A note on optimization modelling of piecewise linear delay costing in the airline industry

Abstract

We present a mathematical model in an integer programming (I.P.) framework for non-linear delay costing in the airline industry. We prove the correctness of the model mathematically. Time is discretized into intervals of, for example, 15 minutes. We assume that the cost increases with increase in the number of intervals of delay in a piecewise linear manner. Computational results with data obtained from Sydney airport (Australia) show that the integer programming non-linear cost model runs much slower than the linear cost model; hence fast heuristics need to be developed to implement non-linear costing, which is more accurate than linear costing. We present a greedy heuristic that produces a solution only slightly worse than the ones produced by the I.P. models, but in much shorter time.