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Path or itinerary based approach for modeling the
origin/destination (OD) shipping model in LINGO.
We are given:
A network of nodes and legs(or arcs, links). Each leg of the network has a capacity limit.
There is a set of origin->destination (OD) pairs of nodes in the network with a demand amount desired to be shipped for each OD pair.
A path is a set of legs starting at an origin node and ending at a destination note. Each path has a profit contribution per unit shipped over this path. There may be several paths for a single OD pair.
We want to decide how much to ship over each path so as to:
Maximize the total profit contribution, subject to
not exceeding the desired demand for any OD pair, and not exceeding the capacity of any leg.
The Path formulation allows you to take into account that paths that are too long from a source to a destination need not be generated;