U.S. Express is an overnight package delivery company based in Atlanta, Georgia. Jet fuel is one of the largest operating costs incurred by the company, and the company wants your assistance in managing this cost. The price of jet fuel varies considerably at different airports around the country. As a result, it seems that it might be wise to "fill up" on jet fuel at airports where it is least expensive. However, the amount of fuel an airline burns depends, in part, on the weight of the plane, and excess fuel makes an airplane heavier and, therefore, less fuel-efficient. Similarly, more fuel is burned on flights from the East Cost to the West Coast ( going against the jet stream) than from the West coast to the east cost ( going with the jet stream)
The following table summarizes the flight schedule or ratation flown nightly by one of the companys plans. For each flight segment, the flight summaries the minimum required and maximum allowable amount of fuel on board at takeoff and the cost of fuel at each point of departure. The final column provides a linear function relating fuel consumption to the amount of fuel on board at take off.
|
Segment
|
Depart
|
Arrive
|
Minimum Fuel Level at Takeoff (in 1000's)
|
Maximum fuel level at take off ( in 1000's)
|
Cost per gallon
|
Fuel used in flight with G Gallons ( in 1000's) on board at takeoff
|
|
1
|
Atlanta
|
San Fran
|
21
|
31
|
$0.92
|
3.20 + 0.45 X G
|
|
2
|
San Fran
|
LA
|
7
|
20
|
.85
|
2.25 + .65 X G
|
|
3
|
LA
|
Chicago
|
18
|
31
|
.87
|
1.80 +.35 X G
|
|
4
|
Chicago
|
Atlanta
|
16
|
31
|
1.02
|
2.20 + .60 X G
|
For instance, if the plane leaves Atlanta for San Fran with 25,000 gallons on board, it should arrive in San Fran with approx. 25 - (3.2 + .45 x 25) = 10.55 thousand gallons of fuel.
The company has many other planes that fly different schedules each night, so the potential cost savings from efficient fuel purchasing is quite significant. But before turning you loose on all of its flight schedules, the company wants you to create a spread sheet model to determine the most economical fuel purchasing plan for the previous schedule. ( hint: keep in mind that the most fuel you would purchase at any departure point is the maximum allowable fuel level for takeoff at the point. Also assume that whatever fuel is on board when the plane returns to Atlanta at the end of the rotation will still be on board when the plane leaves Atlanta for the next evening)
A.) Draw the network diagram for this problem.
B.) implement the model for this problem in your spreadsheet, and solve it
C.) How much fuel should U.S. Express purchase at each departure point, and what is the cost of this purchasing plan?