Lecture 22 Inventory Fundamentals (Continued) Books Introduction to Materials Management, Sixth...

Lecture 22

Inventory Fundamentals (Continued)

Books• Introduction to Materials Management, Sixth Edition, J. R. Tony Arnold, P.E., CFPIM, CIRM, Fleming

College, Emeritus, Stephen N. Chapman, Ph.D., CFPIM, North Carolina State University, Lloyd M. Clive, P.E., CFPIM, Fleming College

• Operations Management for Competitive Advantage, 11th Edition, by Chase, Jacobs, and Aquilano, 2005, N.Y.: McGraw-Hill/Irwin.

• Operations Management, 11/E, Jay Heizer, Texas Lutheran University, Barry Render, Graduate School of Business, Rollins College, Prentice Hall

Objectives

• ABC Controls• ABC analysis• Records accuracy• Cycle counting• Independent vs. dependent demand• Managing inventory in the face of uncertainity

ABC Inventory Control

• Control of inventory is exercised by controlling individual items called stock-keeping units (SKUs).

• An SKU is an individual item in a specific inventory.• Four questions must be answered in controlling

inventory:– What is the importance of the inventory item?– How are they to be controlled?– How much should be ordered at one time?– When should an order be placed?

ABC Inventory Control

• ABC inventory classification answers the first two questions by determining the importance of items and thus allowing different levels of control based on the importance of items.

• Factors affecting the importance of an item include annual dollar usage, unit cost, and scarcity of material.

ABC Inventory Control

• The ABC principle is based on the observation that a small number of items often dominate the results achieved in any situation and represent the most critical values (“Pareto” principle).

• ABC inventory control separates the more significant items from the less important.

• It is used to determine the degree and level of control required.

ABC Inventory Control Methodology

• Calculate the annual dollar usage for each item.• List the items according to their annual dollar

usage.• Calculate the cumulative annual dollar usage and

the cumulative percent of items.• Group items into an A, B, C classification.

ABC Inventory Control

• Control Based on ABC Classification– Two general rules:

• Have plenty of low-value items - C items are only important if there is a shortage of one of them - then they become extremely important - so a supply should always be on hand.

• Use the money and control effort saved to reduce the inventory of high-value items - A items are extremely important and deserve the tightest control and the most frequent review.

A Items 20% of the items account for

80% of the total dollar usage

B Items 30% of the items account for

15% of the total dollar usage

C Items 50% of the items account for

5% of the total dollar usage

ABC Inventory Control

ABC Inventory Control

A Items

B Items

C Items

Tight Control• Complete, accurate records• Regular, frequent review by management• Frequent review of forecasts• Close follow-upNormal Control• Good records• Normal processing

Simplest possible control• Make sure there are plenty• Simple or no records• Large order quantities

ABC Analysis

Divides inventory into three classes based on annual dollar volume Class A - high annual dollar volume Class B - medium annual dollar volume Class C - low annual dollar volume

Used to establish policies that focus on the few critical parts and not the many trivial ones

ABC Analysis

Item Stock

Number

Percent of Number of

Items Stocked

Annual Volume (units) x

Unit Cost =

Annual Dollar

Volume

Percent of Annual Dollar

Volume Class

#10286 20% 1,000 $ 90.00 $ 90,000 38.8% A

#11526 500 154.00 77,000 33.2% A

#12760 1,550 17.00 26,350 11.3% B

#10867 30% 350 42.86 15,001 6.4% B

#10500 1,000 12.50 12,500 5.4% B

72%

23%

ABC Analysis

Item Stock

Number

Percent of Number of

Items Stocked

Annual Volume (units) x

Unit Cost =

Annual Dollar

Volume

Percent of Annual Dollar

Volume Class

#12572 600 $ 14.17 $ 8,502 3.7% C

#14075 2,000 .60 1,200 .5% C

#01036 50% 100 8.50 850 .4% C

#01307 1,200 .42 504 .2% C

#10572 250 .60 150 .1% C

8,550 $232,057 100.0%

5%

ABC Analysis

A Items

B ItemsC Items

Per

cent

of

annu

al d

olla

r us

age

80 –

70 –

60 –

50 –

40 –

30 –

20 –

10 –

0 – | | | | | | | | | |

10 20 30 40 50 60 70 80 90 100

Percent of inventory items

ABC Analysis

Other criteria than annual dollar volume may be used Anticipated engineering changes Delivery problems Quality problems High unit cost

