Chapter 3 Inventory Management Lecture Outline • • • • • • Elements of Inventory Management Inventory Control Systems Economic Order Quantity Models Quantity Discounts Reorder Point Order Quantity for a Periodic Inventory System 13-2 What Is Inventory? • Stock of items kept to meet future demand • Purpose of inventory management • how many units to order • when to order 13-3 Supply Chain Management • Bullwhip effect • demand information is distorted as it moves away from the end-use customer • higher safety stock inventories to are stored to compensate • • • • Seasonal or cyclical demand Inventory provides independence from vendors Take advantage of price discounts Inventory provides independence between stages and avoids work stoppages 13-4 Quality Management in the Supply Chain • Customers usually perceive quality service as availability of goods they want when they want them • Inventory must be sufficient to provide highquality customer service in QM 13-5 Types of Inventory • Raw materials • Purchased parts and supplies • Work-in-process (partially completed) products (WIP) • Items being transported • Tools and equipment 13-6 Two Forms of Demand • Dependent • Demand for items used to produce final products • Tires for autos are a dependent demand item • Independent • Demand for items used by external customers • Cars, appliances, computers, and houses are examples of independent demand inventory 13-7 Inventory Costs • Carrying cost • cost of holding an item in inventory • Ordering cost • cost of replenishing inventory • Shortage cost • temporary or permanent loss of sales when demand cannot be met 13-8 Inventory Control Systems • Continuous system (fixed-order-quantity) • constant amount ordered when inventory declines to predetermined level • Periodic system (fixed-time-period) • order placed for variable amount after fixed passage of time 13-9 ABC Classification • Class A • 5 – 15 % of units • 70 – 80 % of value • Class B • 30 % of units • 15 % of value • Class C • 50 – 60 % of units • 5 – 10 % of value 13-10 ABC Classification PART UNIT COST ANNUAL USAGE 1 2 3 4 5 6 7 8 9 10 $ 60 350 30 80 30 20 10 320 510 20 90 40 130 60 100 180 170 50 60 120 13-11 ABC Classification PART 9 8 2 1 4 3 6 5 10 7 TOTAL VALUE $30,600 16,000 14,000 5,400 4,800 3,900 3,600 3,000 2,400 1,700 % OF TOTAL VALUE 35.9 18.7 16.4 6.3 5.6 4.6 4.2 3.5 2.8 2.0 % OF TOTAL QUANTITY 6.0 5.0 4.0 9.0 6.0 10.0 18.0 13.0 12.0 17.0 % CUMMULATIVE A B C 6.0 11.0 15.0 24.0 30.0 40.0 58.0 71.0 83.0 100.0 $85,400 Example 10.1 13-12 ABC Classification CLASS A B C ITEMS 9, 8, 2 1, 4, 3 6, 5, 10, 7 % OF TOTAL VALUE % OF TOTAL QUANTITY 71.0 16.5 12.5 15.0 25.0 60.0 Example 10.1 13-13 Economic Order Quantity (EOQ) Models • EOQ • optimal order quantity that will minimize total inventory costs • Basic EOQ model • Production quantity model 13-14 Assumptions of Basic EOQ Model • Demand is known with certainty and is constant over time • No shortages are allowed • Lead time for the receipt of orders is constant • Order quantity is received all at once 13-15 Inventory Order Cycle Inventory Level Order quantity, Q Demand rate Average inventory Q 2 Reorder point, R 0 Lead time Order Order placed receipt Lead time Order Order placed receipt Time 13-16 EOQ Cost Model Co - cost of placing order Cc - annual per-unit carrying cost D - annual demand Q - order quantity Annual ordering cost = CoD Q Annual carrying cost = CcQ 2 Total cost = Co D + Q CcQ 2 13-17 EOQ Cost Model Proving equality of costs at optimal point Deriving Qopt Co D CcQ TC = + Q 2 CoD Cc TC = – Q2 + 2 Q C0D Cc 0 = – Q2 + 2 Qopt = 2CoD Cc CoD CcQ = Q 2 Q2 2CoD = Cc Qopt = 2CoD Cc 13-18 EOQ Cost Model Annual cost ($) Total Cost Slope = 0 CcQ Carrying Cost = 2 Minimum total cost CoD Ordering Cost = Q Optimal order Qopt Order Quantity, Q 13-19 EOQ Example Cc = $0.75 per gallon Qopt = 2CoD Cc Qopt = 2(150)(10,000) (0.75) Co = $150 Qopt = 2,000 gallons Orders per year = D/Qopt = 10,000/2,000 = 5 orders/year D = 10,000 gallons CoD CcQ TCmin = + Q 2 