Push and Pull: Efficiency and Robustness
To illustrate efficiency and robustness in financial terms, consider a profit function of the form
Profit = p×throughput - h×WIPwhere p is a unit profit (not including inventory holding costs) and h is a unit holding cost. In push systems we control throughput (via releases) and observe WIP level. In pull systems we control WIP and observe throughput. In either case, we can seek out the control (throughput or WIP) that maximizes the profit level.
To make comparisons possible, we plot the profit as a percent of
optimal control. That is, for the push system, we find the throughput
that makes the profit as large as possible. Then we plot the profit
as a function of the ratio of throughput to optimal throughput. For
instance, when the ratio is 80 percent, this means the throughput is 20
percent below the optimum level; when the ratio is 120 percent, it is 20
percent too high. Likewise, for the pull system, we find the profit
maximizing WIP level and then plot profit as a function of the ratio of
WIP level to optimum WIP level. A ratio of 120 percent now means
that we have 20 percent too much WIP in the system. The results for
a specific example are shown in the following graph.
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Notice that when both systems are optimized, pull achieves a higher level of throughput than push. This illustrates the Pull Efficiency Principle. But even more important is what happens when the controls are not set optimally. When throughput is set 20 percent too low in the push system and WIP is set 20 percent too low in the pull system, the gap is even larger. And when both controls are set 20 percent too high, there is a huge advantage of pull over push. Since, by the Observability Principle it is more difficult to set throughput rate than it is to set WIP level (relative to their respective optimal levels), this robustness result is a major reason for the attractiveness of pull systems. They are simply easier to manage well.