Inventory Management

Lecture Outline

• Elements of Inventory Management• Inventory Control Systems• Economic Order Quantity Models• Quantity Discounts• Reorder Point• Order Quantity for a Periodic Inventory

System

13-2

What Is Inventory?

• Stock of items kept to meet future demand

• Purpose of inventory management• how many units to order

• when to order

13-3

Supply Chain Management

• Bullwhip effect• demand information is distorted as it moves away from

the end-use customer• higher safety stock inventories to are stored to compensate

• Seasonal or cyclical demand• Inventory provides independence from vendors• Take advantage of price discounts• Inventory provides independence between

stages and avoids work stoppages

13-4

Quality Management in the Supply Chain

• Customers usually perceive quality service as availability of goods they want when they want them

• Inventory must be sufficient to provide high-quality customer service in QM

13-5

Types of Inventory

• Raw materials

• Purchased parts and supplies

• Work-in-process (partially completed) products (WIP)

• Items being transported

• Tools and equipment

13-6

Two Forms of Demand

13-7

• Dependent• Demand for items used to produce final

products

• Tires for autos are a dependent demand item

• Independent• Demand for items used by external customers

• Cars, appliances, computers, and houses are examples of independent demand inventory

Inventory Costs

• Carrying cost• cost of holding an item in inventory

• Ordering cost• cost of replenishing inventory

• Shortage cost• temporary or permanent loss of sales when

demand cannot be met

13-8

Inventory Control Systems

13-9

• Continuous system (fixed-order-quantity)• constant amount ordered when inventory declines

to predetermined level

• Periodic system (fixed-time-period)• order placed for variable amount after fixed

passage of time

ABC Classification

• Class A• 5 – 15 % of units

• 70 – 80 % of value

• Class B• 30 % of units

• 15 % of value

• Class C• 50 – 60 % of units

• 5 – 10 % of value

13-10

ABC Classification

13-11

1 $ 60 902 350 403 30 1304 80 605 30 1006 20 1807 10 1708 320 509 510 60

10 20 120

PART UNIT COST ANNUAL USAGE

ABC Classification

13-12

Example 10.1

9 $30,600 35.9 6.0 6.08 16,000 18.7 5.0 11.02 14,000 16.4 4.0 15.01 5,400 6.3 9.0 24.04 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.06 3,600 4.2 18.0 58.05 3,000 3.5 13.0 71.0

10 2,400 2.8 12.0 83.07 1,700 2.0 17.0 100.0

TOTAL % OF TOTAL % OF TOTALPART VALUE VALUE QUANTITY % CUMMULATIVE

A

B

C

$85,400

ABC Classification

13-13

Example 10.1

% OF TOTAL % OF TOTALCLASS ITEMS VALUE QUANTITY

A 9, 8, 2 71.0 15.0B 1, 4, 3 16.5 25.0C 6, 5, 10, 7 12.5 60.0

Economic Order Quantity (EOQ) Models

• EOQ• optimal order quantity that will

minimize total inventory costs

• Basic EOQ model

• Production quantity model

13-14

Assumptions of Basic EOQ Model

• Demand is known with certainty and is constant over time

• No shortages are allowed• Lead time for the receipt of orders is

constant• Order quantity is received all at once

13-15

Inventory Order Cycle

13-16

Demand rate

TimeLead time

Lead time

Order placed

Order placed

Order receipt

Order receipt

Inve

ntor

y Le

vel

Reorder point, R

Order quantity, Q

0

Average inventory

Q

2

EOQ Cost Model

13-17

Co - cost of placing order D - annual demand

Cc - annual per-unit carrying cost Q - order quantity

Annual ordering cost =CoD

Q

Annual carrying cost =CcQ

2

Total cost = +CoD

Q

CcQ

2

EOQ Cost Model

13-18

TC = +CoD

Q

CcQ

2

= – +CoD

Q2

Cc

2

TC

Q

0 = – +C0D

Q2

Cc

2

Qopt =2CoD

Cc

Deriving Qopt Proving equality of costs at optimal point

=CoD

Q

CcQ

2

Q2 =2CoD

Cc

Qopt =2CoD

Cc

EOQ Cost Model

13-19

Order Quantity, Q

Annual cost ($) Total Cost

Carrying Cost =CcQ

2

Slope = 0

Minimum total cost

Optimal order Qopt

Ordering Cost =CoD

Q

EOQ Example

13-20

Cc = $0.75 per gallon Co = $150 D = 10,000 gallons

Qopt =2CoD

Cc

Qopt =2(150)(10,000)

(0.75)

Qopt = 2,000 gallons

TCmin = +CoD

Q

CcQ

2

TCmin = +(150)(10,000)

2,000

(0.75)(2,000)

2

TCmin = $750 + $750 = $1,500

Orders per year =D/Qopt

=10,000/2,000

=5 orders/year

Order cycle time =311 days/(D/Qopt)

=311/5

=62.2 store days

Production Quantity Model

• Order is received gradually, as inventory is simultaneously being depleted• AKA non-instantaneous receipt model

• assumption that Q is received all at once is relaxed

• p - daily rate at which an order is received over time, a.k.a. production rate

• d - daily rate at which inventory is demanded

13-21

Production Quantity Model

13-22

Q(1-d/p)

