One of the ways that airlines operating through major hubs can improve their service is to allow as many transferring passengers as possible who land at one of the scheduled arrival–

departure peaks to carry on with their next flight on the same plane.13 Such through-flight connections must involve flights scheduled for the same type of aircraft, and flights with sufficient arrival to departure time to complete the required servicing.

The number of passengers pi,j arriving on flight i and continuing on flight j at any peak can be estimated in advance. Explain how this problem of optimizing through flights can be modeled as a linear assignment problem by describing the two sets being matched, the collection of feasible pairings, the associated linear costs, and whether the total is to be minimized or maximized.