -

II 18 - - - 7653.53 - - - - - - -

III 19 - - - 8069.27 - - - - - - -

IV 20 - - - 8485.00 - - - - - - -

2017 I 21 - - - 8900.74 - - - - - - -

II 22 - - - 9316.48 - - - - - - -

III 23 - - - 9732.21 - - - - - - -

IV 24 - - - 10147.95 - - - - - - -

0

2000

4000

6000

8000

10000

12000

0 5 10 15 20 25 30

DEM

AN

D

QUARTERS

DEMAND

F

Figure 12: Middle East Demand Forecast – Model 2

36

5.2 Application of the Network Design tool

Since the company considers that the demand will reach its maturity stage at the end of

2017, they can assume that the forecasted demand for the last quarter of 2017 can be a

reasonable indicator for the stable demand in maturity stage. Thus, these values are the input for

the network design problem. From the forecasting model the following regional demand data is

forecasted as the maturity demand, which the cosmetic company needs to satisfy.

Table 11: Network Design Data

Market Demands

Markets Europe America Africa Middle

East Asia

Demand 30000 18500 1450 10000 40000

The following are the existing and potential facility/plant locations and their respective associated costs

as per the data given by the company. Those values have been previously discussed in the “Element of

the problem” paragraph.

Plant Capacities and Costs

Capacity

Fixed Cost /

year

Production

Cost / Unit

Plants

France 25000 $23,000,000.00 $15.00

Germany 18000 $20,000,000.00 $13.00

America 20000 $20,000,000.00 $12.00

South

Africa 12000 $12,000,000.00 $9.00

Dubai 15000 $22,000,000.00 $13.00

Japan 21000 $14,000,000.00 $11.00

India 20000 $11,000,000.00 $10.00

Transportation Costs

Plants France Germany America

South

Africa Dubai Japan India

Market

Europe $1.00 $1.00 $1.60 $1.40 $1.20 $1.80 $1.70

America $1.50 $1.60 $1.00 $2.20 $1.80 $1.70 $2.00

Africa $1.40 $1.40 $2.20 $1.00 $1.50 $1.90 $1.80

Middle

East $1.20 $1.20 $1.80 $1.50 $1.00 $1.80 $1.10

Asia $1.70 $1.70 $2.00 $1.80 $1.10 $1.20 $1.00

37

Variable Production Costs, Transportation Costs and Duties From Plants to Markets

Plants France Germany America

South

Africa Dubai Japan India

Market

Europe $16.40 $16.40 $17.20 $16.00 $16.50 $16.90 $16.80

America $14.00 $14.00 $14.60 $14.40 $14.20 $14.80 $14.70

Africa $13.50 $13.60 $13.00 $14.20 $13.80 $13.70 $14.00

Middle

East $10.40 $10.40 $11.20 $10.00 $10.50 $10.90 $10.80

Asia $14.00 $14.00 $14.60 $14.40 $14.20 $14.80 $14.70

In order to define the optimal solution for the network design problem, we decided to set

two different models. In the first one we assumed that the company opens all the possible new

locations (Germany, South Africa, Dubai and Japan), while in the second one we included the

possibility not to open them if they are not required to satisfy the demand. The basic assumption

is that existing facilities (France, America and India) cannot be closed in both models. The

constraints are that the overall demand has to be satisfied and the production capacity of each

plant cannot be exceeded. After running the Microsoft Excel solver to solve each model, total

costs have been compared and we chose the best solution which minimizes total costs.

5.2.1 Network model when all the locations are opened

The following is the network model which illustrates the total quantity shipped from each

plant location to the respective market with all the facilities opened.

Table 12: Network Model – All Locations Opened

Quantity Shipped

Plants France Germany America

South

Africa Dubai Japan India

Demand

Unsatisfied

Market

Europe 0 0 0 10000 0 0 20000 0

America 0 3500 0 0 15000 0 0 0

Africa 0 0 1450 0 0 0 0 0

Middle East 0 0 0 2000 0 8000 0 0

Asia 25000 14500 500 0 0 0 0 0

Capacity

Unused 0 0 18050 0 0 13000 0

38

From the above network model it is clearly evident that the option of opening all the

facilities at the potential locations is not a wise choice as the unused capacity at locations like

Japan and America is a huge disadvantage, which increases the total costs of the distribution

network.

This above network model costs the company as follows:

Total Cost = $123,444,350.00

5.2.2 Network Model - Capitalized Plant location Network model

As previously discussed in the “Description of the tools” paragraph about the capitalized

plant location model, which when applied to the same network illustrates a large variation and

also uses the plant capacity to the maximum. The basic objective of the problem is to design a

network model that allows the company to have the minimum total cost and at the same time

satisfies the total demand.

The following is the Capitalized Plant Location Network model:

Table 13: Network Design – Capitalized Plant Locations

Quantity Shipped

Plants France Germany America

South

Africa Dubai Japan India

Demand

Unsatisfied

Market

Europe 0 0 0 0 0 20000 10000 0

America 0 3000 15500 0 0 0 0 0

Africa 0 0 1450 0 0 0 0 0

Middle East 0 0 0 0 0 0 10000 0

Asia 25000 15000 0 0 0 0 0 0

Y 1 1 1 0 0 1 1

Capacity

Unused 0 0 3050 0 0 1000 0

Total Cost = $89,461,150.00

39

It is clearly evident that the network generated from Capitalized Plant Location model is

the best model of the two discussed ones because it gives the company less total costs by

suggesting the opening of the plants at Germany and Japan. The outcome of this model also

suggests not to open the facilities located in South Africa and Dubai. In this way, the company

can save $33,983,200.

6. CONCLUSIONS

According to the previous calculation and selected models, we obtained the forecasted

level of demand for the product in its maturity stage. This information allowed us to define and

develop the best network model for the cosmetic company, which is opening the new facilities in

Germany and Japan. This network allows the company to have buffer capacity of 3050 units at

America and 1000 units at Japan plants. Moreover, we noticed that the production capacity at

France, Germany and India will be utilized at their maximum levels giving the company a good

degree of efficiency. This network model gives the company a minimum total cost of

$89,461,150.

7. FUTURE WORK

As the network designed in this project is based on forecasted maturity demand data,

which the company expects to reach in that particular period, the future level of demand can be

different. Thus, the company should analyze the different scenarios that may occur. In this

40

section we provided the analysis of each possible scenario and what is the situation that the

company is going to face, according to each different situation.

- If the demand is similar to the forecasts, the company will have a high rate of efficiency

because the production capacity of three out of five plants is saturated. The unused

capacity at America and Japan will allow the company to have reasonable rate of

flexibility.

- If the maturity stage demand is much higher than the forecasted demand, the company

should increase the total production capacity by opening new facilities or increasing the

capacities of the existing plants.

- If the maturity stage demand is much lower than the forecasted demand, the company has

excess production capacity which can be used to manufacture other similar products or

outsource products for other companies.

41

8. REFERENCES

Ballou, Ronald H. Business Logistics Management. 5th ed. Englewood Cliffs, NJ: Prentice-Hall,

2003.

Chopra, Sunil, and Peter Meindl. Supply Chain Management: Strategy, Planning, and Operation.

5th ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2007.

Coyle, John J.; Langley, C. John; Gibson, Brian J.; Novack, Robert A.; Bardi, Edward J. Supply

Chain Management: A Logistics Perspective. 9th ed. South-Western, 2013.

Kotler, Philip, and Kevin Lane Keller. Marketing Management. 14th ed. Upper Saddle River,

NJ: Prentice Hall, 2012. Print.