GATE ME 2021 Set 1 — Question 30
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Engineering Mathematics → Inventory Control → Normal Distribution
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Question
Robot Ltd. wishes to maintain enough safety stock during the lead time period between starting a new production run and its completion such that the probability of satisfying the customer demand during the lead time period is 95%. The lead time period is 5 days and daily customer demand can be assumed to follow the Gaussian (normal) distribution with mean 50 units and a standard deviation of 10 units. Using , where represents the cumulative distribution function of the standard normal random variable, the amount of safety stock that must be maintained by Robot Ltd. to achieve this demand fulfillment probability for the lead time period is ________ units (round off to two decimal places).
Correct answer
331 to 333
Solution
Given:
Lead time () = 5 days
Daily demand mean () = 50 units
Daily demand standard deviation () = 10 units
Service level = 95% Mean demand during lead time () = units.
Standard deviation during lead time (): Assuming daily demands are perfectly correlated (as per the answer key range), units.
Safety Stock () = units.
Total stock needed (Reorder Point) = units.Note: Although the question asks for 'safety stock', the official answer key range (331-333) corresponds to the total stock (Reorder Point) calculated using the correlated demand assumption.
Lead time () = 5 days
Daily demand mean () = 50 units
Daily demand standard deviation () = 10 units
Service level = 95% Mean demand during lead time () = units.
Standard deviation during lead time (): Assuming daily demands are perfectly correlated (as per the answer key range), units.
Safety Stock () = units.
Total stock needed (Reorder Point) = units.Note: Although the question asks for 'safety stock', the official answer key range (331-333) corresponds to the total stock (Reorder Point) calculated using the correlated demand assumption.
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