Inventory Management Copyright 2006 John Wiley Sons Inc

Inventory Management Copyright 2006 John Wiley & Sons, Inc.

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

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

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

Two Forms of Demand § Dependent § 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. 12 -5

Inventory and Quality Management w Customers usually perceive quality service as availability of goods they want when they want them w Inventory must be sufficient to provide high-quality customer service in TQM Copyright 2006 John Wiley & Sons, Inc. 12 -6

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 Copyright 2006 John Wiley & Sons, Inc. 12 -7

Inventory Control Systems § Continuous system (fixedorder-quantity) § constant amount ordered when inventory declines to predetermined level § Periodic system (fixed-timeperiod) § order placed for variable amount after fixed passage of time Copyright 2006 John Wiley & Sons, Inc. 12 -8

ABC Classification w Class A n n 5 – 15 % of units 70 – 80 % of value w Class B n n 30 % of units 15 % of value w Class C n n 50 – 60 % of units 5 – 10 % of value Copyright 2006 John Wiley & Sons, Inc.

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

ABC Classification: Example (cont. ) PART 9 8 2 1 4 3 6 5 10 7 TOTAL PART VALUE $30, 600 1 16, 000 2 14, 000 3 5, 400 4 4, 800 5 3, 900 3, 600 6 CLASS 3, 000 7 2, 400 A 8 1, 700 B 9 C $85, 400 10 % OF TOTAL UNIT ANNUAL USAGE VALUECOSTQUANTITY % CUMMULATIVE 35. 9 6. 0 $ 60 18. 7 5. 0 350 16. 4 4. 0 30 6. 3 9. 0 5. 680 6. 0 4. 630 10. 0 4. 220 % OF TOTAL 18. 0 ITEMS VALUE 3. 510 13. 0 12. 0 9, 8, 2. 8 2 71. 0 320 17. 0 1, 4, 2. 0 3 16. 5 5107 6, 5, 10, 12. 5 20 Copyright 2006 John Wiley & Sons, Inc. 6. 0 90 11. 0 40 A 15. 0 130 24. 0 30. 0 B 60 100 40. 0 % OF TOTAL 58. 0 180 QUANTITY 71. 0 170 C 83. 0 50 15. 0 100. 0 25. 0 60 60. 0 120 Example 10. 1

Economic Order Quantity (EOQ) Models w EOQ n optimal order quantity that will minimize total inventory costs w Basic EOQ model w 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 Order quantity, Q Inventory Level Demand rate Reorder point, R 0 Lead time Order placed receipt Copyright 2006 John Wiley & Sons, Inc. Lead time Order placed receipt Time

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

EOQ Cost Model Deriving Qopt Co D Cc Q TC = + Q 2 Co D Cc TC = 2 + Q 2 Q C 0 D Cc 0= + Q 2 2 Qopt = 2 Co. D Cc Copyright 2006 John Wiley & Sons, Inc. Proving equality of costs at optimal point Co D Cc Q = Q 2 2 Co. D = Cc Qopt = 2 Co. D Cc

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

EOQ Example Cc = $0. 75 per yard Qopt = 2 Co. D Cc Qopt = 2(150)(10, 000) (0. 75) Co = $150 Qopt = 2, 000 yards Orders per year = = = D/Qopt 10, 000/2, 000 5 orders/year Copyright 2006 John Wiley & Sons, Inc. D = 10, 000 yards Co. D Cc Q 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

Production Quantity Model w An inventory system in which an order is received gradually, as inventory is simultaneously being depleted w AKA non-instantaneous receipt model n assumption that Q is received all at once is relaxed w p - daily rate at which an order is received over time, a. k. a. production rate w d - daily rate at which inventory is demanded Copyright 2006 John Wiley & Sons, Inc.

Production Quantity Model (cont. ) Inventory level Q(1 -d/p) Maximum inventory level Q (1 -d/p) 2 Average inventory level 0 Order receipt period Begin End order receipt Copyright 2006 John Wiley & Sons, Inc. Time

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

Production Quantity Model: Example Cc = $0. 75 per yard Co = $150 d = 10, 000/311 = 32. 2 yards per day 2 Co D Qopt = Cc 1 - d p D = 10, 000 yards p = 150 yards per day 2(150)(10, 000) = Co D Cc Q d TC = Q + 2 1 - p 32. 2 0. 75 1 150 = 2, 256. 8 yards = $1, 329 2, 256. 8 Q Production run = = = 15. 05 days per order p 150 Copyright 2006 John Wiley & Sons, Inc.

Production Quantity Model: Example (cont. ) 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 - = 1, 772 yards Copyright 2006 John Wiley & Sons, Inc. 32. 2 150

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

Quantity Discount Model (cont. ) ORDER SIZE 0 - 99 100 – 199 200+ PRICE $10 8 (d 1) 6 (d 2) TC = ($10 ) TC (d 1 = $8 ) Inventory cost ($) TC (d 2 = $6 ) Carrying cost Ordering cost Q(d 1 ) = 100 Qopt Copyright 2006 John Wiley & Sons, Inc. Q(d 2 ) = 200 12 -25

Quantity Discount: Example QUANTITY PRICE 1 - 49 50 - 89 90+ $1, 400 1, 100 900 Qopt = For Q = 72. 5 For Q = 90 2 Co D = Cc Co = $2, 500 Cc = $190 per computer D = 200 2(2500)(200) = 72. 5 PCs 190 Cc. Qopt Co D TC = + + PD = $233, 784 2 Qopt Cc Q Co D TC = + + PD = $194, 105 2 Q Copyright 2006 John Wiley & Sons, Inc.

Reorder Point Level of inventory at which a new order is placed R = d. L where d = demand rate 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 = d. L = (32. 154)(10) = 321. 54 yards Copyright 2006 John Wiley & Sons, Inc.

Safety Stocks § 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 Copyright 2006 John Wiley & Sons, Inc.

Variable Demand with a Reorder Point Inventory level Q Reorder point, R 0 LT LT Time Copyright 2006 John Wiley & Sons, Inc.

Inventory level Reorder Point with a Safety Stock Q Reorder point, R Safety Stock 0 LT LT Time Copyright 2006 John Wiley & Sons, Inc. 12 -31

Reorder Point With Variable Demand R = d. L + 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 Probability of a stockout Safety stock z d L d. L Demand Copyright 2006 John Wiley & Sons, Inc. R 12 -33

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 = d. L + z d L Safety stock = z d L = 30(10) + (1. 65)(5)( 10) = 326. 1 yards = 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 tb L d z d = average demand rate = the fixed time between orders = lead time = standard deviation of demand tb + L = safety stock I = inventory level Copyright 2006 John Wiley & Sons, Inc. 12 -35

Fixed-Period Model with Variable Demand d = 6 bottles per day d = 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. 12 -36