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One-machine scheduling with allocation of continuously-divisible resource and with no precedence constraints. (English) Zbl 0635.90048

Summary: The efficiently solved one-machine scheduling problems with no precedence constraints are generalized to the case with allocation of continuously- divisible constrained nonrenewable resource. Models of operation are assumed to be duration versus resource amount linear functions. The following optimality criteria are considered: maximum completion time, maximum lateness, maximum cost and weighted sum of completion times. For the problems discussed polynomial-time algorithms are found.

MSC:

90B35 Deterministic scheduling theory in operations research
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References:

[1] J. R. Jackson: Scheduling a Production Line to Minimize Maximum Tardiness. Research Report, University of California at Los Angeles 1955.
[2] L. Lawler: Optimal sequencing of a single machine subject to precedence constraints. Management Sci. 19 (1973), 544-546. · Zbl 0254.90039 · doi:10.1287/mnsc.19.5.544
[3] H. L. Lawler J. K. Lenstra, A. H. G. Rinnooy Kan: Recent developments in deterministic sequencing and scheduling: a survey. Deterministic and Stochastic Scheduling, (M. A. H. Dempster, J. K. Lenstra and A. H. G. Rinnooy Kan, Dordrecht 1982. · Zbl 0482.68035
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