To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Chapter 10 Inventory Management To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved.

Inventory Stock of items held to meet future demand Stock of items held to meet future demand Inventory management answers two questions Inventory management answers two questions How much to order How much to order When to order When to order

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Types of Inventory Raw materials Raw materials Purchased parts and supplies Purchased parts and supplies Labor Labor In-process (partially completed) products In-process (partially completed) products Component parts Component parts Working capital Working capital Tools, machinery, and equipment Tools, machinery, and equipment

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Reasons to Hold Inventory Meet unexpected demand Meet unexpected demand Smooth seasonal or cyclical demand Smooth seasonal or cyclical demand Meet variations in customer demand Meet variations in customer demand Take advantage of price discounts Take advantage of price discounts Hedge against price increases Hedge against price increases Quantity discounts Quantity discounts

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Two Forms of Demand Dependent Dependent Items used to produce final products Items used to produce final products Independent Independent Items demanded by external customers Items demanded by external customers

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Inventory Costs Carrying Cost Carrying Cost Cost of holding an item in inventory Cost of holding an item in inventory Ordering Cost Ordering Cost Cost of replenishing inventory Cost of replenishing inventory Shortage Cost Shortage Cost Temporary or permanent loss of sales when demand cannot be met Temporary or permanent loss of sales when demand cannot be met

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Inventory Control Systems Continuous system (fixed-order- quantity) Continuous system (fixed-order- quantity) Constant amount ordered when inventory declines to predetermined level Constant amount ordered when inventory declines to predetermined level Periodic system (fixed-time-period) Periodic system (fixed-time-period) Order placed for variable amount after fixed passage of time Order placed for variable amount after fixed passage of time

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. ABC Classification System Demand volume and value of items vary Demand volume and value of items vary Classify inventory into 3 categories, typically on the basis of the dollar value to the firm Classify inventory into 3 categories, typically on the basis of the dollar value to the firm PERCENTAGEPERCENTAGE CLASSOF UNITSOF DOLLARS A B3015 C

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. ABC Classification 1$ PARTUNIT COSTANNUAL USAGE Example 10.1

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. ABC Classification Example $ PARTUNIT COSTANNUAL USAGE TOTAL% OF TOTAL% OF TOTAL PARTVALUEVALUEQUANTITY% CUMMULATIVE 9$30, , , , , , , , , , $85,400

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. ABC Classification Example $ PARTUNIT COSTANNUAL USAGE TOTAL% OF TOTAL% OF TOTAL PARTVALUEVALUEQUANTITY% CUMMULATIVE 9$30, , , , , , , , , , $85,400 A B C

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. ABC Classification Example $ PARTUNIT COSTANNUAL USAGE TOTAL% OF TOTAL% OF TOTAL PARTVALUEVALUEQUANTITY% CUMMULATIVE 9$30, , , , , , , , , , $85,400 A B C % OF TOTAL CLASSITEMSVALUEQUANTITY A9, 8, B1, 4, C6, 5, 10,

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. ABC Classification – – – – – 0 0 – |||||| % of Quantity % of Value A B C

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Assumptions of Basic EOQ Model Demand is known with certainty and is constant over time Demand is known with certainty and is constant over time No shortages are allowed No shortages are allowed Lead time for the receipt of orders is constant Lead time for the receipt of orders is constant The order quantity is received all at once The order quantity is received all at once

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. The Inventory Order Cycle Time Inventory Level Reorder point, R Order quantity, Q 0 Figure 10.1

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. The Inventory Order Cycle Demand rate Time Lead time Order placed Order receipt Inventory Level Reorder point, R Order quantity, Q 0 Figure 10.1

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. EOQ Cost Model C o - cost of placing orderD - annual demand C c - annual per-unit carrying costQ - order quantity Annual ordering cost = CoDCoDQQCoDCoDQQQ Annual carrying cost = CcQCcQ22CcQCcQ222 Total cost = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. EOQ Cost Model C o - cost of placing orderD - annual demand C c - annual per-unit carrying costQ - order quantity Annual ordering cost = CoDCoDQQCoDCoDQQQ Annual carrying cost = CcQCcQ22CcQCcQ222 Total cost = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 TC = + CoDQCoDQ CcQ2CcQ2 = + CoDQ2CoDQ2 Cc2Cc2  TC  Q 0 = + C0DQ2C0DQ2 Cc2Cc2 Q opt = 2CoDCc2CoDCc Deriving Q opt Proving equality of costs at optimal point = CoDQCoDQ CcQ2CcQ2 Q 2 = 2CoDCc2CoDCc Q opt = 2CoDCc2CoDCc

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. EOQ Cost Model Order Quantity, Q Annual cost ($) Figure 10.2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. EOQ Cost Model Figure 10.2 Order Quantity, Q Annual cost ($) Ordering Cost = CoDCoDQQCoDCoDQQQ

