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Inventory Management

Ronald S. Lau, Ph.D.

HKUST – ISOM

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Intended learning outcomes

Inventory management and control concepts List the types of inventory and their functions

Describe with examples of different inventory costs

Compare and contrast the commonly used inventory systems

Describe cycle counting and inventory control activities

 Apply ABC classification to establish an appropriate degree ofcontrol for different items

List the assumptions of the basic inventory models

Compute the optimal order size using basic inventory models

Compute the reorder point and safety stock of a probabilistic

EOQ model

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   W   A   T   C   H

   V   I   D

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  n  o   t   t  a  u  g   h   t

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Inventory

4

   i  n  v  e  n

   t  o  r  y  s  o  m  e   t   i  m

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  a  p  a  c   i   t  y

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   T   I   E   D  -

  n  o   t  a  c   h   i  e  v   i

   e  x  c

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Purposes of inventory

Required or unavoidable Regulations or customer expectations

In transit or pipeline inventory

Decoupling points Maintain independence of operations

Buffer against uncertainty

Economic benefits Quantity discounts or reduced overall costs

Potential increase in value

5

   (   l   i   k  e  o   i   l   )

   i   f

  o  n  e  s   l  o  w   d  o  w  n   t   h  e  o   t   h  e  r

   i  s  a   f   f  e  c   t  e   d ,

 

   b  e  s  e  p  a  r  a   t  e   d   t  o   b

   (  w   i  n  e ,  c  o   l   l  e  c   t   i   b   l  e ,  p

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Why avoiding excess inventory?

 “Excess inventory is the root of all evil” (Kiyoshi Suzaki) Tie up working capital

Implications of Little’s law (I = R x T)

Hide problems (e.g., quality, scheduling, communication, etc.)

More storage, handling, damage, and admin expenses, etc.

May become obsolete and worthless

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  a  n  y   t   h   i  n  g  m  o  r  e   t   h  a  n

  y  o  u  n  e  e   d   “  e

  x  c  e  s  s   ”

  p  e  o

  p   l  e   b  e  c  o  m  e  m  o  r  e  c  a  r  e   l  e  s  s ,  n  o   t  c  a  r  e  a   b  o  u   t  q  u  a   l   i   t  y

  m  a  n  y   i  n  v  e  n   t  o  r  y   (  c  o  m  p  a  r  e

   d   t  o   J   I   T ,   l  o  w

   i  n  v  e  n   t  o  r  y ,   h   i

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Types and examples of inventory costs

Holding (or carrying) costs [variable cost] Material handling costs, storage space, warehousing fees

Damage, spoilage, depreciation, obsolescence of materials

Cost of capital, opportunity cost, taxes and insurance

Shortage costs [variable cost] Lost sales and profits, customer dissatisfaction

Expedition costs, penalty charges

Ordering (or setup) costs [fixed cost] Handling charges, preparing orders

Supplier selection, negotiations

Freight and insurance

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Continuous review inventory system vs.Periodic review inventory system

Continuous review system:  An order is triggered when the inventory falls to a specific level

(varied interval of time between orders)

Fixed order quantity inventory model

Decisions: How much to order (Q)? When to order (R)?

Periodic review system: Inventory level is checked periodically (fixed interval of time

between orders)

 An order is placed to bring the inventory level up to a

predetermined level (varied order quantity)

 Also known as fixed time period inventory model

Decisions: How much to order (Q)? How long between orders(T)?

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 ABC classification

 ABC classification is based on the 80/20 principle(critical few, trivial many) Items are not of equal importance

 “A” items account for a small percentage of items but a largepercentage of value

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   8   0   %    P

  r  o   fi   t   f  r  o  m

   2   0   %   o

   f   t   h

  e  c  u  s   t  o  m  e  r  s

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 ABC example

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 Application of ABC analysis

Strategy Inventory Production Distribution

Classification(Examples)

By usage in dollarvalue

By value of finishedproduct

By profitability ofproduct and customer

A(Engines)

Strictly controlled

and counted

Make-to-order Higher service level

B(Brackets)

Controlled reorder

point and quantity

Configure-to-order Med/High service levels

C(Nuts & bolts)

Free issue Make-to-stock Lower service level

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Cycle counting

Inventory accuracy: Do inventoryrecords agree with physical count? Physical count: Suspend operations and

count all stock keeping units (SKUs)

Cycle count: Systematically samplesome SKUs

Cycle counting: How frequent? When? Which items?

