Running head: A-CAT CORP. FORECASTING
A-CAT Corp. Forecasting Analysis
Janis Chartier
Southern New Hampshire University
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A-CAT CORP. FORECASTING
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Abstract
This paper will present a statistical analysis of the A-CAT Corporation: Forecasting case study
(Sharma, 2013). The analysis will review the company’s historical sales and inventory data,
provide an analysis of the data, and recommend the size and timing of the next order of VR-500
voltage regulators.
A-CAT CORP. FORECASTING
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Table of Contents
Introduction ......................................................................................................................... 4
Analysis Plan ...................................................................................................................... 5
Quantifiable Factors ........................................................................................................ 5
Effect on Operational Processes ..................................................................................... 5
Problem Statement .......................................................................................................... 6
Proposed Analysis Strategy ............................................................................................ 6
Statistical Tools and Methods ............................................................................................. 7
Appropriate Family of Statistical Tools .......................................................................... 7
Categories of Provided Data ........................................................................................... 7
Most Appropriate Statistical Tool and its Justification................................................... 8
Best Quantitative Method ............................................................................................... 8
Analysis of Data .................................................................................................................. 9
Outline of Process and its Validity ................................................................................. 9
Analysis of Data and Reliability of Results .................................................................. 10
Data Driven Decision .................................................................................................... 14
Recommendations for Operational Improvements ....................................................... 15
References ......................................................................................................................... 16
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A-CAT Corp. Forecasting Analysis
This paper presents a statistical analysis of the A-CAT Corporation: Forecasting Case
Study (Sharma, 2013). The analysis will review the company’s historical sales and inventory
data, provide an analysis of the data, and recommend the size and timing of the next order of
VR-500 voltage regulators.
Introduction
A-CAT Corporation is a medium-scale company that produces and distributes electrical
appliances to rural customers in the Vidarbha region of India. A-CAT has been in business since
1986 and employs around 40 employees at of their two medium-sized manufacturing plants in
the town of Gondia.
A-CAT Corporation’s flagship product is the VR-500 Voltage Regulator commonly used
in appliances such as refrigerators and television sets. These voltage regulators are a key
component to ensure that appliances are not damaged due to the frequent electrical grid voltage
instabilities and outages. Due to the rural customer base, A-CAT Corporation’s products must
be affordably priced to ensure that the company’s customer base is not lost to competitors.
A-CAT Corporation Vice President, Arun Mittra, has directed Operations Manager,
Shirish Ratnaparkhi, to conduct a statistical analysis of the sales of the VR-500 voltage
regulators in order to determine the correct inventory levels needed to avoid over or
understocking of transformers needed to produce the VR-500. Key stake holders include the ACAT Corporation’s department heads, employees, customers, and the transformer supply vendor.
A-CAT CORP. FORECASTING
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Analysis Plan
Quantifiable Factors
Several quantifiable factors are known. Most of these factors are historical in nature.
These quantifiable factors include the monthly quantity of transformers needed for the
production of voltage regulators from 2006 through 2010. Quarterly sales figures of refrigerators
are also given between 2006 through 2010. Sales of refrigerators are significant as the voltage
regulators are a key component of the appliance.
The construction of quality control charts requires the use of the descriptive statistics
provided. Descriptive statistics including the mean, standard deviation and sample variance are
known for the year 2006 (Sharma, 2013). Descriptive statistics are needed for 2007 through
2010 in order to estimate the mean number of transformers required to produce the voltage
regulators (Sharma, 2013).
A one-way analysis of variance (ANOVA) analysis is included for the years between
2006 and 2008. The results of this analysis indicate there has been a change in the mean number
of transformers required. The transformer requirements are provided for 2009 and 2010 are
given in order to determine the change in the number and mean of transformers required over the
two-year period.
Lastly, sales of refrigerators and the number of transformers required to produce those
refrigerators are given by each quarter and used to forecast the number of transformers required
for future sales.
Effect on Operational Processes
The number of transformers in stock is necessary in order to produce the required number
of VR-500 voltage regulators. If the stock is too low to meet customer demands, the company
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stands to lose sales to competitors. If the stock is too high, the company is essentially wasting
capital funds that could be used for other products also impacting sales revenue.
The number and level of VR-500s produced directly affects the purchasing department,
the manufacturing department and the sales and service department. Purchasing is required to
buy and stock the transformers required to produce the VR-500s. The Manufacturing department
must staff and schedule the appropriate shifts to produce the VR-500s, and the Sales Department
must have the stock available to meet existing and future customer demands.
