How much should I make when product has a fixed shelf life? I should be OK if production does not exceed what I can sell on average before it goes out of code, right? As Johnny Carson might have said, “You are wrong, bell curve breath!”
We live in a world that talks about averages all the time. We assume if the expected average result meets our requirements, things will turn out fine. That is not necessarily true. If it takes an average of 30 minutes to get to work, you should be fine leaving the house with 5 minutes to spare, right? What if the average includes a one in five chance of being stopped by a train for ten minutes? Four out of five days you can get to work in 28 minutes and one out of five days it takes 38 minutes. What time would you leave?
In real life, demand for your product fluctuates. Because of the demand variability, there can be significant risk of obsolescence even when the production run is much less than average demand. The best way to model this variability may be a gamma distribution (see my prior blog: A Probability Distribution for Demand Variability). If so, the gamma probability density function can be used to estimate the expected number of units that will become obsolete for a given starting inventory. See how to calculate the expected obsolescence here.
Using the Gamma Distribution to Determine Expected Obsolescence
Figure 1 shows an example where minimum run of 525 units is less than average demand. In this example demand (sales) has been averaging 200 units per month. The shippable life is three months after manufacture before the customer will no longer accept the product. Average demand of 200 units per month equates to 600 units over the three month shippable life.
It might seem OK to produce 525 units when you expect to sell 600 before it ages out. However, when the variability of demand is considered it becomes clear that there is a significant risk of obsolescence. With a standard deviation of 100 units per month, there is a 36% risk of obsolescence from each run. On average, the expected obsolescence is 35 units out of each run of 525 units.
In considering the potential obsolescence for a given production lot size, starting inventory must include all product in the network, including remaining inventory from prior production. Assuming proper rotation, the oldest inventory will be used first. However, if there is older inventory a more complete analysis would consider each lot of inventory separately.
Figure 2 shows the expected units of obsolescence for different values of starting inventory in the above example. Expected obsolescence is 0 cases for starting inventory of 280 or less. Above 280 it is an increasing curve.
If risk of obsolescence were the only concern, it would be a simple matter to determine the lot size for a given desired probability of obsolescence. This could easily be done using the inverse gamma function in Excel (GAMMA.INV(probability,alpha,beta)). In the example above, the lot size for a 5% probability of obsolescence would be 346 units. However, expected cost of obsolescence is only one factor in determining production lot size.
Other costs for consideration in setting lot size include the changeover (setup) costs and cost of holding inventory. These factors come together in traditional Economic Lot Size (ELS) calculations. For more information on traditional ELS, see my prior blog: how-much-is-enough-without-being-too-much. My next blog will show how to integrate demand variability with traditional ELS calculations to balance the risk of obsolescence and inventory carrying costs with setup costs.