Inventory Management Chapter 15 To Accompany Krajewski Ritzman

Inventory Costs · Interest or Opportunity Cost · Storage and Handling Costs · Taxes,

Inventory Costs · Customer Service · Ordering Cost · Setup Cost · Labor and

Types of Inventory Cycle Inventory Q+0 Average cycle inventory = 2 Safety Stock Inventory

Types of Inventory Cycle inventory = Q/2 = 280/2 = 140 drills Pipeline inventory

Types of Inventory Tutor Estimating Inventory Levels Figure 15. 1 To Accompany Krajewski &

ABC Analysis Percentage of dollar value 100 — Class C Class B 90 —

How Much? When! To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh

Economic Order Quantity To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh

Economic Order Quantity Assumptions 1. Demand rate is constant 2. No constraints on lot

Economic Order Quantity On-hand inventory (units) Receive order Inventory depletion (demand rate) Q Average

Economic Order Quantity Annual cost (dollars) Total cost = HC + OC Figure 15.

Economic Order Quantity Example 15. 2 Annual cost (dollars) 3000 — Total cost =

Economic Order Quantity Current cost Example 15. 2 Annual cost (dollars) 3000 — Total

Economic Order Quantity Current cost Example 15. 2 Annual cost (dollars) 3000 — Bird

Economic Order Quantity Current cost Example 15. 2 Annual cost (dollars) 3000 — 2000

IP On-hand inventory IP Order received OH OH IP Q Q Soup up So

IP On-hand inventory IP Order received Q Soup up So Soup Continuous Review Chicken

Uncertain Demand Figure 15. 8 On-hand inventory IP Order received Q Q Q OH

Reorder Point / Safety Stock Cycle-service level = 85% Probability of stockout (1. 0

Reorder Point / Safety Stock/R Safety stock = z L = 2. 33(22) =

Lead Time Distributions t = 15 t = 26 + 75 Demand for week

Lead Time Distributions t = 15 + 75 Demand for week 1 t =

Lead Time Distributions TABLE 15. 1 PROBABILITY DISTRIBUTION FOR LEAD TIME Lead Time (weeks)

Periodic Review Systems On-hand inventory T IP IP Order received Q 1 OH Order

Periodic Review Systems On-hand inventory T IP IP Order received Q 1 OH Q

Periodic Review Systems On-hand inventory T IP 1 IP IP IP Order Bird feeder—

Periodic Review Systems On-hand inventory T IP 1 IP IP Order Bird feeder— Calculating

Comparison of Q and P Systems · Convenient to administer · Orders may be

ABC Analysis – Solved Problem 2 Figure 15. 14 To Accompany Krajewski & Ritzman

Comparison of P and Q Systems – Solved Problem 6 Figure 15. 15 To

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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 Q+0 Average cycle inventory = 2 Safety Stock Inventory Anticipation Inventory Pipeline inventory = DL = d. L 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 Pipeline inventory = = = DL = d. L (70 drills/week)(3 weeks) 210 drills Example 15. 1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Types of Inventory Tutor Estimating Inventory Levels Figure 15. 1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

ABC Analysis Percentage of dollar value 100 — Class C Class B 90 — Class A 80 — 70 — 60 — 50 — 40 — 30 — 20 — 10 — 0— Figure 15. 2 10 20 30 40 50 60 70 80 90 100 Percentage of items To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

