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Math Meth Oper Res (2002) 56:83–100 A bicriteria stochastic programming model for capacity expansion in telecommunications Morten Riis1, Jørn Lodahl2 1 Department of Operations Research, University of Aarhus, building 530, Ny Munkegade, DK-8000, A ˚ rhus C, Denmark (e-mail: [email protected]) 2 SONOFON, Skelagervej 1, DK-9100, A ˚ lborg, Denmark Manuscript received: December 2001/Final version received: January 2002 Abstract. We consider capacity expansion of a telecommunications network in the face of uncertain future demand and potential future failures of network components. The problem is formulated as a bicriteria stochastic program with recourse in which the total cost of the capacity expansion and the prob- abil ity of fut ure capac it y requi rements to be vi ol ate d ar e si mul taneo usl y minimized. Assuming the existence of a nite number of possible future states of the world, an algorithm for the problem is elaborated. The algorithm de- termines all non-dominated solutions to the problem by a reduced feasible region method, solving a sequence of restricted subproblems by a cutting plane procedure. Computational results are reported for three di¤erent problem in- stances, one of which is a real-life problem faced by SONOFON, a Danish communi cations networ k operator. Key words: Capacity expansion, telecommunications, stochastic programming, integer programming, bicrite ria optimization 1 Introd uction Capacity expansion problems is an important class of problems arising in many contexts. Uncertainty is almost always an inherent feature of the system being modeled, and the importance of taking due account of this uncertainty when formulating the problem as an optimization problem is well-recognized. This paper is concerned with capacity expansion of a telecommunications network in an uncertain environment. The uncertainties facing the network operator are assumed to be twofold. Some arises due to the inherent uncer- tainty involved in the assessment of future demand, and some is due to the potential future failure of nodes or edges in the network. Previous studies have mainly dealt with these issues separately. Capacity expansion problems with uncertain future demand have been considered by authors such as Dempster,

Riis M., Lodahl J.-a Bicriteria Stochastic Programming Model for Capacity Expansion in Telecommunications (2002)

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