You run a company that is determining its order quantity and re-order point for one of its products where the demand rate is a random variable and it operates under a continuous review policy. In addition, both the order quantity and re-order point can take continuous values. Annual demand for the product is normally distributed with mean 3600 and standard deviation 300. The fixed order cost of the product is $7500 and the monthly holding costs are $15 per product. The product is backlogged at a cost of $250 per product that is backlogged. Finally, lead time for the product is 2 months. (a) Determine the mean and the standard deviation of lead time demand. (b) Determine the optimal (Q, R) pair. If you are using the table from class slides, you may use the closest listed value to the one under consideration in your calculation. You may stop the method to solve for (Q, R) when consectutive Q values or R values are within .5 of one another. (c)Determine the reorder point if the company decides to re-order the EOQ and it wishes to maintain a Type 2 service level with β = .98.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...