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 \(\phi^{-1}(0.95) = 1.64\), where \(\phi\) 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).

Hint:

Safety stock accounts for variability in demand and lead time. It can be calculated using the standard normal distribution for a given probability of demand satisfaction.

Answer 1

Correct Answer: 331

The safety stock can be calculated using the formula: \[ \text{Safety Stock} = \phi^{-1}(0.95) \times \sigma \times \sqrt{L}, \] where:
- \(\phi^{-1}(0.95) = 1.64\) (the z-value for a 95% probability),
- \(\sigma = 10\) (the standard deviation of daily demand), - \(L = 5\) days (the lead time).
Substituting the values: \[ \text{Safety Stock} = 1.64 \times 10 \times \sqrt{5} = 1.64 \times 10 \times 2.236 = 36.7. \] Thus, the amount of safety stock that must be maintained is approximately: \[ \boxed{331 \, \text{to} \, 333 \, \text{units}}. \]