What is goal-seeking behavior?

Goal-seeking behavior is the pattern in which a quantity rises or falls toward a goal and approaches it ever more slowly. It is produced by a loop that measures the gap between the goal and the current state and acts to shrink it. It matters because it describes thermostats, inventory control, hiring, and budgets, and shows how fast a system can reach a target.

How it works

The structure is a balancing feedback loop. The correction each period is the gap divided by an adjustment time. A larger gap gives a bigger correction, so progress is fast at first and slow near the target. The curve is an exponential approach, and after about three adjustment times the system has closed roughly 95 percent of the gap.

With a delay in the loop, the correction acts on old information. The system may then pass the goal and swing back, which is oscillation instead of smooth approach. Another cause of missing a goal is a goal that itself drifts downward when it is not reached. The first things to ask about any goal-seeking system are what the goal is, how the gap is measured, and how long the adjustment takes. The equilibrium is reached when the gap is zero.

Example

Say a warehouse wants 1,000 units in stock and holds 400. The adjustment time is 5 weeks, so each week it orders (1,000 − 400) / 5, which is 120 units. The gap falls to 480 and the next order is 96, then 77, and so on. After 5 weeks stock is about 800, and after 15 weeks about 950. This is an illustration with round numbers.

How to model it in Machinations

Use a Pool for the stock and a Register for the goal. A Source feeds the Pool at a rate defined by a formula: goal minus Pool, divided by the adjustment time. Play and chart the Pool. Use a Lever on the adjustment time to compare slow and quick approaches.