Question

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Weekly demand for a particular product averages 60 units, with a standard deviation of 5. This item is managed with a fixed-order-interval model. The order interval is 4 weeks, and this item has a certain lead time of 1 week. The desired service level is 97.5 percent. Assume that it is now time to place another order, and there are 23 units on hand. How many units should be ordered?

In a single-period inventory situation, the probabilities that demand will be 1, 2, 3, or 4 units are 0.1, 0.4, 0.3, and 0.2, respectively. If 3 units are stocked, what is the probability of selling all of them?

Answer 1

Calculate the order quantity with the following information: Weekly demand- 60 units Standard deviation-5 Order-interval - 4 weeks Lead time-1week Service level = 97.5% Z-value for desired service level of 97.5% is 1.96 (from normal distribution table) Calculate the order quantity using the following formula: ROP- Weekly demand during lead time plus fixed interval t z x VLead time x standard deviation of the demand per weelk On hand inventory (60x(4+1))+(1.96x5x (4+1))-23 300 + 21.913-23 - 298.913-299 units Therefore, |299 units should be ordered

The probabilities of demand are as follows: P(1) 0.1, P(2) 0.4, P(3) 0.3, P(4)-0.2 If three units are stocked, it will get sold only if the demand is equal to or greater than 3 units When demand is greater than or equal to 3 units, it can be either 3 or 4 units. Calculate the probability of all the units getting sold as follows: P-1-(P(3)+P(4) 1-(0.3+0.2) -0.5 Therefore, the probability of sell all of them is 0.5 i.e. 50%)