Branch-and-price-and-cut algorithms for solving the reliable h-paths problem

Andreas, April K.; Smith, J. Cole; Küçükyavuz, Simge

doi:10.1007/s10898-007-9254-x

Cited by 21 publications

(13 citation statements)

References 17 publications

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“…Chen, Kim, Zhou, and Chootinan () propose a stochastic bi‐level optimization model for minimizing the total travel time budget required to satisfy the predefined reliability constraint. Andreas, Smith, and Küçükyavuz () consider the h ‐path network routing problem to minimize transportation cost subject to a specified reliability requirement such that at least one path retains reliability beyond minimum level. Desai and Sen () apply a branch‐and‐bound algorithm for designing a reliable transportation network by assuming that there exists an arbitrary set of risk mitigation resources in each arc with its constraints.…”

Section: Literature Reviewmentioning

confidence: 99%

Reliable Supply Chain Network Design

et al. 2015

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Risk management in supply chains has been receiving increased attention in the past few years. In this article, we present formulations for the strategic supply chain network design problem with dual objectives, which usually conflict with each other: minimizing cost and maximizing reliability. Quantifying the total reliability of a network design is not as straightforward as total cost calculation. We use reliability indices and develop analytical formulations that model the impact of upstream supply chain on individual entities' reliability to quantify the total reliability of a network. The resulting multiobjective nonlinear model is solved using a novel hybrid algorithm that utilizes a genetic algorithm for network design and linear programming for network flow optimization. We demonstrate the application of our approach through illustrative examples in establishing tradeoffs between cost and reliability in network design and present managerial implications.

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Section: Literature Reviewmentioning

confidence: 99%

Reliable Supply Chain Network Design

et al. 2015

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“…In addition to Benders feasibility cuts, we propose two additional sets of valid inequalities for the chanceconstrained Steiner tree problem (2). The first set of valid inequalities is based on the concept of probabilistic Steiner p-cuts.…”

Section: Additional Valid Inequalitiesmentioning

confidence: 99%

“…We refer to this problem (2) as the chance-constrained Steiner tree problem. Note that our problem reduces to the case of reliably connecting a single pair of nodes when |T | = 2, and reduces to reliably connecting all pairs of nodes when T = V, both of which are studied in Song and Luedtke [28].…”

Section: Introductionmentioning

confidence: 99%

“…fails to connect T in scenario 3, and therefore is infeasible to the chance-constrained Steiner tree problem (2).…”

Section: Introductionmentioning

confidence: 99%

“…Chance-constrained programs are difficult to solve because the feasible region of the corresponding formulation is in general nonconvex. In our problem (2), there are a finite number of edge failure scenarios, although this number could be very large in general (up to 2 |E| ). To make it computationally tractable, a sample average approximation (SAA) with a moderate number of scenarios is solved, where the set of scenarios is generated by drawing a sample from the collection of all possible scenarios (Luedtke and Ahmed [24]).…”

Section: Introductionmentioning

confidence: 99%

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Chance‐constrained multi‐terminal network design problems

Song

Zhang

2015

Naval Research Logistics

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We consider a reliable network design problem under uncertain edge failures. Our goal is to select a minimum‐cost subset of edges in the network to connect multiple terminals together with high probability. This problem can be seen as a stochastic variant of the Steiner tree problem. We propose two scenario‐based Steiner cut formulations, study the strength of the proposed valid inequalities, and develop a branch‐and‐cut solution method. We also propose an LP‐based separation for the scenario‐based directed Steiner cut inequalities using Benders feasibility cuts, leveraging the success of the directed Steiner cuts for the deterministic Steiner tree problem. In our computational study, we test our branch‐and‐cut method on instances adapted from graphs in SteinLib Testdata Library with up to 100 nodes, 200 edges, and 17 terminals. The performance of our branch‐and‐cut method demonstrates the strength of the scenario‐based formulations and the benefit from adding the additional valid inequalities that we propose. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 321–334, 2015

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The most reliable flight itinerary problem

2018

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Travel itineraries between many origin‐destination (OD) pairs can require multiple legs, such as several trains, shared rides or flights, to arrive at the final destination. Travelers expect transparent reliability information to help improve decision‐making for multi‐leg itineraries. We focus on airline travel and making a priori decisions about flight itineraries based on the reliability of arriving at the destination within the travel time budget. We model the reliability of multi‐leg itineraries and, given publicly available data, create probability distributions of flight arrival and departure times. We use these values in our reliability calculations for the entire itinerary. We implement a stochastic network search algorithm that finds the most reliable flight itinerary (MRFI). We also implement several ideas to improve the efficiency of this network search. Computational experiments help identify characteristics of the MRFI for a diverse set of OD pairs.

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Branch-and-price-and-cut algorithms for solving the reliable h-paths problem

Cited by 21 publications

References 17 publications

Reliable Supply Chain Network Design

Reliable Supply Chain Network Design

Chance‐constrained multi‐terminal network design problems

The most reliable flight itinerary problem

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