## Abstract

A dial-a-flight problem (DAFP) is described as experienced by a tourist airline operating in Botswana. Typically, a daily schedule is drawn up manually by a team of experienced schedulers a few days before the day in question. In this research, the problem is modeled and optimized using a composite variable formulation of a multi-commodity network flow model. The method takes many of the problem constraints into account at the variable creation stage, reducing the problem size in terms of variables and constraints. As such the method is mostly suitable for highly constrained problems. Six daily lists of booking requests were supplied by the airline, and these were set up and solved. The results are compared with the actual costs incurred by the airline on the day in question. Additional ten lists of booking requests of various sizes were created and solved, and the results compared to results from an integer linear programming (ILP) formulation.

## Keywords

Air taxi Airline scheduling Multi-commodity network## Mathematics Subject Classification

90-04## Notes

## References

- Armacost AP, Barnhart C, Ware KA (2002) Composite variable formulations for express shipment service network design. Interfaces 36(1):1–20Google Scholar
- Armacost AP, Barnhart C, Ware KA, Wilson AM (2004) UPS optimizes its air network. Interfaces 34(1):15–25CrossRefGoogle Scholar
- Barnhart C, Boland NL, Clarke LW, Johnson EL, Nemhauser GL, Shenoi RG (1998) Flight string models for aircraft fleeting and routing. Transp Sci 32(3):208–220CrossRefGoogle Scholar
- Barnhart C, Johnson E, Nemhauser G, Savelsbergh M, Vance P (1998) Branch-and-price: column generation for solving huge integer programs. Oper Res 46:316–329CrossRefGoogle Scholar
- Boland N, Hewitt M, Marshall L, Savelsbergh M (2017) The continuous-time service network design problem. Oper Res 65:1303–1321CrossRefGoogle Scholar
- Braekers K, Caris A, Janssens GK (2014) Exact and meta-heuristic approach for a general heterogeneous dial-a-ride problem with multiple depots. Transp Res Part B Methodol 67:166–186CrossRefGoogle Scholar
- Clarke LW, Johnson EL, Nemhauser GL, Zhu Z (1997) The aircraft rotation problem. Ann Oper Res 69:33–46CrossRefGoogle Scholar
- Cohn A, Barnhart C (2006) Composite-variable modeling for service parts logistics. Ann Oper Res 144(1):17–32CrossRefGoogle Scholar
- Cordeau J, Laporte G, Potvin J, Savelsbergh M (2004) Transportation on demand. In: Transportation, North-Holland, pp 429–466Google Scholar
- Cubillos C, Urra E, Rodríguez N (2009) Application of genetic algorithms for the DARPTW problem. Int J Comput Commun Control 4:127–136CrossRefGoogle Scholar
- Detti P, Papalini F, de Lara GZM (2017) A multi-depot dial-a-ride problem with heterogeneous vehicles and compatibility constraints in healthcare. Omega 70:1–14CrossRefGoogle Scholar
- Engineer FG, Nemhauser GL, Savelsbergh MWP (2011) Dynamic programming-based column generation on time expanded networks: application to the dial-a-flight problem. INFORMS J Comput 23:105–119CrossRefGoogle Scholar
- Erdmann A, Nolte A, Noltemeier A, Schrader R (2001) Modeling and solving an airline schedule generation problem. Ann Oper Res 107:117–142CrossRefGoogle Scholar
- Espinoza D, Garcia R, Goycoolea M, Nemhauser GL, Savelsbergh MWP (2008) Per-seat, on-demand air transportation part 1: problem description and an integer multicommodity flow model. Transp Sci 42(3):263–278CrossRefGoogle Scholar
- Federal Aviation Authority (2012) Electronic code of federal regulations Title 14 Chapter 1 Subchapter F Part 91.1059. Government Publishing Office (US). https://www.ecfr.gov/cgi-bin/text-idx?node=14:2.0.1.3.10#se14.2.91_11059. Accessed 21 July 2012
- Google Earth (2012) Google Inc. https://earth.google.com/web/@-20.0230228,22.18064645,683.38909086a,484407.35871971d,35y,0h,0t,0r. Accessed 21 July 2012
- Ho SC, Szeto YK, Leung JMY, Petering M, Tou WH (2018) A survey of dial-a-ride problems: literature review and recent developments. Transp Res Part B MethodolGoogle Scholar
- Jorgensen RM, Larsen J, Bergvinsdottir KB (2007) Solving the dial-a-ride problem using genetic algorithms. J Oper Res Soc 58:1321–1331CrossRefGoogle Scholar
- Kim D, Barnhart C (2007) Flight schedule design for a charter airline. Comput Oper Res 34:1516–1531CrossRefGoogle Scholar
- Muelas S, LaTorre A, Peña J-M (2015) A distributed VNS algorithm for optimizing dial-a-ride problems in large-scale scenarios. Transp Res Part C Emerg Technol 54:110–130CrossRefGoogle Scholar
- Papadakos N (2009) Integrated airline scheduling. Comput Oper Res 36(1):176–195CrossRefGoogle Scholar
- Ronen D (2000) Scheduling charter aircraft. J Oper Res Soc 51(3):258–262CrossRefGoogle Scholar
- Schilde M, Doerner KF, Hartl RF (2014) Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem. J Oper Res 238(1):18–30CrossRefGoogle Scholar
- Sefofane Marketing Brochure (2008)Google Scholar
- Subramanian R, Scheff RP, Quillinan JD, Wiper DS, Marsten RE (1994) Coldstart: fleet assignment at delta air lines. Interfaces 24(1):104–120CrossRefGoogle Scholar
- Vanderbeck F, Wolsey L (1996) An exact algorithm for IP column generation. Oper Res Lett 19:151–159CrossRefGoogle Scholar
- Velasco N, Castagliola P, Dejax P (2009) A memetic algorithm for a pick-up and delivery problem by helicopter. In: Bio-inspired algorithms for the vehicle routing problem, Springer, Berlin, pp 173–190Google Scholar
- Weide O, Ryan D, Ehrgott M (2010) An iterative approach to robust and integrated aircraft routing and crew scheduling. Comput Oper Res 37(5):833–844CrossRefGoogle Scholar