lecture7-2k - AEB 6182 Lecture VII Professor Charles Moss...

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AEB 6182 Lecture VII Professor Charles Moss 1 Farm Portfolio Problem: Part III Lecture VII I. Target Motad A. The target MOTAD model is a two-attribute risk and return model. 1. Return is measured as the sum of the expected return of each activity multiplied by the activity level. 2. Risk is measured as the expected sum of the negative deviations of the solution results from a target-return level. 3. Risk is then varied parametrically so that a risk-return frontier can be traced out. B. Mathematically, the model is stated as max ( ) x j j j n ij j j n i rj j j n r r r r n E z c x st a x b T c x y p y = - - = = = = = 1 1 1 1 0 l where: 1. x j is the activity level for crop j. 2. c j is the expected return on crop j. 3. a ij is the technical coefficient in column I of row j. 4. b j is the right hand side of that technical row. 5. c rj is the r th outcome for activity j 6. T is the target loss 7. y r is the transfer of the negative deviation 8. λ is the target loss. C. The decision process can then be expressed as a locus of points where the whole farm plan maximizes expected income subject to a target level of negative deviation. II. Discrete Sequential Stochastic Programming A. Target MOTAD, direct expected utility, and even MOTAD begin to develop the concept of constraints being stochastic or met with some level of probability. 1. In target MOTAD, income under a certain state exceeds the target level of income with some probability. 2. In direct expected utility maximization the level of wealth transferred to the objective function was represented by a constraint which had some level of probability. 3. In MOTAD, we minimized the expected negative deviations which implied stochastic constraints.
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AEB 6182 Lecture VII Professor Charles Moss 2 4. However, in each of these cases, the primary impact of stochastic constraints was on the objective function or some threshold level of risk (as was the case in target MOTAD). B. The variant of model that we want to develop is referred to as Discrete Sequential Stochastic Programming (DSSP), although other names have been attributed to it. This work grows out of work by Cocks, and focuses on decision processes which are strung out over a discrete number of decision periods. 1.
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lecture7-2k - AEB 6182 Lecture VII Professor Charles Moss...

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