You are managing a computer store and are trying to determine the number of computers to keep in stock. Your current policy is to order 1100 computers whenever end-of-month inventory is 400 computers or less. Each time an order is placed a fixed cost of $600 and a variable cost of $1500 per computer is incurred. Computers are sold for $2800. If you don't have any computers in stock a customer buys a computer from a competitor. At the end of each month, there is a holding cost of $10 for each computer in stock. Orders are placed at the end of a month and are delivered in approximately 4 weeks. For example, if you order at the end of Month 1, the delivery will take place at the end of Month 2, and the new computers can be sold starting in Month 3 (the computers will be added to the stock before inventory is taken at the end of Month 2 - the holding cost applies to all inventory at the end of the month). Assume that demand for computers each month is a random variable that is normally distributed with mean 400 and standard deviation 100 and at the beginning of Month 1 you have 200 computers. You may round the normal variable to integer to make sure the demand is integer. For simplicity, negative demand is allowed. Create a simulation model for evaluating this inventory restocking policy for the next 2 years. Assume that salvage value for items that remain in stock at the end of Month 24 is $100 per item, and you do not reorder at the end of Month 24.
a) What is the expected profit for the next 2 years using this inventory restocking policy? What is the standard deviation and 95% confidence interval? What is the probability of the profit less than $7.5M?
b) According to your current policy, your reorder quantity is 1100 and reorder point is 400. If fixing the reorder quantity to 1100, what is the optimal reorder point? Specify the value in the multiples of 100. Denote by P1 the optimal reorder point you find.
c) Now fixing the reorder point to P1, what is the optimal reorder quantity? Specify the value in the multiples of 100. Denote by R1 the optimal reorder quantity you find.
d) Is the R1 equal to 1100? Explain the reason why it is equal or not equal.