Result 4: The Spring-Damper Hybrid Model

I combined the "spring" model and the "damper" model and got some interesting results.

First, let's see what happens to the average cost when you add damping mechanism to the spring-only model.

Figure 1: Average cost vs. Sensitivity (to the "spring" term)

It widened the range of sensitivity coefficient (to the "spring" or the inventory level itself) for small Sensitivity Coefficients.

Next, what happens to the effect of target inventory on the cost-minimizing Sensitivity Coefficients?

Figure 2

Although it hard to see in this figure, it did decrease the global minimum cost a little. It also lowered the cost for small Target Inventory levels.

So, what the behaviors of inventory levels at the global minimum when you add an anchoring mechanism to the damper-only model? First, recall when there are only dampers in the chain, it looks like:

Figure 3

By adding a "spring" to each node, it now looks like:

Figure 4

Clearly, the fluctuations are repressed even more, backlogs have been reduced and the four inventory levels are really moving together now.

This is the best result I could get with the spring-damper hybrid model.