Decomposition methods for the two-stage stochastic Steiner tree problem

Leitner, Markus; Ljubić, Ivana; Luipersbeck, Martin; Sinnl, Markus

doi:10.1007/s10589-017-9966-x

Cited by 5 publications

(5 citation statements)

References 36 publications

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“…Given that the subproblems are nonlinear and require considerable computational e↵orts, it is better to extract as much information as possible at each iteration by adding multiple cuts each time the Benders subproblem is called. This leads to the multicut approach (see, e.g., , You and Grossmann (2013), Leitner et al (2018)).…”

Section: Generalized Benders Decompositionmentioning

confidence: 99%

Budgeting in International Humanitarian Organizations

Fard

Ljubić

Papier

2022

M&SOM

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Problem definition: International humanitarian organizations (IHOs) prepare a detailed annual allocation plan for operations that are conducted in the countries they serve. The annual plan is strongly affected by the available financial budget. The budget of IHOs is derived from donations, which are typically limited, uncertain, and to a large extent earmarked for specific countries or programs. These factors, together with the specific utility function of IHOs, render budgeting for IHOs a challenging managerial problem. In this paper, we develop an approach to optimize budget allocation plans for each country of operations. Academic/practical relevance: The current research provides a better understanding of the budgeting problem in IHOs given the increasing interest of the operations management community for nonprofit operations. Methodology: We model the problem as a two-stage stochastic optimization model with a concave utility function and identify a number of analytical properties for the problem. We develop an efficient generalized Benders decomposition algorithm as well as a fast heuristic. Results: Using data from the International Committee of the Red Cross, our results indicate 21.3% improvement in the IHO’s utility by adopting stochastic programming instead of the expected value solution. Moreover, our solution approach is computationally more efficient than other approaches. Managerial implications: Our analysis highlights the importance of nonearmarked donations for the overall performance of IHOs. We also find that putting pressure on IHOs to fulfill the targeted missions (e.g., by donors or media) results in lower beneficiaries’ welfare. Moreover, the IHOs benefit from negative correlation among donations. Finally, our findings indicate that, if donors allow the IHO to allocate unused earmarked donations to other delegations, the performance of the IHO improves significantly.

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Section: Generalized Benders Decompositionmentioning

confidence: 99%

Budgeting in International Humanitarian Organizations

Fard

Ljubić

Papier

2022

M&SOM

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“…In a recent Networks article, Rehfeldt et al [199] transformed the PCSTP and the MWCS into the SAP and used dual ascent as a tool for reducing the input size. For two STP generalizations, namely the stochastic STP and the Steiner tree‐star problem, dual‐ascent techniques have been successfully applied by Leitner et al [152] and by Bardossy and Raghavan [15] and Leitner et al [154], respectively.…”

Section: Dual‐ascent Methodsmentioning

confidence: 99%

“…If this lower bound exceeds a known upper bound (i.e., the objective value of the best incumbent solution), node i and all its incident edges can be removed [228]. Following these concepts, subsequent contributions to reduction tests are made for deterministic [102, 180, 228], stochastic [152], node‐weighted variants of the STP [153, 199], or special instances stemming from VLSI design [225]. A recent comprehensive collection of reduction tests for node‐weighted variants of the STP is given in Rehfeldt et al [199].…”

Section: Reduction Testsmentioning

confidence: 99%

“…For two‐stage stochastic STP , Leitner et al [152] combined two types of decomposition techniques which can be seen as dual to each other, namely Benders decomposition and Lagrangian relaxation. The authors demonstrated that using these two powerful decompositions in a combined framework creates synergetic effects and allows one to attack the stochastic STP from multiple angles so as to exploit different types of problem‐structures.…”

Section: Lagrangian Relaxationsmentioning

confidence: 99%

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Solving Steiner trees: Recent advances, challenges, and perspectives

Ljubić

2020

Networks

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The Steiner tree problem (STP) in graphs is one of the most studied problems in combinatorial optimization. Since its inception in 1970, numerous articles published in the journal Networks have stimulated new theoretical and computational studies on Steiner trees: from approximation algorithms, heuristics, metaheuristics, all the way to exact algorithms based on (mixed) integer linear programming, fixed parameter tractability, or combinatorial branch‐and‐bounds. The pervasive applicability and relevance of Steiner trees have been reinforced by the recent 11th DIMACS Implementation Challenge in 2014 and the PACE 2018 Challenge. This article provides an overview of the rich developments from the last three decades for the STP in graphs and highlights the most recent computational studies for some of its closely related variants.

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“…Theoretically, the problem has been of interest to the community for decades, starting with the inclusion in Karp's 21 NP-Complete problems (Karp 1972). Since then, it has been studied extensively in approximation algorithm design (Kou, Markowsky, and Berman 1981;Takakashi 1980;Wu, Widmayer, and Wong 1986;Byrka et al 2010), stochastic algorithms (Gupta and Pál 2005;Gupta, Hajiaghayi, and Kumar 2007;Kurz, Mutzel, and Zey 2012;Leitner et al 2018) and online algorithms (Imase and Waxman 1991;Berman and Coulston 1997;Angelopoulos 2008Angelopoulos , 2009. Practically, the Steiner tree problem is fundamental for many network problems such as fiber optic networks (Bachhiesl et al 2002), social networks (Chiang et al 2013;Lappas et al 2010), and biological networks (Sadeghi and Fröhlich 2013).…”

Section: Introductionmentioning

confidence: 99%

Learning-Augmented Algorithms for Online Steiner Tree

Moseley

2022

AAAI

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This paper considers the recently popular beyond-worst-case algorithm analysis model which integrates machine-learned predictions with online algorithm design. We consider the online Steiner tree problem in this model for both directed and undirected graphs. Steiner tree is known to have strong lower bounds in the online setting and any algorithm’s worst-case guarantee is far from desirable. This paper considers algorithms that predict which terminal arrives online. The predictions may be incorrect and the algorithms’ performance is parameterized by the number of incorrectly predicted terminals. These guarantees ensure that algorithms break through the online lower bounds with good predictions and the competitive ratio gracefully degrades as the prediction error grows. We then observe that the theory is predictive of what will occur empirically. We show on graphs where terminals are drawn from a distribution, the new online algorithms have strong performance even with modestly correct predictions.

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Decomposition methods for the two-stage stochastic Steiner tree problem

Cited by 5 publications

References 36 publications

Budgeting in International Humanitarian Organizations

Budgeting in International Humanitarian Organizations

Solving Steiner trees: Recent advances, challenges, and perspectives

Learning-Augmented Algorithms for Online Steiner Tree

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