Journal of applied mathematics & informatics
- 제26권5_6호
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- Pages.889-900
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- 2008
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- 2734-1194(pISSN)
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- 2234-8417(eISSN)
STOCHASTIC SINGLE MACHINE SCHEDULING WITH WEIGHTED QUADRATIC EARLY-TARDY PENALTIES
- Zhao, Chuan-Li (School of Mathematics and System Science, Shenyang Normal University) ;
- Tang, Heng-Yong (School of Mathematics and System Science, Shenyang Normal University)
- 발행 : 2008.09.30
초록
The problem of scheduling n jobs on a single machine is considered when the machine is subject to stochastic breakdowns. The objective is to minimize the weighted squared deviation of job completion times from a common due date. Two versions of the problem are addressed. In the first one the common due date is a given constant, whereas in the second one the common due date is a decision variable. In each case, a general form of deterministic equivalent of the stochastic scheduling problem is obtained when the counting process N(t) related to the machine uptimes is a Poisson process. It is proved that an optimal schedule must be V-shaped in terms of weighted processing time when the agreeable weight condition is satisfied. Based on the V-shape property, two dynamic programming algorithms are proposed to solve both versions of the problem.