In Lorex, we are looking at a situation in the workplace where we can potentially utilize the concepts we are talking about this week: how to frame/describe a pool of values into a kind of distribution, then utilize that for decision making.
1. every time we produce a batch of bottles of the new drug, we are concern about what would be the number of rejects. It is because rejects are costly in the sense that we have to sell them at a lower price. So, the first question is if we were to produce a batch with a certain fill-target, how many defects should we expect?
2. If we know how many to expect, then we can calculate the revenue associated with the batch and also the related costs. Then we can estimate profit.
3. The decision on what should be the fill target should depend on the profit level associates with each. For example, we know that if we have a higher fill target, the we should expect less defects. But to go with that is the average cost of the ingredients used in each bottle will be higer. It is a matter of which one is higher.
In order to deal with these type of operational issues(which organizations have to do a lot) you have to follow some framework for analysis.
Step 1:What are we trying to decide?
We certainly want to know what fill target should we recommend. The issues is that defects(bottles that are under 10oz will cost 20% of price). But on the other hand if we target a high fill target, it costs more in ingredients. So we need to understand the trade-offs.
Step 2:How would you measure it?
In this case we should be concern about profit. But it is not always the case because in operations, a lot of times we only worry about the cost. But since we are given the price etc, we can use profit as what we want to measure in order to decide what target level we recommend.
Then one of the questions we need to address is the defective rate. In order to understand this, we need to know if we start the machine rolling, what will the volume of the bottles be like? That is why they sampled 144 bottles. As you can see the weight of the bottles, based on the sample, varies. For the sample, they targeted 10.2oz, the bottles were all over the map with 12 of the bottles under 10oz(defective). If you plot the 144 bottles, it kind of centered around 10.2oz(as expected or else something else is wrong with your machine). Well, it does look kind of like a normal distribution. If you think it is good enough to be considered normally distributed, then life is relatively easy for you. Because if you target 10.2oz, with a standard deviation of .16oz(measured in the sample), you can theoretically find out what percentage of your bottles will likely be under 10oz. In this case, it is about 10%. But you don¿t have to assume that it is normally distributed. You can always use 12 out of 144 as your defective rate(8%) as observed in the sample run. Then you problem is then what about 10.3oz, 10.1oz? For example, I know the shampoo folks in Downey for Unilever simply makes run for different fill target and then observe the defective rates. There are plus and minus for that. For Lorex, let say we can assume that they are normally distributed. IF you are real picky, you can use Chi-Square Statistical Test to validate that. We will cover that at a later time in this course. By the way in Excel, there are all kinds of functions that can calculate the % for you. It is under FUNCTION.
Now that we know the potential fill target and corresponding defective rate of the bottles(just an estimate), we can move on and try to figure out the profit correspond to each potential fill target.
Step 3:Data Collection
We know most of the data (someone collected that for us). But we have to massage them. For example, how do we calculate revenue, costs, etc.
Step 4:Analysis.
Because we have most of the data we need, including pricing information, we can make our decision base on profit estimates. It is appropriate to set up a P&L statement(Profit & Loss) so we can examine profit at different fill level. We know as we increase our fill level, we will use more ingredients but also reduce defects.
First we have to decide on a time period or quantity, and I would suggest one batch. Because the cost figures are by batch. Each batch will yield about 169,088 oz. We can then calculate how many cases we can fill with a specific fill level, then we can calculate the defective rate(discussed before), then we can calculate the revenue. Ingredient cost(and all other blending related costs) per batch is the same for all levels. But the filling costs(labor, materials, overhead) are dependent on the number of bottles/cases and should be adjusted according for each fill level. So is re-packaging cost for seconds.
Step 5:Decision.
With the cost information calculated, then we have the profit estimates for each fill targets and then we can make our decision based on that. What we have to be careful is that we are not looking at service levels here. We are assuming no goodwill cost and the only penalty for defects is the reduction in price. Also, we are assuming that we can sell everything we produce, including unlimited amount of defects.
As you can see there is nothing that you don't already know technically. But learning how to frame and approach the problem is a different story. Please give it a try and post your spreadsheet and questions here so we can discuss.
One approach is that in order to estimate defective rate(bottles under 10oz) for different fill levels under consideration, they counted the number of bottles that were defective and convert that to a percentage. Since the sample was for 10.2 oz fill target, then for 10.3 fill target, just add .1oz to each one of the 144 weights. Now that is one approach.
Another approach is mine where I just assume that the bottles produced in the long run would be normally distributed. Then I can use the mean and std dev and use the NORMDIST function in Excel to calculate the defective rate for each fill target under consideration.
Of course, as I mentioned in my posting that some companies(such as Unilever's shampoo production in Downey) will just make multiple sample runs of 144 for each of the potential fill target, count the defects for each and use that percentage.
These are just three different ways of doing it and obviously have pros and cons for each. For example using my way, the defective rate for 10.2oz fill target was 10.56%. The First way will yield 8.33%. Big difference in this situation.
I want to talk a little about the pros and cons here. Please feel free to comment.
My way of assuming normalcy, it is easy to do calculation but I need to be quite sure that I can assume normalcy or else all the calculation will fall apart. The first way is basing more on the sample truly. But think what if that sample was really not too representative, it would create wrong assumptions. The Unilever way is better than the First way but more costly because you hae to make all those extra runs of 144. Which one is better? No such thing. Just depends on your rationale and tendency. But I am sure you appreciate the fact that choosing one instead of another can significantly impact your decision. So, often times you can't look for just one correct answer. Difference in perfectly acceptable approaches can change the decision completely.
In order to compare the different fill target level, in order to compare apple with apple, we need to decide on a fixed amount of output so we can compare gross margins. We can compare the gross margins for different fill target levels based on one bottle of production, or a case. A case probably would make more sense. Or we can choose gross margin for a month as comparison. Another choice is to calculate gross margin by batch(5000 liters). This would be probably more logical because most of the cost figures are by batch. But if you are doing it by batch, you have to remember that the blending costs are not going to change if you change fill target. But depends on the fill target, the filling costs and seconds packaging will be different because these are based on the number of bottles.
For easy comprehension, I would suggest by batch.