Basics of time-dependent scheduling

Gawiejnowicz, Stanisław

doi:10.1007/978-3-540-69446-5_5

Cited by 155 publications

(91 citation statements)

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“…Subsequent contributions to the theory of scheduling, beginning with Johnson (1954), focus on minimizing the time needed to complete heterogeneous jobs on a discrete number of machines. Because of their combinatorial nature these types of problems are often NP-hard and require an algorithmic approach (Veinott and Wagner 1962;Gawienjnowicz 2008). For the cash-flow switching problem with a single switching time, we pursue a semi-analytical approach.…”

Section: Literaturementioning

confidence: 99%

Optimal switching between cash-flow streams

Weber

2017

Math Meth Oper Res

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We consider the problem of finding the optimal time to switch between two measurable cash-flow streams. A complete characterization of the set of solutions is obtained in terms of adjoint variables which measure the available gain from deviations. An iterative procedure for the computation of the adjoint variables is provided. The results are generalized to multiple switching times, multiple cash-flow streams, switching costs, as well as switch-triggered cash-flow streams that arise in equipmentreplacement problems.

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Section: Literaturementioning

confidence: 99%

Optimal switching between cash-flow streams

Weber

2017

Math Meth Oper Res

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“…The contributing factors to varying processing times may be machine or worker learning, machine deterioration, production system upgrades or technological shocks. Gawienjnowiz (2008) provides a wide variety of applications and to date results on scheduling with time-dependent jobs. Time-dependent scheduling models can be classified into three general categories.…”

Section: Introductionmentioning

confidence: 99%

Minimizing total completion time on a single machine with step improving jobs

Kim

Oron

2015

Journal of the Operational Research Society

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Production systems often experience a shock or a technological change, resulting in performance improvement. In such settings, job processing times become shorter if jobs start processing at, or after, a common critical date. This paper considers a single machine scheduling problem with step-improving processing times, where the effects are job-dependent. The objective is to minimize the total completion time. We show that the problem is NP-hard in general and discuss several special cases which can be solved in polynomial time. We formulate a Mixed Integer Programming model and develop an LP-based heuristic for the general problem. Finally, computational experiments show that the proposed heuristic yields very effective and efficient solutions.

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“…Under a time-dependent effect, the actual processing time of a job is a function of the start time of the job. Leaving aside less popular cumulative effects initiated by [5] and [6], the studies on the positional and the time-dependent effects have formed the bulk of publications in the area; see, e.g., a survey [7] and the book [8], the latter providing a comprehensive exposition on scheduling with time-dependent processing times. These two effects can be further classified as being either job-dependent or job-independent.…”

Section: Introductionmentioning

confidence: 99%

“…Although more exotic models have also been considered (see, e.g., [8] and [9] for reviews), many authors pose questions regarding their practical relevance. Thus, in this paper we concentrate on linear time-dependent effects.…”

Section: Introductionmentioning

confidence: 99%

Combining time and position dependent effects on a single machine subject to rate-modifying activities

Rustogi

Strusevich

2014

Omega

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Citation for this version held on GALA:Rustogi, Kabir and Strusevich, Vitaly (2014) Combining time and position dependent effects on a single machine subject to rate-modifying activities. London: Greenwich Academic Literature Archive. We introduce a general model for single machine scheduling problems, in which the actual processing times of jobs are subject to a combination of positional and timedependent effects, that are job-independent but additionally depend on certain activities that modify the processing rate of the machine, such as, e.g., maintenance. We focus on minimizing two classical objectives: the makespan and the sum of the completion times. The traditional classification accepted in this area of scheduling is based on the distinction between the learning and deterioration effects, on one hand, and between the positional effects and the start-time dependent effects, on the other hand. Our results show that in the framework of the introduced model such a classification is not necessary, as long as the effects are job-independent. The model introduced in this paper covers most previously known models. The solution algorithms are developed within the same general framework and their running times are no worse than those available earlier for problems with less general effects.

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Basics of time-dependent scheduling

Cited by 155 publications

References 0 publications

Optimal switching between cash-flow streams

Optimal switching between cash-flow streams

Minimizing total completion time on a single machine with step improving jobs

Combining time and position dependent effects on a single machine subject to rate-modifying activities

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