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Conditional Value-at-Risk Optimization Applications in Decision Making Problems

Eskandarzadeh, Saman | 2014

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 46310 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Eshghi, Kourosh; Modarres Yazdi, Mohammad
  7. Abstract:
  8. In this thesis, the Conditional Value-at-Risk measure (CVaR) is used in two basic decision making problems under uncertainty. This measure is used previously in the field of risk management. The first problem is decision tree problem which is a multi-stage stochastic decision problem. In this problem, the risk of a decision maker is estimated by CVaR measure and a linear programming model is presented by using disjunctive programming theory. The importance of the developed model is in its generality for modeling all problems with decision tree structure. Then, its computational performance is compared to intuitive nonlinear programming models for the problem. Moreover, the presented model can be extended to mathematical programming problems whose feasible space can be represented by finite inclusion-union operations on polyhedral sets. The second problem is a production planning problem under stochastic yield which is defined as a one-stage stochastic decision making problem. This problem has many applications in industries ranging from agricultural to petrochemicals production. Two models for this problem are presented in which price and target production quantity are decision variables. The first model, which is based on the dominant approach toward dealing with risk, addresses one aspect of risk from the decision maker’s standpoint. The goal in this model is to optimize the CVaR of profit. For this model, it is proved that with increasing the risk aversity of a decision maker, the optimal selling price increases and the probability of shortage decreases. Since risk, most of the time is a multi-faceted concept for decision makers, we develop another model. The second model, using CVaR measure provide the possibility of controlling the risk or so-called shaping the risk. Risk shaping is defined by adding some constraints which limits the risk of loss from several aspects. For the resulting model which is nonlinear and nonconvex, an efficient solution methodology is also presented
  9. Keywords:
  10. Decision Making Tree ; Random Efficiency ; Production Planning ; Coherent Risk Measure ; Conditional Value at Risk ; Coherent Risk Measure ; Conditional Value at Risk ; Decision Making Problems Under Uncertainty ; Risk Shaping ; Risk Shaping

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