Daya
You mention a few things that aren't correct.
"It was not good practice to deploy inly 1 job server for multiple developer." - it IS normal practice to do this and most installations will have this, only with a high number of concurrent users, and/or adapter usage would multiple job servers be required.
"If you execute the job from multiple designer then it will take maximum time for execution because if one Job will complete then only other will start." - job execution is not synchronous, multiple jobs can always be executed in parallel.
"If you schedule also then it will take more time for completion" - I'm not sure why you think this, it is also wrong.
"Create Server Group for each department and add department job server in each server group" - server groups are only going to help if you have multiple servers to distribute the load, a little pointless on a single server.
Michael