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

Economic Order Quantity On-hand inventory (units) Receive order Inventory depletion (demand rate) Q Average cycle inventory Q — 2 Figure 15. 3 1 cycle Time To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Economic Order Quantity Annual cost (dollars) Total cost = HC + OC Figure 15. 4 Holding cost (HC) Ordering cost (OC) Lot Size (Q) To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Economic Order Quantity Example 15. 2 Annual cost (dollars) 3000 — Total cost = Q D ( H) + ( S) 2 Q 2000 — Holding cost = Q ( H) 2 1000 — Ordering cost = 0— | 50 | 100 | 150 | 200 | 250 | 300 | 350 D ( S) Q | 400 Lot Size (Q) To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Economic Order Quantity Example 15. 2 Annual cost (dollars) 3000 — Total cost = 2000 — Q D ( H) + ( S) 2 Q Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0. 25 ($60/unit) = $15 S = $45 Q = 390 units Holding cost = Q ( H) 2 1000 — Q D C= (H) + (S) 2 Q | 50 | 100 | 150 Ordering cost = | 200 C 0 — = $2925 + $108 = $3033 | 250 | 300 | 350 D ( S) Q | 400 Lot Size (Q) To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Economic Order Quantity Current cost Example 15. 2 Annual cost (dollars) 3000 — Total cost = 2000 — Q D ( H) + ( S) 2 Q Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0. 25 ($60/unit) = $15 S = $45 Q = 390 units Holding cost = Q ( H) 2 1000 — Q D C= (H) + (S) 2 Q | 50 | 100 | 150 Ordering cost = | 200 C 0 — = $2925 + $108 = $3033 | 250 Lot Size (Q) | 300 | 350 D ( S) Q | 400 Current Q To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Economic Order Quantity Current cost Example 15. 2 Annual cost (dollars) 3000 — Total cost = 2000 — Q D ( H) + ( S) 2 Q Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0. 25 ($60/unit) = $15 S = $45 Q = 468 units Holding cost = Q ( H) 2 1000 — Q D C= (H) + (S) 2 Q | 50 | 100 | 150 Ordering cost = | 200 C 0 — = $3510 + $90 = $3600 | 250 Lot Size (Q) | 300 | 350 D ( S) Q | 400 Current Q To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Economic Order Quantity Current cost Example 15. 2 Annual cost (dollars) 3000 — Bird feeder costs Q D Total cost = D(H )(18 + /week)(52 ( S) = weeks) = 936 units 2 Q H = 0. 25 ($60/unit) = $15 S = $45 Q = EOQ 2000 — EOQ = Q Holding cost = Q D(H) 2 DS 2 C= (H) + (S) 2 H Q 1000 — Ordering cost = 0— Example 15. 3 | 50 | 100 | 150 | 200 | 250 Lot Size (Q) | 300 | 350 D ( S) Q | 400 Current Q To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Economic Order Quantity Current cost Example 15. 