A manufacturing company produces several semi$-$finished products $($A$,$ B$,$ C and

D$)$ that are integrated in the final products. Due to the high customization

requirements, it is not possible to keep the semi$-$finished goods on stock, which

means that the demanded parts have to be produced every week. To do so$,$ four

machines are available and each machine is dedicated to exactly one product.

The machines are generally available for $40$ hours per week because they require

labour to be run. Each additional hour on one of the machines $($overtime$)$ costs

$40.$

The company knows from experience that demand for each of the semi$-$finished

products is either low, medium, or high in each week. The probabilities are

equally distributed $(->$ one third for each scenario$)$ and the amount of required

products stays the same for each scenario $($due to how they are implemented in

the final products$).$

The following table gives more information:

Semi$-$finished

Product

Production

Time $($hours$)$

Demand $($low$)$ Demand

$($medium$)$

Demand $($high$)$

A $2162024$

B $481012$

C $8456$

D $1324048$

Sometimes it happens that some machines require overtime while others are

idle $($but the labour still has to be paid for $40$ hours$).$ It is possible to upgrade

machines so that they can produce more than one semi$-$finished product, but

this costs $3,000$ per machine per additional semi$-$finished product.

$1$ Calculate the expected overtime costs for the current, dedicated system

$2$ Calculate the weekly savings if you implement a $2-$flexibility$-$system. Is it

worth to invest?

$3$ How does the $2-$flexibility$-$system perform in comparison to total

flexibility?