Inventorylevel

(1-d/p)Q2

Time0

Orderreceipt period

Beginorder

receipt

Endorder

receipt

Maximuminventory level

Averageinventory level

Production Quantity Model

13-23

p = production rate d = demand rate

Maximum inventory level =Q - d

=Q 1 -

Qp

dp

Average inventory level = 1 -Q2

dp

TC = + 1 -dp

CoD

Q

CcQ

2

Qopt =2CoD

Cc 1 - dp

Production Quantity Model

13-24

Cc = $0.75 per gallon Co = $150 D = 10,000 gallons

d = 10,000/311 = 32.2 gallons per day p = 150 gallons per day

Qopt = = = 2,256.8 gallons

2CoD

Cc 1 - dp

2(150)(10,000)

0.75 1 - 32.2150

TC = + 1 - = $1,329dp

CoD

Q

CcQ

2

Production run = = = 15.05 days per orderQp

2,256.8150

Production Quantity Model

13-25

Number of production runs = = = 4.43 runs/yearDQ

10,0002,256.8

Maximum inventory level =Q 1 - = 2,256.8 1 -

=1,772 gallons

dp

32.2150

Solution of EOQ Models With Excel

13-26

The optimal ordersize, Q, in cell D8

Solution of EOQ Models With Excel

13-27

The formula for Qin cell D10

=(D4*D5/D10)+(D3*D10/2)*(1-(D7/D8))

=D10*(1-(D7/D8))

Solution of EOQ Models With OM Tools

13-28

Quantity Discounts

13-29

Price per unit decreases as order quantity increases

TC = + + PDCoD

Q

CcQ

2

where

P = per unit price of the itemD = annual demand

Quantity Discount Model

13-30

Qopt

Carrying cost

Ordering cost

Inve

ntor

y co

st (

$)

Q(d1 ) = 100 Q(d2 ) = 200

TC (d2 = $6 )

TC (d1 = $8 )

TC = ($10 ) ORDER SIZE PRICE

0 - 99 $10

100 – 199 8 (d1)

200+ 6 (d2)

Quantity Discount

13-31

QUANTITY PRICE

1 - 49 $1,400

50 - 89 1,100

90+ 900

Co =$2,500

Cc =$190 per TV

D =200 TVs per year

Qopt = = = 72.5 TVs2CoD

Cc

2(2500)(200)190

TC = + + PD = $233,784 CoD

Qopt

CcQopt

2

For Q = 72.5

TC = + + PD = $194,105CoD

Q

CcQ

2

For Q = 90

Quantity Discount Model With Excel

13-32

=(D4*D5/E10)+(D3*E10/2)+C10*D5=IF(D10>B10,D10,B10)

Reorder Point

13-33

• Inventory level at which a new order is placed

R = dLwhere

d = demand rate per periodL = lead time

Reorder Point

13-34

Demand = 10,000 gallons/year

Store open 311 days/year

Daily demand = 10,000 / 311 = 32.154 gallons/day

Lead time = L = 10 days

R = dL = (32.154)(10) = 321.54 gallons

Safety Stock

• Safety stock• buffer added to on hand inventory during lead

time

• Stockout • an inventory shortage

• Service level • probability that the inventory available during

lead time will meet demand

• P(Demand during lead time <= Reorder Point)

13-35

Variable Demand With Reorder Point

13-36

Reorderpoint, R

Q

LT

Time

LT

Inve

nto

ry le

vel

0

Reorder Point With Safety Stock

13-37

Reorderpoint, R

Q

LTTime

LT

Inve

nto

ry le

vel

0

Safety Stock

Reorder Point With Variable Demand

13-38

R = dL + zd L

where

d =average daily demandL =lead time

d =the standard deviation of daily demand

z =number of standard deviationscorresponding to the service levelprobability

zd L =safety stock

Reorder Point For a Service Level

13-39

Probability of meeting demand during lead time = service level

Probability of a stockout

R

Safety stock

dLDemand

zd L

Reorder Point For Variable Demand

13-40

The paint store wants a reorder point with a 95% service level and a 5% stockout probability

d= 30 gallons per dayL= 10 days

d= 5 gallons per day

For a 95% service level, z = 1.65

R= dL + z d L

= 30(10) + (1.65)(5)( 10)

= 326.1 gallons

Safety stock= z d L

= (1.65)(5)( 10)

= 26.1 gallons

Determining Reorder Point with Excel

13-41

The reorder pointformula in cell E7

Order Quantity for a Periodic Inventory System

13-42

Q = d(tb + L) + zd tb + L - I

where

d= average demand ratetb= the fixed time between ordersL= lead time

d= standard deviation of demand

zd tb + L= safety stockI= inventory level

Periodic Inventory System

13-43

Fixed-Period Model With Variable Demand

13-44

d= 6 packages per dayd= 1.2 packagestb= 60 daysL= 5 daysI= 8 packagesz= 1.65 (for a 95% service level)

Q= d(tb + L) + zd tb + L - I

= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8

= 397.96 packages

Fixed-Period Model with Excel

13-45

Formula for ordersize, Q, in cell D10