When It is imperative to look at

When
considering expanding, companies should determine whether to make the expansion
a medium or large scale project.  By
carefully analyzing the data, we can make an educated prediction since new
products involves an uncertainty, which for planning purposes may be low demand,
medium demand, or high demand.  As a vice
president of the Bell Computer Company, the data would be analyzed to determine
the best path for the company’s expansion.

Case 1: Bell Computer Company

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Profit Associated with the Two
Expansions

Medium-Scale

Large-Scale

Expansion Profits

Expansion Profits

Annual Profit
($1000s)

P(x)

Annual Profit
($1000s)

P(x)

Demand

Low

50

20%

0

20%

Medium

150

50%

100

50%

High

200

30%

300

30%

Expected Profit ($1000s)

145

140

 

Maximizing Expected
Profit

For maximizing the
profit, the company can strive for the large-scale expansion which seems to be ideal
for a high demand.  The assertive
expansion assuming the company will have high demand offers a profit range of $300,000
vice the $200,000 in profits that are anticipated by the medium-scale expansion.
 In the other hand, there is a great
level of uncertainty because everything is dependent on the
demand for the product.  Looking at the
bigger picture, the medium scale expansion has higher expected value than
large-scale expansion project.  Therefore,
the medium-scale expansion is preferred for the objective of maximizing
expected profit in it’s entirely.  By
just knowing the expected profit value, it does not provide adequate information
to make an educated decision when it comes to expanding the company.  It is imperative to look at the variance.  The variance measures how far a set of random
values are from the mean.  In this case,
it will provide us with the deviation of profit margins, thus a low variance is
more favorable for maximizing the profit. 
The medium-scale expansion with a variance of 2725 is more desirable
than a large-scale expansion with a variance of 12400 because the profit
deviation is much less with the medium-scale expansion.

Risk Analysis for Medium-Scale Expansion

Demand

Annual Profit (x)
$1000s

Probability P(x)

(x – µ)

(x – µ)2

(x – µ)2 *
P(x)

Low

50

20%

-95

9025

1805

Medium

150

50%

5

25

12.5

High

200

30%

55

3025

907.5

?2 =

2725

? =

52.2015325

Risk Analysis for Large-Scale Expansion

Demand

Annual Profit (x)
$1000s

Probability P(x)

(x – µ)

(x – µ)2

(x – µ)2 *
P(x)

Low

0

20%

-140

19600

3920

Medium

100

50%

-40

1600

800

High

300

30%

160

25600

7680

?2 =

12400

? =

111.355287

 

Minimizing the Risk

The standard deviation
is used to measure the deviation of data values which in a way measures the
associated risk.  A standard deviation
with low values provides us with a lower risk assessment, and a standard
deviation with a high value is indicative that associated risk is higher.  From the data above, the medium-scale
expansion is ideal for minimizing the uncertainty the company might be willing
to assume as the standard deviation is twice as small as the large scale
expansion.  The large-scale expansion
offers a higher profit maximum; however, it has a zero profit minimum that
could be unfavorable for the company’s expansion.  The medium-scale expansion may offer the $200,000
profit in comparison to the $300,000 attain by the large scale expansion, but it
has a favorable profit at a low demand of $50,000 compared to the no profit generated
by the large-scale expansion.  Also, the
medium-scale expansion offers a $150,000 profit with a medium demand contrasted
to $100,000 with the large expansion. 
The overall risk associated with the medium scale expansion is much
favorable than the large-scale expansion.

 

Case 2:  Kyle Bits and Bytes

Abstract

Kyle Bits and Bytes, a
retailer of computing products sells a variety of computer-related products.  Kyle’s most popular products is an HP laser
printer.  The average weekly demand is
200 units.  Lead time for a new order
from the manufacturer to arrive is one week. 
 If the
demand for printers were constant, the retailer would re-order when there were
exactly 200 printers in inventory.  However,
Kyle learned demand is a random variable.  An analysis of previous weeks reveals the weekly demand standard
deviation is 30.  He wants
the probability of running short (stock-out) in any week to be no more than 6%.    

Re-Order
Point

In this case of Kyle Bits and
Bytes, D = 200/7 units, L = 7 days and ? = 30/7. Maximum accepted probability
of stock out is 6%. Using the z-table to determine the z-value at 0.94, z
equals 1.56.  The re-order point is
calculated by multiplying the average daily usage rate by the lead time and
adding the safety stock (Average daily usage rate x Lead time) + Safety stock.   Therefore, the following formula can be used
to calculate the re-ordering point: R = D*L + z*?*?L, Where D = average daily
demand, L = lead time, ? = standard deviation of daily demand, and z = number
of standard deviations corresponding to the service level probability due to
the constant demand.  By conducting the
calculation in the excel table below, the re-order point (R) is equal to
217.69.

Kyle Bits and Bytes Re-Order Point

Reorder Point (R)= Average daily usage rate *Lead time + Safety
stock

R= DL + z*?*?L

 

D=200/7

L=7 days

z=1.56

?=30/7

?L=?7

 

28.57

7.00

1.56

4.29

2.65

R =

217.6887373

Safety Stock =

17.69

 

Safety
Stock

The safety stock is a buffer stock
used against unexpected events that depleted the company’s stock or to account
for unexpected manufacturing delays.  For
Kyle’s Bits and Bytes, the maximum probability of stock-out accepted is
6%.  To calculate the safety stock, the
following formula is used:  Safety Stock=z*?*?L,
where L = lead time, ? = standard deviation of daily demand, and z = number of
standard deviations corresponding to the service level probability because the
demand is constant.  Therefore, the
standard deviation of lead time is used to calculate the safety stock.  From the table above, it was determined that
the safety stock for the Kyles’s Bits and Bytes is 18 units.  The company should maintain 18 units safety
stock of HP laser printer to avoid stock out.