Problem Statement
In recent months, the sales of the VR-500 have declined. The various department
managers are interested in the cost of stocking the transformers required to make the VR-500s.
Too much inventory puts a strain on capital money that could be employed elsewhere to improve
profit margins. There is also a need to ensure that sufficient supply is on hand and to provide a
consistent strategy for ordering the transformers. As there is currently only one supplier for the
transformers, the purchase price could be negatively impacted if orders are inconsistent and
unpredictable. Therefore, it is also necessary to ensure consistent transformer purchase orders to
avoid any increases in prices by the supplier.
Proposed Analysis Strategy
The amount of stock is dependent on variables including sales, inaccurate forecasts, lead
times for the materials needed and manufacturing time (King, 2011). The current proposed
analysis strategy is to review the historical data provided. We can use the normal distribution
and z-scores to determine how to meet demand with a 95 percent confidence level (King, 2011).
Since we have historical data, we will employ a similar ANOVA analysis to the one provided in
the case study, as well as various “time-series” data analysis. This is based on the assumption
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that the sales are related to the previous year’s sales, that they change over time, and that there
appear to be seasonal or time-related variances in the number of transformers required and VR500s produced (Sharpe, DeVeaux, & Vellman, 2015). Specific “time-series” analysis tools will
be included in the upcoming milestones for this report.
Statistical Tools and Methods
Appropriate Family of Statistical Tools
We have been provided the data sets in the case addendum and within the case exhibits
and we would be employing a range of statistical tools for analyzing the data sets to generate our
results. As we read the case study we need to understand that most of the data would be analyzed
through the use of the descriptive statistics and performing the hypothesis tests such as the One
Way ANOVA or the One Sample T-test.
There are a range of different statistical software out there to analyze the data based on
these methods such as SPSS, excel, Stata etc. The assumption on the basis of which we have
selected this statistical tool and the method as specified above is that the data sets that we have
been provided with are simple and the number of observations is small.
Categories of Provided Data
The decision variable of the case study is the demand quantity of the voltage regulators
that are either demanded or sold by the company. The level of measurement on which this
variable is measured is scale. Nominal and ordinal data are also other important levels of
measurement but the case study, exhibits and addendum does not provide us with any of such
data types.
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This is the reason due to which using SPSS or any other statistical tools would not be
appropriate and it would complicate the analysis of the data. All the data within the case study is
of the scale category and scale variables can be appropriately and easily analyzed within the
excel spreadsheet software. Therefore, it is highly important to make use of such simplistic
statistical tool for driving the decision and finding recommendations for the business problems.
Most Appropriate Statistical Tool and its Justification
As stated previously, we have seen that there is no use of any kind of ordinal or nominal
data and all the data sets that we have been provided are in the form of the scale measurement.
Hence, we would be employing the use of the excel spreadsheet to perform the analysis and
generate the descriptive statistics of the data (Chou, 2001). All the hypothesis tests and the
forecasting model would be generated within the excel spreadsheet.
There are two specific justifications for selecting this statistical tool. The first one is that
scale data can be easily analyzed using the different formulas and techniques, tests and methods
that are provided within the excel spreadsheet package and secondly, the data analysis performed
in excel would be more reliable and easier for us as the data sample is short (Chou, 2001).
Best Quantitative Method
We have employed a range of different quantitative methods for performing the analysis
of the data for this case. First of all, we have forecasted the data for the years 2009 and 2010
using the simplest forecasting technique that is the simple moving average technique (Freedman,
2005). Next, we have generated the descriptive statistics for the entire data set for the year 2006
to 2010 (Chou, 2001).
This is highly important as it would guide the operational managers to remove all sorts of
the discrepancies from the data and resolve the issues faced by them. We have employed no
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external sources to extract additional data for the company and all the data sets provided within
the case, exhibits and addendum have been used to perform the statistical analysis. Along with
this, we have employed a range of hypothesis tests such as the one sample t-test and the one-way
ANOVA test for determining the significance of the change in average number of regulators.
Finally, we have employed the linear regression model to generate the most appropriate
forecasting model for the company.
Analysis of Data
Outline of Process and its Validity
This is the analysis section of the report and the most important part of the entire report.
Here we state the outline of the process of analysis and its validity. Before performing any of the
analysis, we have forecasted the data for the demand quantities of the voltage regulators for the
years 2009 and 2010 as stated previously. The method of forecasting user here is the simple
moving average method for the past three months of the preceding three years (Freedman, 2005).
