Multi-service mesh networks allow existence of guaranteed delay Quality-of-Service (QoS) traffic streams such as Voice over IP and best effort QoS traffic streams such as file transfer. We present an optimization that performs a linear search for the minimum number of TDMA slots required to support the guaranteed QoS flows. At each stage of the search a linear integer program is solved to find if there is a feasible schedule supporting the required end-to-end bandwidth and delay. Our optimization results in a relative order of transmissions in the frame that guarantees a maximum end-to-end delay in the network. The ordering of the transmissions can be used later to find feasible schedules with the Bellman-Ford algorithm on the conflict graph for the network. We use the optimization in numerical simulations showing the efficiency of 802.16 mesh networks with VoIP traffic.