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Given a set of locations and periods, a number of people or commodities arrive at each location each period, desiring to be tranported to other locations. It takes a specified amount of time for a bus to travel from location i to location j, and people do not want to wait a long time, and each bus has a finite capacity, how should we route the buses, so that people get transported to their desired locations without having to wait very long?
This is a discrete time model. The period length should be just short enough to accurately approximate travel times and wait times. E.g., if the average tolerable wait time is 6 minutes and the trip times is are multiples of 9 minutes, then a period length of 3 minutes should give an accurate approximation. The longer the period length, the fewer the number of periods needed to model a given interval of time, and thus more manageable is a problem with lots of locations;