Delay resulting from scheduling inefficiencies is what we seek to minimize in our model. In a perfect world, the total delay would equal the sum of random delays for every plane. If we knew beforehand the random delay of every plane, we could set the flight schedule in such a manner that we would leave the appropriate gap in between each flight to account for this delay. For example, say we knew a flight scheduled at 6:00 am had a random delay of 25 minutes. We would then optimally schedule the next flight at 6:30 am and not 6:15 am to account for this random delay. Unfortunately, the random delay is not known so the total delay for a single flight may also include additional delay that results from inefficient scheduling.
Inefficient scheduling delay may be explained more clearly in an example. The Figure below contains a portion of a potential scheduling decision made by our program.
Inefficient scheduling delay may be explained more clearly in an example. The Figure below contains a portion of a potential scheduling decision made by our program.
In the example, there would be flights scheduled at 6:00 am (Flight #1) and 6:30 am (Flight #2). The gate would be empty at 6:15 am and 6:45 am. From the exponential distribution, the random delays for Flight #1 and Flight #2 happened to be 40 minutes and 5 minutes respectively. Again, this random delay is uncontrollable and will occur regardless of scheduling decisions. Due to the random delay, Flight #1 will not depart until 6:40 am. This impacts Flight #2 because it now will not be able to begin the boarding process until the next available 15 minute interval. In this example, that interval is at 6:45 am. The 15 minutes of delay for Flight #2 from 6:30 am to 6:45 am is what we call delay due to scheduling inefficiencies. The total delay for Flight #2 is now 20 minutes, or random delay plus scheduling inefficiency delay.