Geodesic
Optimal scheduling of passenger air transportation in regional network
Matematičeskoe modelirovanie, Tome 32 (2020) no. 9, pp. 73-86

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This paper deals with the problem of air passenger transportation optimal planning. The aim is to minimize renting and operational costs, taking into account heterogeneous fleet, feasibility of multiple visits to the same location, restrictions on the set of available airways, etc. Two multi-index formalizations — as a binary linear programming problem and as a mixed-integer linear programming problem (depending on the consideration of time windows for takeoffs and landings) — are presented for the regarded task. In the future constructed analytical model can become the basis for the development of the globally optimal schedules approximation algorithms.
Keywords: vehicle routing problem, multiple trips, mixed-integer linear programming. 
@article{MM_2020_32_9_a4,
     author = {I. P. Bogdanov},
     title = {Optimal scheduling of passenger air transportation in regional network},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {73--86},
     publisher = {mathdoc},
     volume = {32},
     number = {9},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_9_a4/}
}
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I. P. Bogdanov. Optimal scheduling of passenger air transportation in regional network. Matematičeskoe modelirovanie, Tome 32 (2020) no. 9, pp. 73-86. http://geodesic.mathdoc.fr/item/MM_2020_32_9_a4/