Beni Asllani University of Tennessee at Chattanooga Chapter 12 Inventory Management Operations Management - 5th Edition Roberta Russell & Bernard W. Taylor, III Beni Asllani University of Tennessee at Chattanooga Copyright 2006 John Wiley & Sons, Inc.

Lecture Outline Elements of Inventory Management Inventory Control Systems Economic Order Quantity Models Quantity Discounts Reorder Point Order Quantity for a Periodic Inventory System Copyright 2006 John Wiley & Sons, Inc.

What Is Inventory? Stock of items kept to meet future demand Purpose of inventory management how many units to order when to order Copyright 2006 John Wiley & Sons, Inc.

Types of Inventory Raw materials Purchased parts and supplies Work-in-process (partially completed) products (WIP) Items being transported Tools and equipment Copyright 2006 John Wiley & Sons, Inc.

Inventory and 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 stop-pages Copyright 2006 John Wiley & Sons, Inc.

Two Forms of Demand Dependent Independent Demand for items used to produce final products Tires stored at a Goodyear plant are an example of a dependent demand item Independent Demand for items used by external customers Cars, appliances, computers, and houses are examples of independent demand inventory Copyright 2006 John Wiley & Sons, Inc.

Inventory and Quality Management Customers usually perceive quality service as availability of goods they want when they want them Inventory must be sufficient to provide high-quality customer service in TQM Copyright 2006 John Wiley & Sons, Inc.

Inventory Costs Carrying cost Ordering cost Shortage 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 Copyright 2006 John Wiley & Sons, Inc.

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 Copyright 2006 John Wiley & Sons, Inc.

ABC Classification Class A Class B Class C 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 Copyright 2006 John Wiley & Sons, Inc.

ABC Classification: Example 1 $ 60 90 2 350 40 3 30 130 4 80 60 5 30 100 6 20 180 7 10 170 8 320 50 9 510 60 10 20 120 PART UNIT COST ANNUAL USAGE Copyright 2006 John Wiley & Sons, Inc.

ABC Classification: Example (cont.) 1 $ 60 90 2 350 40 3 30 130 4 80 60 5 30 100 6 20 180 7 10 170 8 320 50 9 510 60 10 20 120 PART UNIT COST ANNUAL USAGE TOTAL % OF TOTAL % OF TOTAL PART VALUE VALUE QUANTITY % CUMMULATIVE 9 $30,600 35.9 6.0 6.0 8 16,000 18.7 5.0 11.0 2 14,000 16.4 4.0 15.0 1 5,400 6.3 9.0 24.0 4 4,800 5.6 6.0 30.0 3 3,900 4.6 10.0 40.0 6 3,600 4.2 18.0 58.0 5 3,000 3.5 13.0 71.0 10 2,400 2.8 12.0 83.0 7 1,700 2.0 17.0 100.0 $85,400 A B C % OF TOTAL % OF TOTAL CLASS ITEMS VALUE QUANTITY A 9, 8, 2 71.0 15.0 B 1, 4, 3 16.5 25.0 C 6, 5, 10, 7 12.5 60.0 Example 10.1 Copyright 2006 John Wiley & Sons, Inc.

Economic Order Quantity (EOQ) Models optimal order quantity that will minimize total inventory costs Basic EOQ model Production quantity model Copyright 2006 John Wiley & Sons, Inc.

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 Copyright 2006 John Wiley & Sons, Inc.

Inventory Order Cycle Demand rate Time Lead time Order placed Order receipt Inventory Level Reorder point, R Order quantity, Q Copyright 2006 John Wiley & Sons, Inc.

EOQ Cost Model Co - cost of placing order D - annual demand Cc - annual per-unit carrying cost Q - order quantity Annual ordering cost = CoD Q Annual carrying cost = CcQ 2 Total cost = + Copyright 2006 John Wiley & Sons, Inc.

EOQ Cost Model TC = + CoD Q CcQ 2 = + Q2 Cc TC Q 0 = + C0D Qopt = = + Q2 Cc TC Q 0 = + C0D Qopt = 2CoD Deriving Qopt Proving equality of costs at optimal point = CoD Q CcQ 2 Q2 = 2CoD Cc Qopt = Copyright 2006 John Wiley & Sons, Inc.

EOQ Cost Model (cont.) Order Quantity, Q Annual cost ($) Total Cost Ordering Cost = CoD Q Slope = 0 Minimum total cost Optimal order Qopt Carrying Cost = CcQ 2 Copyright 2006 John Wiley & Sons, Inc.

EOQ Example Cc = $0.75 per yard Co = $150 D = 10,000 yards Qopt = 2CoD 2(150)(10,000) (0.75) Qopt = 2,000 yards TCmin = + CoD Q CcQ 2 TCmin = + (150)(10,000) 2,000 (0.75)(2,000) TCmin = $750 + $750 = $1,500 Orders per year = D/Qopt = 10,000/2,000 = 5 orders/year Order cycle time = 311 days/(D/Qopt) = 311/5 = 62.2 store days Copyright 2006 John Wiley & Sons, Inc.

