A bicriteria approach to minimize number of tardy jobs and resource consumption in scheduling a single machine

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Abstract

We extend the classical scheduling problem of minimizing the number of tardy jobs in a single-machine to the case where the job processing times are controllable by allocating a continuous and non-renewable resource to the processing operations. Our aim is to construct an efficient trade-off curve between the number of tardy jobs and total resource consumption using a bicriteria approach. Most of the research on scheduling with controllable resource-dependent processing times is done either to a linear resource consumption function or to a specific type of convex resource consumption function. We, in contrast, analyze the problem for a more general type of convex decreasing resource consumption function, which guarantees a very robust analysis that can be applied to a wide range of problems. We present four different variations of the problem and prove them to be NP-hard. We then present a polynomial time algorithm to solve an important special case of the problem and also suggest and compare the performances of three different heuristic algorithms.

Original languageEnglish
Pages (from-to)298-307
Number of pages10
JournalInternational Journal of Production Economics
Volume119
Issue number2
DOIs
StatePublished - 1 Jun 2009

Keywords

  • Complexity
  • Controllable processing times
  • Deterministic scheduling
  • Resource allocation

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