Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty

Bodur, Merve; Luedtke, James

doi:10.1287/mnsc.2016.2455

Cited by 48 publications

(19 citation statements)

References 64 publications

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“…Our computational results show that adding parametric inequalities that convexify the second stage formulation significantly reduces the total solution time taken to solve these problems. We utilize an efficient implementation of the L-shaped method for TSS-MIPs which utilizes Benders' cuts within branch-and-cut approach, and incorporates various techniques to enhance [9], aggregate [34], consolidate [36], and reactivate Benders' cut. We refer to our implementation as the modified L-shaped method; see Appendix B for details.…”

Section: Contributionsmentioning

confidence: 99%

“…Mixed integer rounding enhanced Benders' cuts. Recently, Bodur and Luedtke [9] strengthen the quality of the Benders' cuts through mixed integer rounding (MIR) procedure. The idea behind this method is to pair Benders' cuts developed in two consecutive iterations and then apply MIR aggregation technique to derive a new "strengthened" Benders' cut.…”

Section: B Implementation Of Modified L-shaped Algorithm For Tss-mipsmentioning

confidence: 99%

See 1 more Smart Citation

Tight Second Stage Formulations in Two-Stage Stochastic Mixed Integer Programs

Bansal¹,

Huang²,

Mehrotra³

2018

SIAM J. Optim.

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We study two-stage stochastic mixed integer programs (TSS-MIPs) with integer variables in the second stage. We show that under suitable conditions, the second stage MIPs can be convexified by adding parametric cuts a priori. As special cases, we extend the results of Miller and Wolsey (Math Program 98(1):73-88, 2003) to TSS-MIPs. Furthermore, we consider second stage programs that are generalizations of the well-known mixing (and continuous mixing) set, or certain piecewise-linear convex objective integer programs. These results allow us to relax the integrality restrictions on the second stage integer variables without effecting the integrality of the optimal solution of the TSS-MIP. We also use four variants of the two-stage stochastic capacitated lot-sizing problems as test problems for computational experiments, and present tight second-stage formulations for these problems. Our computational results show that adding parametric inequalities that a priori convexify the second stage formulation significantly reduces the total solution time taken to solve these problems.

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Section: Contributionsmentioning

confidence: 99%

Section: B Implementation Of Modified L-shaped Algorithm For Tss-mipsmentioning

confidence: 99%

Tight Second Stage Formulations in Two-Stage Stochastic Mixed Integer Programs

Bansal¹,

Huang²,

Mehrotra³

2018

SIAM J. Optim.

View full text Add to dashboard Cite

show abstract

“…Considering the fact that using callbacks prevents CPLEX from utilizing dynamic search, we specify the MIP search method for both algorithms as traditional branch-and-cut. Following an acceleration technique suggested in Bodur and Luedtke (2016), we initialize the RMP of the scenario decomposition-based algorithm with optimality and feasibility cuts associated with an initial first-stage solution to benefit from the possible improvement obtained from the automatically created CPLEX cuts. In particular, our initial solution locates two facilities at Mobile and Orlando with the smallest size.…”

Section: Computational Studymentioning

confidence: 99%

Two-stage stochastic programming under multivariate risk constraints with an application to humanitarian relief network design

2019

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In this study, we consider two classes of multicriteria two-stage stochastic programs in finite probability spaces with multivariate risk constraints. The first-stage problem features a multivariate stochastic benchmarking constraint based on a vector-valued random variable representing multiple and possibly conflicting stochastic performance measures associated with the second-stage decisions. In particular, the aim is to ensure that the associated random outcome vector of interest is preferable to a specified benchmark with respect to the multivariate polyhedral conditional value-at-risk (CVaR) or a multivariate stochastic order relation. In this case, the classical decomposition methods cannot be used directly due to the complicating multivariate stochastic benchmarking constraints. We propose an exact unified decomposition framework for solving these two classes of optimization problems and show its finite convergence. We apply the proposed approach to a stochastic network design problem in a pre-disaster humanitarian logistics context and conduct a computational study concerning the threat of hurricanes in the Southeastern part of the United States. Our numerical results on these large-scale problems show that our proposed algorithm is computationally scalable.

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“…Consequently, appropriate constraints need to be devised so that feasible assignments respect each given priority rule. From this standpoint, our work mimics Bodur and Luedtke (2016), where the authors use job-to-server assignment variables to capture dynamics under the shadow-tandem priority rule.…”

Section: Literature Reviewmentioning

confidence: 99%

Robust Multiclass Queuing Theory for Wait Time Estimation in Resource Allocation Systems

2019

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In this paper, we study systems that allocate different types of scarce resources to heterogeneous allocatees based on predetermined priority rules—the U.S. deceased-donor kidney allocation system or the public housing program. We tackle the problem of estimating the wait time of an allocatee who possesses incomplete system information with regard, for example, to his relative priority, other allocatees’ preferences, and resource availability. We model such systems as multiclass, multiserver queuing systems that are potentially unstable or in transient regime. We propose a novel robust optimization solution methodology that builds on the assignment problem. For first-come, first-served systems, our approach yields a mixed-integer programming formulation. For the important case where there is a hierarchy in the resource types, we strengthen our formulation through a drastic variable reduction and also propose a highly scalable heuristic, involving only the solution of a convex optimization problem (usually a second-order cone problem). We back the heuristic with an approximation guarantee that becomes tighter for larger problem sizes. We illustrate the generalizability of our approach by studying systems that operate under different priority rules, such as class priority. Numerical studies demonstrate that our approach outperforms simulation. We showcase how our methodology can be applied to assist patients in the U.S. deceased-donor kidney waitlist. We calibrate our model using historical data to estimate patients’ wait times based on their kidney quality preferences, blood type, location, and rank in the waitlist. This paper was accepted by Yinyu Ye, optimization.

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Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty

Cited by 48 publications

References 64 publications

Tight Second Stage Formulations in Two-Stage Stochastic Mixed Integer Programs

Tight Second Stage Formulations in Two-Stage Stochastic Mixed Integer Programs

Two-stage stochastic programming under multivariate risk constraints with an application to humanitarian relief network design

Robust Multiclass Queuing Theory for Wait Time Estimation in Resource Allocation Systems

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