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Decision Making under Uncertainty

Decision Making under Uncertainty. The maximin criterion. A decision table for the food manufacturer ( Daily profits)           Demand (no. of batches) 1 2 Course of action Produce 1 batch $200 $200 Produce 2 batches –$600 $400.

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Decision Making under Uncertainty

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  1. Decision Making under Uncertainty

  2. The maximin criterion A decision table for the food manufacturer (Daily profits)           Demand (no. of batches) 1 2 Course of action Produce 1 batch $200 $200 Produce 2 batches –$600 $400

  3. The Expected Monetary Value (EMV) criterion Another decision table for the food manufacturer (Daily profits)   Demand (no. of batches) 1 2 Probability 0.3 0.7 Course of action Produce 1 batch $200 $200 Produce 2 batches –$600 $400

  4. Calculating expected profits Produce one batch: Expected daily profit = (0.3  $200) + (0.7  $200) = $200 Produce two batches: Expected daily profit = (0.3  –$600) + (0.7  $400) = $100

  5. Sensitivity analysis

  6. Limitations of the EMV criterion • It assumes that the decision maker is neutral to risk • It assumes a linear value function for money • It considers only one attribute - money

  7. Single-attribute utility:A decision tree for the conference organizer

  8. Applying utilities to the conference organizer’s decision

  9. A utility function for the conference organizer - indicating she is risk averse

  10. Interpreting utility functions

  11. The drug company research department’s problem

  12. Utility function for product development time

  13. Allais’s paradox

  14. Multi-attribute Utility

  15. Utility independence Attribute A is utility independent of attribute B, if the decision maker’s preferences for gambles involving different levels of A, but the same level of B, do not depend on the level of attribute B…

  16. Utility independence

  17. Utility functions for overrun time and project cost

  18. The project manager’s utilities for overrun and cost Overrun Cost of (weeks) Utility project ($) Utility 0 1.0 50 000 1.00 1 0.9 60 000 0.96 3 0.6 80 000 0.90 6 0.0 120 000 0.55 140 000 0.00

  19. Multi-attribute utility function u(x1,x2) =k1u(x1) + k2u(x2) + k3u(x1)u(x2) where: k3 = 1– k1– k2

  20. Determining k1

  21. Determining k2

  22. The project manager’s decision tree with utilities

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