Quantum communication networks are emerging as a promising technology that could constitute a key building block in future communication networks in the 6G era and beyond. These networks have an inherent feature of parallelism that allows them to boost the capacity and enhance the security of communication systems. Recent advances led to the deployment of small- and large-scale quantum communication networks with real quantum hardware. In quantum networks, entanglement is a key resource that allows for data transmission between different nodes. However, to reap the benefits of entanglement and enable efficient quantum communication, the number of generated entangled pairs must be optimized. Indeed, if the entanglement generation rates are not optimized, then some of these valuable resources will be discarded and lost. In this paper, the problem of optimizing the entanglement generation rates and their distribution over a quantum memory is studied. In particular, a quantum network in which users have heterogeneous distances and applications is considered. This problem is posed as a mixed integer nonlinear programming optimization problem whose goal is to efficiently utilize the available quantum memory by distributing the quantum entangled pairs in a way that maximizes the user satisfaction. An interior point optimization method is used to solve the optimization problem and extensive simulations are conducted to evaluate the effectiveness of the proposed system. Simulation results show the key design considerations for efficient quantum networks, and the effect of different network parameters on the network performance.