By whom?

Impact of technology on inventorymanagement

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  o   t   h  e  r  w   i  s  e

   t   h  e  s   t  o  c   k  w   i   l   l   u  p   d  a   t  e  c  o  n   t   i  n  u  o  u  s   l  y   i   f  n

  u  n   i  v  e  r

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  o  n   l  y

  s

   i  n   f  o  r

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Effect of inventory inaccuracy

Financial statement and tax complications

Increased stock-outs Reduced customer service level

Increased levels of safety stock 

Disruptions during replenishment Order the wrong items

Order the wrong quantity

Errors magnified in upstream business partners’planning (more bullwhip effect)

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 Achieving the goal of zero inventory?

The dilemma: Keep inventories as low as possible whileproviding acceptable customer service

Performance measures Inventory turnover = Cost of goods sold / Avg. inventory Days of supply (inventory) = 365 / Inventory turnover

Weeks of supply (inventory) = 52 / Inventory turnover

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Dell’s supply chain performance example

Dell’s FY2005 example Given: COGS = $40,103M and Inventory = $459M

Inventory turnover = 40,103 / 459 = 87.4 turns per year

Days of supply = 365 / 87.4 = 4.2 days

Dell’s FY2013 example: Given: COGS = $44,754M and Inventory = $1,382M

Inventory turnover = 44,754 / 1,382 = 32.4 turns per year

Days of supply = 365 / 32.4 = 11.3 days

Implications?

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Dell’s stock prices as a reflection of itsbusiness performance

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18.0%

10.5%

12.7%

15.0%

16.7%

2000 2001 2002 2003 2004

Worldwide Market Share

18.0%

10.5%

12.7%

15.0%

16.7%

2000 2001 2002 2003 2004

Worldwide Market Share

Dell

S&P5002005

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Economic order quantity model

EOQ basic assumptions: Demand for the product is constant and known

Lead time (time from ordering to receipt) is constant and known

Each order is received all at once

No back order is allowed

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Optimal EOQ

H2

Q +SQ

D +DC=TC

Total annual cost =

 Annualpurchase

cost

 Annualordering

cost

 Annualholding

cost+ +

TC Total annual cost

D Demand

C Cost per unit

Q Order quantity

S Setup or ordering costR Reorder point

L Lead time

H Annual holding cost

EOQ attempts to minimize TC:

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Optimal EOQ

Ordering costs

COST

Holding costs

Total stocking costs

QOPT Q

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H

DS2EOQ =

Economic Order Quantity Reorder Point

R = d L

Time

Inventory Level

Q

L

R

2

QTC = DC + H +

Q

DS

Total Annual Cost = Annual

Purchase Cost Annual

Holding Cost+

 AnnualOrdering Cost

+

Total Stocking Cost

# of orders placed in a year 

Average inventory

d

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Economic production quantity model

Time

Inventory

Q

Usage only

I max

d

p

p – d

Production& Usage

p = production rate

d = usage

p > d

 Assumptions:

Similar to EOQ except that each order is received gradually

Mainly for in-house production

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Formulas for EPQ model

Q =H

DS2

p - d

p

I max =p

p – d

Q

2

I maxTC = DC + H +Q

DS

 Average inventory2

I max=

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Inventory Management

Example – EPQ Model

The Dakota Electronics Corporation manufactures a certain component for its computer

products. The annual demand for the component is 10,000 units. The annual inventorycarrying cost is $10 per unit, and the cost of preparing an order and making productionsetup for the order is $100. The company operates 250 days per year. The machine usedto manufacture this part has a production rate of 200 units per day and cost is $15 per unit.

a. Find the EPQ.

b. How many lots are to be produced per year?c. What is the maximum inventory level?

d. What is the total cost per year?

e. A supplier offers to sell a similar component for $15.20 per unit with a service chargeof $25 per order. Should the company accept the offer?

Given:

D = 10,000 units per year 

H = $10 per unit per year 

S = $100 per order 

d = 10,000 / 250 = 40 units per day

p = 200 units per day

C = $15 per unit

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Inventory Management

D = 10,000 units per year 

H = $10 per unit per year 

S = $100 per order 

d = 10,000 / 250 = 40 units per day

p = 200 units per day

C = $15 per unit

a. Find the EPQ.

