Both transportation and assignment problems are members of a category of lp problems called network flow problems
Network flow problems are a type of combinatorial optimization problem in which the input is a flow network (a graph with numerical capacities on its edges) and the goal is to construct a flow with numerical values on each edge that respect the capacity constraints and have incoming flow.
A company, for example, may want to ship packages from Los Angeles to New York City by using trucks to transport between intermediate cities. If the route connecting two cities only has one truck and each truck has a maximum load, the graph describing the transportation options will be a flow network.
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