$[25$ points$]$ In the hand simulation of the simple processing system, suppose that the queue

discipline was changed so that when the drill press becomes idle and finds parts waiting in

queue, instead of taking the first one, it instead takes the one that will require the shortest

processing time $($this is sometimes called an SPT queue discipline$).$ To make this work, you$$ll

need to assign a second attribute to parts in the system when they arrive, representing what

their service time at the drill press will be$.$ Redo the hand simulation. Is this a better rule? From

what perspective?

$2.[35$ points$]$ In the hand simulation of the simple processing system, suppose the drill press is

taken down for burn$-$in maintenance at time $4$ minutes, and it takes $4$ minutes to do this work

and bring it back up; it then stays up for the rest of the $20-$minute simulation length. If there$$s

a part in service when the drill press goes down, it just sits there, its processing suspended until

the drill press comes back up$,$ when it$$s resumed and needs just its remaining processing time

$($its processing does not have to start over from scratch$).$ During the down time, the arrival

process of new parts continues without regard to down time. Regard the drill press as being

busy when it$$s down, and defi ne the time in system of a part to include the time it sits in the

drill press but not being worked on if it$$s unlucky enough to be in service when the drill press

is taken down. Using the same input data, carry out this simulation by hand and note any

differences in the output performance measures from the original model.

$3.[40$ points$]$ Increase the sample size on the news vendor problem from $30$ days to $150.$ As in the

original problem, use the same realized demands in column E for all values of q$.$ Don$$t forget

to change the statistical$-$summary and histogram cells appropriately at the bottom of the

columns, as well as the cells referred to in the various graphics. What is the effect on the

results? Based on your results, about what sample size $($in days$)$ would be needed to bring the

maximum half$-$width of all five confidence intervals down to under $\backslash$pm $$1\mathrm{.}50?$