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 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 of 50 units and a standard deviation of 10 units. Using ϕ-1 (0.95) = 1.64, where ϕ 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 fulfilment probability for the lead time period is ______ units (round off two decimal places).
Answer :
Correct answer is : 16.4
Service level = 95%, Z = ϕ-1 (0.95) = 1.64, Lead time period = 5
Mean distribution = 50 units, standard deviation = 10 units
Since the Lead time period is 5 so the total standard deviation is :
σ =
σ1 = σ2 = σ3 = σ4 = σ5 = 10
σ = = 22.36
Saftey stock = Z × σ = 1.64 × 22.36 = 36.67
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