A business case is needed to justify why replacement/additional resources are necessary in order to either maintain or improve service delivery for the University as a whole.
If your business case is not robust enough it could result in resource requests being denied. Writing a detailed and thought-through business case could save time in getting a position filled if you anticipate the questions that may be asked through the approval process.
The length of and detail within your case will depend on a number of things. Here are some of the areas that might help in putting a case together. Not all will be relevant but will give you a good starting point.