ABC Analysis

Policies employed may include More emphasis on supplier development

for A items Tighter physical inventory control for A

items More care in forecasting A items

Record Accuracy

Accurate records are a critical ingredient in production and inventory systems

Allows organization to focus on what is needed

Necessary to make precise decisions about ordering, scheduling, and shipping

Incoming and outgoing record keeping must be accurate

Stockrooms should be secure

Cycle Counting

Items are counted and records updated on a periodic basis

Often used with ABC analysis to determine cycle

Has several advantages Eliminates shutdowns and interruptions Eliminates annual inventory adjustment Trained personnel audit inventory accuracy Allows causes of errors to be identified and

corrected Maintains accurate inventory records

Cycle Counting Example

5,000 items in inventory, 500 A items, 1,750 B items, 2,750 C items

Policy is to count A items every month (20 working days), B items every quarter (60 days), and C items every six months (120 days)

Item Class Quantity Cycle Counting Policy

Number of Items Counted per Day

A 500 Each month 500/20 = 25/day

B 1,750 Each quarter 1,750/60 = 29/day

C 2,750 Every 6 months 2,750/120 = 23/day

77/day

Control of Service Inventories

Can be a critical component of profitability

Losses may come from shrinkage or pilferage

Applicable techniques include1. Good personnel selection, training, and

discipline

2. Tight control on incoming shipments

3. Effective control on all goods leaving facility

Independent Versus Dependent Demand

Independent demand - the demand for item is independent of the demand for any other item in inventory

Dependent demand - the demand for item is dependent upon the demand for some other item in the inventory

Holding, Ordering, and Setup Costs

Holding costs - the costs of holding or “carrying” inventory over time

Ordering costs - the costs of placing an order and receiving goods

Setup costs - cost to prepare a machine or process for manufacturing an order

Holding Costs

Category

Cost (and range) as a Percent of Inventory Value

Housing costs (building rent or depreciation, operating costs, taxes, insurance)

6% (3 - 10%)

Material handling costs (equipment lease or depreciation, power, operating cost)

3% (1 - 3.5%)

Labor cost 3% (3 - 5%)

Investment costs (borrowing costs, taxes, and insurance on inventory)

11% (6 - 24%)

Pilferage, space, and obsolescence 3% (2 - 5%)

Overall carrying cost 26%

Holding Costs

Category

Cost (and range) as a Percent of Inventory Value

Housing costs (building rent or depreciation, operating costs, taxes, insurance)

6% (3 - 10%)

Material handling costs (equipment lease or depreciation, power, operating cost)

3% (1 - 3.5%)

Labor cost 3% (3 - 5%)

Investment costs (borrowing costs, taxes, and insurance on inventory)

11% (6 - 24%)

Pilferage, space, and obsolescence 3% (2 - 5%)

Overall carrying cost 26%

Holding costs vary considerably depending on the

business, location, and interest rates. Generally

greater than 15%, some high tech items have holding

costs greater than 50%.

MANAGING INVENTORY IN THE FACE OF UNCERTAINTY

The Newsvendor Problem

You are the GaTech Barnes & Noble Merchandise Buyer

#BB12 - Final Four tee

100% cotton -shirt with Final Four logo$21.98. 

It’s Sunday, March 28, 2004.The Jackets just made it to theFinal Four.

Before heading out to celebrate,you need to call your T-shirt supplier and order Final Four merchandise.

