Case: Air Traffic Controller School $($ATCS$)$

ATCS provides training for future air traffic controllers. One of the skills air traffic controllers need is the ability to sequence aircraft for landing purposes. The controller decides who lands immediately and who goes into a holding pattern. The following data are provided to you, the student, to develop an acceptable landing sequence. Any sequence that results in an aircraft not being scheduled to land before it runs out of remaining flying time is unacceptable. The following aircraft are currently awaiting your decision as to their landing sequence.

$\backslash$table$[[\backslash$table$[[$Flight$],[$Number$]],\backslash$table$[[$Minutes$],[$on Runway$]],\backslash$table$[[$Remaining$],[$Flying Time$],[($minutes$)]],\backslash$table$[[$Cost per$],[$Minute of$],[$Flying Time $($$$)]]],[101,2\mathrm{.}00,10,100],[118,3\mathrm{.}00,15,150],[217,2\mathrm{.}75,8,125],[8076,1\mathrm{.}50,5,80],[219,3\mathrm{.}50,12,200],[894,1\mathrm{.}75,19,150],[024,2\mathrm{.}50,16,400],[616,3\mathrm{.}25,22,300]]$

There are many ways to sequence this group of aircraft waiting to land. Since cost is an obvious factor, consider a sequence that minimizes total cost to land the aircraft. Multiply the cost per minute of flying time by the remaining number of minutes. This gives you the maximum cost associated with an airplane

circling in a holding pattern until the last possible moment.

$($a$)$ Develop a landing sequence that gives priority to those aircraft with the highest cost of slack time $($excess flying time multiplied by cost per minute of flying time$).$ For example, Flight $616\text{'}$s $18\mathrm{.}75$ minutes of slack time $(22-3\mathrm{.}25$ times $$300$ per minute means that if Flight $616$ does not land until its time is all used up$,$ it incurs an extra flying cost of $$5,625.$ Make a Gantt chart showing the landing sequence and evaluate the sequence in terms of performance. Calculate mean flow time, mean lateness, and average number of planes in the system.

$($b$)$ Develop a sequence using SPT as a priority rule. Make a Gantt chart showing the landing sequence and evaluate the sequence in terms of performance. Calculate mean flow time, mean lateness, and average number of planes in the system.

$($c$)$ Develop a third sequence using EDD $($earliest due date$)$ as a priority rule. The plane with the least amount of flying time remaining has the highest priority. Make a Gantt chart showing the landing sequence and evaluate the sequence in terms of performance. Calculate mean flow time, mean lateness, and average number of planes in the system. Calculate the total cost associated with this sequence $($flow time multiplied by cost per minute of flying time for each flight$).$

$($d$)$ Try to develop an alternative sequence that lands all of the aircraft safely and reduces the total cost.