What is "Productivity?"

In one of my stats classes, a nursing student mentioned that they measure productivity at her hospital. It's measured this way:

"To get the productivity ratio; you take the total number of hours worked by nursing ( all nurses on the unit) and divide that by the total number of patients on the unit at midnight. For example if there are 4 nurses per shift and they work 12 hour shifts then that is 96 hours; then say there are 30 patients on the unit at midnight; divide 96(nursing hours worked) by 30(# of patients) = 3.2."

In my consulting practice, my clients often tell me about productivity numbers. This, to me, is one of the compelling questions for those of us in the quality profession: what is "productivity?" To keep the discussion going with my student, I posted the following, to raise some of the issues I've seen organizations struggle with over the years:

This is one problem with many of the metrics used for "productivity." By trying to boil it down to the simplest, easiest to use ratio, you leave out a lot of important information. What is productivity in nursing? Is it just being there? Clocking in and clocking out? Most of the nurses I know work pretty hard, but even the amount of work completed wouldn't necessarily reflect the value of a nurse. A number of years ago, a paradigm came out called ABC (for Activity-Based Costing) that measured productivity in terms of activity...how much were you actually doing? Seems reasonable, but it doesn't necessarily reflect value, any more than motion reflects progress.

Nursing can be a lot like being in the Military. I can't tell you how many watches I stood in 20 years...tens of thousands of hours where no one took a shot at anyone. If my job was to kill enemies, then most of the time, I was a waste of taxpayer dollars. Did that mean we didn't need to be there? Our job was not to be constantly doing something, but to be alert and vigilant so that if something did happen, we could take immediate action.
Similarly, there are nights, even in Emergency Rooms, that are slow. Would you send everyone home, to keep your productivity numbers high? Or is there value in having some knowledgeable and experienced caregivers there for the probable event of an emergency?
What is the productivity measure tied to? Can you show that a higher ratio correlates to better outcomes? Higher profits? If it's just cost-cutting, it's hardly "productivity;" it's just lack of having to pay for "non-productivity."
The point is, productivity is difficult to measure, and productivity is in the eye of the recipient. What the patient may value, the administrator may not. What the doctor may value, the HMO may not. What the nurse may value, the patient may not (one example; waking a surgical patient up every hour during the night to check vitals).

Of course, I guess the whole point boils down to value...who defines that, how you prioritize the "whos." This is where you must be able to understand something about systems thinking.