Graduation season is just around the corner. It’s the time of year when local grocery stores and discount retailers sprout seasonal aisles filled with tassels, mortarboards, and congratulations signs. For stores that rely on these kinds of seasonal sales, it’s an important time of year – but it can also be a difficult planning task: What’s the right number of seasonal items to stock?
The question reminds me of the classic “newsvendor problem,” one of my favorite cases from business school. Imagine you’re a street vendor looking to sell newspapers, and you have to buy your newspapers at the start of the day, before you know what the demand will be for the papers you’re looking to sell. How many do you buy? If you under-stock relative to demand, you miss out on valuable sales that you could have made. On the other hand, if you over-stock relative to demand, you’re stuck holding leftover newspapers that you’ll be unable to sell tomorrow because they’re literally “old news.”
To imagine a more realistic scenario, consider stores stocking decorations for graduation season. If a particular store runs out of festive decorations before the end of the season, they lose sales to competitors and may even lose customers in the long term. Conversely, if they buy too much and have stock remaining after the season, they must generally sell the excess inventory at a steep discount – potentially at a loss.
The Hypothetical Scenario
The “newsvendor model” helps find the right balance in cases like this. To see how it works, imagine that our client is Hank’s Grocery and is weighing whether to buy a batch of decorative tassel table-toppers. Assume it would cost Hank’s $0.50 per unit purchased, but Hank’s could sell each unit for $1.00. Unfortunately, any quantity that is purchased but remains unsold after the season would have to be put on clearance at the deeply discounted price of $0.25 per unit – in other words, sold for a loss. Hank’s marketing team has estimated that there would be demand for 2,000 table topper units, but given uncertainty puts the standard deviation at 500.
Our hypothetical, normally distributed demand would look something like this:
How many table toppers should Hank’s purchase? Our goal is to balance the cost of over-stocking and the cost of under-stocking. We do this by comparing the marginal benefit of selling one more unit (i.e., the retail price minus the wholesale cost) to the marginal cost of over-stocking (i.e., the retail price minus any “salvage” value). The formula, which provides what is called the optimal service level, looks like the following:
In our case, ($1.00-$0.50)/($1.00-$0.25) = 0.667. Note that this gives you the optimal service level, not the optimal quantity. To translate the optimal service level into a quantity, we need to look back at our demand distribution.
Looking at our demand curve, we need to find the quantity at which the cumulative probability of demand is 66.67%. You can find this quantity in two ways: First, you can create a demand table like the one shown below that maps out the demand, probability of demand, and cumulative probability based on the specified distribution. Second, you can use Excel’s normal distribution functions (since I’ve assumed demand is normally distributed). In this case, using the NORM.INV function along with our demand curve’s mean (2,000) and standard deviation (500) shows that Hank’s should purchase 2,215 table topper units (i.e., =NORM.INV(0.667,2000,500) = 2215).
Putting It to Work for You
The newsvendor model applies in any situation in which an optimal inventory level needs to be determined before demand is known, by balancing the costs of over-stocking (e.g., product obsolescence, holding costs, etc.) against the costs of under-stocking (e.g., lost sales, dissatisfied customers, etc.).
At Credera, we use the newsvendor model and similar frameworks to help our strategy and ecommerce clients think through their company’s unique business challenges from a quantitative perspective.