The Newsvendor Model

3.5 Placing a One-Time Order Under Uncertain Demand (The "Newsvendor" Model)

The last environment we will consider for the purposes of inventory management is the situation faced every day by managers of fashion products, by retailers of perishable products, all the way down to the local fruit or newspaper vendor. Here we assume that the demand is over a short selling season, which does not afford us with the luxury of ordering more than once for our selling season. Hence all the inventory we order must arrive before the selling season starts (or it is a major loss), and the replenishment lead time does not really matter here, paradoxically because it is so important!

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We can also ignore the fixed costs of ordering in many cases, as that is the cost of doing business, and if the fixed costs are too high, we may not enter the business at all. Hence, the only remaining question is how much to order for the selling season in order to trade-off the cost of shortages (underage), and the cost of holding (overage) at the end of the selling season. Hence, we can always compute the Target Service Level based on our internal trade-offs as:

Target Service Level = Shortage Cost Per Unit / (Shortage Cost Per Unit + Holding Cost Per Unit).

 In this case, since the lead time is irrelevant, we just compute the average and standard deviation of demand during the entire selling season.

Hence the Order Quantity = Avg. Demand During Selling Season + z x Standard Deviation of Demand During the Selling Season.

 The Safety Stock in this case is just the second term:

z x Standard Deviation of Demand During the Selling Season, where the safety factor z= NORMSINV(Target Service Level).

 Again, we see that the framework for determining the order quantity (which is the inventory we stock for the selling season) is similar to the framework for determining the Base-Stock level, and the Reorder Point in the previous models.