EPQ =H

DS2

p - d

p=

10

( 10,000 ) ( 100 )2= 500 units

200 - 40

200

b. How many lots are to be produced per year?

No. of lots =Q

D=

500

10,000= 20

c. What is the maximum inventory level?

I max =p

p – dQ = = 400 units

200

200 – 40500

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Inventory Management

D = 10,000 units per year 

H = $10 per unit per year 

S = $100 per order 

d = 10,000 / 250 = 40 units per day

p = 200 units per day

C = $15 per unit

d. What is the total cost per year?

2

I maxTC = DC + H +Q

DS

2

400

= 10,000 (15) + (10) + 500

10,000

(100) = $154,000 per year 

Time

Inventory

Q = 500

Usage only

IMAX = 400 d = 40

p = 200

p – d

Production& Usage

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Inventory Management

e. A supplier offers to sell a similar component for $15.20 per unit with a service charge

of $25 per order. Should the company accept the offer?S = $25 per order C = $15.2 per unit

H

DS2EOQ = =

10

(10000) (25)2= 224 units

2

QTC = DC + H + Q

DS

2

224= 10000 (15.2) + (10) +

224

10000(25) = $154,236 per year 

Time

Inventory

Q = 224

L

R d

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Inventory Management

Summary

Total cost: To make ($154,000) vs. buy ($154,236)

Other considerations in make vs. buy decisions:

Storage requirementMake (400) vs. Buy (224)

Use of existing equipment after production is haltedShadow price = ?Salvage value = ?

Quality and reliability of suppliers

Strategic implications of outsourcing

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EOQ with quantity discount (price break)model

 Assumptions: Same as EOQ except that the product cost is a function oforder quantity.

Solution procedureStep 1: Start at the lowest unit cost.

Step 2: Compute the EOQ.

Step 3: If the EOQ is not feasible: Choose the next higher unit cost and goto step 2.If the EOQ is feasible: Compute the total cost for the feasible EOQ.

Step 4: Compute the total costs for each and every higher price break

points. The optimal order quantity corresponds to the one whichminimizes the total cost.

(Note: The only potential candidates for optimal solution are the feasibleEOQ and its higher price break points.)

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Inventory Management

Example – EOQ with Quantity Discount (Price-Break) Model

The annual demand for a product X is 40,000 units. The cost to process an order is $25,

and the annual inventory holding cost rate is 20% of the product cost. Given below theprice schedule for product X, find the optimal Q with the minimum total cost.

Quantity Unit Cost1 - 1,499 $ 2.351,500 - 2,499 2.302,500 - 2,999 2.253,000+ 2.20

Given:

D = 40,000 units per year S = $25 per order 

i = 0.2 (or 20%)

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Inventory Management

Quantity Unit Cost1 - 1,499 $2.35

1,500 - 2,499 2.302,500 - 2,999 2.253,000+ 2.20

D = 40,000 units per year 

S = $25 per order 

i = 0.2 (or 20%)

i C

DS2EOQ = =

( 0.2 ) ( 2.20 )

( 40,000 ) ( 25 )2= 2,132 units

For C = $ 2.20

  Infeasible EOQ ! 

i C

DS2EOQ = =

( 0.2 ) ( 2.25 )

( 40,000 ) ( 25 )2= 2,108 units

For C = $ 2.25

  Infeasible EOQ ! 

i C

DS2EOQ = =

( 0.2 ) ( 2.30 )

( 40,000 ) ( 25 )2= 2,085 units

For C = $ 2.30

  Feasible EOQ ! 

