Please solve the attached questionCASE STUDY

Shall It Be Postponed?

Foxcompany $($Fox$)$ Co$.$ Ltd$.$ was founded in $1974$ in

Taiwan as a manufacturer of electrical components for

computers. With strong research and development

efforts, by $2011,$ it had accumulated more than $25,000$

patents granted worldwide. Fox is now one of the

world's $500$ biggest companies, according to Fortune

magazine. Its biggest production operation is located in

Shenzhen Longlong Science & Technology Park,

which covers more than $3$ square km with $15$ factories.

Not only does Fox have dormitories, a hospital, and a

fire brigade, but it also broadcasts its own TV channel

within the park.

Fox is highly specialized in producing computer

components and produces and packages private$-$label

components for various famous brand names, including

Acer, Apple, Dell, and Hewlett$-$Packard. The compo$-$

nents manufactured are basically identical but are

labeled and packaged differently for the various cus$-$

tomers. The Shenzhen manufacturing facility replen$-$

ishes a distribution center $($DC$)$ in Taiwan where the

lead time is nine weeks. Fox adopts a continuous

review policy to manage the inventory at its DC and

wants to maintain a cycle service level of $95$ percent

for all orders.

The previous month had been challenging: Apple

asked for $5,000$ extra units than were available at the DC$,$

whereas Acer and Dell ordered $3,500$ units and $4,000$

units fewer, respectively. Although there was sufficient

inventory available at the DC in the form of basic prod$-$

uct, Fox was not able to meet Apple's demand because

the excess inventory available was labeled and nackaged

for Acer and

Dell.As a result Fox lost the extra business

opportunity and surplus inventory because of the wrong

labels and packaging.

Labeling and Packaging at the DC

To allow more flexibility for Fox production to accept such

additional orders from customers by simply switching the

inventory, the senior logistics supply chain manager pro$-$

poses to postpone the labeling and packaging work to the

DC$,$ where the lead time of manufacturing and transporta$-$

tion remains unchanged. As a consequence, Fox would be

able to meet Apple's sudden additional order more readily

if other customers $($e$.$g$.,$ Acer$)$ placed a smaller order.

However, the management at the DC worried about

the additional labeling and packaging work. Moreover, a

detailed study revealed that the postponement would cost

$$1$ more per unit. In particular, the DC managers believed

that those $$1$ increases in cost per unit would be held against

them once the process was changed and they would be

under pressure to lower costs. They also thought the added

workload would affect the overall service level of the DC$.$

Evaluating the Two Options

A task force was set up to look into this matter. It would

focus its study mainly on three major components$-$moth$-$

erboards, graphics cards, and chassis$-$ and the four key

customers$-$Acer, Apple, Dell, and HP$.$ Weekly demand is

shown in Table $12-9.$ In each case, the mean denotes the

average demand per week, and SD denotes the standard

deviation of the demand per week. Furthermore, all

demands follow the normal distribution pattern. Fox

incurred a total cost of $$100$ per motherboard, $$50$ per

graphics card, and $$30$ per chassis. As per the rule of

thumb of the industry, Fox used a holding cost of $30$ per$-$

cent when making all inventory decisions. The task force

studied the impact of postponement on safety inventories

before providing its final recommendation.

TABLE $12-9$ Distribution of Weekly Demand by Product and Customer

Questions

What is the annual inventory cost before postponement?

How would the inventory cost change if postponement

were implemented? Evaluate the change in inventory costs

as the correlation coefficient of demand between any pair

of customer varies from $0$ to $0\mathrm{.}5$ to $1\mathrm{.}0.$

Should Fox postpone its labeling and packaging process to

the DC$?$ Would the answer change if the additional cost of

labeling and packaging at the DC were reduced to $$0\mathrm{.}5$

$($from the current $$1)?$