Last session, we saw how small changes in operational variables can have big financial rewards. One tool that helped us understand that relationship between operational variables and financial variables is the KPI tree, where KPI stands for Key Performance Indicators. Kpi tree is a powerful way to visualize the relationship between the many operational variables and the financial bottom line. Kpi tree is also the starting point for a sensitivity analysis, that will formally let us identify those operational variables that yield the biggest financial improvements. Let's go back to our restaurant example from the last session and see KPI trees in action. The number that we care about in the restaurant is the daily profit. What drives this profit? Profit is simply revenue minus cost. What drives the revenue here? Revenue is driven by the flow rate, the number of customers that we serve, times the dollars that we make per customer. In our example, there was $six per customer. Flow rate, in turn, is defined as a minimum between demand and capacity. The capacity is driven by the bottleneck because that was a step with the lowest capacity between stations one, two, and three. In our case, station two was a bottleneck and that was, in turn, driven by the processing time of station two which consisted of the time of putting the onions on the sandwich, lettuce, tomato, everything else to boxing the napkin along with the order. On the cost side of the business, we have fixed and variable cost. The variable costs are driven simply by the number of sandwiches that we make times the dollars per sandwich or the dollars per order. These, in turns, are driven by the ingredients in the sandwich, including the bread, the meat, the cheese, the vegetables and again, everything all the way up to the napkin. So, you can think of the KPI tree as basically one big mathematical equation that combines the many variables that showed up in our spreadsheet analysis before that ultimately drive profits, in one visual way. Evaluating changes in the leaves of the tree and predicting the impact on profits is the idea of sensitivity analysis. For example, we can ask ourselves, how much more profits do we make if we can put the onions on the sandwich pasta? How much more profit will we make if we reduce our fixed cost, if we would source our bread any cheaper? Mathematically, this correspond to a derivative. We take the partial derivative of profit with respect to an operational variable. In practice, however, as we saw in the previous session, evaluating the input of change is much easier and doesn't require any Calculus. All we have to do is build an Excel spreadsheet and evaluate the changes. Why was the impact of a productivity change so big on profits? Think about our business from a financial perspective. That's plot. Revenue and cost is a function of flow rate, our revenue is not quite simple. They go up at a slope of $six for every customer that we serve. Our costs, however, are a little different. Remember, that we have to pay $250 in terms of fixed cost, plus another $60 of labor. This amount of money we have to spend even if we don't sell any sandwiches. From then onwards, this line slopes up, but now at a much lower slope than the revenue curve. In fact, the slope is simply $1.50 per customer capturing our variable cost. You see that here, we have a point at which we start making money. This is typically called the breakeven point. In our baseline analysis in the previous session, we noticed that we were just beyond the breakeven point. We made a little bit of profit. However, from then onwards, adding an additional customer through the system has a very strong marginal effect. Every customer that we serve brings us $4.50 that go right into the bottom line. Is seduce worth the squeeze? Changing an operation is hard and there are many operation variables, that we could focus on. The KPI tree is a powerful tool that helps us identify those operations variables that we should focus on. The KPI tree is also a powerful visual that helps us understand the causal system that connects all these operational variables with the financial bottom line. So, I suggest to you that you always start any operational improvement projects by first, mapping out the process, drawing out the process flow diagram, then you do the process analysis, calculating the operational variables that we introduced in the first module, and then you build a KPI tree that help you understand how these operational variables drive financial performance.