Feasibility in transportation networks with supply eating arcs

Dye, Shane; Tomasgård, Asgeir; Wallace, Stein W.

doi:10.1002/(sici)1097-0037(199805)31:3<165::aid-net3>3.0.co;2-d

Cited by 6 publications

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“…The multiple node service provision problem is exactly a transportation network with so-called supply eating arcs. Dye et al [5] discuss the question of determining whether a solution exists for which all demand is met in the multiple node problem. They also provide a brief discussion of the similarities of this problem with other classical mixed integer programs.…”

Section: Relationship To Other Problems and Complexitymentioning

confidence: 99%

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Approximation algorithms and relaxations for a service provision problem on a telecommunication network

Dye

Stougie

Tomasgård

2003

Discrete Applied Mathematics

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Section: Relationship To Other Problems and Complexitymentioning

confidence: 99%

“…In [5] it is shown that deciding feasibility of the multiple node service provision in the sense that no request needs to be rejected is NP-complete. In this paper we study optimization of both the single node and the multiple node problem.…”

Section: Introductionmentioning

confidence: 99%

Approximation algorithms and relaxations for a service provision problem on a telecommunication network

Dye

Stougie

Tomasgård

2003

Discrete Applied Mathematics

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“…The related feasibility problem (i.e., the problem of finding a feasible solution that satisfies all demand, under the assumption that such a solution exists) has the structure of a Transportation Network with Supply Eating Arcs (TSEA) [10]. It is interesting to note that the deterministic feasibility problem of TSEA is NP-complete in the strong sense, see [10]. In [10], an algorithm is also given that solves the TSEA feasibility problem when r(i, j) = r( j).…”

Section: A Deterministic Service Provision Modelmentioning

confidence: 99%

“…It is interesting to note that the deterministic feasibility problem of TSEA is NP-complete in the strong sense, see [10]. In [10], an algorithm is also given that solves the TSEA feasibility problem when r(i, j) = r( j).…”

Section: A Deterministic Service Provision Modelmentioning

confidence: 99%

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Tomasgård¹,

Audestad²,

Dye³

et al. 1998

Annals of Operations Research

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In memory of Åsa HallefjordThe purpose of this paper is to formally describe new optimization models for telecommunication networks with distributed processing. Modern distributed networks put more focus on the processing of information and less on the actual transportation of data than we are traditionally used to in telecommunications. This paper introduces new approaches for modelling decision support at operational, tactical and strategic levels. One of the main advantages of the technological framework we are working within is its inherent flexibility, which enables us to dynamically plan and consider uncertainty when decisions are made. When we present the models, emphasis is placed on the modelling discussions around the shift of focus towards processing, the new technological aspects, and how to utilize flexibility to cope with uncertainty.

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The stochastic single resource service‐provision problem

Dye

Stougie

Tomasgård

2003

Naval Research Logistics

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The service‐provision problem described in this paper comes from an application of distributed processing in telecommunications networks. The objective is to maximize a service provider's profit from offering computational‐based services to customers. The service provider has limited capacity and must choose which of a set of software applications he would like to offer. This can be done dynamically, taking into consideration that demand for the different services is uncertain. The problem is examined in the framework of stochastic integer programming. Approximations and complexity are examined for the case when demand is described by a discrete probability distribution. For the deterministic counterpart, a fully polynomial approximation scheme is known S. Dye, L. Stougie, and A. Tomasgard, Approximation algorithms and relaxations for a service provision problem on a telecommunication network, Working Paper #2‐98, Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Trondheim, Norway, 1998, Discrete Appl Math, to appear. We show that introduction of stochasticity makes the problem strongly NP‐hard, implying that the existence of such a scheme for the stochastic problem is highly unlikely. For the general case a heuristic with a worst‐case performance ratio that increases in the number of scenarios is presented. Restricting the class of problem instances in a way that many reasonable practical problem instances satisfy allows for the derivation of a heuristic with a constant worst‐case performance ratio. Worst‐case performance analysis of approximation algorithms is classical in the field of combinatorial optimization, but in stochastic programming the authors are not aware of any previous results in this direction. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003

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Feasibility in transportation networks with supply eating arcs

Cited by 6 publications

References 1 publication

Approximation algorithms and relaxations for a service provision problem on a telecommunication network

Approximation algorithms and relaxations for a service provision problem on a telecommunication network

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The stochastic single resource service‐provision problem

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