Using Fuzzy Numbers in Network Design Optimization Problems

The fluctuations that have taken place in the worldwide economy over the past few years make it difficult to estimate the costs of the equipment that have to be used in order to design a telecommunications network. The literature is replete with prescriptive integer programming models for various network design problems that do not take into account the problems inherent vagueness due to equipment costs. This paper considers the real-world wavelength division multiplexing (WDM) network design problem. The vagueness that appears in this problem is assumed and handled by means of fuzzy-set-based methodologies. A fuzzy integer linear programming model is then proposed to be used as an auxiliary model to solve the former problem. With the purpose to obtain cost-effective network designs, this model is then solved using Cplex, which is a commercial high-performance optimization engine.