Chapter 13 Inventory Management

Lecture Outline • • • • • • •

Role of Inventory in SCM Elements of Inventory Management Inventory Control Systems Economic Order Quantity Models Quantity Discounts Reorder Point Order Quantity for a Periodic Inventory System

Copyright 2011 John Wiley & Sons, Inc.

13-2

Role of Inventory in SCM • U.S. companies carry $1.1 trillion dollar in inventory spread out along the supply chain. • Cost of holding inventory includes: • • • • • •

Insurance Obsolescence Depreciation Interest Opportunity cost Storage cost

Copyright 2011 John Wiley & Sons, Inc.

13-3

Role of Inventory in SCM • Why to hold inventories? • To meet customer demand for a product (Safety or buffer stock). • To meet demand that is seasonal or cyclical. • Stocks of parts and raw material is kept to meet variations in supplier deliveries. • To take advantage of price discount or as a hedge against anticipated price increase (Walmart stores). • The cost of ordering might be so high. • Within a facility, to provide independence between production stages and to avoid work stoppages. Copyright 2011 John Wiley & Sons, Inc.

13-4

Role of Inventory in SCM • Many emerging practices in inventory management is due in large part to advances in information technology (IT). • Examples of IT advances: • • • •

Enterprise resource planning (ERP) systems. Bar codes Radio frequency identification (RFID) Point of sales data

Copyright 2011 John Wiley & Sons, Inc.

13-5

Role of Inventory in SCM • Examples of successful SCM practices: • • • •

Vendor managed inventory (VMI). Continuous replenishment program (CRP) Supplier hubs Third party logistics (3PL)

• Bullwhip effect: • Demand information is distorted as it moves away from the end-use customer • Higher safety stock inventories are stored to compensate

Copyright 2011 John Wiley & Sons, Inc.

13-6

What Is Inventory? • Stock of items kept to meet future demand • Purpose of inventory management • How many units to order • When to order

• Types of inventories: • • • • •

Raw materials Purchased parts and supplies Work-in-process (partially completed) products (WIP) Items being transported Tools and equipment

Copyright 2011 John Wiley & Sons, Inc.

13-7

Two Forms of Demand • 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

Copyright 2011 John Wiley & Sons, Inc.

13-8

Inventory Costs • Carrying (holding) cost • Cost of holding an item in inventory • Expressed as • dollar value per unit basis per time period • Percentage of the value of an item

• Ordering cost • Cost of replenishing inventory • Expressed as a dollar amount per order (independent of the order size).

• Shortage (Stockout) cost • Temporary or permanent loss of sales when demand cannot be met

Copyright 2011 John Wiley & Sons, Inc.

13-9

Inventory Control Systems • Continuous system (fixed-order-quantity) • constant amount ordered when inventory declines to predetermined level (Checkbook)

• Periodic system (fixed-time-period) • order placed for variable amount after fixed passage of time (University bookstore)

Copyright 2011 John Wiley & Sons, Inc.

13-10

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

Copyright 2011 John Wiley & Sons, Inc.

13-11

ABC Classification PART

UNIT COST

ANNUAL USAGE

1 2 3 4 5 6 7 8 9 10

$ 60 350 30 80 30 20 10 320 510 20

90 40 130 60 100 180 170 50 60 120

Copyright 2011 John Wiley & Sons, Inc.

13-12

ABC Classification PART

9 8 2 1 4 3 6 5 10 7

TOTAL VALUE

% OF TOTAL VALUE

$30,600 16,000 14,000 5,400 4,800 3,900 3,600 3,000 2,400 1,700

35.9 18.7 16.4 6.3 5.6 4.6 4.2 3.5 2.8 2.0

% OF TOTAL QUANTITY

6.0 5.0 4.0 9.0 6.0 10.0 18.0 13.0 12.0 17.0

% CUMMULATIVE

A B C

6.0 11.0 15.0 24.0 30.0 40.0 58.0 71.0 83.0 100.0

$85,400

Example 10.1 Copyright 2011 John Wiley & Sons, Inc.

13-13

ABC Classification

CLASS A B C

ITEMS 9, 8, 2 1, 4, 3 6, 5, 10, 7

% OF TOTAL VALUE

% OF TOTAL QUANTITY

71.0 16.5 12.5

15.0 25.0 60.0

Example 10.1 Copyright 2011 John Wiley & Sons, Inc.

13-14

Economic Order Quantity (EOQ) Models • EOQ • optimal order quantity that will minimize total inventory costs

• Basic EOQ model • Production quantity model

Copyright 2011 John Wiley & Sons, Inc.

13-15

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

Copyright 2011 John Wiley & Sons, Inc.

13-16

Inventory Order Cycle

Inventory Level

Order quantity, Q

Demand rate

Average inventory

Q 2

Reorder point, R

0

Copyright 2011 John Wiley & Sons, Inc.

