9.8 Tools: Newsvendor Model

Take a look at Figure 9-10. So far, we have focused on how you make decisions for items that you hold in inventory for weeks, months, or even years. But, you can't hold some things—like newspapers or fresh foods—in inventory indefinitely. High-tech and fast-fashion items also become obsolete quickly. For these "perishable" products that are unsaleable after a very short shelf life, the is the tool you need to use.

Figure 9-10: Different Inventory Models: Newsvendor Model

Imagine you own a newsstand. Every day, you have to decide how many newspapers you should order from the publisher for delivery and sale the next day. You have some idea of what customer demand for tomorrow's newspaper might be, but you cannot be sure. In this context, what costs do you need to consider? Ordering and holding costs are no longer relevant. You have to order every day and old news has no value. However, two costs are relevant to your decision:

: If you order too few newspapers, you will incur stockouts.
: If you order too many newspapers, you will be left with unsaleable newspapers at the end of the day.

Figure 9-11: Newspapers, like Flowers are Perishable.

By now, you probably see where the term "newsvendor model" comes from. Despite the name, the model is useful whenever you place a single order for each selling season (one day for a newspaper). For example, you would use the newsvendor model for the following: gowns for graduation day, desktop calendars for next year, flowers for Valentine's Day, costumes for Halloween, and Christmas trees for Christmas. All of these examples share the two key features:

Your customers will only buy these products during a limited selling period.
You need to make stocking decisions knowing that future replenishments may not be possible (after all, you can't just grow a Christmas tree if inventory is running low by December 22nd).

As you might guess, the newsvendor model is sometimes referred to as a single-period model.

How does the newsvendor model work? When managing perishable products, your goal is to minimize total costs by trading off the costs of understocking and the costs of overstocking. In a newsvendor context, the amount of inventory you want to hold is determined by your optimal in-stock probability [F(Q*)]—that is, how often you want inventory to be in stock. The optimal in-stock probability is defined by what is called the :

F (Q^{*}) = \frac{C_{u}}{C_{u} + C_{o}}

Where cU is the cost of understocking per unit and cO is the cost of overstocking per unit.

Let's return to our newspaper example and calculate the optimal in-stock probability. You have calculated the following:

The cost of understocking is $0.50—the profit you lose for each out-of-stock newspaper.
The cost of overstocking be $0.30—the money you paid to purchase a single newspaper from the publisher ($0.20) and the cost of disposing of a leftover copy ($0.10).

These numbers would yield an optimal in-stock rate of 62.5%. The formula is:

F (Q^{*}) = \frac{C_{u}}{C_{u} + C_{o}} = \frac{.5}{.5 + .3} = 62.5 %

Does this result seem intuitive to you? Given that cU is $0.50 and cO is $0.30, it is clearly more desirable (cheaper) to overstock than to understock. It makes sense to target an in-stock rate of greater than 50%. Now what if you reversed the values? If your cost of understocking ( cU) is $0.30 and your cost of overstocking ( cO) is $0.50, you're optimal in-stock rate is 37.5%. The lower cost of understocking shifts the balance in favor of an in-stock rate of less than 50%.

Now that you know what your optimal in-stock rate is, let's look at how you use this information to calculate your order quantity. Figure 9-12 shows a normal demand distribution. Remember the notation: Average demand is D and the standard deviation of demand is sD. If you place an order equal to average demand, the resulting in-stock probability is 50%. If you want to achieve an in-stock rate of greater than 62.5%, you need to order more than average demand. The greater your desired in-stock target, the larger your order quantity will be. In more formal terms, the newsvendor quantity is determined as follows:

$Q^{*} = D + z \times s D$

Where z is the number of standard deviations you need to add to average demand to obtain your desired in-stock rate F(Q*).

Figure 9-12: The Newsvendor Quantity

Let's look at a simple numerical example: ScareMart sells Halloween costumes and operates out of an abandoned warehouse from August 15 to October 31. Since all merchandise is sourced from China, ScareMart must place its orders by April for delivery by August. Over the past three years, average demand for ScareMart's top seller, a vampire costume, was 2,350 units. The standard deviation of demand ( sD) was 840 units. ScareMart pays $4.20 per costume (delivered) and sells the costume for $29.99. Any costumes that don't sell are liquidated to HalloDiscounts.com for a mere $1.99 on November 1st. What is your optimal in-stock probability? What is your optimal order quantity? Watch the video for a brief tutorial.

Let's run the numbers. You begin by calculating your optimal in-stock probability as follows:

F (Q^{*}) = \frac{C_{u}}{C_{u} + C_{o}} = \frac{25.79}{25.79 + 2.21} = .92

Now that you know your .92 optimal in-stock probability, you need to look up your z-score in a standard normal probability distribution table. A .92 in-stock probability gives you a z-score of 1.41. The calculations for your optimal order quantity look as follows:

$Q^{*} = D + z \times s D = 2, 350 + 1.41 \times 840 = 3, 536$

Have you ever been hungry—really hungry because there was not enough food? According to statistics from the United Nations Food and Agriculture Organization, one in eight people worldwide are undernourished. 1 The sad irony is that one third of all food destined for human consumption is wasted every year. 2 In the U.S. alone, a stunning $165 billion price tag on annual food waste. 3 To add insult to injury, food waste represents the largest component of solid waste in U.S. cities. What is the source of the waste? In developing countries, the losses occur primarily during processing and production. In industrialized nations, retailers and consumers are the primary wasters.

You may be wondering, "Why does this paradox of excess and shortage in food supplies exist?" Consider two reasons.

Distribution: Food simply is not where it is needed. A number of startups have emerged that attempt to remedy this. Firms like CropMobster let farmers donate excess food inventory to charities. Apps such as SpoilerAlert link consumers that have leftover food items with those in need.
Inventory Management: Just like in a newsvendor situation, farmers must anticipate demand well in advance and plant accordingly. This can easily lead to overproduction—and lower crop prices. To preserve already razor-thin margins, farmers often leave their orchards and fields unharvested, creating more food waste.

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