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. ABC Analysis A processes of diving the items into three classes, according to their annual dollar usage. Thumb rule: Class A: About 20% of items- Top 80% of $ usage Class B: About 30% of items - Next 15% of $ usage Class C: About 50% of items – Bottom 5% of $ usage

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. ABC Analysis – Problem #5 ItemUnit costDemand$ Usage A ,220 D ,690 X ,500 U ,075 L ,035 S ,604 X ,603 L ,005 28,732

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. ABC Analysis – Problem #5 Item Unit costDemand$ Usage % of $ usageCum. %Class D , % U , %54.9% A , %66.1% L , %76.6% L ,0057.0%83.6% S ,6045.6%89.2% X ,6035.6%94.8% X ,5005.2%100.0% 28,732

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 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. Economic Order Quantity Effects of change EOQ = 2DS H Change in demand rate (D) Change in setup cost (S) Change in holding cost (H) Error in estimating D, H, and S

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. How much to order? Two systems Continuous review (Q) system (aka: Reorder point (ROP) system) Place order when IP = ROP Periodic review (P) system Place an order at regular intervals of time

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. 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. 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