What is a good probability distribution to model fluctuating demand? Is the Normal distribution applicable? How can you estimate a probability distribution when history is unreliable?
Understanding demand variability is key to setting an inventory strategy. Demand variability directly affects the safety stock calculation. Demand variability and shelf life interact to affect production frequency, thus affecting cycle stock. An accurate model of demand variability is essential, especially if you have products with limited shelf life that will lose value if demand is less than expected.
This is the second in a series of blogs on the topic of lot sizing to determine optimal batch quantity for production or ordering in uncertain times. The first blog in this series covered the traditional methodology for Economic Lot Size (ELS). Upcoming blogs will show how to integrate traditional ELS with the demand distribution covered in this blog and how to estimate a demand distribution when history is unreliable.
What is the best probability distribution to use for demand variability?
The Normal distribution is so engrained into business and engineering training that we often default to it for everything. However, it may not always be the best probability distribution to use in modelling demand fluctuation for a given time period. If the mean is several standard deviations above 0, the Normal distribution probably works OK for this application. But if you are modelling low volume items, you will probably find that the Normal distribution incorrectly models a significant tail of probability of less than zero demand.
I have had good success using the Gamma Distribution to model demand variability. A key feature of the Gamma distribution is that it cannot have negative values. You cannot have negative shipments (some systems show customer returns as negative demand, however for Demand Planning they should be ignored or treated as a reductions of the original shipment). Figure 1 illustrates the flexibility of the gamma distribution for different types of demand situations. For higher volume items gamma distribution can very closely resemble the normal distribution, but it also works well for lower volume items that tend to be more skewed.
Gamma distributions are defined by two parameters, alpha & beta.
Mean = alpha * beta
Standard deviation = beta * sqrt(alpha)
The gamma distribution can easily be applied to inventory analysis in Excel using GAMMA.DIST(x,alpha,beta,cumulative) for cumulative distribution function or probability density function.
Have you used the gamma distribution to model demand variability? If so, please comment below on how you applied it and what your results were.
References
T. A. Burgin, 1975. The Gamma Distribution and Inventory Control Operational Research Quarterly (1970-1977), Vol. 26, No. 3, Part 1 (Sep., 1975), pp.507-525
R. D. Snyder, 1984. Inventory control with the gamma probability distribution European Journal of Operational Research Volume 17, Issue 3, September 1984, Pages 373-381
Ashkan Mirzaee, 2017. Alternative Methods for Calculating Optimal Safety Stock Levels