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We are given a
+ number of units that must be shipped from i to j each period,
+ the lead time to ship from i to j,
+ the capacity of the containers that carry the units to be shipped.
The containers must satisfy conservation of flow as they move about the system, i.e., they cannot be created or destroyed, except in period 1 in which we insert as many containers as we wish at each city. A container may physically correspond to whatever the user wishes, e.g., actual containers, trucks, railroad cars, airplanes, etc.
This is a discrete time model where the unit of time is called a "period". A period could be a hour, a half day, a day, etc., whatever the user decides. The model need not know what unit of time the user chose, as long as the user is consistent.
A crucial piece of input data is the travel time matrix. It is a matrix of integers specifying how many periods it takes a container to be moved from one city to another. A variety of objectives are possible. Below we choose the objective of minimizing the number of containers needed in total.