Sumif And Data Sorting.

I have 3 worksheets in the same workbbook named Payment Distribution, Invoice Detail, and Corporate Phones respectively. Payment distribution has 3 columns (Corp, Dept, Cost). This worksheet is protected against changes. Invoice Detail has 2 columns (Deptartment, Charges). This worksheet is a workable worksheet.
Corporate PHones has 4 columns, (Phone #, Dept, Name, charges) with mulitple listings per row.

SUMif is used in the Invoice Detail worksheet for the department numbers and the subtotal of those charges for department numbers. The Payment Distribution worksheet contains a reference to a cell in Invoice detail for that department.

If I add a new department listing to Invoice detail and then sort the department numbers numerically, how can I get the forumla for SUMif to maintain the same no matter how I sort the data? It is causing issues if I sort the departments numerically if I add the new department to the bottom of the list.