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Optimizing Profit through Stochastic Programming: The Street Vendor and Farmer Problems

Explore the street vendor and farmer problems through stochastic programming to maximize expected profit, make risk-neutral decisions, and evaluate the value of information like Expected Value of Perfect Information and Value of the Stochastic Solution. This model formulation involves making first-stage decisions without full information, followed by corrective actions based on real-time data, showcasing the value of information in decision-making processes.

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Optimizing Profit through Stochastic Programming: The Street Vendor and Farmer Problems

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  1. Stochastic programming

  2. Street vendor problem

  3. The farmer problem

  4. Maximizing the Expected Profit (long-run profit, risk-neutral decisions )

  5. Expected Value of Perfect Information (EVPI)

  6. Expected Value of Perfect Information (EVPI)

  7. Expected Value of Perfect Information (EVPI)

  8. Expected Value of Perfect Information (EVPI)

  9. The Value of the Stochastic Solution (VSS)

  10. The Value of the Stochastic Solution (VSS)

  11. Profits based on Mean Value

  12. Profits based on Mean Value

  13. The Value of the Stochastic Solution (VSS)

  14. General Model Formulation • We have a set of decisions to be taken without full information on some random events, which we call first-stage decisions (x) • Later, full information is received on the realization of some random vector ξ, and second-stage or corrective actions (recourse) y are taken • We assume that the probability distribution of ξ is known a priori • The preceding examples illustrate such models

  15. Two-stage stochastic program with recourse – linear programming implicit form

  16. Value of information for stochastic solution

  17. Expected Value of Perfect Information (EVPI)

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