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Inventory Management

Quantity Unit Cost1 - 1,499 $2.35

1,500 - 2,499 2.302,500 - 2,999 2.253,000+ 2.20

D = 40,000 units per year 

S = $25 per order 

i = 0.2 (or 20%)

For C = $ 2.20, infeasible EOQ Q = 3,000

For C = $ 2.25, infeasible EOQ Q = 2,500

For C = $ 2.30, EOQ = 2,085 (feasible)

Total cost for C = $ 2.30, Q = 2,085

2

QTC = DC + iC +

Q

DS

2

2,085TC = 40,000 (2.30) + (0.2)(2.30) +

2,085

40,000(25) = $ 92,959.17 per year 

Total cost for C = $ 2.25, Q = 2,500

2

2,500TC = 40,000 (2.25) + (0.2)(2.25) +

2,500

40,000(25) = $ 90,962.50 per year 

Total cost for C = $ 2.20, Q = 3,000

2

3,000TC = 40,000 (2.20) + (0.2)(2.20) +

3,000

40,000(25) = $ 88,993.33 per year 

Min. total cost = $ 88,993.33 per year Optimal Q = 3000

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Inventory Management

EOQ with quantity discount model

Q

Cost

@ 2.20

@ 2.25

@ 2.30

@ 2.35

3,0002,5001,500

92,959

90,96288,993

2,132

2,085

2,108

Optimal

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Inventory Management

Optimal solution found at the feasible EOQ

Q

Cost

Optimal solution found at one of theprice break point

Q

Cost

Optimal

Optimal

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Probabilistic demand during lead time

 Averagedemandduring LT

Reorder point

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Probabilistic EOQ model

 Assumptions: Same as EOQ except that the demand during lead time fluctuates.

R = d L + Z L

0 z

Service level

Z = 2.05

Reorder point

e.g. SL = 98%

LT demand Safety Stock

SD of demand during lead time

L dL =

L = d12 + d2

2 + … + dL2

If d12 = d2

2 = … = dL2

Order quantity

H

DS2EOQ =

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Inventory Management

Example – Probabilistic EOQ Model

The annual demand for a product is 15,600 units. The weekly demand is 300 units with a

standard deviation of 90 units. The cost to place an order is $31.20, and the time fromordering to receipt is four weeks. The annual inventory carrying cost is $0.10 per unit.

Find the reorder point necessary to provide a 98 percent service probability.

Suppose the production manager is asked to reduce the safety stock of this item by 50percent. If she does so, what will the new service probability be?

D = 15,600 units per year 

d = 300 units per week

w = 90 units per week

S = $31.2 per order 

H = $0.1 per unit per year 

L = 4 weeks

SL = 98%

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Inventory Management

Find the reorder point necessary to provide a 98 percent service probability.

D = 15600 units per year 

d = 300 units per week

w = 90 units per week

S = $31.2 per order 

H = $0.1 per unit per year 

L = 4 weeks

SL = 98%

R = d L + Z L

0 z

SL = 98%

Z = 2.05

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Inventory Management

Find the reorder point necessary to provide a 98 percent service probability.

D = 15600 units per year 

d = 300 units per week

w = 90 units per week

S = $31.2 per order 

H = $0.1 per unit per year 

L = 4 weeks

SL = 98%

R = d L + Z L

0 z

SL = 98%

Z = 2.05

L wL =

4 (90) = 180 unitsL =

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Inventory Management

Find the reorder point necessary to provide a 98 percent service probability.

D = 15,600 units per year 

d = 300 units per week

w = 90 units per week

S = $31.2 per order 

H = $0.1 per unit per year 

L = 4 weeks

SL = 98%

R = d L + Z L

0 z

SL = 98%

Z = 2.05

L wL =

4 (90) = 180 unitsL =R = 300 (4) + 2.05 (180)

= 1,200 + 369 = 1,569 units

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Inventory Management

Find the reorder point necessary to provide a 98 percent service probability.

D = 15600 units per year 

d = 300 units per week

w = 90 units per week

S = $31.2 per order 

H = $0.1 per unit per year 

L = 4 weeks

SL = 98%

R = d L + Z L

R = 300 (4) + 2.05 (180)

= 1200 + 369 = 1569 units

Suppose the production manager is asked to reduce the safety stock of this item by 50percent. If she does so, what will the new service probability be?

SS = Z L = 369

Reduce safety stock by 50%   New SS = 369 / 2 = 184.5 185

L

SSZ = = 1.03

180

185=   SL = 84.8% (from the normal distribution table)

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Inventory Management

ServiceLevel

SafetyStock

10.5

Effect of service level on safety stock

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Other inventory models

Fixed-time period models Time interval between orders is a constant

Order quantity is a variable

Single-period models Newsboy problems (for short life cycle products)

Perishable or seasonal demand products

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