Robust scheduling of a two-machine flow shop with uncertain processing times

Kouvelis, Panos; Daniels, Richard L.; Vairaktarakis, George L.

doi:10.1080/07408170008963918

Cited by 157 publications

(100 citation statements)

References 11 publications

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“…The size of the scheduling instances that can be solved to guaranteed optimality remains limited but is comparable with the size of problems solvable by other combinatorial-optimization approaches to scheduling under uncertainty (see, e.g., Daniels and Carrillo 1997;Daniels and Kouvelis 1995;or Kouvelis et al 2000). An additional complication of the stability objective is the fact that optimal schedules need not (and generally will not) be active.…”

Section: Discussionmentioning

confidence: 99%

“…Stochastic job duration D i is modelled by means of discrete scenarios, a choice that was also made by, e.g., Daniels and Carrillo (1997), Daniels and Kouvelis (1995), Kouvelis and Yu (1997), and Kouvelis et al (2000). Specifically, let a random variable L i denote the increase in d i if i is 'disrupted', which takes place with probability π i ; D i equals the baseline duration d i with probability (1 − π i ).…”

Section: Definitions and Objective Functionmentioning

confidence: 99%

See 1 more Smart Citation

Scheduling for stability in single-machine production systems

Leus

Herroelen

2007

J Sched

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Robust scheduling aims at the construction of a schedule that is protected against uncertain events. A stable schedule is a robust schedule that changes only little when variations in the input parameters arise. This paper presents a model for single-machine scheduling with stability objective and a common deadline. We propose a branch-andbound algorithm for solving an approximate formulation of the model. The algorithm is exact when exactly one job is disrupted during schedule execution.

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Section: Discussionmentioning

confidence: 99%

Section: Definitions and Objective Functionmentioning

confidence: 99%

Scheduling for stability in single-machine production systems

Leus

Herroelen

2007

J Sched

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“…Hence, robustness can be provided by forcing a schedule to fulfill a bunch of scenarios, sampled according to expected realizations of the uncertainty. Searching for a single schedule for all scenarios is often used in the robust literature [9]. However, a less conservative option is using a multi-stage stochastic optimization [16], which benefits from the assumption that the uncertainty can be measured in the short future, so decisions could be adapted accordingly.…”

Section: Center For Advanced Process Systems Engineering (Capse) Intmentioning

confidence: 99%

Robust multi-objective scheduling in an evaporation network

Palacı́n

Pitarch

Prada

et al. 2017

2017 25th Mediterranean Conference on Control and Automation (MED)

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Abstract-Considering uncertainty in continuous production processes is key to compute short-time optimal schedules which can be trusted in practice. This paper proposes a twostep stochastic approach to the robust scheduling of several evaporation plants. This approach considers the possibility of reacting in the future once the uncertainty materializes. Each evaporator has different features (capacity, equipment, etc.) and the individual performance is affected by external factors and fouling effects. Moreover, a multi-objective analysis has been carried out to provide a decision support for the operator who must take the concrete decisions about load allocation and cleaning tasks along a time horizon. The problem has been solved by discretizing the time horizon and adapting the general-precedence method to deal with an unknown number of tasks. The nonlinear behavior of each plant is approximated by surrogate linear models obtained experimentally, providing thus solutions in acceptable time.

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“…Kouvelis et al (2000) and Kasperski et al (2012) considered a min-max regret version of the two-machine flow shop scheduling problem with uncertain processing times, using the makespan as the performance measure of interest. Kouvelis et al (2000) proved NP-hardness and developed exact and heuristic methods. Kasperski et al (2008) showed strong NP-hardness and established approximability.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Let where * s σ is a schedule to minimize the makespan under scenario s. Since this problem is known to be NP-hard (Kouvelis and Daniels, 2000), however, we consider the problem satisfying ordered properties, defined as follows: Under each scenario q can be interpreted as the time associated with machine i, such as in setting or fine-tuning the machine. In this case, processing jobs can start after machine set-up is completed.…”

Section: Introductionmentioning

confidence: 99%

Min-Max Regret Version of an m-Machine Ordered Flow Shop with Uncertain Processing Times

Park¹,

Choi²

2015

Management Science and Financial Engineering

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We consider an m-machine flow shop scheduling problem to minimize the latest completion time, where processing times are uncertain. Processing time uncertainty is described through a finite set of processing time vectors. The objective is to minimize maximum deviation from optimality for all scenarios. Since this problem is known to be NPhard, we consider it with an ordered property. We discuss optimality properties and develop a pseudo-polynomial time approach for the problem with a fixed number of machines and scenarios. Furthermore, we find two special structures for processing time uncertainty that keep the problem NP-hard, even for two machines and two scenarios. Finally, we investigate a special structure for uncertain processing times that makes the problem polynomially solvable.

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Robust scheduling of a two-machine flow shop with uncertain processing times

Cited by 157 publications

References 11 publications

Scheduling for stability in single-machine production systems

Scheduling for stability in single-machine production systems

Robust multi-objective scheduling in an evaporation network

Min-Max Regret Version of an m-Machine Ordered Flow Shop with Uncertain Processing Times

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