In this paper, we study the impact of different resource allocation schemes, transmission coordination mechanisms among base stations, and user association rules in the context of the downlink of a heterogeneous network comprising of a macro base station overlaid with a pool of low-power pico base stations. We formulate flow-based models for the joint optimization of resource allocation, user association, user scheduling and transmission coordination under a proportional fair throughput objective for two types of resource allocation, i.e, Full Sharing (FS) and Channel Splitting (CS), and two types of transmission coordination, i.e., no coordination and ONOFF coordination. Our formulations allow us to obtain exact solutions for small to medium sized networks. The numerical results show that the performance of FS without transmission coordination among BSs is much worse than CS without coordination. However, FS with our coordination mechanism performs as well as CS with coordination. Interestingly, FS and CS with coordination do not perform much better than CS without coordination. Our study provides a message that we might not need to go for the complexity of transmission coordination among BSs depending upon the resource allocation scheme.