Optimization: Objectives & Constraints

Optimization is maximizing a desired objective function subject to given constraint relations.

Hospitals have to make profit, otherwise they cannot grow, or buy new machines, or get better qualified (meaning more expensive) doctors. They must provide the best medical care and treat patients in a manner that does not offend the patient's dignity. Given that a hospital has positioned itself for a certain type of customer, in its day-to-day operation its charges are no longer a variable.

So what should be the objective function and what the constraint? Should it maximize profit under the constraint that patient care and handling does not fall below some minimum threshold? Or should it maximize the patient experience under the constraint of some minimum profit?

What of software companies? Should you maximize thruput (executable lines of code, function points) per person and minimize Quality (documentation, reviews, unit tests, ...) subject to the constraint that acceptance checks are passed? Or should you maximize Quality subject to the constraint of minimum thruput acceptable by the customer?

(True story: We once undertook work that the customer wanted done in 7 months. We said, we would deliver but without testing. The customer said that was okay as long as it was top quality. The project proceeded. After 7 months till about another 18 months all lived through interesting times.)

What we choose as objective and what we set as threshold for the constraints depends on how we see ourselves. It is what we are - and are not. It is about our values.

One objective is not intrinsically superior to another. What is important, however, is that objectives, and constraint limits, must be consistent through out the organization. That is what forms the culture of the organization.