You are in charge of the replenishment of component A. The annual demand is 20,000 units. The purchasing cost is $50 dollars per component. Placing an order has a fixed cost of $500 and a fixed lead-time of 2 weeks. The cost of capital is 10% per year.

a. (6 points) Determine the optimal ordering level for component A. What is the total annual holding + ordering + purchasing cost? What is the optimal Reorder Point?

b. (6 points) Suppose that you decide to order component A only 4 times per year. What is the total annual holding + ordering + purchasing cost in this case?

c. (7 points) Effect of pooling: Disregarding b., suppose that the manager of another location has contacted you to consolidate your inventory orders and storage with hers. The characteristics of the second location are identical to yours. If you decide to order jointly, what would be the optimal ordering quantity? What is the effect of this consolidation on the total cost associated with ordering and holding inventory?

d. (6 points) Disregarding c., consider a second component, B, whose annual demand is 30,000 and purchasing cost is $40/unit. To save on ordering cost, you have decided to coordinate the orders of the two components, so that every order will be placed for both components at the same time. The ordering cost in this case is $720. How many orders you will place per year? What are the optimal ordering levels for components A and B?