This thesis is concerned with an Airline Gate Assignment problem that seeks to allocate gates to aircraft at an airport, using the objective of minimizing passenger walking distances. The problem is modeled as a variant of the quadratic assignment problem with set packing constraints. The quadratic objective function is then transformed into an equivalent linearized form by applying the first-order linearization technique of Sherali and Adams [1989, 1990]. In addition to linearizing the problem, the application of this technique generates additional constraints that provide a tighter linear programming representation. A suitable solution process that exploits the structure of the linearized problem is developed. Test results are presented using realistic data obtained from USAIR.