9.4 Inventory as Insurance: Uncertainty And Risk

Imagine your job is to anticipate demand for and procure supply of chicken wings. You know customers eat millions of chicken wings every day. You also know that they consume more wings during sporting events, causing spikes in demand. Now, a question: How many wings do you think people ate during the 2016 Super Bowl weekend? Americans alone consumed a stunning 1.3 BILLION chicken wings. 1 How do you accurately predict such a wild swing in demand? Every year, this Super Bowl surge raises fears of a chicken wing shortage. 2 By contrast, what do you do if you plan on this demand surge, but fans eat egg rolls instead?

As a customer, you've encountered the consequences of managers' inability to accurately forecast demand. That is, you wanted to buy something, but it was out of stock. Or, you bought something that was marked down 70% so the retailer could "move excess inventory." Customer driven demand uncertaintyRefers to the degree of variability of demand; often measured as the standard deviation of demand. makes it tough for you to get inventory just right. It is almost impossible to anticipate customer demand when promotional price wars, new product introductions, and other factors lead customers to switch among brands or products—after they enter the store. Because customer demand is a moving target, you need to carry inventory as insurance—this is called inventory " safety stockInventory used as buffer to protect against potential stockouts. ."

Now, imagine you are a production planner on Boeing's 737 assembly line. You are executing to your production plan when you get a call. The person on the other end of the line tells you that a train carrying fuselages from your Kansas supplier derailed in Montana. What do you do now? Who could plan for a train derailment? The loss of these fuselages has thrown "a wrench in [your] tightly choreographed, far-flung aerospace supply chain." 3 You order replacement fuselages, but lead time goes up, delaying your customer deliveries. Although this is an extreme example, the many causes of lead time uncertaintyRefers to the degree of variability of demand; often measured as the standard deviation of lead times. increase the risk of a stockoutAlso called out-of-stock event which occurs when demand for an item cannot be filled from existing inventory. , causing headaches for you. Safety stock can help insure against unexpectedly long lead times.

Together, demand and lead time uncertainty introduce risk, complicating your decision-making process and increasing your costs. The bottom line: Greater risk raises the likelihood that things will go wrong. You face a dilemma: You can choose to hold more safety stock to avoid stockouts when demand is greater than you expected or when incoming shipments are delayed. Or, you can choose to forego such buffer inventory and live with the risk of stocking out. Each option brings unique costs. You are thus faced with a tradeoff. Let's explicitly conceptualize this tradeoff so we can develop a model to help you make the best, lowest-cost decisions.

Figure 9-1 depicts demand and lead-time uncertainties. As you can see, the distributions are normal. In the top left, the distribution of demand is shown with mean D and standard deviation sD. The distribution of lead times is likewise defined by mean lead time L and the standard deviation of lead times sL. We are concerned with the combination of these two distributions, which are called the distribution of lead time demandProbability distribution of customer demand during lead times. It combines demand and lead time distributions and is defined by its mean (average demand during the average lead time) and the standard deviation of lead time demand. (shown in red in(shown in red inFigure 9-1) with mean LTD and standard deviation sLD.

Now, imagine you are a textile merchant who is purchasing a pencil skirt from a supplier. Consider the following:

• Average customer demand per day ( D) is 80 units.

• Average order fulfillment lead time ( L) is 10 days.

What is your average lead time demand ( LTD)? Answer: Multiply your average lead time by your average daily demand; that is, 80*10 = 800 units. As you now know, both the customer demand and the lead time may vary, meaning your actual demand may be more or less than 800 units. The standard deviation of lead time demand ( sLD) measures how much variance you have experienced in the past. As variance increases, you find it harder to accurately forecast lead time demand. As a result, you either need to hold more inventory to buffer against this uncertainty or risk losing sales if demand is higher than normal.

The standard deviation of lead time demand ( sLD) is your primary measure of uncertainty and risk. Unfortunately, measuring sLD is a little messy. You have to combine the characteristics of the demand and lead time distributions. The resulting distribution is called the convoluted standard deviation of lead time demand. It is defined as:

$$sLD=\sqrt{L\cdot s{D}^2+D^2\cdot s{L}^2}$$

What you need to remember is that this measure of risk draws on all four parameters that define the lead time ( L, sL) and demand ( D, sD) distributions.