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SINGLE-MACHINE SCHEDULING PROBLEMS WITH AN AGING EFFECT
Zhao, Chuan-Li,Tang, Heng-Yong 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.25 No.1
This paper considers single machine scheduling problems where the processing time of a job increases as a function of its position in the sequence. In this model, the later a given job is scheduled in the sequence, the longer its processing time. It is shown that the optimal schedule may be very different from that of the classical version of the problem. We introduce polynomial solutions for the makespan minimization problem, the sum of completion times minimization problem and the sum of earliness penalties minimization problem. For two resource constrained problems, based on the analysis of the problems, the optimal resource allocation methods are presented, respectively.
Stochastic single machine scheduling with weighted quadratic early-tardy penalties
Chuan-li Zhao,Heng-yong Tang 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.5
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.
STOCHASTIC SINGLE MACHINE SCHEDULING WITH WEIGHTED QUADRATIC EARLY-TARDY PENALTIES
Zhao, Chuan-Li,Tang, Heng-Yong Korean Society of Computational and Applied Mathem 2008 Journal of applied mathematics & informatics Vol.26 No.5
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.