After this the actual analysis including of descriptive statistics, hypothesis tests like oneway ANOVA, one sample t-test and forecasting models like regression analysis have been
performed. Following this outlined process would lead to data driven decision, because it
addresses all the issues step by step and most of these methods have been used by the company
in the past so they are valid for the company’s data (Chou, 2001). Finally, regression analysis
would be new for the company and it would guide the data driven process by formulating the
most appropriate statistical model for the company.
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Analysis of Data and Reliability of Results
As stated in the process outline, we have first generated the descriptive statistics for the
entire data including the data for 2009 and 2010 that we forecasted. These descriptive would be
utilized by the managers within the operational department to prepare the control charts and the
confidence limits for processes. The Vice President of A-Cat have requested these descriptive
and these are shown in the table below:
DESCRIPTIVE STATISTICS 2007-2010
2007
2008
2009
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Confidence Level (95.0%)
898.667
39.529
864.000
-
990.333
41.950
941.000
-
136.931
18750.061
-0.609
0.772
394.000
739.000
1133.000
10784.000
12.000
87.002
896.722
32.835
852.167
-
145.320
21117.879
-0.853
0.650
448.000
798.000
1246.000
11884.000
12.000
92.332
2010
928.574
36.480
887.556
-
113.745
12937.896
-1.214
0.738
307.333
783.333
1090.667
10760.667
12.000
72.270
126.372
15969.834
-1.055
0.791
344.444
809.111
1153.556
11142.889
12.000
80.293
If we look at the average demand of the transformers, then the demand first the
demand has declined from 2008 to 2009 but then it had increased by a much higher percentage
from 2009 to 2010. The maximum demand had been experienced in 2010 which is around 1154
units approximately. Furthermore, the trend of the variability of demand shows that standard
deviation has reduced in 2009-2010 as compared to the previous period of 2006-2008. The 95%
confidence level is also calculated for transformer demand for each of these years.
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After, analyzing the descriptive of the data set, we determine the change in the
mean number of transformers over the same period. Previously, the vice president of operations
determined the mean number of transformers required for producing voltage regulators based on
the demand of regulators in 2006. However, now we have the demand for the year 2010 as well.
Hence, we determine once again that whether the mean number of the transformers needed to
manufacture voltage regulators has changed significantly over the years or not. This has been
analyzed by performing the one-sample t-test. The hypothetical mean for this test is set at 1000
units since the management believes that the mean number of the transformers to be produced is
likely to exceed 1000 units. The test results are shown below:
ONE SAMPLE T-TEST ( Based upon 2010 data)
Count
Mean
Standard Deviation
Standard Error
12
928.57
126.37
36.48
Hypothetical Mean
Alpha
Tails
Df
t stat
P value
T crit
Significance
1000
0.05
1
11
-1.9579
3.80%
2.2010
YES
The t-value of the test is less than the critical value and the p value is also less than the
level of significance of 0.05, therefore, we can conclude that the mean number of transformers
required are significantly high over these years and the actual mean number of transformers
required to produce the voltage regulators is equal to or greater than 1000 units.
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Next, we use the one-way ANOVA test to determine that whether the change in the mean
number of the transformers required for manufacturing the voltage regulators is significant over
these years or not. This test had been previously tested by the operational managers based on the
data of the demand of transformers from 2006 to 2008 however, since we have a much bigger
data set from 2006 to 2010, therefore, this needs to be tested again. The results of this test are
shown in the table below:
Groups
2006
2007
2008
2009
2010
Count
12
12
12
12
12
SUMMARY
Sum
9614
10784
11884
10760.667
11142.889
Source of Variation
Between Groups
Within Groups
ANOVA
SS
df
224511.81 4
833758.02 55
Total
1058269.8 59
Average
801.167
898.667
990.333
896.722
928.574
MS
56127.953
15159.237
F
3.703
Variance
7020.515
18750.061
21117.879
12937.896
15969.834
P-value
0.010
F crit
2.540
The summary statistics in the first table show that the mean number of transformers had
increased between 2006 to 2008, then declined in 2009 and then again increased in 2010 by a
much higher percentage. The significance value of 0.01 and the F critical value of 2.540 then it
could be concluded that the results of this test are significant and the mean numbers of the
transformers has changed significantly from the year 2006 to 2010.
