Stochastic fuzzy multi-objective backbone selection and capacity allocation problem under tax-band pricing policy with different fuzzy operators

In this paper, we investigate a multi-objective optimization problem that a telecom bandwidth broker (BB) faces when acquiring and selling bandwidth in an uncertain market environment in which there exists several backbone providers (BPs) and end users. The proposed model incorporates two important goals: maximizing expected profit and minimizing expected loss capacity within realistic constraints such as BPs’ capacity, meeting the end users’ bandwidth requests and satisfying the Quality of Service requests of end users’, considering stochastic capacity loss rates of BPs. The fuzzy set theory and stochastic programming techniques are employed to handle the non-deterministic nature of telecommunication network setting due to the presence of vagueness and randomness of information. The model is formulated in such a way that it simultaneously considers the randomness in demand and determines the allocation of end users’ bandwidth requests into purchased capacity based on tax-band pricing scheme. As solution strategies, two different fuzzy operators, namely max–min and weighted additive max–min, are integrated into a resulting two-stage multi-objective stochastic linear programming model. Then, algorithms are provided to solve and to compare methodologies with deterministic approaches. Finally, the proposed algorithms are tested on several randomly generated test scenarios to provide managerial insight to decision makers of BB companies.