To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Inventory Management Chapter 15

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Inventory Costs  Interest or Opportunity Cost  Storage and Handling Costs  Taxes, Insurance, and Shrinkage

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Inventory Costs  Customer Service  Ordering Cost  Setup Cost  Labor and Equipment Utilization  Transportation Costs  Payments to Suppliers

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Types of Inventory Cycle Inventory Average cycle inventory = Q Safety Stock Inventory Anticipation Inventory Pipeline Inventory Pipeline inventory = D L = dL

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Types of Inventory Cycle inventory=Q/2 =280/2 =140 drills Example 15.1 Pipeline inventory=D L =dL =(70 drills/week)(3 weeks) =210 drills

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Types of Inventory Figure 15.1 Tutor Estimating Inventory Levels

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. ABC Analysis Percentage of items Percentage of dollar value — — — — — — — — — — 0 0 — Figure 15.2 Class C Class A Class B

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. How Much? When! When!

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Economic Order Quantity

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Economic Order Quantity 1.Demand rate is constant 2.No constraints on lot size 3.Only relevant costs are holding and ordering/setup 4.Decisions for items are independent from other items 5.No uncertainty in lead time or supply Assumptions

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Economic Order Quantity Figure 15.3 Inventory depletion (demand rate) Receive order 1 cycle On-hand inventory (units) Time Q AveragecycleinventoryQ—2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Economic Order Quantity Annual cost (dollars) Lot Size (Q) Figure 15.4 Holding cost (HC) Ordering cost (OC) Total cost = HC + OC

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Example — — — 0 0 — |||||||| Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQ Economic Order Quantity

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQ Example — — — 0 0 — |||||||| Lot Size (Q) Annual cost (dollars) Economic Order Quantity Bird feeder costs C = (H) + (S) Q2Q2 DQDQ D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 390 units C = $ $108 = $3033

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved — — — 0 0 — |||||||| Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQ Bird feeder costs C = (H) + (S) Q2Q2 DQDQ D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 390 units C = $ $108 = $3033 CurrentcostCurrentQ Example 15.2 Economic Order Quantity

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved — — — 0 0 — |||||||| Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQ Bird feeder costs C = (H) + (S) Q2Q2 DQDQ D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 390 units C = $ $108 = $3033 CurrentcostCurrentQ Example 15.2 Economic Order Quantity

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved — — — 0 0 — |||||||| Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQ Bird feeder costs C = (H) + (S) Q2Q2 DQDQ D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $ S = $45 Q = 468 units CurrentcostCurrentQ Example 15.2 Economic Order Quantity C = $ $90 = $3600

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved — — — 0 0 — |||||||| Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQCurrentcostCurrentQ Example 15.2 Economic Order Quantity Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = EOQ C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H Example 15.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved — — — 0 0 — |||||||| Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQCurrentcostCurrentQ Example 15.2 Economic Order Quantity Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H Example 15.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved — — — 0 0 — |||||||| Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQCurrentcostCurrentQ Example 15.2 Economic Order Quantity Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H Example 15.3 C = $562 + $562 = $1124

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved — — — 0 0 — |||||||| Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQCurrentcostCurrentQ Example 15.2 Economic Order Quantity Example 15.3 Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H C = $562 + $562 = $1124 Lowestcost Best Q (EOQ)

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Example 15.2 Economic Order Quantity Example — — — 0 0 — |||||||| Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQCurrentcostCurrentQ Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H C = $562 + $562 = $1124 Lowestcost Best Q (EOQ)

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Lowestcost Best Q (EOQ) Example 15.2 Economic Order Quantity Figure — — — 0 0 — |||||||| Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQCurrentcostCurrentQ Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H C = $562 + $562 = $1124

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Lowestcost Best Q (EOQ) Example 15.2 Economic Order Quantity Example — — — 0 0 — |||||||| Lot Size (Q) Annual cost (dollars) Total cost = (H) + (S) DQQ2 Holding cost = (H) Q2 Ordering cost = (S) DQCurrentcostCurrentQ Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 C = (H) + (S) Q2Q2 DQDQ EOQ = 2DS H C = $562 + $562 = $1124 Time between orders TBO EOQ = = 75/936 = year EOQ D TBO EOQ = (75/936)(12) = 0.96 months TBO EOQ = (75/936)(52) = 4.17 weeks TBO EOQ = (75/936)(365) = days

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. How Much? When! When!

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Continuous Review Soup Figure 15.7 Time On-hand inventory R TBO L TBO L TBO L Orderreceived Orderreceived Q OH OrderplacedIPOrderreceived Q OH Orderplaced IP Orderreceived OrderplacedIPQ OH

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time On-hand inventory R TBO L TBO L TBO L Orderreceived Q OH Orderplaced IP Orderreceived Q OH OrderplacedIPOrderreceived Q OH Orderplaced IP Orderreceived Continuous Review Soup Example 15.4 Chicken Soup R= Average demand during lead time = (25)(4) = 100 cases IP= OH + SR – BO = – 0 = 210 cases

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Uncertain Demand Figure 15.8 Time On-hand inventory TBO 1 TBO 2 TBO 3 L1L1L1L1 L2L2L2L2 L3L3L3L3 R Orderreceived Q Orderplaced Orderplaced OrderreceivedIPIP Q Orderplaced Q Orderreceived Orderreceived OH

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Reorder Point / Safety Stock Figure 15.9 Average demand during lead time Cycle-service level = 85% Probability of stockout (1.0 – 0.85 = 0.15) zLzLzLzL R