Production Quantity Model An inventory system in which an 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 Copyright 2006 John Wiley & Sons, Inc.

Production Quantity Model (cont.) Q(1-d/p) Inventory level (1-d/p) Q 2 Time Order receipt period Begin order receipt End Maximum inventory level Average Copyright 2006 John Wiley & Sons, Inc.

Production Quantity Model (cont.) p = production rate d = demand rate Maximum inventory level = Q - d = Q 1 - Q p d Average inventory level = 1 - 2 TC = + 1 - CoD CcQ Qopt = 2CoD Cc 1 - Copyright 2006 John Wiley & Sons, Inc.

Production Quantity Model: Example Cc = $0.75 per yard Co = $150 D = 10,000 yards d = 10,000/311 = 32.2 yards per day p = 150 yards per day Qopt = = = 2,256.8 yards 2CoD Cc 1 - d p 2(150)(10,000) 0.75 1 - 32.2 150 TC = + 1 - = $1,329 d p CoD Q CcQ 2 Production run = = = 15.05 days per order Q p 2,256.8 150 Copyright 2006 John Wiley & Sons, Inc.

Production Quantity Model: Example (cont.) Number of production runs = = = 4.43 runs/year D Q 10,000 2,256.8 Maximum inventory level = Q 1 - = 2,256.8 1 - = 1,772 yards d p 32.2 150 Copyright 2006 John Wiley & Sons, Inc.

P = per unit price of the item Quantity Discounts Price per unit decreases as order quantity increases TC = + + PD CoD Q CcQ 2 where P = per unit price of the item D = annual demand Copyright 2006 John Wiley & Sons, Inc.

Quantity Discount Model (cont.) Qopt Carrying cost Ordering cost Inventory cost ($) Q(d1 ) = 100 Q(d2 ) = 200 TC (d2 = $6 ) TC (d1 = $8 ) TC = ($10 ) ORDER SIZE PRICE 0 - 99 $10 100 – 199 8 (d1) 200+ 6 (d2) Copyright 2006 John Wiley & Sons, Inc.

Quantity Discount: Example QUANTITY PRICE 1 - 49 $1,400 50 - 89 1,100 90+ 900 Co = $2,500 Cc = $190 per computer D = 200 Qopt = = = 72.5 PCs 2CoD Cc 2(2500)(200) 190 TC = + + PD = $233,784 CoD Qopt CcQopt 2 For Q = 72.5 TC = + + PD = $194,105 CoD Q CcQ 2 For Q = 90 Copyright 2006 John Wiley & Sons, Inc.

Reorder Point Level of inventory at which a new order is placed R = dL where d = demand rate per period L = lead time Copyright 2006 John Wiley & Sons, Inc.

Reorder Point: Example Demand = 10,000 yards/year Store open 311 days/year Daily demand = 10,000 / 311 = 32.154 yards/day Lead time = L = 10 days R = dL = (32.154)(10) = 321.54 yards Copyright 2006 John Wiley & Sons, Inc.

Safety Stocks Safety stock Stockout Service level 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 Copyright 2006 John Wiley & Sons, Inc.

Variable Demand with a Reorder Point point, R Q LT Time Inventory level Copyright 2006 John Wiley & Sons, Inc.

Reorder Point with a Safety Stock point, R Q LT Time Inventory level Safety Stock Copyright 2006 John Wiley & Sons, Inc.

Reorder Point With Variable Demand R = dL + zd 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 zd L = safety stock Copyright 2006 John Wiley & Sons, Inc.

Reorder Point for a Service Level Probability of meeting demand during lead time = service level a stockout R Safety stock dL Demand zd L Copyright 2006 John Wiley & Sons, Inc.

Reorder Point for Variable Demand The carpet store wants a reorder point with a 95% service level and a 5% stockout probability d = 30 yards per day L = 10 days d = 5 yards per day For a 95% service level, z = 1.65 R = dL + z d L = 30(10) + (1.65)(5)( 10) = 326.1 yards Safety stock = z d L = (1.65)(5)( 10) = 26.1 yards Copyright 2006 John Wiley & Sons, Inc.

Order Quantity for a Periodic Inventory System Q = d(tb + L) + zd tb + L - I where d = average demand rate tb = the fixed time between orders L = lead time sd = standard deviation of demand zd tb + L = safety stock I = inventory level Copyright 2006 John Wiley & Sons, Inc.

Fixed-Period Model with Variable Demand d = 6 bottles per day sd = 1.2 bottles tb = 60 days L = 5 days I = 8 bottles z = 1.65 (for a 95% service level) Q = d(tb + L) + zd tb + L - I = (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8 = 397.96 bottles Copyright 2006 John Wiley & Sons, Inc.

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