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Forecast Model for the Voltage Regulators
We have employed the linear regression analysis in excel spreadsheet by taking sales as
the independent variable and demand as the dependent variable to generate the forecast model
(Draper, 1998). The regression statistics and ANOVA results are shown in the tables below for
this model:
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
Regression
Residual
Total
df
1
18
19
93%
86%
85%
179.47
20
SS
3485332.92
579756.88
4065089.80
ANOVA
MS
3485332.92
32208.72
F
108.21
Significance F
0%
The statistics of the regression model in table 1 show that the relationship between the
demand of the transformers and the sales of the refrigerators is 93% which is highly strong and
positive. If sales increases, then the demand of regulators also increase (Cohen, 2003) (Chou,
2001). Also, if we look at the adjusted r square value then the percentage change in the demand
of the regulators as a result of the sales of the refrigerators is 85% which is also quite high and
provides enough evidence for the relationship between sales of refrigerators and demand of
regulators (Draper, 1998). The sig value of the ANOVA is 0.000 and this suggests that the model
is fitted and significant. The coefficients table is shown below:
Coeffici
ents
Standard
Error
t
Stat
Pvalu
e
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
A-CAT CORP. FORECASTING
Intercept
Sales of
Refrigerators
1233.49
9
0.315
7.36
167.475
5
10.4
0.030
02
14
0.00
0
0.00
0
881.64
7
1585.3
52
881.647
1585.35
2
0.251
0.379
0.251
0.379
The coefficients table shows that if the sales of the refrigerator is increased by a single
unit then the demand for the regulators is increased by 0.315. This is the most appropriate
forecast model that should be used by the management of A-Cat for forecasting the demand of
the voltage regulators.
Overall, the analysis has shown us reliable results and this is evident by the high adjusted
r square of the regression model. The entire analysis is reliable because it is consistent as it is
based on historical data of the company and forecasted data for 2009 and 2010. The descriptive
statistics also suggest that the company is following rational trends for the demand of its
regulators. Hence, the entire analysis performed in reliable.
Data Driven Decision
The data driven decision that we have reached to is that management should produce at
least 1000 units or more than 1000 units of the transformers for manufacturing the voltage
regulators to avoid overstocking and understocking and to meet the actual demand of the
customers in the market (Nelder, 1990). Secondly, in future the management should not rely on
intuition to estimate the demand of regulators but it should make use of the above regression
model to forecast the future demand. Managers should never rely on their intuitions and they
need to follow a rational forecasting approaches. Finally, the operational managers of the
company need to determine other factors, internal or external, that might have an impact on the
demand of transformers and then include those factors in the forecasting model (Ellis, 2010).
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Recommendations for Operational Improvements
The analysis plan states that it is highly important to determine the right number of the
transformers to manufacture the right number of the voltage regulators. For operational
managers, this would enhance operational efficiency and they would not end up under-stocking
or overstocking the units. Regarding, the external stakeholders, the customers would be happy if
their complete demand is met on time. It is recommended for the managers of A-Cat that they
make use of the appropriate and authentic models for estimating the demand of their products
especially their main product, voltage regulators (Nelder, 1990).
The company needs to manufacture more than 1000 units of the transformers in future
years. Managers should never rely on their intuition for forecasting future demand but they
should make use of the regression model for estimate the future demand based upon the sales of
the refrigerators. This would help the company to overcome the issues of overstocking and
under-stocking and the customers would be always satisfied and the risks of lost sales would no
longer exist in the company.
Lastly, this is the best option for the company and it would lead to operational
improvement. This is because this model has enough room to incorporate other factors that might
have an impact on the demand of the voltage regulators. These factors could be regional factors
within the market of Vidarbha and other rural market areas. When these factors are incorporated
within the multiple regression model, then they would generate more accurate forecasts and
hence boost the sales for A-Cat Corporation.
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References
Draper, N.R.; Smith, H. (1998). Applied Regression Analysis (3rd ed.). John Wiley.
Chou, Y.-l. (2001). Statistical Analysis. Holt International .
Cohen, J., Cohen P., West, S.G., & Aiken, L.S. (2003). Applied multiple regression/correlation
analysis for the behavioral sciences. (2nd ed.) Hillsdale, NJ: Lawrence Erlbaum
Associates
Ellis, K. (2010). Production Planning and Inventory Control. McGraw-Hill. ISBN 0-412-03471-9
Freedman, D. (2005). Statistical Models: Theory and Practice,. Cambridge University Press.
King, P. L. (2011, July & Aug.). Crack the Code: Understanding Safety Stock and Mastering Its
Equations. APICS Magazine, 33-35.
Nelder, J. A. (1990). The knowledge needed to computerise the analysis and interpretation of
statistical information. . In Expert systems and artificial intelligence: the need for
information about data. Library Association Report .
Sharma, J. (2013). A CAT CORP: Forecasting. HBS No. 13377. U.S.A: IVEY Publishing.
Sharpe, N. R., D., D. V., & Velleman, P. F. (2015). Business statistics. Boston: Pearson
Education.