Risk-averse single machine scheduling: complexity and approximation

Kasperski, Adam; Zieliński, Paweł

doi:10.1007/s10951-019-00599-6

Cited by 13 publications

(5 citation statements)

References 42 publications

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“…A branch-and-bound approach was proposed for the stochastic single machine scheduling problem with uncertain processing time and release time in Urgo and Váncza (2019) to minimise the valueâĂŘatâĂŘrisk of the maximum lateness, and for a flow shop stochastic scheduling approach minimising the CVaR of the residual work content in Urgo (2019). Kasperski and Zieliński (2019) discussed a wide class of single-machine scheduling problems with uncertain job processing times and due dates and applied risk measure criteria (VaR and CVaR) to obtain an optimal solution. Meloni and Pranzo (2020) evaluated the conditional value-at-risk of the makespan for a resource-constrained project scheduling problem where, for each activity, an interval for processing times is defined in the integer domain and the evaluation of quantile-and superquantiles-based risk measures for the interval-valued processing times in scheduling problems is addressed in Meloni and Pranzo (2023).…”

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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“…Urgo et al [19] apply a branch-and-bound approach for the stochastic single machine scheduling problem with uncertain processing time and release time aims at minimizing the value-at-risk of maximum lateness. Kasperski et al [29] discuss a wide class of single machine scheduling problems with uncertain job processing times and due dates, and applied risk measure approaches (VaR and CVaR) to get a solution. Meloni et al [30] evaluate the conditional value-at-risk of makespan for a resource constrained project scheduling problem in which for each activity only the interval for its integer valued duration is known.…”

Section: State Of Artmentioning

confidence: 99%

Scheduling Remanufacturing Activities for the Repair of Turbine Blades: An Approximate Branch and Bound Approach to Minimize a Risk Measure

Liu

Urgo

2021

Lecture Notes in Mechanical Engineering

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Refurbished products are gaining importance in many industrial sectors, specifically high-value products whose residual value is relevant and guarantee the economic viability of the remanufacturing at an industrial level, e.g., turbine blades for power generation. In this paper we address the scheduling of re-manufacturing activities for turbine blades. Parts entering the process may have very different wear state or presence of defects. Thus, the repair process is affected by a significant degree of uncertainty. To cope with this, the proposed approach pursues robust schedules minimizing the risk associated to a timely completion time. An approximate branch and bound algorithm is developed grounding on the estimation of the lower bound of the makespan. The viability and efficiency of the approach is assessed through computational experiments grounding on the industrial case under study and a comparison is operated among alternative scheduling approaches.

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“…. , b K , respectively, with Pr[X = a i ] = Pr[Y = b i ] and a i ≤ γb i for each i ∈ [K] and some fixed γ ≥ 0, the inequality CVaR α [X] ≤ γCVaR α [Y] holds (see, e.g., [17]), we get:…”

Section: Tablementioning

confidence: 99%

Two-stage combinatorial optimization problems under risk

Goerigk

Kasperski

Zieliński

2020

Theoretical Computer Science

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In this paper a class of robust two-stage combinatorial optimization problems is discussed. It is assumed that the uncertain second stage costs are specified in the form of a convex uncertainty set, in particular polyhedral or ellipsoidal ones. It is shown that the robust two-stage versions of basic network and selection problems are NP-hard, even in a very restrictive cases. Some exact and approximation algorithms for the general problem are constructed. Polynomial and approximation algorithms for the robust two-stage versions of basic problems, such as the selection and shortest path problems, are also provided.Typically, the first stage costs are known while the second stage costs can only be predicted to belong to an uncertainty set U . First such models were discussed in [16,18,26,23], where the robust two-stage spanning tree and perfect matching problems were considered. In these papers, the uncertainty set U contains K explicitly listed scenarios. Several negative and positive complexity results for this uncertainty representation were established. Some of them have been recently extended in [19], where also the robust two-stage shortest path problem has been investigated. In [25] and [13] the robust two-stage selection problem has been explored. The problem is NP-hard for discrete uncertainty representation but it is polynomially solvable under a special case of polyhedral uncertainty set, called continuous budgeted uncertainty (see [13]).Robust two-stage problems belong to the class of three-level, min-max-min optimization problems. In mathematical programming, this approach is also called adjustable robustness (see, e.g. [5,31]). Namely, some variables must be determined before the realization of the uncertain parameters, while the other part are variables that can be chosen after the realization. Several such models have been recently considered in combinatorial optimization, which can be represented as a 0-1 programming problem. Among them there is the robust two-stage problem discussed in this paper, but also the robust recoverable models [11,12] and the k-adaptability approach [9]. In general, problems of this type can be hard to solve exactly. A standard approach is to apply row and column generation techniques, which consists in solving a sequence of MIP formulations (see, e.g., [32]). However, this method can be inefficient for larger problems, especially when the underlying deterministic problem is already NP-hard. Therefore, some faster approximation algorithms can be useful in this case.In this paper we consider the class of robust two-stage combinatorial problems under convex uncertainty, i.e. when the uncertainty set U is convex. Important special cases are polyhedral and ellipsoidal uncertainty, which are widely used in single-stage robust optimization. Notice that in the problems discussed in [16,18,26,23], U contains a fixed number of scenarios, so it is not a convex set. The problem formulation and description of the uncertainty sets are provided in Section 2. The complexity status of ba...

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Risk-averse single machine scheduling: complexity and approximation

Cited by 13 publications

References 42 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

Scheduling Remanufacturing Activities for the Repair of Turbine Blades: An Approximate Branch and Bound Approach to Minimize a Risk Measure

Two-stage combinatorial optimization problems under risk

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