In the health system inefficiency leads to poor use of scarce expensive resources. Lengthy patient treatment waiting time can result from inefficiency in scheduling. The use of state-of-the art multi-agent and distributed computing technologies can provide a solution to address this problem. However, distributed optimisation in such a multi-agent setting poses an important challenge that requires protocols to enable agents to optimise shared objectives without necessarily revealing all of their private constraints. In this study we show that if the problem is expressed as a Dynamic Distributed Constraint Optimisation Problem a powerful algorithm such as SBDO can be deployed to solve it. As SBDO can be deployed in a grid all of the advantages of grid computing are also gained.