I recently encountered a postponement/pooling issue that I thought I'd make an example out of. The following problem explains how postponement can result in pooling for a product with a steady lead time, known average demand, and known standard deviations of that demand. In other words, you know exactly how long it takes you get it and you have a very good idea as to how many you will sell.
There are two main products. The DD1 and the DD2. The DD1 has a production time of 19 days with an average daily demand of 1,000 and a daily standard deviation of 180 units. The DD2 has a also has a 20 day production time, average weekly demand of 1,200 and standard deviation of 200 units. We want to find out what the optimal safety stock levels should be. Both products have a 98% service level set.
If you recall, the safety stock formula has two terms. The first term is the cycle stock and second term is the safety stock. We are only going to look at safety stock (choosing to ignore cycle stock because this model has little affect on the cycle stock investment). The term in the inventory equation for safety stock can be rearranged so variations in lead time are not taken into account, which is perfect for this example because lead times are constant. The following formula is that variation:
Safety Stock=z*standard deviation*SQRT(Lead Time)
z is a statistical tool used to correllate service level with standard deviations. In order to find a z-value for a 98% service level, use the following formula in Excel:
This equals 2.05
Now we have the inputs we need for our safety stocks:
DD1 Formula Inputs
Lead Time=20 days (this is the production time and in considered the lead time because it is the time it takes to make more units if all units in production run out).
DD2 Formula Inputs
Lead Time=20 days
Total safety stock inventory is 3,490 units (sum of DD1+DD2)
This is localized optimization for inventory without postponement. The next post will discuss the inventory model when postponement is put into place.