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

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.