What should the new organizational structure look like? Where should I put each person, specifically managers?

The new structure will use matrix organizational form as follows:
1. All managers will be under ISD Director directly including Project Manager X and Project Manager Y.
2. Associate Director position will not be needed.
3. Project Manager X and Project Manager Y will cross their project responsibility with the line management functional responsibility to give project managers more authorities and to have a balanced power between line and project managers. This balanced power will be beneficial in sharing the resources of the Operations Manager who controls more than 50%.
4. The supervisors and secretary pool can be realigned to be under the Administrative Services Manager.

When should I announce the new organizational change? Should it be at the same time as my appointment or at a later date?

You should announce the new organizational change at same time as your appointment so that the employees can adjust and plan accordingly. Also, this will show that you have an insight and you are aware of the current potential problems of the ISD. The announcement should made in a way that provides an idea to all employees within the division that there will be an upcoming change to the organizational structure and their input will be appreciated and considered.

Should I invite any of my people to provide input to the organizational restructuring? Can this be used as a technique to ease power plays?

Yes of course you should invite them and collect input. By doing this, they will feel that they have contributed and added their personal touch to the change which will limit the resistance and increase the support. In addition, this technique will show that you are not enforcing the change but you are solving the problems that have impacts on the entire