Stochastic Scheduling

Sarin, Subhash C.; Nagarajan, Balaji; Liao, Lizi

doi:10.1017/cbo9780511778032

Cited by 24 publications

(14 citation statements)

References 55 publications

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“…Although able to consider the impact of extreme scenarios, this criteria ignores the actual probability distributions linked to uncertain parameters, resulting in possible overcautious decisions (Tolio and Urgo 2013). To incorporate the available information on stochastic variables, the variance of the objective function could be considered, together with the expected value, to optimise the expectation-variance tradeoff (De et al 1992;Sarin et al 2010).…”

Section: Literature Reviewmentioning

confidence: 99%

A branch-and-bound approach to minimise the value-at-risk of the makespan in a stochastic two-machine flow shop

Liu

Urgo

2023

International Journal of Production Research

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Planning and scheduling approaches in real manufacturing environments entail the need to cope with random attributes and variables to match the characteristics of real scheduling problems where uncertain events are frequent. Moreover, the capability of devising robust schedules, which are less sensitive to the disruptive effects of unexpected events, is a major request in real applications. In this paper, a branch-and-bound approach is proposed to solve the two-machine permutation flow shop scheduling problem with stochastic processing times. The objective is the minimisation of the value-at-risk of the makespan, to support decisionmakers in the trade-off between the expected performance and the mitigation of the impact of extreme scenarios. A Markovian Activity Network (MAN) model is adopted to estimate the distribution of the makespan and assess the value-at-risk for both partial and complete schedules. Phasetype distributions are used to enable general distributions for processing times while maintaining the capability to exploit a Markovian approach. The effectiveness and performance of the proposed approach are demonstrated through a set of computational experiments.

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Section: Literature Reviewmentioning

confidence: 99%

A branch-and-bound approach to minimise the value-at-risk of the makespan in a stochastic two-machine flow shop

Liu

Urgo

2023

International Journal of Production Research

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“…In this paper, we assume the execution cycles of task v j follow normal distribution w(v j ) ∼ N (μ j , σ 2 j ) [12], [14], [16]. An important fact about normal random variables is that if Y j is normally distributed with expected value μ j and variance σ 2…”

Section: A the Execution Time On Single Processormentioning

confidence: 99%

“…However, in pioneering works [16], [18], Clark developed a method to recursively estimate the expected value and variance of the greatest of a finite set of random variables that are normally distributed. Hence, Clark's method can be applied recursively to find the desired expected value and variance of Makespan.…”

Section: B the Maximum Execution Time On Hcsmentioning

confidence: 99%

“…(20) 10 Compute task v j system probability Eq. (21) 11 end 12 Find the suitable processor and frequency pair with minimal system probability for the given task 13 Assign task v j to the corresponding processor frequency 14 Update the processor expected execution time and varinace 15 end 16 Compute Makespan use Eq. (6), total energy consumption use Eq.…”

Section: Algorithm 1: the Ests Algorithmmentioning

confidence: 99%

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Energy-Aware Scheduling Algorithm for Task Execution Cycles with Normal Distribution on Heterogeneous Computing Systems

Yin

2012

2012 41st International Conference on Parallel Processing

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In the past few years, many energy-aware scheduling algorithms have been developed primarily using the dynamic voltage-frequency scaling (DVFS) capability which has been incorporated into recent commodity processors. However, these techniques are unsatisfied with optimizing both schedule length and energy consumption. Furthermore, most algorithms schedule tasks according to their average case execution time and not consider the task's execution cycles with probability distribution in real-world. In recognition of this, we study the problem of scheduling independent stochastic tasks with normal distribution, deadline and energy consumption budget constraints on a heterogeneous platform. We first formulate this energyaware stochastic scheduling problem as a linear programming, which maximize the guaranteed confidence probabilities under deadline and energy consumption budget constraints. Then, we propose a heuristic energy-aware stochastic tasks scheduling algorithm (ESTS) to solve this problem, which can achieve high schedule performance for independent tasks with lower complexity. Our extensive simulation performance evaluation study, based on randomly generated stochastic applications and real-world applications, clearly demonstrate that our proposed heuristic algorithm can improve system guaranteed confidence probability and has a good trade-off between schedule length and energy consumption.

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“…For a general batch process without energy integration, delays are handled in a proactive or reactive manner. In the case of a proactive approach, a robust schedule is generated at the design stage by using stochastic modeling. − On the other hand, a reactive approach focuses on developing a new schedule (rescheduling) based on the current state of operation and the remaining time horizon. − It is worth noting that such a reactive scheduling, triggered by a process disturbance, can also affect practical heat recovery in the case of heat-integrated designs. In a different vein, integration of scheduling and dynamic optimization/advanced control has also been proposed to address delays arising out of processing time variations. − However, incorporation of heat integration into such integrated approaches is challenging and has not been pursued yet.…”

Section: Introductionmentioning

confidence: 99%

Robustness Analysis of Heat-Integrated Batch Process Networks

Shahane

Jogwar

Mathpati

2018

Ind. Eng. Chem. Res.

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Heat integration in batch processes strongly depends on the production schedule due to time-dependent availability of hot and cold process streams. Schedule delays in batch process operation are inevitable and can significantly reduce the practical benefits promised by heat integration. This paper presents a systematic framework to analyze the effect of schedule delays on achievable heat recovery in batch process systems. To this end, a time delay analysis method is proposed to generate heat recovery profile as a function of stream delay. The analysis computes maximum theoretical heat recovery (with a modified heat exchanger network) as well as practically achievable heat recovery (with the same network). The results of time delay analysis are then used to define three robustness measures to assess the sensitivity of a heat-integrated batch process network toward schedule delays. The presented framework allows identification of sensitive process streams as well as provides an operational measure to screen competing design alternatives. Two relevant example systems are considered to illustrate the effectiveness of the proposed framework.

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Stochastic Scheduling

Cited by 24 publications

References 55 publications

A branch-and-bound approach to minimise the value-at-risk of the makespan in a stochastic two-machine flow shop

A branch-and-bound approach to minimise the value-at-risk of the makespan in a stochastic two-machine flow shop

Energy-Aware Scheduling Algorithm for Task Execution Cycles with Normal Distribution on Heterogeneous Computing Systems

Robustness Analysis of Heat-Integrated Batch Process Networks

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