Lead time Order Order placed receipt

Lead time Order Order placed receipt

Time

13-17

EOQ Cost Model Co - cost of placing order Cc - annual per-unit carrying cost

D - annual demand Q - order quantity

Annual ordering cost =

Co D Q

Annual carrying cost =

CcQ 2

Total cost =

Copyright 2011 John Wiley & Sons, Inc.

CoD + Q

CcQ 2

13-18

EOQ Cost Model Proving equality of costs at optimal point

Deriving Qopt CoD CcQ TC = + Q 2 CoD Cc TC = – Q2 + 2 Q C0D Cc 0 = – Q2 + 2 Qopt =

2CoD Cc

Copyright 2011 John Wiley & Sons, Inc.

CoD CcQ = Q 2 Q2

2CoD = Cc

Qopt =

2CoD Cc

13-19

EOQ Cost Model Annual cost ($)

Total Cost Slope = 0 CcQ Carrying Cost = 2

Minimum total cost

CoD Ordering Cost = Q Optimal order Qopt

Copyright 2011 John Wiley & Sons, Inc.

Order Quantity, Q

13-20

EOQ Example Cc = $0.75 per gallon Qopt =

2CoD Cc

Qopt =

2(150)(10,000) (0.75)

Co = $150

Qopt = 2,000 gallons Orders per year = D/Qopt = 10,000/2,000 = 5 orders/year Copyright 2011 John Wiley & Sons, Inc.

D = 10,000 gallons

CoD CcQ TCmin = + Q 2 TCmin

(150)(10,000) (0.75)(2,000) = + 2,000 2

TCmin = $750 + $750 = $1,500 Order cycle time = 311 days/(D/Qopt) = 311/5 = 62.2 store days 13-21

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

Copyright 2011 John Wiley & Sons, Inc.

13-22

Production Quantity Model Inventory level

Q(1-d/p)

Maximum inventory level

Q (1-d/p) 2

Average inventory level

0 Order receipt period

Begin End order order receipt receipt

Copyright 2011 John Wiley & Sons, Inc.

Time

13-23

Production Quantity Model p = production rate

d = demand rate

Maximum inventory level = Q - Q d p

=Q1- d p Average inventory level =

Q 12

d p

2CoD Qopt =

d Cc 1 p

CoD CcQ d TC = Q + 2 1 - p

Copyright 2011 John Wiley & Sons, Inc.

13-24

Production Quantity Model Cc = $0.75 per gallon Co = $150 d = 10,000/311 = 32.2 gallons per day

2CoD Qopt =

Cc 1 - d p

D = 10,000 gallons p = 150 gallons per day

2(150)(10,000) =

CoD CcQ d TC = Q + 2 1 - p

32.2 0.75 1 150

= 2,256.8 gallons

= $1,329

2,256.8 Q Production run = = = 15.05 days per order 150 p Copyright 2011 John Wiley & Sons, Inc.

13-25

Production Quantity Model Number of production runs =

10,000 D = = 4.43 runs/year 2,256.8 Q

Maximum inventory level = Q 1 -

d p

= 2,256.8 1 -

32.2 150

= 1,772 gallons

Copyright 2011 John Wiley & Sons, Inc.

13-26

Quantity Discounts Price per unit decreases as order quantity increases TC =

CoD Q

CcQ + + PD 2

where P = per unit price of the item D = annual demand

The total inventory cost function must now include the purchase price of the item being ordered Copyright 2011 John Wiley & Sons, Inc.

13-27

Quantity Discount Model ORDER SIZE 0 - 99 100 – 199 200+

PRICE $10 8 (d1) 6 (d2)

TC = ($10 ) TC (d1 = $8 )

Inventory cost ($)

TC (d2 = $6 )

Carrying cost

Ordering cost Q(d1 ) = 100 Qopt Copyright 2011 John Wiley & Sons, Inc.

Q(d2 ) = 200 13-28

Quantity Discount QUANTITY 1 - 49 50 - 89 90+ Qopt =

PRICE $1,400 1,100 900 2CoD = Cc

Co = $2,500 Cc = $190 per TV D = 200 TVs per year

2(2500)(200) = 72.5 TVs 190

For Q = 72.5

CcQopt CoD TC = + 2 + PD = $233,784 Qopt

For Q = 90

CcQ CoD TC = + 2 + PD = $194,105 Q

Copyright 2011 John Wiley & Sons, Inc.

13-29

Quantity Discount Model With Excel

=IF(D10>B10,D10,B10)

Copyright 2011 John Wiley & Sons, Inc.

=(D4*D5/E10)+(D3*E10/2)+C10*D5

13-30

Reorder Point •

Inventory level at which a new order is placed

•

For the basic EOQ model, which has a constant demand and constant lead time:

R = dL where d = demand rate per period L = lead time

Copyright 2011 John Wiley & Sons, Inc.

13-31

Reorder Point 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

Copyright 2011 John Wiley & Sons, Inc.

13-32

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