Scheduling Problem In Assignmentmodel

Introduction:

Scheduling problem is also the part of a management problems which is used to  arranging air flights or bus  transport or rail transport. The peculiarities of this type of problem is that one flight / train / bus leaves form a station with some flight number / train number / bus number. After reaching the destination, the same plane / train/bus leave that place (destination) and reach the hometown with different number.

Scheduling problem:

Our problem here is how to arrange a limited number of planes with crew / trains with crew / bus with crew between two places to make the trips without inconvenience, by allowing required lay over time. Lay over time means the time allowed for

crew to take rest before starting.

Example: For the following Airline time table between Bangalore and Mumbai it is required to pair to and forflights for the same crew, so as to minimize the lay over time of the crew on ground away from Headquarters. It is possible to assign Bangalore or Bombay as the head quarter. Decide the pairing of flightsand headquarters of the concerned crew. It is stipulated that the same crew cannot undertake nextflight, within one hour of the arrival. That is one hour is the layover time.

Solution

•          Now let us consider the layover times separately for crew based at Mumbai and crew based at Bangalore.
•         flight No. 101 leaves Mumbai at 6.30 a.m. and reaches Bangalore at 7.45 a.m.
•         Unless the crew takes one our rest, they cannot fly the airplane. So if the crew cannot leave Bangalore until 8.45 a.m. So there is no chance for the crew to go for flight No. 102.
•        But they can go as flight Nos. 103, 106, 108 and 110. As we have to minimize the flyover time, we can take the nearest flight i.e. 103.
•         The flight 103 leaves Bangalore at 11.00 a.m. By 11.00 a.m. the crew might have spent time at Bangalore from 7.45 a.m. to 11.00 a.m. That is it has spent 3 hours and 15 minutes.
•         If we convert 3 hours and 15 minutes in terms of quarter hours, it will become 13-quarter hours.
•         Similarly the flight 102 which arrives at Mumbai at 8.00 a.m. wants to leave as flight 101 at 6.30 a.m. it has to leave next day morning.
•        Hence the layover time will be 22 hours and 30 minutes. Likewise, we can work out layover time for all flights and we can write two matrices, one for crew at Mumbai and other for crew at Bangalore.