Case Study for Logan International

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1. a. Per plane delay times
λ=50: 6.54 minutes/ plane
λ=55: 12.52 minutes/ plane
λ=59: 60.5 minutes/ plane

Delay costs
Arrival rate| 50| 55| 59|
Turbo| 6.54(348+0.7*15*25.7)60=$67.07| 12.5(348+0.7*15*25.7)60=$128.32| 60.5(348+0.7*15*25.7)60=$620.02| Jet| 6.54(1585+0.7*150*25.7)60=$467.29| 12,5(1585+0.7*150*25.7)60=$893.95| 60.5(1585+0.7*150*25.7)60=$4319.5| Regional Jet| 6.54(632+0.7*50*25.7)60=$167.07| 12.5(632+0.7*50*25.7)60=$319.62| 60.5(632+0.7*50*25.7)60=$1544.37|

b. Delay costs according to FAA
There are only delay costs associated with an arrival rate of 59, delay time: 60.5-15= 45.5

Arrival rate| 50| 55| 59|
Turbo| 0| 0| 45.5(348+0.7*15*25.7)60=$466.30|
Jet| 0| 0| 45.5(1585+0.7*150*25.7)60=$3248.62|
Regional Jet| 0| 0| 45.5(632+0.7*50*25.7)60=$1161.49|

c. We think 20-30 minutes would be a reasonable definition of delay because there shouldn’t be delay costs associated with delays under 30 minutes because it’s not a lot of time.

d. PPP is a good solution if it can reduce the arrival rate by even a small amount, say 5 planes. By reducing it from 59 to 55, per plane delay times will decrease dramatically, as will delay costs.

2. a. Revenue per plane
Turbo| Jet| Regional Jet|
15*0.7*240=2520| 150*0.7*400=42000| 50*0.7*160=5600|

% of fee/ revenue
Landing Fee| 200| 250| 300|
Turbo| 2002520=7.9%| 2502520=9.9%| 3002520=11.9%|
Jet| 20042000=0.48%| 25042000=0.6%| 30042000=0.71%|
Regional Jet| 2005600=3.6%| 2505600=4.5%| 3005600=5.4%|

We think having a fee of at least 3% of revenue would be significant. For all landing fees, turboprobs and regional jets would feel a significant impact, conventional jets would not. Turboprobs would be the most affected.

b. Per plane delay times
λ=40: 3.6 minutes/ plane
λ=45: 4.57 minutes/ plane
λ=55: 12.52 minutes/ plane

i. Delay cost
Arrival rate| 40| 45| 55|
Turbo| 3.6(348+0.7*15*25.7)60=$37.07| 4.57(348+0.7*15*25.7)60=$46.85| 12.5(348+0.7*15*25.7)60=$128.32| Jet| 3.6(1585+0.7*150*25.7)60=$257.01| 4.57(348+0.7*15*25.7)60=$326.36| 12,5(1585+0.7*150*25.7)60=$893.95| Regional Jet| 3.6(632+0.7*50*25.7)60=$91.89| 4.57(348+0.7*15*25.7)60=$116.69| 12.5(632+0.7*50*25.7)60=$319.62| Total cost

Arrival rate| 40| 45| 55|
Landing fee| 300| 250| 200|
Turbo| 37.07+300=337.07| 46.85+250=296.85| 128.32+200=328.32| Jet| 257.01+300=557.01| 326.36+250=576.36| 893.95+200=1093.95| Regional Jet| 91.89+300=391.89| 116.69+250=366.69| 319.62+200=519.62| All planes prefer the lowest total cost so turboprobs prefer a $250 landing fee, Jets prefer a $300 landing fee and regional jets prefer a $250 landing fee. ii. PPPs effect on delays definitely depend on the particular mix of planes because certain types of planes are more impacted than others.

40% turbo, 18% regional, 42% conventional
No fee (λ=50)| $200 fee| $250 fee| $300 fee|
0.4*67+0.18*167+0.42*467=253| 0.4*328+0.18*519+0.42*1094=684| 0.4*297+0.18*367+0.42*576=427| 0.4*337+0.18*392+0.42*557=439|

A $200 landing fee would have the most impact if your arrival rate was more than 55 because it would generate the most money and would reduce the planes to 55. If the arrival rate is less than 55 you would chose a landing fee of $300 because it generates more money and reduces the arrival rate to 40.

iii. 5% turbo, 30% regional, 65% conventional
No fee (λ=50)| $200 fee| $250 fee| $300 fee|
0.05*67+0.3*167+0.65*467=357| 0.05*328+0.3*519+0.65*1094=883| 0.05*297+0.3*367+0.65*576=499| 0.05*337+0.3*392+0.65*557=497| c. With this combination a $200 landing fee would also have the most impact because it would generate the most money if the arrival rate was over 55. If the arrival rate is under 55, a $250 fee would be most effective. 3.

a. The fundamental condition is, the value of lambda (arrival rate) must be smaller than mui (capacity rate) is violated in...
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