How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of.
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How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality Albert Einstein 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 2500 2 1000 3 1900 4 1500 5 3900 6 1000 7 200 8 1000 9 8000 10 9000 11 500 12 400 Unit Cost 330 70 500 100 700 915 210 4000 10 2 200 300 Annual $ Value 825000 70000 950000 150000 2730000 915000 42000 4000000 80000 18000 100000 120000 Group A: Perpetual Group C: Periodic Item Number 8 5 3 6 1 4 12 11 9 2 7 10 Annual Demand 1000 3900 1900 1000 2500 1500 400 500 8000 1000 200 9000 Unit Cost 4000 700 500 915 330 100 300 200 10 70 210 2 Annual % of Total Classification $ Value 4000000 A 2730000 67% A 950000 B 915000 B 825000 27% B 150000 C 120000 C 100000 C 80000 C 70000 C 42000 C 18000 6% C 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 64 4800 200 48 3600 250 38.4 2880 300 32 2400 350 27.4 2057 400 24 1800 450 21.3 1600 500 19.2 1440 550 17.5 1309 600 16 1200 650 14.8 1108 700 13.7 1029 750 12.8 960 800 12 900 850 11.3 847 900 10.7 800 Annual Ordering Cost Ordering Cost Order Size Number of Orders Ordering Cost 50 192 14400 100 96 7200 150 64 4800 200 48 3600 16000 250 38.4 2880 14000 300 32 2400 12000 350 27.4 2057 10000 400 24 1800 450 21.3 1600 8000 500 19.2 1440 6000 550 17.5 1309 4000 600 16 1200 2000 650 14.8 1108 0 700 13.7 1029 100 200 300 400 750 0 12.8 960 500 Order Size 800 12 900 850 11.3 847 900 10.7 800 D S Q 600 700 800 900 1000 The Inventory Cycle Quantity on hand Inventory Usage rate 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. Q0 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 250 125 2000 6000 300 150 2400 5000 350 175 2800 400 200 3200 4000 450 225 3600 3000 500 250 4000 2000 550 275 4400 1000 600 300 4800 0 650 325 5200 0 100 200 300 400 500 600 700 350 5600 Order Size 750 375 6000 800 400 6400 850 425 6800 900 450 7200 Q H 2 700 800 900 1000 Total Cost Order Size Number of Orders 50 192 100 96 150 64 200 48 250 38.4 300 32 350 27.4 16000 400 24 450 21.3 14000 500 19.2 550 17.5 12000 600 16 650 14.8 10000 700 13.7 750 12.8 8000 12 800 850 11.3 900 6000 10.7 Ordering Cost Average Inventory 14400 25 7200 50 4800 75 3600 100 2880 125 2400 150 2057 175 1800 200 1600 225 1440 250 1309 275 1200 300 1108 325 1029 350 960 375 900 400 847 425 800 450 Carrying Cost Total Ord&Carr. Cost 400 14800 800 8000 1200 6000 1600 5200 2000 4880 2400 4800 2800 4857 3200 5000 3600 5200 4000 5440 4400 5709 4800 6000 5200 6308 5600 6629 Ordering Cost 6000 6960 Carrying Cost 6400 7300 6800 7647 Total Ord&Carr. Cost 7200 8000 4000 2000 0 200 400 600 800 1000 ost 0 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) = 0.9×3000=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 Assignment 12a.1 A toy manufacturer uses approximately 32000 silicon chips annually. The Chips are used at a steady rate during the 240 days a year that the plant operates. Annual holding cost is 60 cents per chip, and ordering cost is $24. Determine the following: 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 (working days 240/year)? d) What is the total cost? Assignment 12a.2 Victor sells a line of upscale evening dresses in his boutique. He charges $300 per dress, and sales average 30 dresses per week. Currently, Vector orders 10 week supply at a time from the manufacturer. He pays $150 per dress, and it takes two weeks to receive each delivery. Victor estimates his administrative cost of placing each order at 225. His inventory charring cost including cost of capital, storage, and obsolescence is 20% of the purchasing cost. Assume 52 weeks per year. a) Compute Vector’s total annual cost of inventory system (carrying plus ordering but excluding purchasing) under the current ordering policy? b) Without any EOQ computation, is this the optimal policy? Why? c) Compute Vector’s total annual cost of inventory system (carrying plus ordering but excluding purchasing) under the optimal ordering policy? d) What is the ordering interval under optimal ordering policy? e) What is average inventory and inventory turns under optimal ordering policy? Inventory turn = Demand divided by average inventory. Average inventory = Max Inventory divided by 2. Average inventory is the same as cycle inventory. Assignment 12a.3 Complete Computer (CC) is a retailer of computer equipment in Minneapolis with four retail outlets. Currently each outlet manages its ordering independently. Demand at each retail outlet averages 4,000 per week. Each unit of product costs $200, and CC has a holding cost of 20% of the product cost per annum. The fixed cost of each order (administrative plus transportation) is $900. Assume 50 weeks per year. The holding cost will be the same in both decentralized and centralized ordering systems. The ordering cost in the centralized ordering is twice of the decentralized ordering system. Decentralized ordering: If each outlet orders individually. Centralized ordering: If all outlets order together as a single order. a) b) c) d) e) Compute EOQ in decentralized ordering Compute the cycle inventory for one outlet and for all outlets. Compute EOQ in the centralized ordering Compute the cycle inventory for all outlets and for one outlet Compute the total holding cost + ordering cost (not including purchasing cost) for the decentralized policy f) Compute the total holding cost plus ordering cost for the centralized policy