TWO- STAGE-PROGRAMMING UNDER RISK WITH DISCRETE OR DISCRETE APPROXIMATED CONTINUOUS DISTRIBUTION FUNCTIONS

To solve the complete problem of two-stage-programming under risk involving random variables with discrete distribution functions only, this paper presents an efficient algorithm by using the Dantzig/Wolfe decomposition principle. If the recourse matrix is a positive or negative identy matrix applying this algo-rithm an efficient approach is derived for this structure of the problem. By using this approach, under the assumptions i) only the second stage matrix is a continuous random variable, ii) either the expectation of the random matrix is known or there is a good estimate at least, iii) every row of the random matrix is a transformation of only one continuous random variable with known range, it is shown, that the solution of the two-stage-programming problem under risk with an identy as a recourse matrix can be approximated arbitrary exait ly by generating a discrete random matrix with unknown distribution function. av-^-'i-