A Time-Flow Approach for Scheduling and Routing of Fly-in Safari Airplanes

Abstract

A touristic company that offers fly-in safaris is faced with the challenge to route and schedule its fleet of aircrafts in an optimal way. Over the course of a given time horizon several groups of tourists have to be picked up at airports and flown to their destinations within a certain time window. Furthermore the number of available seats, the consumption of fuel, the maximal takeoff weight, and restrictions on the detour of the individual groups have to be taken into account. A flow-over-flow formulation on the time expanded graph of the airports was used in the literature in combination with a so called time-free relaxation in order to solve this problem with a solver for MILP. We give an alternative MILP formulation of the problem, that still allows for similar relaxation techniques to be used. This formulation, however, also allows for the construction of graphs which can be interpreted as intermediate graphs between the time-free and the (totally) time-expanded graph and therefore yield stronger relaxations. With knowledge obtained from the solutions of these relaxations the number of vertices that have to be expanded in order to guarantee feasibility is reduced significantly. On the benchmark set this lead to a decrease of the average computation time and a significant reduction of the remaining optimality gaps.