2 Annual cost (dollars) 3000 — Bird feeder costs Q D Total cost = D(H )(18 + /week)(52 ( S) = weeks) = 936 units 2 Q H = 0. 25 ($60/unit) = $15 S = $45 Q = 75 2000 — EOQ = Q Holding cost = Q D(H) 2 DS 2 C= (H) + (S) 2 H Q 1000 — Ordering cost = 0— Example 15. 3 | 50 | 100 | 150 | 200 | 250 Lot Size (Q) | 300 | 350 D ( S) Q | 400 Current Q To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Economic Order Quantity Current cost Example 15. 2 Annual cost (dollars) 3000 — Bird feeder costs Q D Total cost = D(H )(18 + /week)(52 ( S) = weeks) = 936 units 2 Q H = 0. 25 ($60/unit) = $15 S = $45 Q = 75 2000 — EOQ = 1000 — Q Holding cost = Q D(H) 2 DS 2 C= (H) + (S) 2 H Q C = $562 + $562 = $1124 Ordering cost = 0— Example 15. 3 | 50 | 100 | 150 | 200 | 250 Lot Size (Q) | 300 | 350 D ( S) Q | 400 Current Q To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Economic Order Quantity Current cost Example 15. 2 Annual cost (dollars) 3000 — Bird feeder costs Q D Total cost = D(H )(18 + /week)(52 ( S) = weeks) = 936 units 2 Q H = 0. 25 ($60/unit) = $15 S = $45 Q = 75 2000 — EOQ = 1000 — Q Holding cost = Q D(H) 2 DS 2 C= (H) + (S) 2 H Q C = $562 + $562 = $1124 Ordering cost = Lowest cost 0— Example 15. 3 | 50 | 100 | 150 | 200 | 250 | 300 | 350 | 400 D ( S) Q Current Best Q Lot Size (Q) Q (EOQ) To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Economic Order Quantity Current cost Example 15. 2 Annual cost (dollars) 3000 — Bird feeder costs Q D Total cost = D(H )(18 + /week)(52 ( S) = weeks) = 936 units 2 Q H = 0. 25 ($60/unit) = $15 S = $45 Q = 75 2000 — EOQ = 1000 — Q Holding cost = Q D(H) 2 DS 2 C= (H) + (S) Q C = $562 + $562 = $1124 Ordering cost = Lowest cost 0— Figure 15. 6 2 H | 50 | 100 | 150 | 200 | 250 | 300 | 350 | 400 D ( S) Q Current Best Q Lot Size (Q) Q (EOQ) To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Economic Order Quantity Current cost Example 15. 2 Annual cost (dollars) 3000 — 2000 — Bird feeder costs Time between orders Q D Total cost = D(H + /week)(52 ( S) = )(18 weeks) = 936 units 2 Q EOQ = $15 HTBO = 0. 25 ($60/unit) = = 75/936 = 0. 080 year EOQ D S = $45 Q = 75 Q Holding cost = Q D(H) 2 DS TBO = (75/936)(12) = 0. 96 months 2 C= (H) + (S) EOQ =EOQ 2 Q H TBOEOQ = (75/936)(52) = 4. 17 weeks C = $562 + $562 = $1124 D days TBOEOQ = (75/936)(365) = 29. 25 Ordering cost = ( S) 1000 — Lowest cost Q 0— Example 15. 3 | 50 | 100 | 150 | 200 | 250 | 300 | 350 | 400 Current Best Q Lot Size (Q) Q (EOQ) To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

