Two Stage Programming Under Risk With Discrete Or Discrete Approximated Continuo

Cover Two Stage Programming Under Risk With Discrete Or Discrete Approximated Continuo
Two Stage Programming Under Risk With Discrete Or Discrete Approximated Continuo
Michael Werner
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The solution r=l of (26)supplies the vector of simplexmultipliers a .
Then we have to check up whether it is possible to generate any y „, , with g, Kg+i -d -a'Y, . 1 > (27) g r g, Kg+l which is not yet considered in the solution r=l of (26) : By assumption iii)the random vector y is a transformation y (C ) of only one random g V g g variable (for example ^ ) with known range K, . ? J- So we have to solve the G problems c := d + a'-y (^ ) ->■ min g g r 'g'^g' (28) Si ^ S ^ Su which means the mi
...nimizing of a linear or nonlinear function defined over a given range.
d + a^-y (° ) and determine 1 g=l, 2, ... , G } = ?H . (29) 11 If c- there is no vector Y „, which is able to improve the last solution g - g'^g"^^ of (26). The last solution of (26)is optimal and feasible for any outcome of the continuous random variable Y- By using the dual variables of (26) we can generate the solution v of (24) and (22) which is also feasible for any outcome of the continuous random variable Y- If Y (C ) means a linear function of r, then only the two points C, , C with the 'g g g gl gu related outcomes of Y have to be considered.


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