a) What is the optimal level of safety stock?  b) What is the probability of stock out?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter9: Decision Making Under Uncertainty
Section: Chapter Questions
Problem 46P
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Krishna cables requires aluminium for its factory. The probability distributions of the daily usage rate and the lead time for procurement are given below. (These distributions are independent.) 

Daily Usage Rate in Tonnes: 2, 3, 4 

Probability: 0.2, 0.6, 0.2 

Lead time in days: 25, 35, 45 

Probability: 0.2, 0.5, 0.3 

The stockout cost is estimated at ₹8,000 per ton and the carrying cost is ₹2,000 per ton per year. 

Question.1) a) What is the optimal level of safety stock? 

b) What is the probability of stock out? 

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