A quantum network allows us to connect quantum information processors to achieve capabilities that are not possible using classical computation. Quantum network protocols typically require several entangled states available simultaneously. Previously, an entanglement generation process was analysed where, at each time step, we generate an entangled state with success probability p. Here, we consider adaptive entangled state generation with more flexibility. At each time step, our process chooses a protocol (p_i, F_i) from a discrete number of entanglement generation protocols. An entangled state is generated successfully with probability p_i, and its fidelity F_i defines how close the entangled state is to an ideal Bell state. The new state is subject to depolarising noise in the quantum memory. Because of the memory noise, states are discarded after a certain number of time steps t_i when they are no longer useful to our application. We model our process as a Markov decision process and derive a policy π to generate n entangled states with minimal expected time Eπ[τ]. We analyse the offered improvement of the optimal policy of our adaptive entanglement generation process over the previously studied static process. We conclude that this improvement becomes more significant as the required number of links in memory increases.