How many do you order?

The Newsvendor Framework

• One chance to decide on the stocking quantity for the product you’re selling

• Demand for the product is uncertain• Known marginal profit for each unit sold and known

marginal loss for the ones that are bought and not sold• Goal: Maximize expected profit

Examples where the Newsvendor framework is appropriate

• Perishable goods– Meals in a cafeteria– Dairy foods

• Short selling season– Christmas trees, toys– Flowers on Valentine’s day– Fashion clothes, seasonal clothes– Newspapers

The Newsvendor Problem

• Newsvendor selling the AJC• Sells the papers for $1.00• Buys them for 70 cents• Leftover papers sold at discount: 20 cents each.• He will definitely have at least 35 customers, but no more

than 40: – 35 customers with probability 0.10– 36 customers with probability 0.15– 37 customers with probability 0.25– 38 customers with probability 0.25– 39 customers with probability 0.15– 40 customers with probability 0.1

How Many Papers Should He Buy To Maximize His Expected Profit?

Marginal analysis

x

Probabili-ty that demand = x

P = Prob. of selling the xth unit

(1-P)=Prob. of NOT selling the xth unit

P x $0.3=Expected profit from selling xth unit

(1-P) x $0.5=Expected loss from NOT selling xth unit

Expected NET profit from stocking xth unit

<35 0

35 0.1 1.0 0 $0.30 $0 $0.30

36 0.15

37 0.25

38 0.25

39 0.15

40 0.1

>40 0

Marginal analysis

x

Probabili-ty that demand = x

P = Prob. of selling the xth unit

(1-P)=Prob. of NOT selling the xth unit

P x $0.3=Expected profit from selling xth unit

(1-P) x $0.5=Expected loss from NOT selling xth unit

Expected NET profit from stocking xth unit

<35 0

35 0.1 1.0 0 $0.30 $0 $0.30

36 0.15 0.9 0.1 $0.27 $0.05 $0.22

37 0.25

38 0.25

39 0.15

40 0.1

>40 0

Marginal analysis

x

Probabili-ty that demand = x

P = Prob. of selling the xth unit

(1-P)=Prob. of NOT selling the xth unit

P x $0.3=Expected profit from selling xth unit

(1-P) x $0.5=Expected loss from NOT selling xth unit

Expected NET profit from stocking xth unit

<35 0

35 0.1 1.0 0 $0.30 $0 $0.30

36 0.15 0.9 0.1 $0.27 $0.05 $0.22

37 0.25 0.75 0.25 $0.225 $0.125 $0.10

38 0.25

39 0.15

40 0.1

>40 0

Marginal analysis

x

Probabili-ty that demand = x

P= Prob. of selling the xth unit

(1-P)=Prob. of NOT selling the xth unit

P x $0.3=Expected profit from selling xth unit

(1-P) x $0.5=Expected loss from NOT selling xth unit

Expected NET profit from stocking xth unit

<35 0

35 0.1 1.0 0 $0.30 $0 $0.30

36 0.15 0.9 0.1 $0.27 $0.05 $0.22

37 0.25 0.75 0.25 $0.225 $0.125 $0.10

38 0.25 0.50 0.50 $0.15 $0.25 $-0.10

39 0.15 0.25 0.75 $0.075 $0.375 $-0.30

40 0.1 0.1 0.9 $0.03 $0.45 $-0.42

>40 0 0 1 $0.0 $0.50 $-0.50

Marginal analysis

x

Probability that demand = x

P= Prob. of selling the xth unit

(1-P)=Prob. of NOT selling the xth unit

P x $0.3=Expected profit from selling xth unit

(1-P) x $0.5=Expected loss from NOT selling xth unit

Expected NET profit from stocking xth unit

<35 0

35 0.1 1.0 0 $0.30 $0 $0.30

36 0.15 0.9 0.1 $0.27 $0.05 $0.22

37 0.25 0.75 0.25 $0.225 $0.125 $0.10

38 0.25 0.50 0.50 $0.15 $0.25 $-0.10

39 0.15 0.25 0.75 $0.075 $0.375 $-0.30

40 0.1 0.1 0.9 $0.03 $0.45 $-0.42

>40 0 0 1 $0.0 $0.50 $-0.50

Decreasing marginal returns to each additional unit.

