Resource allocation with quality of service constraints is one of the most challenging problems in elastic optical networks which is normally formulated as an MINLP optimization program. In this paper, we focus on novel properties of geometric optimization and provide a heuristic approach for resource allocation which is very faster than its MINLP counterpart. Our heuristic consists of two main parts for routing/traffic ordering and power/spectrum assignment. It aims at minimization of transmitted optical power and spectrum usage constrained to quality of service and physical requirements. We consider three routing/traffic ordering procedures and compare them in terms of total transmitted optical power, total received noise power and total nonlinear interference including self- and cross-channel interferences. We propose a posynomial expression for optical signal to noise ratio in which fiber nonlinearities and spontaneous emission noise have been addressed. We also propose posynomial expressions that relate modulation spectral efficiency to its corresponding minimum required optical signal to noise ratio. We then use the posynomial expressions to develop six geometric formulations for power/spectrum assignment part of the heuristic which are different in run time, complexity and accuracy. Simulation results demonstrate that the proposed solution has a very good accuracy and much lower computational complexity in comparison with MINLP formulation. As example for European Cost239 optical network with 46 transmit transponders, the geometric formulations can be more than 59 times faster than its MINLP counterpart. Numerical results also reveal that in long-haul elastic optical networks, considering the product of the number of common fiber spans and the transmission bit rate is a better goal function for routing/traffic ordering sub-problem.