Optimized schedules for airline routes

Increasing flight frequency on airline routes tends to reduce. user delay costs but increase airline operating costs. Flight frequency should vary as demand intensity changes at various times of day. Models are presented here for optimizing the departure times of flights on single airline routes with time-dependent demand. An analytic model is developed to find the departure times that minimize average schedule delay per passenger for given flight frequencies and to identify the algebraic relations among the variables. Using an analytic approach, the departure times of flights that minimize airline operating cost and users' waiting cost are determined. To minimize the objective function, it is found that the headways should be inversely proportional to the square root of demand intensity near the departure times. Computer models for both cost minimization and profit maximization are developed to solve the problems with relaxed assumptions and verify the numerical results obtained analytically.