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The Allocation of Aircraft to Routes--An Example of Linear Programming Under Uncertain Demand

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  • Allen R. Ferguson

    (The RAND Corporation)

  • George B. Dantzig

    (The RAND Corporation)

Abstract

The purpose of this paper is to illustrate an application of linear programming to the problem of allocation of aircraft to routes in order to maximize expected profits when there is uncertain customer demand. The approach is intuitive; the theoretical basis of this work is found in an earlier study. The allocations are compared with those obtained under the usual procedure of assuming a fixed demand equal to the expected value. The computational procedure is similar to the fixed demand case, with only slightly more computational effort required. This paper is intended both for readers interested in routing (and analogous resource allocation) problems and for those interested in studying an example of an application of linear programming under uncertainty.

Suggested Citation

  • Allen R. Ferguson & George B. Dantzig, 1956. "The Allocation of Aircraft to Routes--An Example of Linear Programming Under Uncertain Demand," Management Science, INFORMS, vol. 3(1), pages 45-73, October.
    • Handle: RePEc:inm:ormnsc:v:3:y:1956:i:1:p:45-73
    DOI: 10.1287/mnsc.3.1.45
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    Cited by:

    1. Marcel Klatt & Axel Munk & Yoav Zemel, 2022. "Limit laws for empirical optimal solutions in random linear programs," Annals of Operations Research, Springer, vol. 315(1), pages 251-278, August.
    2. Alan S. Manne, 1958. "A Target-Assignment Problem," Operations Research, INFORMS, vol. 6(3), pages 346-351, June.
    3. Francisco Barahona & Stuart Bermon & Oktay Günlük & Sarah Hood, 2005. "Robust capacity planning in semiconductor manufacturing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(5), pages 459-468, August.
    4. Powell, Warren B., 2019. "A unified framework for stochastic optimization," European Journal of Operational Research, Elsevier, vol. 275(3), pages 795-821.
    5. Shakeel Javaid & Dr. S.N. Gupta, 2008. "Capacitated Stochastic Fractional Transshipment Problem," Journal of Commerce and Trade, Society for Advanced Management Studies, vol. 3(1), pages 84-93, April.
    6. Cynthia Barnhart & Peter Belobaba & Amedeo R. Odoni, 2003. "Applications of Operations Research in the Air Transport Industry," Transportation Science, INFORMS, vol. 37(4), pages 368-391, November.
    7. Listes, O.L. & Dekker, R., 2002. "A scenario aggregation based approach for determining a robust airline fleet composition," Econometric Institute Research Papers EI 2002-17, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    8. Güzin Bayraksan & David P. Morton, 2011. "A Sequential Sampling Procedure for Stochastic Programming," Operations Research, INFORMS, vol. 59(4), pages 898-913, August.
    9. V. Balachandran & Suresh Jain, 1975. "Optimal Facility Location under Random Demand with General Cost Structure," Discussion Papers 149, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Barry C. Smith & Ellis L. Johnson, 2006. "Robust Airline Fleet Assignment: Imposing Station Purity Using Station Decomposition," Transportation Science, INFORMS, vol. 40(4), pages 497-516, November.
    11. Wu, Yue, 2010. "A dual-response forwarding approach for containerizing air cargoes under uncertainty, based on stochastic mixed 0-1 programming," European Journal of Operational Research, Elsevier, vol. 207(1), pages 152-164, November.
    12. Dangalchev, Chavdar A., 2000. "Optimization of the transportation expense of a firm with contractual supplies," Transportation Research Part B: Methodological, Elsevier, vol. 34(3), pages 203-217, April.
    13. Spyros Kontogiorgis, 2000. "Practical Piecewise-Linear Approximation for Monotropic Optimization," INFORMS Journal on Computing, INFORMS, vol. 12(4), pages 324-340, November.
    14. Warren B. Powell, 2016. "Perspectives of approximate dynamic programming," Annals of Operations Research, Springer, vol. 241(1), pages 319-356, June.
    15. Ovidiu Listes & Rommert Dekker, 2005. "A Scenario Aggregation–Based Approach for Determining a Robust Airline Fleet Composition for Dynamic Capacity Allocation," Transportation Science, INFORMS, vol. 39(3), pages 367-382, August.
    16. Algo Carè & Simone Garatti & Marco C. Campi, 2014. "FAST---Fast Algorithm for the Scenario Technique," Operations Research, INFORMS, vol. 62(3), pages 662-671, June.
    17. Dupacova, Jitka, 2002. "Applications of stochastic programming: Achievements and questions," European Journal of Operational Research, Elsevier, vol. 140(2), pages 281-290, July.
    18. Richard W. Cottle, 2005. "George B. Dantzig: Operations Research Icon," Operations Research, INFORMS, vol. 53(6), pages 892-898, December.

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