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**Unformatted text preview: **311 O PERATION M ANAGEMENT I NFORMATION AND O PERATIONS M ANAGEMENT M ARSHALL S CHOOL OF B USINESS T EACHING N OTE ON I NVENTORY M ANAGEMENT Inventory Models with Uncertain Demand: In previous classes we discussed the EOQ model. One of the major assumptions behind the EOQ model is that demand is known with certainty. Clearly, such an assumption is a limiting assumption. In most situations the demand is not known with certainty. In this note we describe the models that address demand uncertainty, and the tools that are commonly used to deal with uncertain demand. Inventory models with uncertain demand are divided into two major sub-classes: Periodic review and continuous review. In periodic review the manager observes the inventory at the beginning of every period (day, week month) and based on the observation the manager makes a purchasing decision. In continuous review the inventory is monitored continuously, and the manager can make decisions at any point of time. We concentrate on periodic review systems. How to capture uncertainty? Before we describe the models we need to clearly define what we mean by “uncertain demand”. Typically by saying that the demand is uncertain we mean that the level of the realized demand may be one of several different values. For example, the demand for books in February may be 100, but it may also be 150 or 200 books. Usually we know more than just the potential values of the demand. We know which of the potential values are more likely to realize and which are less likely. We capture the likelihood by using a probability distribution. For example, the probability of the demand being 100 is 0.1, being 150 is 0.6, and the probability of the demand realizing the value 200 is 0.3. How do we know the probability distribution of the demand? We can calculate the probability distribution from past data. Suppose we collected demand data for the last 30 months. The data is available at Table 1. Clearly, from the past data, it is impossible to forecast with certainty the demand realization in the next month. But we can use the frequency of the demand realizations to estimate the probabilities that the demand realization will have a given value. In table 1 below, we observe that the demand realization was 100, 3 times out of 30, (periods 11, 12 and 15), it was 150, 18 times and it was 200, 9 times. P AGE 1 311 OPERATIONS MANAGEMENT Given this data we conclude that the probability that the realized demand will be 100 is 3/30 = 0.1 Similarly, the probability that the realized demand will have a value of 150 is 18/ 30 =0.6. Similarly, the probability that the realized demand will have a value of 150 is 18/ 30 =0....

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