How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to Please Click on the Following Recorded Lecture https://www.csun.edu/~aa2035/CourseBase/Inventory/Inventory.ToShare/Ch12a.html Importance of Inventory A typical hospital spends about 20% of its budget on medical, surgical, and pharmaceutical supplies. For all hospitals it adds up to $150 billion annually. The average inventory in US economy about $1.13 trillion on $9.66 trillion of sales. About $430 billion in manufacturing, $230 billion in wholesaler, $411 billion in retail. What happens when a company with a large Work In Process (WIP) and Finished Goods (FG) inventory finds a market demand shift to a new product? Two choices: Fire-sell all WIP and FG inventories and then quickly introduce the new product Significant losses Finish all WIP inventory and sell all output before introducing the new product Delay and reduced market response time Inventory Classified Inputs inventory Raw materials and Parts
In-process inventory Parts and products that are being processed Parts and products to decouple operations (line balancing inventory). Parts and products to take advantage of Economies of Scale (batch inventory). Outputs inventory To meet anticipated customer demand (average inventory and safety stock). To smooth production while meeting seasonal demand (seasonal inventory). In transit to a final destination to fill the gap between production and demand lead times (pipeline inventory). Inventory Poor inventory management hampers operations, diminishes customer satisfaction, and increases operating costs. A typical firm probably has tied in inventories about 30 percent of its Current Assets 90 percent of its Working Capital (Current Assets Current Liabilities) Understocking; lost sales, dissatisfied customers. Overstocking; tied up funds (financial costs), storage and safe keeping (physical cost), change in customer preferences (obsolescence cost). Periodic Inventory [Counting] Systems At the beginning of each period, the existing inventory level is identified and the additional required volume to satisfy the demand during the period is ordered. The quantity of order is variable but the timing of order is fixed. Re-Order Point (ROP) is defined in terms of time.
One-Bin System (Periodic) Order Enough to Refill Bin Physical count of items made at periodic intervals. Disadvantage: no information on inventory between two counts. Advantage: order for several items are made at the same time. Perpetual Inventory Systems When inventory reaches ROP an order of EOQ (Economic Order Quantity) units is placed. The quantity of order is fixed but the timing of order is variable. ROP is defined in terms of quantity (inventory on hand). Two-Bin System (Perpetual) Order One Bin of Inventory Full Empty Keeps track of removals from inventory continuously, thus monitoring current levels of each item. A point-of-sales (POS) system record items at the time of sale. A classification Approach: ABC Analysis ABC Analysis in terms of dollars invested, profit potential, sales or usage volume, and stockout penalties. Perpetual for class A, Periodic for class C. Item Annual Number Demand 1
330 100 300 200 10 70 210 2 Annual % of Total Classification $ Value A 4000000 67% A 2730000 B 950000 B 915000 27% B 825000 C 150000 C 120000 C 100000 C 80000
C 70000 C 42000 6% C 18000 The Basic Inventory Model: Economic Order Quantity Only one product Demand is known and is constant throughout the year Each order is received in a single delivery Lead time does not vary -Two costs Ordering Costs: Costs of ordering and receiving the order Holding or Carrying Costs: Cost to carry an item in inventory for one year Unit cost of product is not incorporated because we assume it is fixed. It does not depends on the ordering policy. The Basic Inventory Model Annual demand for a product is 9600 units. D = 9600 Annual carrying cost per unit of product is $16. H = 16 Ordering cost per order is $75. S = 75 a) How much should we order each time to minimize our total cost? b) How many times should we order?
c) What is the length of an order cycle (288 working days/year)? d) What is the total cost? Do NOT worry if you do not get integer numbers. Ordering Cost D = Demand in units / year Q = Order quantity in units / order Number of orders / year = D Q S = Order cost / order Annual order cost = D S Q Annual Ordering Cost Order Size Number of Orders Ordering Cost 50 192 14400 100 96 7200 150
Q 600 700 800 900 1000 The Inventory Cycle Usage rate Inventory Quantity on hand Receive order Time When the quantity on hand is just sufficient to satisfy demand in lead time, an order for EOQ is placed At the instant that the inventory on hand falls to zero, the order will be received (Screencam tutorial on DVD)
Inventory The Inventory Cycle Q Q = Order quantity At the beginning of the period we get Q units. At the end of the period we have 0 units. Q 0 Q 2 2 0 Q/2 Average Inventory / Period & Average Inventory / year This is average inventory / period. Average inventory / period is also known as Cycle Inventory What is average inventory / year ? Time Time Inventory Carrying Cost Q = Order quantity in units / order
Q 2 Average inventory / year = H = Inventory carrying cost / unit / year Annual carrying cost = Q H 2 Annual Carrying Cost Carring Cost Order Size Average Inventory Carrying Cost 50 25 400 100 50 800 150 75 1200 8000 200 100 1600 7000
5440 4400 5709 4800 6000 5200 6308 5600 6629 Ordering Cost 6000 6960 Carrying Cost 6400 7300 Total Ord&Carr. Cost 6800 7647 7200 8000 EOQ TC (Q / 2) H ( D / Q ) S EOQ is at the intersection of the two costs. (Q/2)H = (D/Q)S Q is the only unknown. If we solve it
EOQ = 2DS = H 2(Annual Demand )(Order or Setup Cost ) Annual Holding Cost Back to the Original Questions Annual demand for a product is 9600 units. D = 9600 Annual carrying cost per unit of product is $16. H = 16 Ordering cost per order is $75. S = 75 a) How much should we order each time to minimize our total cost? b) How many times should we order? c) What is the length of an order cycle (288 working days/year)? d) What is the total cost? What is the Optimal Order Quantity 2 DS EOQ H D = 9600, H = 16, S = 75 2(9600)(75)
EOQ 300 16 How Many Times Should We Order? Annual demand for a product is 9600 units. D = 9600 Economic Order Quantity is 300 units. EOQ = 300 Each time we order EOQ. How many times should we order per year? D/EOQ 9600/300 = 32 What is the Length of an Order Cycle? Working Days = 288/year 9600 units are required for 288 days. 300 units is enough for how many days? (300/9600)(288) = 9 days What is the Optimal Total Cost The total cost of any policy is computed as: TC (Q / 2) H ( D / Q ) S The economic order quantity is 300. TC (300 / 2)16 (9600 / 300)75 TC 2400 2400 TC 4800 This is optimal policy that minimizes total cost.
Centura Health Hospital Centura Health Hospital processes a demand of 31200 units of IV starter kits each year (D=31200), and places an order of 6000 units at a time (Q=6000). There is a cost of $130 each time an order is placed (S = $130). Inventory carrying cost is $0.90 per unit per year (H = $0.90). Assume 52 weeks per year. What is the average inventory? Average inventory = Q/2 = 6000/2 = 3000 What is the total annual carrying cost? Carrying cost = H(Q/2) = 0.93000=2700 How many times do we order? 31200/6000 = 5.2 What is total annual ordering cost? Total ordering cost = S(D/Q) Ordering cost = 130(5.2) = $676
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