Finding the Best Plan Within Limits

The idea

An optimization problem has three parts. The decisions: what I can change, such as the order of jobs. The constraints: what I must not break, such as safety rules or a machine's available hours. The objective: a score that defines best, such as the fewest hours late. A solver then searches for the choice with the best score. First-principles thinking (Reasoning From the Ground Up) helps here, because building the model forces me to say what the goal and the assumptions actually are.

An example

The Scheduling Optimization Lab on this site has seven jobs waiting for one machine, and switching between job types costs an hour of setup. Simple rules, like running the job due soonest first, beat most possible orders but still fall well short of the best one. Checking all 5,040 possible orders finds the true best for the lab's score. But that score is a choice: five points for each hour late, two for each setup, and a small amount for the finish time. Change those weights and the best order can change. The math is exact; the values behind it are mine.

What I think (and don't know)

Optimization finds the best plan for a model, but the world rarely holds still. When other people respond with goals of their own, the problem becomes a game rather than a calculation (Choices That Depend on Other People). Because the best plan on paper can be fragile when timing varies, I like to test it with simulation (Simulating a System Event by Event). And some things I care about, like love, should not be scored at all (Love Is Not Something to Maximize).

Questions I'm still exploring

• Which things I value can never be written into a score, and how should a plan respect them?
• When is a simple rule of thumb good enough compared with the best possible plan?
• How much should a plan give up on paper so that it holds up when things go wrong?

Sources and further reading

• Frederick S. Hillier and Gerald J. Lieberman, Introduction to Operations Research (McGraw-Hill)