IP On-hand inventory IP Order received OH OH IP Q Q Soup up So Soup Continuous Review Q OH R Order placed L TBO Time Figure 15. 7 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

IP On-hand inventory IP Order received Q Soup up So Soup Continuous Review Chicken Soup Q R = Average demand during lead time OH = (25)(4) = 100 OH cases OH R IP = OH + SR – BO Order = 10 + 200 – 0 = 210 cases placed Order placed L TBO Time Example 15. 4 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Uncertain Demand Figure 15. 8 On-hand inventory IP Order received Q Q Q OH R L 1 TBO 1 Order placed L 2 TBO 2 L 3 Time TBO 3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Reorder Point / Safety Stock Cycle-service level = 85% Probability of stockout (1. 0 – 0. 85 = 0. 15) Average demand during lead time R z L Figure 15. 9 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Reorder Point / Safety Stock/R Safety stock = z L = 2. 33(22) = 51. 3 = 51 boxes Cycle-service level = 85% Reorder point = ADDLT + SS = 250 + 51 = 301 boxes Probability of stockout (1. 0 – 0. 85 = 0. 15) Average demand during lead time R z L Example 15. 5 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Lead Time Distributions t = 15 t = 26 + 75 Demand for week 1 t = 15 + 75 Demand for week 2 Figure 15. 10 t = 15 225 Demand for three-week lead time = 75 Demand for week 3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Lead Time Distributions t = 15 + 75 Demand for week 1 t = 26 Bird feeder Lead Time Distribution t = 1 week t = 15 + s. L = st 75 Safety Demand for week 2 d = 18 L =5 stock = z L = t = 15 2 L=2 = 7. 1 225 for 9 units 1. 28(7. 1)Demand = 9. 1 or three-week lead time Reorder point = d. L + Safety stock = 2(18) + 9 = 45 units Example 15. 6 = 75 Demand for week 3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Lead Time Distributions t = 15 + 75 Demand for week 1 t = 26 Bird feeder Lead Time Distribution t = 1 week t = 15 d = 18 L=2 Reorder point = 2(18) + 9 = 45 units + 225 75 936 C= ($15) + ($45) + 9($15) Demand for 75 2 75 three-week lead time Demand for week 2 t = 15 C = $562. 50 + $561. 60 + $135 = $1259. 10 Example 15. 6 = 75 Demand for week 3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Lead Time Distributions TABLE 15. 1 PROBABILITY DISTRIBUTION FOR LEAD TIME Lead Time (weeks) Probability for Lead Time 1 2 3 4 5 0. 35 0. 45 0. 10 0. 05 TABLE 15. 2 PROBABILITY DISTRIBUTION FOR DEMAND Demand (units per week) Probability of Demand 10 13 18 23 26 0. 10 0. 20 0. 40 0. 20 0. 10 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Lead Time Distributions t = 15 t = 26 + 75 Demand for week 1 t = 15 + 75 Demand for week 2 t = 15 225 Demand for three-week lead time = Figure 15. 11(a) 75 Demand for week 3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Lead Time Distributions t = 15 t = 26 + 75 Demand for week 1 t = 15 + 75 Demand for week 2 t = 15 225 Demand for three-week lead time = Figure 15. 11(b) 75 Demand for week 3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Lead Time Distributions t = 15 t = 26 + 75 Demand for week 1 t = 15 + 75 Demand for week 2 t = 15 225 Demand for three-week lead time = Figure 15. 11(c) 75 Demand for week 3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Lead Time Distributions t = 15 t = 26 + 75 Demand for week 1 t = 15 + 75 Demand for week 2 t = 15 225 Demand for three-week lead time = Figure 15. 11(d) 75 Demand for week 3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Periodic Review Systems On-hand inventory T IP IP Order received Q 1 OH Order received OH Q 2 IP Q 3 Order received IP 1 IP 3 IP 2 Order placed L L P Figure 15. 12 L P Time Protection interval To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Periodic Review Systems On-hand inventory T IP IP Order received Q 1 OH Q 2 IP 1 IP 3 IP 2 Order received IP = OH + SR – BO Q 3 Q t = T - IPt OH T = 400 OH = 0 BO = 5 SR = 0 Order placed IP = 0 + 0 – 5 = – 5 sets Q = 400 – (– 5) = 405 sets L L P Example 15. 7 TV Set - P System IP L P Time Protection interval To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Periodic Review Systems On-hand inventory T IP 1 IP IP IP Order Bird feeder— Calculating P and T received Q 3 = 90% t = cycle/service level Q 118 units L = 2 weeks OH OH Q 2 EOQ = 75 units D = (18 units/week)(52 weeks) = 936 units EOQ 75 P= (52) = 4. 2 or 4 weeks D 936 Order placed P+L = t P + L = 5 placed 6 = 12 units IP 3 IP 2 T = Average demand during the protection interval + Safety stock = d (P + L) + z P + L L = (18 units/week)(16 weeks) + 1. 28(12 units) = 123 units Time P P Example 15. 8 Protection interval To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Periodic Review Systems On-hand inventory T IP 1 IP IP Order Bird feeder— Calculating P and T received Q 3 = 90% t = cycle/service level Q 118 units L = 2 weeks OH OH Q 2 EOQ = 75 units D = (18 units/week)(52 weeks) = 936 units IP 3 IP 2 IP P = 4 weeks Order placed C= L Order 936 placed 4(18) ($15) + ($45) + 15($15) 2 4(18) C = $540 + $585 + $225 = $1350 L P Example 15. 8 T = 123 units P L Time Protection interval To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Periodic Review Systems On-hand inventory T IP IP Order received Q 1 OH Order received OH Q 2 IP Q 3 Order received IP 1 IP 3 IP 2 Order placed L L P Figure 15. 13 L P Time Protection interval To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Comparison of Q and P Systems · Convenient to administer · Orders may be combined · IP only required at review Q Systems · 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.

Comparison of P and Q Systems – Solved Problem 6 Figure 15. 15 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.