Safety stock =1.56*(30/7) * ?7 = 17.69 = 18 units

z = 1.56

? = 30/7

L = 7 days

Safety stock = z*?*?L

The order will be placed when the inventory

level reaches 218 units. When the service level is at a 94% means, there is

0.94 probability, that the firm will meet the demand during lead time. It

means, the probability of stock out is 6%. When we calculate the safety stock,

it leaves us with 18 units of safety HP printers that will remain in stock

before we eventually run out of them.

R = (200/7) *7 + 1.56*(30/7) * ?7

= 200 + 17.69 = 217.69

z = 1.56

? = 30/7

L = 7 days

d = 200/7 units

Reorder point R = dL + z*?*?

In

the most part we need to understand that they are having a big ratio, with

those being out of stock and none to come for a week. Its making their job

harder for Kyle’s sales associated with the company. Therefore, Kyle Bits business

must see what can they do to gain a manufacturing team to produce more products

for them. If they want to expand the manufacturing company, then he would need to

acquire more businesses within. By doing so, this manufacturing company can

make more products that way they can sell quick. The problem they have with HP

laser printers is the demand is not consistent it be switching up and down,

which leads to less of them being manufactured. They are trying to accomplish

the sells for their company so, they can make more sell as other companies and

have advertising and more expansions. Kyle Bits and Bytes can lead to

purchasing printers if they can keep up with their business being manufactured,

but the demand may leave them with some or none as it continues to sell. The reorder

point; Inventory level at which order should be placed:

Kyle

Bits and Bytes has a retail business of computing products. This case Kyle’s

most sells are the HP laser printer, to be very important it gets sold out quickly.

This product is getting sold quick, is making an average on a weekly demand of

200 units, and the lead time is about one week. However, the demand is not

constantly. From the scenario Kyle has been observing that the weekly demand has

a standard deviation of 30. He needs to know when should he be placing an order/

reorder point, and inventory level so that there is no stock-out. If Kyle runs

out he won’t be able to fulfill an order due to stock-out, Kyle will lose all

the sales and possibly additional sale that has been placed. Kyle put a maximum

acceptable probability because he can’t be stock-out in a week at a 6%. In the

scenario Kyle Bits wants to know, what should be the re-order point and how

many HP laser printers should be in stock before running out.

Case 2: Kyle Bits and Bytes

We

have decided for the management, and as a vice president we would go with the

large-scale expansion. Just because it has a lower deviation as the calculation

shows on the Excel spreadsheet it will show the medium and large scales

operations.

Large

scale: 111.3553

Medium

scale: 52.20153

As

the standard deviation will follow to be measure for both data values. The

standard deviation will be calculated by the square root of the variance. The

lower the variance the lower risk it has, and the higher deviation will be considered

as a high risk. The standard deviation for both cases are:

Large

scale: 12,400

Medium

scale: 2,725

expansion project, because the large

scale has a lower expansion. For the medium scale, expansion is preferred for making

an objective of maximizing profit. However, they are expecting the value is not

enough to take an informed decision. But is also important to know how profits

can deviate from the expected value. Variance will be used for both risk

analysis to measures how far a set of random values are spread from the mean

value. The higher of variance means the random values are spread far from its

mean with a standard deviation. This will determine the risk factor for the

management to decide which one to pick. The variance for both expansion cases

are:

The medium scale expansion alternative has higher expected

value than the large-scale

Large scale expansion: $140

Medium scale expansion: $145

When dealing with an expected value is like anticipating with

a value of an action that comes with multiple outcomes. But first, we need to

determine the probability of the occurrence of each outcome of each medium scale

and high scale analysis. The expected value for the bell computer will be

calculated by multiplying each possible outcome, and by the probability of

occurrence of outcome, and adding all those values. The expected value of

medium scale expansion and large-scale expansion will help all the management to

choose the expansion option that is most likely to generate on a higher profit.

As we expected the value of the two expansions

are:

The bell computer company has two alternative expansion

options: a medium scale, and a large scale. The medium scale expansion and large-scale

expansion, has a demand to be in between low, medium, or high with a probability

of 0.2, 0.5, and 0.3 respectively. For the medium scale expansion, the profits

in case of low, medium and high demand is $50,000, $150,000 and $200,000

respectively. As for the large scaling

expansion, the profits are case of low, medium, and high demand of $0, $100,000

and $300,000 respectively. Their management team is facing a big dilemma, they

can’t choose between the medium scale or the large-scale expansion. We are expecting

for the large-scale expansion, to have a greater potential to generate on a

higher profit in case of high demand scale, the large-scale expansion will

generate lower profit than the medium-scale expansion. In this case, they are

looking at the low profit demands, just because the large-scale expansion is results

as a nil profit. However, the medium-scale expansion is escalating more risk

than the large-scale expansion.

Case 1: Bell Computer Company

The bell computer company wants to do a determination on

which expansion to choose for the new computer products coming out. For this

case, we are going to determine whether to choose the expansion from the medium

scale or the large scale. Accordingly, the first case will show how to use the

mean and standard deviation of probability distributions to decide,

specifically by having expansion strategy. Additionally, the second case will help

determine the point in which a manager should re-order a printer so, they do

not run out of stock using normal distribution.