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Tang, Hengyong,Zhao, Chuanli 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.25 No.1
In this paper we research the problem in which the objective is to minimize the sum of squared deviations of job expected completion times from the due date, and the job processing times are stochastic. In the problem the machine is subject to stochastic breakdowns and all jobs are preempt-repeat. In order to show that the replacing ESSD by SSDE is reasonable, we discuss difference between ESSD function and SSDE function. We first give an express of the expected completion times for both cases without resampling and with resampling. Then we show that the optimal sequence of the problem V-shaped with respect to expected occupying time. A dynamic programming algorithm based on the V-shape property of the optimal sequence is suggested. The time complexity of the algorithm is pseudopolynomial.
L-SHAPED ALGORITHM FOR TWO STAGE PROBLEMS OF STOCHASTIC CONVEX PROGRAMMING
Tang, Hengyong,Zhao, Yufang 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.13 No.1
In this paper we study two stage problems of stochastic convex programming. Solving the problems is very hard. A L-shaped method for it is given. The implement of the algorithm is simple, so less computation work is needed. The result of computation shows that the algorithm is effective.