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Minimum cost problem

Consider a variant of the cargo flight loading problem with two types of cargo, reserved and on-spot. Reserved cargo, with quantity denoted by aij, has to be transported from city i to city j. On-spot cargo, with the maximum quantity denoted by bij, is optional with a unit profit of rij. The problem is to maximum the profit of the flight, by determining the quantity xijof each on-spot cargo to load. For your reference, below is the network flow model for the original one-type cargo flight loading problem, where p is the capacity of the flight.

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