Heh, at my school we call IE's "Imaginary Engineers". But in all honesty, it's a pretty broad program and if I were to get a dual major in another engineering discipline, it'd be IE probably (I'm an EE).
It is kind of a dying field though (if not in the workforce, than at least in school there's a lot less people in it now than before).
As to what they do, here's a pretty good definition that I found:
Industrial engineers (IEs) figure out how to do things better. They engineer processes and systems that improve quality and productivity. IEs make significant contributions to their employers by saving money while making the workplace better for fellow workers. In addition to manufacturing, industrial engineers apply their skills in a variety of settings. Here are a few examples:
As a management engineer in a hospital, you may help doctors and nurses make the best use of their time in treating patients. You may also design procedures for optimum use of medical facilities to help bring the cost of healthcare down.
As an ergonomist in a television manufacturing plant, you may change the tools workers use to assemble televisions to reduce the risk of repetitive stress injuries.
As an operations analyst for an airline, you may design a bar coding system for identifying and transporting passengersâ?? luggage to ensure that it does not get lost.
As a quality engineer for a public gas and electric company, you may improve customer satisfaction by designing a process to schedule service calls around the availability of the customer.
So you can probably see why they're referred to as "Imaginary Engineers". Typically there is not much R&D involved and that's what is generally thought of as the core of engineering (it's what I think of anyway). It's more about efficiency, which is certaintly important. Just not what you think of right away when you hear "engineering". Hope this helps, good luck.