TCmin (150)(10,000) (0.75)(2,000) = + 2,000 2 TCmin = $750 + $750 = $1,500 Order cycle time = 311 days/(D/Qopt) = 311/5 = 62.2 store days 13-20 Production Quantity Model • Order is received gradually, as inventory is simultaneously being depleted • AKA non-instantaneous receipt model • assumption that Q is received all at once is relaxed • p - daily rate at which an order is received over time, a.k.a. production rate • d - daily rate at which inventory is demanded 13-21 Production Quantity Model Inventory level Q(1-d/p) Maximum inventory level Q (1-d/p) 2 Average inventory level 0 Order receipt period Begin End order order receipt receipt Time 13-22 Production Quantity Model p = production rate d = demand rate Maximum inventory level = Q - Q d p =Q1- d p Average inventory level = Q d 12 p 2CoD Qopt = d Cc 1 p CoD CcQ d TC = Q + 2 1 - p 13-23 Production Quantity Model Cc = $0.75 per gallon Co = $150 d = 10,000/311 = 32.2 gallons per day 2CoD Qopt = Cc 1 - d p D = 10,000 gallons p = 150 gallons per day 2(150)(10,000) = CoD CcQ d TC = Q + 2 1 - p 32.2 0.75 1 150 = 2,256.8 gallons = $1,329 2,256.8 Q Production run = = = 15.05 days per order 150 p 13-24 Production Quantity Model Number of production runs = 10,000 D = = 4.43 runs/year 2,256.8 Q Maximum inventory level = Q 1 - d p = 2,256.8 1 - 32.2 150 = 1,772 gallons 13-25 Solution of EOQ Models With Excel The optimal order size, Q, in cell D8 13-26 Solution of EOQ Models With Excel The formula for Q in cell D10 =(D4*D5/D10)+(D3*D10/2)*(1-(D7/D8)) =D10*(1-(D7/D8)) 13-27 Solution of EOQ Models With OM Tools 13-28 Quantity Discounts Price per unit decreases as order quantity increases CoD CcQ TC = + + PD Q 2 where P = per unit price of the item D = annual demand 13-29 Quantity Discount Model ORDER SIZE 0 - 99 100 – 199 200+ PRICE $10 8 (d1) 6 (d2) TC = ($10 ) TC (d1 = $8 ) Inventory cost ($) TC (d2 = $6 ) Carrying cost Ordering cost Q(d1 ) = 100 Qopt Q(d2 ) = 200 13-30 Quantity Discount QUANTITY 1 - 49 50 - 89 90+ Qopt = PRICE $1,400 1,100 900 2CoD = Cc Co = $2,500 Cc = $190 per TV D = 200 TVs per year 2(2500)(200) = 72.5 TVs 190 For Q = 72.5 CcQopt Co D TC = + 2 + PD = $233,784 Qopt For Q = 90 CcQ CoD TC = + 2 + PD = $194,105 Q Copyright 2011 John Wiley & Sons, Inc. 13-31 Quantity Discount Model With Excel =IF(D10>B10,D10,B10) =(D4*D5/E10)+(D3*E10/2)+C10*D5 13-32 Reorder Point • Inventory level at which a new order is placed R = dL where d = demand rate per period L = lead time 13-33 Reorder Point Demand = 10,000 gallons/year Store open 311 days/year Daily demand = 10,000 / 311 = 32.154 gallons/day Lead time = L = 10 days R = dL = (32.154)(10) = 321.54 gallons 13-34 Safety Stock • Safety stock • buffer added to on hand inventory during lead time • Stockout • an inventory shortage • Service level • probability that the inventory available during lead time will meet demand • P(Demand during lead time <= Reorder Point) 13-35 Inventory level Variable Demand With Reorder Point Q Reorder point, R 0 LT LT Time 13-36 Inventory level Reorder Point With Safety Stock Q Reorder point, R Safety Stock 0 LT Time LT 13-37 Reorder Point With Variable Demand R = dL + zd L where d = average daily demand L = lead time d = the standard deviation of daily demand z = number of standard deviations corresponding to the service level probability zd L = safety stock 13-38 Reorder Point For a Service Level Probability of meeting demand during lead time = service level Probability of a stockout Safety stock zd L dL Demand R 13-39 Reorder Point For Variable Demand The paint store wants a reorder point with a 95% service level and a 5% stockout probability d = 30 gallons per day L = 10 days d = 5 gallons per day For a 95% service level, z = 1.65 R = dL + z d L Safety stock = z d L = 30(10) + (1.65)(5)( 10) = (1.65)(5)( 10) = 326.1 gallons = 26.1 gallons 13-40 Determining Reorder Point with Excel The reorder point formula in cell E7 13-41 Periodic Inventory System 13-42 Fixed-Period Model with Excel Formula for order size, Q, in cell D10 13-43