Executive Summary:
A new approach to estimating demand for products and services has been created by Professors Ed Fox, Bezalel Gavish, and John Semple of SMU Cox. The "truer" demand curve has the potential to revolutionize business by allowing organizations to estimate and forecast demand quicker and more accurately.
Background
For decades, companies have typically estimated demand using the normal distribution with its classic bell-shaped curve. A more sophisticated distribution is the lognormal, particularly when demand data is not symmetric, such as when it's heavy-tailed or skewed. The lognormal distribution usually fits the demand data better, resulting in better forecasts. This becomes important for managers deciding how much inventory to carry and staff to schedule. Not enough inventory or staff means lost sales; too much inventory or staff means unnecessary costs.
The authors derived their distribution from first principles, focusing on the purchase timing of individual customers. Fox explains, "If we have detailed data about customer transactions, the time between those transactions can be used to derive a distribution for total demand." He continues, "So, we started with the timing between transactions. We then derived the Birnbaum-Saunders (BISA) distribution (normally used in fatigue life studies) as an appropriate distribution for counting demand (and is well suited to many business uses). This distribution fits the demand data better than standard or even lognormal distributions. We approximate the true demand distribution, if you will, by going back to first principles."
Using the BISA
The authors exploit two types of estimation techniques for the BISA distribution: BISA-I, which is estimated using transaction time data, and BISA-S, which is estimated using sales data. The proliferation of electronic scanning devices in retail cash registers and electronic ticket dispensing devices in queues enables the widespread collection of transaction time data. Because BISA-I is tied to transaction time data, you can predict overall demand quickly and accurately. Fox explains, "If we know the time between transactions, we can tell you for any time period-whether it's a day, week, or month-what the demand distribution will be. Additionally, we can get the shape of the demand distribution much more quickly. If there are 20 sales a day, we can tell you the demand distribution within a week (given the transaction times) whereas it might have taken months to forecast using just sales data." BISA-I gives you an idea about the shape of the demand distribution (curve) quicker.
Managers setting inventory levels or forecasting may use either BISA-S or I. Both may be applied to other counting processes, too. For example, one could use the BISA to model the number of patients (or customers) walking in the door, maybe for emergency room staffing decisions. "We plan to use the BISA-S with data we have from 7-Eleven stores," say Fox. "We want to see how price changes, weather, and other variables impact demand; and then we will see if 'the fit' improves." These demand analysis methods could also be used in the natural sciences, social sciences, or in other disciplines where the time between transactions can be determined or things can be counted, which is most anything. One could even count the number of sunspots.
The Important Tail
Does BISA-S work better with higher counts? Frequent sales, like in coffee shops, work best; sales of diamond necklaces at Tiffany's would be tough. Fox says, "The more sales data, the better it works-where counts are higher. You especially care about what's going on in the upper tail (when the counts are highest); that's where demand is greatest. The normal distribution underestimates what's going on in the upper tail, when it matters, as does the Poisson distribution." He continues, "In this case, you would have stock-outs and understaffing. This is where the action is. If you want to be in stock 95 percent of the time vs. 90 percent of the time, you care about being accurate where demand is highest. Our model fits considerably better when demand is high, and can thus forecast better for capacity planning decisions."
One important motivation for the authors' research was that sales are not an accurate representation of demand if there are stock outs. No sales are possible after the available inventory is used up, essentially slicing off the demand data. Researchers and practitioners have been trying to fill in the missing part. Fox adds, "If you look at transaction data and the timing of sales, it's only the last one before a re-stock where you could have been out of stock. So, the relationship between time of purchase and counts can tell what demand would have been had there not been an out-of-stock situation. You can also reverse this scenario and say item by item how long you were out of stock. With this method, managers can also determine when sales were lost, even without observing an out of stock."
Firms make their decisions about inventory and staffing when demand is highest, and the BISA distribution fits better in high demand situations than other distributions. This new methodology therefore has the potential to change how demand is modeled and how countless decisions are made.
"Robust Count Distributions with Application to Demand Modeling" by Edward Fox, Bezalel Gavish, and John Semple of SMU Cox is under review.
Written by Jennifer Warren. |
