Alpha Engineering $($AE$)$ produces and sells, among many other products, a portable scanner. AE faces

challenges in its factory and retail store. Your team is hired to help.

AE has $38$ employees in its factory. They are categorized by their expertise into three categories:

expert $($E$),$ experienced $($P$)$ and beginner $($B$).$ The number of employees in each category is given in

Table $1.$

These three categories differ in their monthly productivity, and employees can team up to raise

productivity. For example, an expert working alone can make $15$ products per month, while an expert

and an experienced employee working together $($E$+$P$)$ can produce $29$ products per month. There are

a total of seven possible team configurations, shown in Table $2.$

Each team occupies a machine $($an employee working individually is also considered a team$).$ The

company has $18$ machines, three of which are old and can only be operated by one employee $($of any

category$).$ All the employees are hired on salary and the company does not want to recruit or lay off

any of them. Assume that labor is a sunk cost and can be ignored in this analysis. Finding a way to

form teams for these $38$ employees to maximize the factory$$s monthly productivity becomes AE$$s first

key objective.

AE has two opportunities to improve its productivity. AE can choose to take one of the opportunities

or neither, but not both.

First, a competitor proposes a process redesign that involves improving the workflow and factory

layout. If AE takes this offer, the redesign can reduce the number of single$-$operator machines from $3$

to $1.$ The cost for this offer is five products per month given to the competitor.

The second opportunity to improve productivity is a strategic alliance. If this strategic alliance is

formed, there is a $50\%$ chance that it will be successful. If it is successful, it will increase the

productivity of $($E$+$B$)$ and $($P$+$B$).$ If it is unsuccessful, then the alliance will only increase the

productivity of $($E$+$B$).$ Forming the strategic alliance does not change productivity of any other team

configuration. The resulting productivity of these teams is given in Table $3.$ The cost of this

opportunity is ten products per month given to the strategic ally. This cost is incurred regardless of

the alliance$$s success.

AE also faces challenges in its store. First, AE produces at its maximum productivity in every month

and uses the produced product to meet demand only in that month. For simplicity, assume that all

the product will be produced and available for sale at the beginning of each month. Any unsold

inventory in that month will be discarded so that inventory does not carry over to next month. For

example, if AE$$s monthly productivity $($as a result of the decision on team formation$)$ is $100$ units,

then $100$ units are available at the beginning of each month at its store to meet the demand in that

month and any unsold inventory at the end of month will be discarded.

The net profit per unit is $$10.$ Based on historical data, the number of customers per month is a

normal distribution $(\backslash$mu $=60,$ s$=20).$ The number of products purchased by each customer follows a

triangular distribution with a minimum of zero, maximum of $30,$ and most likely purchase of $20$

units.

When AE cannot satisfy a customer$$s demand, there is a $60\%$ chance that the customer will file a

complaint. In that case, AE will pay the customer a penalty $($i$.$e$.,$ store credit or coupon$)$ of $$5$ per

unsatisfied demand. For example, suppose a customer demands $10$ units and AE has only $4$ units of

inventory available, then this customer has $6$ units of unsatisfied demand. In this case AE will earn

$$10*4=$$$40$ from this customer. If the customer files a complaint $(60\%$ likely$),$ then AE will incur a

penalty cost of $$5*6=$$$30$ for this customer, meaning that AE$$s revenue from this customer will be

$$40-$$$30=$$$10.$

AE$$s sale of the portable is on the rise. As mentioned earlier, it faces an average demand of $60$

customers per month. A recent market research finds that its average number of customers per month

will increase over time, as shown in Table $4.$ Assume that Year $1$ is the current year and that all other

parameters remain constant.

Once optimized, the maximum productivity is fixed for the next five years. Since maximum

productivity is fixed while store demand is projected to increase, AE anticipates paying more penalties

due to unsatisfied demand each year.

You will prepare a report that addresses the following topics:

$$ The most productive way to organize the employees in the factory

$$ Your recommendation on which, if any, opportunity to take

$$ Projection of future losses