Journal ArticleDOI
Algorithms and Complexity Analysis for Robust Single-Machine Scheduling Problems
Bita Tadayon,J. Cole Smith +1 more
TLDR
This paper constructs three alternative uncertainty sets, each of which defines job processing times that can simultaneously occur, and examines the problem of identifying a set of worst-case processing times with respect to a fixed schedule.Abstract:
In this paper, we study a robust single-machine scheduling problem under four alternative optimization criteria: minimizing total completion time, minimizing total weighted completion time, minimizing maximum lateness, and minimizing the number of late jobs. We assume that job processing times are subject to uncertainty. Accordingly, we construct three alternative uncertainty sets, each of which defines job processing times that can simultaneously occur. The robust optimization framework assumes that, given a job schedule, a worst-case set of processing times will be realized from among those allowed by the uncertainty set under consideration. For each combination of objective function and uncertainty set, we first analyze the problem of identifying a set of worst-case processing times with respect to a fixed schedule, and then investigate the problem of selecting a schedule whose worst-case objective is minimal.read more
Citations
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Journal ArticleDOI
Distributionally robust single machine scheduling with risk aversion
TL;DR: The results convincingly show that the DR-SMSP model is able to enhance the robustness of the optimal job sequence and achieve risk reduction with a small sacrifice on the optimality of the mean value.
Journal ArticleDOI
Robust scheduling with budgeted uncertainty
TL;DR: It is proved that the robust version of minimizing the weighted completion time on a single machine is in the strong sense.
Journal ArticleDOI
Robust combinatorial optimization with knapsack uncertainty
TL;DR: The exact and approximation algorithms that extend the iterative algorithms proposed by Bertismas and Sim (2003) are provided and an approximation scheme is provided for the corresponding robust problem.
Journal ArticleDOI
Distributionally robust scheduling on parallel machines under moment uncertainty
TL;DR: A min-max distributionally robust model, which minimizes the worst-case expected total flow time out of all probability distributions in this set, which doesn’t require exact probability distributions which are the basis for many stochastic programming models, and utilizes more information compared to the interval-based robust optimization models.
Journal ArticleDOI
Exact Algorithms for Distributionally β-Robust Machine Scheduling with Uncertain Processing Times
TL;DR: It is shown that there exists a parameterized assignment problem (PAP), such that its optimal solutions are also optimal for the original problem, and there are efficient parametric search methods for the DRS models to handle uncertain processing times.
References
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Book
Introduction to Algorithms
TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
BookDOI
Introduction to Stochastic Programming
John R. Birge,Franois Louveaux +1 more
TL;DR: This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability to help students develop an intuition on how to model uncertainty into mathematical problems.
Book ChapterDOI
Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey
TL;DR: In this article, the authors survey the state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory, and indicate some problems for future research and include a selective bibliography.
Journal ArticleDOI
The Price of Robustness
Dimitris Bertsimas,Melvyn Sim +1 more
TL;DR: In this paper, the authors propose an approach that attempts to make this trade-off more attractive by flexibly adjusting the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations.