On stochastic machine scheduling with general distributional assumptions

Abstract A set of stochastic jobs is to be processed on a single machine which is subject to breakdowns and repairs. Under quite general conditions on the job's processing times, the uptimes and the repairtimes of the machine, we find a simple optimal permutation policy for the weighted sum of an increasing function of the completion times. Some optimal policies for two special cases, which have not been investigated in the literature, are given. Moreover, an upper bound is established on the loss incurred when a processing policy is adopted under a simplifying assumption of exponential processing requirements

[1]  Michael Pinedo,et al.  A note on minimizing the expected makespan in flowshops subject to breakdowns , 1995 .

[2]  Ali Allahverdi,et al.  Scheduling on a two-machine flowshop subject to random breakdowns with a makespan objective function , 1995 .

[3]  Ali Allahverdi,et al.  Scheduling on M parallel machines subject to random breakdowns to minimize expected mean flow time , 1994 .

[4]  Kevin D. Glazebrook,et al.  Scheduling stochastic jobs on a single machine subject to breakdowns , 1984 .

[5]  Kevin D. Glazebrook,et al.  On Nonpreemptive Policies for Stochastic Single-Machine Scheduling with Breakdowns , 1991, Probability in the Engineering and Informational Sciences.

[6]  Cheng-Shang Chang,et al.  On the optimality of LEPT and cµ rules for machines in parallel , 1992, Journal of Applied Probability.

[7]  Wei Li,et al.  Stochastic scheduling on a single machine subject to multiple breakdowns according to different probabilities , 1995, Oper. Res. Lett..

[8]  Ali Allahverdi,et al.  Two-machine ordered flowshop scheduling under random breakdowns , 1994 .

[9]  J. George Shanthikumar,et al.  Scheduling Multiclass Single Server Queueing Systems to Stochastically Maximize the Number of Successful Departures , 1989, Probability in the Engineering and Informational Sciences.

[10]  Esther Frostig,et al.  A Note on Stochastic Scheduling on a Single Machine Subject to Breakdown–The Preemptive Repeat Model , 1991, Probability in the Engineering and Informational Sciences.

[11]  Kevin D. Glazebrook,et al.  Evaluating the effects of machine breakdowns in stochastic scheduling problems , 1987 .

[12]  Michael Pinedo,et al.  A Note on Stochastic Scheduling on a Single Machine Subject to Breakdown and Repair , 1988, Probability in the Engineering and Informational Sciences.

[13]  A.H.G. Rinnooy Kan,et al.  Single‐machine scheduling subject to stochastic breakdowns , 1990 .

[14]  J. B. G. Frenk,et al.  A General Framework for Stochastic One-machine Scheduling Problems with Zero Release Times and No Partial Ordering , 1991, Probability in the Engineering and Informational Sciences.

[15]  Ali Allahverdi,et al.  Two-Stage Production Scheduling with Separated Set-up Times and Stochastic Breakdowns , 1995 .

[16]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .