General stochastic single-machine scheduling with regular cost functions

Authors:
X. Zhou;X. Cai
Affiliations:
Department of Applied Mathematics, The Hong Kong Polytechnic University Hung Hom, Kowloon, Hong Kong;Department of Systems Engineering & Engineering Management The Chinese University of Hong Kong Shatin, N.T., Hong Kong
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1997

Citing 3
Cited 3

Scheduling independent jobs with stochastic processing times and a common due date on parallel and identical machines

Annals of Operations Research
Minimizing total tardiness on one machine is NP-hard

Mathematics of Operations Research
A polynomial time algorithm for a chance-constrained single machine scheduling problem

Operations Research Letters

STOCHASTIC SCHEDULING WITH PREEMPTIVE-REPEAT MACHINE BREAKDOWNS TO MINIMIZE THE EXPECTED WEIGHTED FLOW TIME

Probability in the Engineering and Informational Sciences
Single-machine scheduling to stochastically minimize maximum lateness

Journal of Scheduling
Stochastic Scheduling Subject to Preemptive-Repeat Breakdowns with Incomplete Information

Operations Research

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Abstract

We examine a stochastic scheduling model with n jobs and a single machine, where the processing times of the jobs are random variables with arbitrary distributions, and the machine is subject to stochastic breakdowns. Two types of regular performance measures, the total cost and the maximum cost, with general cost functions are investigated. We derive conditions under which a sequence in nondecreasing stochastic order of processing times minimizes the total expected cost, whereas a sequence in nondecreasing stochastic order of due dates minimizes the maximum expected cost. In addition, results on almost sure minimization of the total stochastic cost or the maximum stochastic cost are also provided. Applications of the general results to various special cases with commonly studied measures like mean weighted flowtime, mean weighted tardiness, weighted number of tardy jobs, maximum tardiness, etc., are discussed, which extend the previous results on these cases to more general situations.