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Exercise 12:
Exercise 12: Order Quantity Whenfaced withplacingperiodicorders for a componentpartor a raw materialinput,the decision as to the size of the order (and thus the frequency with which the order is placed) involves balancing the cost of ordering and the cost of holding inventory. A large order quantity reduces the ordering cost but increases the inventory cost. The effects of a small order quantity are just the opposite. Suppose that annual requirements for the part occur at a relatively constant and known rate over the year (e.g., no seasonality). If R is the estimated annual requirement (in units) and Q is the chosen order quantity, then the firm will place R/ Q orders per year. If S is the cost of placing an order, the total cost of those orders will be (S×R/ Q). If the order quantity is Q, the average inventory carried will be Q/2. If C is the unit cost of each part (in dollars) and I is the inventory holding charge as a fraction of unit cost, then the annual inventory holding cost will be (I×C×Q/2). The total annual cost (ordering plus inventory holding) is given by: where the first term is the annual ordering cost and the second term is the annual inventory holding cost. Build a spreadsheet modelthat will calculate total annual costforthe following situation: R = 2,000 units per year C = $2.00 per unit S = $25.00 per order I = 0.25 (i.e., 25% oftheunit cost) Q = 1,000 units 1. Present the table and then graph the relationship between total annual cost and Q. What is the best Q? 2. Graph the relationship between total annual cost and Q for S values of $15, $20, and $25. Does the optimal order quantity increase or decrease with S? Why?