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Reorder Point / Safety Stock Example 15.5 Average demand during lead time Cycle-service level = 85% Probability of stockout (1.0 – 0.85 = 0.15) zLzLzLzL R Safety Stock/R Safety stock= z  L = 2.33(22) = 51.3 = 51 boxes Reorder point= ADDLT + SS = = 301 boxes

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Lead Time Distributions Figure  t = Demand for week 1  t = Demand for three-week lead time + 75 Demand for week 2  t = 15 = 75 Demand for week 3  t = 15

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Lead Time Distributions Example 15.6  t = Demand for week 1  t = Demand for three-week lead time + 75 Demand for week 2  t = 15 = 75 Demand for week 3  t = 15 t = 1 week d = 18 L = 2  L =  t L = 5 2 = 7.1 Safety stock= z  L = 1.28(7.1) = 9.1 or 9 units Reorder point= dL + Safety stock = 2(18) + 9 = 45 units Bird feeder Lead Time Distribution

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Lead Time Distributions Example 15.6  t = Demand for week 1  t = Demand for three-week lead time + 75 Demand for week 2  t = 15 = 75 Demand for week 3  t = 15 Reorder point= 2(18) + 9 = 45 units t = 1 week d = 18 L = 2 Bird feeder Lead Time Distribution C = ($15) + ($45) + 9($15) C = $ $ $135 = $

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Lead Time Distributions TABLE 15.1PROBABILITY DISTRIBUTION FOR LEAD TIME Lead Time (weeks)Probability for Lead Time TABLE 15.2PROBABILITY DISTRIBUTION FOR DEMAND Demand (units per week)Probability of Demand

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Lead Time Distributions  t = Demand for week 1  t = Demand for three-week lead time + 75 Demand for week 2  t = 15 = 75 Demand for week 3  t = 15 Figure 15.11(a)

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Lead Time Distributions Figure 15.11(b)  t = Demand for week 1  t = Demand for three-week lead time + 75 Demand for week 2  t = 15 = 75 Demand for week 3  t = 15

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Lead Time Distributions  t = Demand for week 1  t = Demand for three-week lead time + 75 Demand for week 2  t = 15 = 75 Demand for week 3  t = 15 Figure 15.11(c)

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Lead Time Distributions  t = Demand for week 1  t = Demand for three-week lead time + 75 Demand for week 2  t = 15 = 75 Demand for week 3  t = 15 Figure 15.11(d)

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Periodic Review Systems Figure PP Time On-hand inventory T Q1Q1Q1Q1 Orderplaced L Orderplaced Orderreceived Orderreceived Orderplaced Q2Q2Q2Q2 Q3Q3Q3Q3 Orderreceived OH LL Protection interval IP 1 IP 3 IP 2 IPIPIP OH

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. PP Time On-hand inventory T Q1Q1Q1Q1 Orderplaced L Orderplaced Orderreceived Orderreceived Orderplaced Q2Q2Q2Q2 Q3Q3Q3Q3 Orderreceived OH LL Protection interval IP 1 IP 3 IP 2 IPIPIP OH Periodic Review Systems Example 15.7 T = 400BO = 5 OH = 0SR = 0 IP = – 5 = –5 sets Q = 400 – (–5) = 405 sets TV Set - P System IP = OH + SR – BO Q t = T - IP t

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. PP Time On-hand inventory T Q1Q1Q1Q1 Orderplaced L Orderplaced Orderreceived Orderreceived Orderplaced Q2Q2Q2Q2 Q3Q3Q3Q3 Orderreceived OH LL Protection interval IP 1 IP 3 IP 2 IPIPIP OH Example 15.8 Periodic Review Systems Bird feeder— Calculating P and T T= Average demand during the protection interval + Safety stock = d (P + L) + z  P + L = (18 units/week)(16 weeks) (12 units) = 123 units EOQ = 75 units D = (18 units/week)(52 weeks) = 936 units  t = 18 units L = 2 weeks cycle/service level = 90% P = (52) = (52) = 4.2 or 4 weeks EOQ D  P+L =    P + L = 5 6 = 12 units

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. PP Time On-hand inventory T Q1Q1Q1Q1 Orderplaced L Orderplaced Orderreceived Orderreceived Orderplaced Q2Q2Q2Q2 Q3Q3Q3Q3 Orderreceived OH LL Protection interval IP 1 IP 3 IP 2 IPIPIP OH Example 15.8 Periodic Review Systems Bird feeder— Calculating P and T EOQ = 75 units D = (18 units/week)(52 weeks) = 936 units  t = 18 units L = 2 weeks cycle/service level = 90% P = 4 weeks T = 123 units C = ($15) + ($45) + 15($15) 4(18) (18) C = $540 + $585 + $225 = $1350

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. PP Time On-hand inventory T Q1Q1Q1Q1 Orderplaced L Orderplaced Orderreceived Orderreceived Orderplaced Q2Q2Q2Q2 Q3Q3Q3Q3 Orderreceived OH LL Protection interval IP 1 IP 3 IP 2 IPIPIP OH Figure Periodic Review Systems

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. PP Time On-hand inventory T Q1Q1Q1Q1 Orderplaced L Orderplaced Orderreceived Orderreceived Orderplaced Q2Q2Q2Q2 Q3Q3Q3Q3 Orderreceived OH LL Protection interval IP 1 IP 3 IP 2 IPIPIP OH Figure Periodic Review Systems

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Comparison of Q and P Systems P Systems Q Systems  Convenient to administer  Orders may be combined  IP only required at review  Individual review frequencies  Possible quantity discounts  Lower, less-expensive safety stocks

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. ABC Analysis – Solved Problem 2 Figure 15.14

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Comparison of P and Q Systems – Solved Problem 6 Figure 15.15