Humans are a passive species. Well, maybe not really. I mean that when there are 10 jobs to be done people will get 10 jobs done, and when there are 20 jobs they will get 20 jobs done.
What if your company is full of people who will take on what they are given but don't like to go out of their way to accept more work? Take the process we proposed in the post titled, The Ever-Changing Inquiry Management Process; you might find your customer service department full of "unresolved inquiries."
So how do you ensure inquiries are resolved in a timely manner? Put simply, you make sure all the work is always assigned to someone. In other words, there will be tasks that are [A] already owned by someone (in the "Allocated" state), and tasks that are [B] waiting for someone to accept them (in the "Offered" state), so you just get rid of the latter types, one by one.
Most workflow systems are equipped with a way to allocate work outside the system, as is Questetra BPM Suite. Another thing you could do is include the function into the workflow itself. Leaders can consider the content and difficulty of each inquiry, as well as the workload and expertise of each employee, when assigning each incoming task. Just keep in mind that if all leaders are on vacation, this workflow won't flow.