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. EOQ Cost Model Order Quantity, Q Annual cost ($) Carrying Cost = CcQCcQ22CcQCcQ222 Ordering Cost = CoDCoDQQCoDCoDQQQ Figure 10.2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. EOQ Cost Model Slope = 0 Total Cost Order Quantity, Q Annual cost ($) Minimum total cost Optimal order Q opt Q opt Carrying Cost = CcQCcQ22CcQCcQ222 Ordering Cost = CoDCoDQQCoDCoDQQQ Figure 10.2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. EOQ Example C c = $0.75 per yardC o = $150D = 10,000 yards Q opt = 2CoD2CoDCcCc2CoD2CoDCcCc 2(150)(10,000)(0.75) Q opt = 2,000 yards TC min = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 (150)(10,000)2,000(0.75)(2,000)2 TC min = $750 + $750 = $1,500 Orders per year =D/Q opt =10,000/2,000 =5 orders/year Order cycle time =311 days/(D/Q opt ) =311/5 =62.2 store days Example 10.2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. EOQ with Noninstantaneous Receipt Q(1-d/p) Inventorylevel (1-d/p) Q2 Time 0 Maximum inventory level Average Figure 10.3

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. EOQ with Noninstantaneous Receipt Q(1-d/p) Inventorylevel (1-d/p) Q2 Time 0 Order receipt period BeginorderreceiptEndorderreceipt Maximum inventory level Average Figure 10.3

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. EOQ with Noninstantaneous Receipt p = production rated = demand rate Maximum inventory level =Q - d =Q 1 - Qpdp Average inventory level = 1 - Q2 dp TC = dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Q opt = 2C o D C c 1 - dp

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Production Quantity C c = $0.75 per yardC o = $150D = 10,000 yards d = 10,000/311 = 32.2 yards per dayp = 150 yards per day Q opt = = = 2,256.8 yards 2C o D C c 1 - dp 2(150)(10,000) TC = = $1,329 dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Production run = = = days per order Qp2, Example 10.3

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Production Quantity C c = $0.75 per yardC o = $150D = 10,000 yards d = 10,000/311 = 32.2 yards per dayp = 150 yards per day Q opt = = = 2,256.8 yards 2C o D C c 1 - dp 2(150)(10,000) TC = = $1,329 dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Production run = = = days per order Qp 2, Number of production runs = = = 4.43 runs/year DQDQ 10,000 2,256.8 Maximum inventory level =Q 1 - = 2, =1,772 yards dpdp Example 10.3

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Quantity Discounts Price per unit decreases as order quantity increases Price per unit decreases as order quantity increases TC = + + PD CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 where P = per unit price of the item D = annual demand

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Quantity Discounts Price per unit decreases as order quantity increases Price per unit decreases as order quantity increases TC = + + PD CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 where P = per unit price of the item D = annual demand ORDER SIZEPRICE $ ( d 1 ) ( d 2 )

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Quantity Discount Model Figure 10.4 Inventory cost ($)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Quantity Discount Model Figure 10.4 Q opt Carrying cost Ordering cost Inventory cost ($) Q( d 1 ) = 100 Q( d 2 ) = 200 TC ( d 2 = $6 ) TC ( d 1 = $8 ) TC = ($10 )

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Quantity Discount Model Figure 10.4 Q opt Carrying cost Ordering cost Inventory cost ($) Q( d 1 ) = 100 Q( d 2 ) = 200 TC ( d 2 = $6 ) TC ( d 1 = $8 ) TC = ($10 )

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Quantity Discount QUANTITYPRICE $1, , C o =$2,500 C c =$190 per computer D =200 Q opt = = = 72.5 PCs 2CoD2CoDCcCc2CoD2CoDCcCc2(2500)(200)190 TC = + + PD = $233,784 C o D Q opt C c Q opt 2 For Q = 72.5 TC = + + PD = $194,105 CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 For Q = 90 Example 10.4

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. When to Order Reorder Point is the level of inventory at which a new order is placed R = dL where d = demand rate per period L = lead time

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Reorder Point Example Demand = 10,000 yards/year Store open 311 days/year Daily demand = 10,000 / 311 = yards/day Lead time = L = 10 days R = dL = (32.154)(10) = yards Example 10.5

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Safety Stocks Safety stock Safety stock buffer added to on hand inventory during lead time buffer added to on hand inventory during lead time Stockout Stockout an inventory shortage an inventory shortage Service level Service level probability that the inventory available during lead time will meet demand probability that the inventory available during lead time will meet demand

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Variable Demand with a Reorder Point Figure 10.5 Reorder point, R Q Time Inventory level 0

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Variable Demand with a Reorder Point Figure 10.5 Reorder point, R Q LT Time LT Inventory level 0

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Reorder Point with a Safety Stock Figure 10.6 Reorder point, R Q LT Time LT Inventory level 0 Safety Stock

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 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

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Reorder Point for a Service Level Probability of meeting demand during lead time = service level Probability of a stockout R Safety stock dL Demand z  d L Figure 10.7

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 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) = yards Safety stock= z  d L = (1.65)(5)( 10) = 26.1 yards Example 10.6

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Order Quantity for a Periodic Inventory System Q = d(t b + L) + z  d t b + L - I where d= average demand rate t b = the fixed time between orders L= lead time  d = standard deviation of demand z  d t b + L= safety stock z  d t b + L= safety stock I= inventory level

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Fixed-Period Model with Variable Demand d= 6 bottles per day  d = 1.2 bottles t b = 60 days L= 5 days I= 8 bottles z= 1.65 (for a 95% service level) Q= d(t b + L) + z  d t b + L - I = (6)(60 + 5) + (1.65)(1.2) = bottles