Question

You are the scheduling coordinator for a small but growing airline. You must schedule exactly one flight out of Chicago to each of the following cities: Atlanta, Los Angeles, New York, and Peoria. The available departure slots are 8 a.m., 10 a.m., and 12 noon. Your airline has only two departure lounges so at most 2 flights can be scheduled per slot. Demand data suggests the following expected profit contribution per flight as a function of departure time:

Expected Profit Contribution in $1000s
	Time
Destination	8	10	12
Atlanta	10	9	8.5
Los Angeles	11	10.5	9.5
New York	17	16	15
Peoria	6.4	2.5	-1

Formulate a model to solve this problem.

Excel answer only

Answer 1

Answer:

Formulation:

Let Xjk be he number of flights scheduled to be departed for location-j at hour-k for j=1 (Atlanta), 2 (LA), 3 (NY), 4 (Peoria) and k=1 (8 am), 2 (10 am), 3 (12 noon)

Max Z = 10 X11 + 9 X12 + 8.5 X13 + 11 X21 + 10.5 X22 + 9.5 X23 + 17 X31 + 16 X32 + 15 X33 + 6.4 X41 + 2.5 X42 - 1 X43

Subject to,

Xj1 + Xj2 + Xj3 = 1 for j=1,2,3,4

X1k + X2k + X3k + X4k <= 2 for k=1,2,3

Xjk >= 0

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