A major liquor store finds that it sells an average of 100 bottles a week of regular 750 ml bottles of Jameson Irish Whiskey. Assume that there are 50 weeks in a year, and the demand occurs at a constant rate. The holding costs are estimated to be $2 per bottle per year. The liquor store currently purchases whiskey once in every two weeks, and a new order arrives exactly when the previous batch is completely sold out. Each order placed with the supplier costs the liquor store $10. Answer the following questions. (a) What is the current order cycle length? Express your answer in years. Round your answer to two decimals if needed.
(b) What is the current order size? Recall that a new order arrives exactly at the moment when the previous batch is sold out.
(c) What is the average inventory of Jameson whiskey at this liquor store?
(d) With the current order quantity, how much does the liquor store spend per year on ordering the inventory of Jameson whiskey?
(e) With the current order quantity, what are their inventory holding costs per year?
(f) What order quantity would have minimized their total annual inventory costs? Assume that they will change their order schedule accordingly: that is, they may order more or less frequently than once in two weeks. Round your answer to the closest integer (i. e., no order quantities like 10.5 bottles are allowed)
(g) What is the annual management-cost penalty the liquor store is currently paying for using the order quantity other than the optimal one? To find it, subtract the current total annual inventory cost associated with EOQ from their current annual inventory costs. Express your answer in dollars (not percentage change!), round to two digits if necessary.
(h) Based on your answer to the previous question, would you recommend that the liquor store changes their ordering policy? Why or why not? What property of the EOQ formula comes to your mind?
(i) Now assume that the demand for Jameson has doubled, that is, they now are selling 200 bottles per week. Let us see how it changes the inventory costs. Calculate the new EOQ and the total annual costs the liquor store will incur if they use the optimal order quantity. Enter the new total annual cost of ordering and holding the inventory here, round to two decimal points if needed.
(j) In the previous question, the demand for whiskey has doubled, and hence the amount the liquor store spends on purchasing the inventory should exactly double, too (they need to buy as many bottles as they will sell). Assuming that they use the optimal ordering policy (or something close to that), will they costs of ordering and carrying the inventory double, too? What do you think are the implications of that?