Single-machine scheduling with general costs under compound-type distributions
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We investigate the problem of scheduling n jobs on a single machine with the following features. The cost functions are general stochastic processes, which can be used to model the effects of stochastic price fluctuations, stochastic due times, etc., and the stochastic processing times follow a class of distributions, which includes exponential, geometric, and other families of distributions. Such a class of distributions is characterized by its characteristic functions. The optimal policies for these scheduling problems, both without precedence constraints, or with precedence in the form of nonpreemptive chains, are discussed, respectively.
KeywordsStochastic scheduling Single machine Stochastic cost functions Due dates Characteristic functions Increment order Convexity order
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- Bagga, P. C. and K. R. Kalra, “Single machine scheduling problem with quadratic functions of completion times—a modified approach,” Journal of Information & Optimization Sciences, 2, 103–108 (1981).Google Scholar
- Bertoin, J., Lévy Processes. Cambridge University Press, New York, 1996.Google Scholar
- Bisgaard, T. M. and S. Zoltan, Characteristic Functions and Moments Sequences: Positive Definiteness in Probability, Nova Science (2000).Google Scholar
- Derman, C., G. Lieberman, and S. Ross, “A renewal decision problem,” Management Science, 24, 554–561 (1978).Google Scholar
- Glazebrook, K. D., “Scheduling tasks with exponential service times on parallel processors,” Journal of Applied Probability, 16, 658–689 (1979).Google Scholar
- Kämpke, T., “Optimal scheduling of jobs with exponential service times on identical parallel processors,” Operations Research, 37, 126–133 (1989).Google Scholar
- Pinedo, M., Scheduling: Theory, Algorithms, and Systems, 2nd edn., Prentice Hall, Englewood Cliffs (2002).Google Scholar
- Pinedo, M. and S.H. Wie, “Inequalities for stochastic flowshops and job shops,” Applied Stochastic Models and Data Analysis, 2, 61–69 (1986).Google Scholar
- Righter, R., “Scheduling,” in: M. Shaked and J. G. Shanthikumar (Eds.), Stochastic Orders and Their Applications. Academic, Boston, 1994, pp. 381–428.Google Scholar
- Rothkopf, M. H., “Scheduling with random service times,” Management Science, 12, 437–447 (1966).Google Scholar