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Applied stochastic programming models and computation

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This overview of stochastic programming reflects its development from 1955 to 2006. Major milestones include the introduction of first models and algorithms, the airline scheduling problem, chance-constrained programming, and advanced methods like Nested Benders decomposition. The study reviews diverse applications, novel models, and computational papers. Notably, finance applications are prevalent, showcasing the growing significance of stochastic programming in various fields. The findings highlight a substantial increase in applications, demonstrating the importance of stochastic methods in decision-making under uncertainty.

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Applied stochastic programming models and computation

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  1. Applied stochastic programming models and computation H.I. Gassmann Dalhousie University

  2. Outline • Introduction to stochastic programming • Scope of study • Results

  3. Milestones in stochastic programming 1955 – First models and algorithms (Dantzig; Beale) 1956 – Airline scheduling problem (Ferguson and Dantzig) 1959 – Chance-constrained programming (Charnes and Cooper) 1969 – L-shaped method (van Slyke and Wets) 1984 – Nested Benders decomposition (Birge) 1989 – Russell Yasuda Kasai model (Cariño et al.) 1995 – OSL/SE (IBM) 2003 – van der Vlerk’s on-line bibliography on SP contains 3840 entries 2006 – EURO application prize (Zenios et al.)

  4. Two-stage recourse model

  5. Multistage recourse model

  6. Chance-constraint model

  7. Integrated chance-constraints

  8. Scope of the study • Included • Applications and novel models • Computational papers • All types of stochastic programs • Illustrative and “industrial-strength” models • Not included • Theoretical papers • New algorithms for old models • Randomly generated problems

  9. The sources • Research bibliographies • Stancu-Minasian and Wets (1976) • P. Birge (1984) • Van der Vlerk (2003) • Citation indexes • Online searches Result: 144 models

  10. Papers by year

  11. Papers by application area

  12. How published?

  13. Features

  14. Features by decade

  15. Number of stages

  16. Number of stages per decade

  17. Scope of the application

  18. Conclusions • SP applications are getting more numerous • Finance applications dominate • Considerable breadth of other applications

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