Optimal Airplanes’ Paths For Minimizing Airline Company’s Cost Subjected to Passengers’ Demand: Formulation and Verification

A new formulation which addresses a new/specific/practical problem facing the airline industry, such as “Optimal Airplanes’ Paths For Minimizing Airline Company’s Cost Subjected to Passengers’ Demand”, is presented in this paper. If the flying paths are explicitly used as unknown variables, then one has to deal with a very large number of unknown variables. To avoid such bottlenecks, our proposed approach consists of finding which city-pair flight legs are flown and how many times the optimum flight paths will use these flight legs. With this obtained information, the optimum flight paths can be obtained by a post-processing phase! The mentioned “Optimal Airplanes’ Paths” problem can be formulated as a nonlinear integer programming (NLIP) problem. Numerical results are also included in this paper to validate the proposed NLIP formulation.