Daily, there are approximately $50,000$ flights operated by commercial airlines. Every aircraft, all baggage, every crew member, and all travelers must be at the correct location at the correct moment, and planes require maintenance and refueling.
Above all, airplanes cannot crash while landing at any of the crowded airports. This presents an exceptionally intricate logistical problem that cannot be solved without math and Operations research.
Moreover, airlines aim to cut costs by establishing a more efficient network where aircraft follow the optimal paths and are never left idle, empty, or out of operation. This can be accomplished by employing algorithms from Graph theory.
Comparable difficulties occur when organizing trains, buses, mail distribution, or urgent services.
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