X*=37

Solution

Start from 35, buy an additional paper only if you expect to make extra profits.

Let’s generalize!c: costr: selling prices: salvage valueMP: marginal profit from selling a stocked unit = r-cML: marginal loss from NOT selling a stocked unit = c-sx: the number of newspapers you buy.P(x): the probability that the xth newspaper is sold = P(D ≥ x)

Solution

Buy one more unit only if the expected net profit of doing so is positive.

Buying x is profitable ifP(x) MP - (1-P(x)) ML ≥0P(x) ≥ ML / (MP + ML)

Critical ratio:Pc=ML / (MP + ML)

Optimal solution: Buy largest x such thatP(x) ≥ Pc

Solution

In this problem: MP = $1-$0.70 = $0.30ML = $0.70 -$0.20 = $0.50

Pc=ML / (MP+ML) = 50 / (50+30) = 0.625

Buy largest x such that P(selling xth unit) ≥ Pc

Marginal analysis

x

Probability that demand = x

P= Prob. of selling the xth unit

(1-P)=Prob. of NOT selling the xth unit

P x $0.3=Expected profit from selling xth unit

(1-P) x $0.5=Expected loss from NOT selling xth unit

Expected NET profit from stocking xth unit

<35 0

35 0.1 1.0 0 $0.30 $0 $0.30

36 0.15 0.9 0.1 $0.27 $0.05 $0.22

37 0.25 0.75 0.25 $0.225 $0.125 $0.10

38 0.25 0.50 0.50 $0.15 $0.25 $-0.10

39 0.15 0.25 0.75 $0.075 $0.375 $-0.30

40 0.1 0.1 0.9 $0.03 $0.45 $-0.42

>40 0 0 1 $0.0 $0.50 $-0.50

Pc = 0.625

X*=37

Now Let’s Assume that Demand is Normally Distributed

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

DEMAND

PR

OB

AB

ILIT

Y D

EN

SIT

Y

=37.5m

=1.44

How do we find order quantity X*?

MP=0.30ML=0.50

P(selling the xth unit) =P(Demand ≥ x)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

DEMAND

PR

OB

AB

ILIT

Y

m

P(Demand≥x)P(Demand<x)

x

Remember solution: Buy largest x such that P(selling xth unit) ≥ Pc

Solution with continuous distribution:Choose X* such that P (D≥ X*) = Pc

Solution: Choose X* such that P (D ≥ X*) = Pc Choose X* such that P (D < X*) = 1-Pc

X*

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

DEMAND

PR

OB

AB

ILIT

Y

mINCREASE X*

DECRESE COST OF LOST SALES

INCREASE COST DUE UNSOLD ITEMS

P(D≥ X*)

DECREASE X*

INCREASE COST OF LOST SALES

DECREASE COST DUE TO UNSOLD ITEMS

Newsvendor: Solution with Normal Distribution

• Remember: MP = 0.30; ML = 0.50• Then Pc is

Pc=ML / (MP+ML)=50/(50+30)=0.625• Look at the z table to find the z corresponding to

1-Pc = 0.375– In this case: z=-0.32

• X*= + z = 37.5 + (-0.32) 1.44 = 37.04

What Do We Learn from the Newsvendor?

• Forecasts are always wrong. A demand estimate that only gives the mean is too simple, you also need the standard deviation.

• The optimal order quantity depends on the relative cost of stocking too much and stocking too little.

• The smaller the standard deviation, the closer will be the order to the mean.

End of Lecture 22