Single machine scheduling with nonlinear cost functions

doi:10.1016/0305-0548(91)90033-N

Computers & Operations Research

Volume 18, Issue 3, 1991, Pages 317-322

https://doi.org/10.1016/0305-0548(91)90033-N Get rights and content

Abstract

The problem of scheduling n jobs with a single machine where each job has a differentiable cost function and the total cost being minimized is studied. A heuristic solution procedure is proposed. The algorithm is also applicable when the cost functions are piecewise diflerentiable. Running time of the algorithm is O(n²). The effectiveness of the algorithm is evaluated and is shown that in many cases the algorithm picks an optimal order. The algorithm proposed here empirically is compared with linearized algorithm by Fisher and Krieger [1].

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Citation Excerpt :
For examples, a group of flow shop problems with state-dependent processing times were first introduced by Sriskandarajah and Goyal (1989), continued by Sriskandarajah and Wagneur (1991) and Wagneur and Sriskandarajah (1993a,b), as well as extended by Finke and Jiang (1997). Alidaee (1991) considered a few single machine scheduling problems with nonlinear cost functions. Janiak and Kovalyov (1996) considered a class of resource dependent scheduling problems.
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^∗: Bahrain Alidaee is Assistant Professor at West Texas State University. He holds the B.Sc. in Business Administration from the University of Tehran, Iran, the M.B.A. in Industrial Management from the University of North Texas and the Ph.D. in Mathematical Sciences from the University of Texas at Arlington. His principal research interest is in scheduling and sequencing, game theory and matroid theory. He has published in the journals of Theory and Decisions, Applied Mathematics Letters, Journal of the Operational Research Society and The Logistic and Transportation Review.

View full text

Single machine scheduling with nonlinear cost functions

Abstract

Ann. disc. Math.

Ann. disc. Math.

Ops Res. Lett.

OMEGA Int. J. Mgmt Sci.

Computers Ops Res.

J. Ops Mgmt.

Analysis of a linearization heuristic for single-machine scheduling to minimize profit

Mathl Program

Various optimizers for single-stage production

Nav. Res. Logist. Q.

Finding an optimal sequence by dynamic programming: an extension to precedence-related tasks

Ops Res.

A dynamic programming approach to sequencing problems

J. Soc. ind. appl. Math.