Inv How-To Manual v Erwin Opalla

July 2008

INVENTORY MANAGEMENTHOW-TO MANUAL Version 2.3

Erwin OpallaOttobrunnJuly 2008

July 2008page 2 /

TABLE OF CONTENT

Safety Stock CalculationG

Lot Sizing ModelsF

Problems with Minimum Order QuantitiesE

Practical Application of Inventory ManagementD

Misleading Inventory TurnsC

Basics of ForecastingB

Financial Background and Implication of Inventory ManagementA

SubjectChapter

July 2008page 3 /

By Lord Kalvin

“When you can measure what you are speaking about and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind.”

MEASURE YOUR BUSINESS

July 2008

CHAPTER A

FINANCIAL BACKGROUND AND IMPLICATION OF INVENTORY MANAGEMENT

July 2008page 5 /

FINANCIAL BASICS OF INVENTORY

Many companies try to reduce cost and increase cash flow by tighter control and management of inventory, reducing for example excess inventory.

“Excess inventory is any quantity much larger than needed, desired, or required!”

But many companies are unaware of the amount of excess and obsolete inventory. Excess inventory is all inventory that does not have true demand (orders) or anticipated demand (forecasted orders). The sales force is usually concerned with the most current goods that produce the highest margins. So over time excess and obsolete inventory build up, tie up cash which is not available any longer for future investments.

The next slides should explain some basic financial concepts in relation to inventory management. The main purpose of any manufacturing company is to make a profit. So the understanding of the underlying financials is crucial for anyone being involved in inventory management.

July 2008page 6 /

INVENTORY THOUGHTS

Inventory is an investment, just like the money spent for capital equipment, product development or advertising. Its sole purpose is to generate income. Excess inventory is something not producing any return for the company.

Inventory is classified as a current asset on the balance sheet, which means it is expected to be consumed or converted to cash in less than a year. Buying excess inventory has immediately a negative impact on cash flow.

Too much inventory, more than 1 year-of-supply for example, may not be longer worth its original cost. In this case auditors request that money is set aside in the form of obsolescence reserve for obsolete, slow-moving and/or excess inventory. The resulting obsolescence expense hits immediately the profit line.

Excess inventory results in unnecessary capital investment in the form of a) warehouses stocking the excess, b) workers to handle and transport the goods, c) insurance, damages, shrinkage etc.

July 2008page 7 /

CONFLICTING INVENTORY OBJECTIVES

AREA TYPICAL RESPONSE FOCUS

Marketing / Sales We need all products from our sales catalog in our warehouse available at all times to beat competition. Inventory is too low!

High availability of ALL goods.

Production If we can produce in larger lot sizes our set-up cost will go down, reducing our unit cost and avoiding manufacturing variances.

Large lot sizes. Low unit cost.

Purchasing We can reduce our unit cost if we buy larger quantities using quantity discounts.

Large lot sizes. Low unit cost.

Finance Where do we get the funds from to pay for this high level of inventory? The levels should be lower. High inventory levels affect negatively our liquidity.

Low total inventory carrying cost.

Warehousing We are out of space. We need another warehouse to stock all the goods.

Less space and low holding cost.

(Adopted from Tersine: Principles of Inventory and Materials Management)

July 2008

RETURN-ON-ASSETS

July 2008page 9 /

INDICATORS OF SUCCESS

Today customers expect goods with a high quality at low cost in shortest lead-time. For example, to get the same revenue as a year ago most companies face the dilemma to sell more products, from a volume point of view, but at lower prices affecting negatively their profitability. The question is, what strategy should be chosen to stay competitive and profitable?

Quality

Price

Lead time

Being competitive and making profit in today’s business environment is crucial for the survival of manufacturing companies.

There are at least three indicators of being successful:

1. Quality, 2. Price, 3. Lead time

July 2008page 10 /

STRATEGIC APPROACH

The DuPont Corporation was the first major company recognizing the importance of looking at both Profit Margin and Total Asset Turns in assessing the performance of an organization.

For this reason the Return-on-Asset ratio (Net Profit After Tax / Total Assets) was broken down into the Profit Margin and Total Assets Turns. This breakdown provides a lot of insight for management on how to improve the profitability of a company.

Assets TotalSales

SalesTaxAfter Profit Net

TurnsAsset TotalMarginProfit Assets Total

TaxAfter Profit Net ROA

×=

×=

=

July 2008page 11 /

STRATEGIC APPROACH

The owner or stockholder invests money in a company to get a return in the form of a profit. If the profit is too low the investor might decide putting his money in a bank, because of higher return, or close down the company and invest in a different one. In the past managers focused on the margin earned and have ignored the turnover of assets. But excessive funds tied up in assets can reduce profitability as well as excessive expenses.

Return-on-Equity represents the profitability of funds invested by the owners and should be as high as possible, but it could be high for wrong reasons if total assets were financed with too much debt!

July 2008page 12 /

MODIFIED DUPONT FORMULA

Legend:* Net Profit Margin = Net Profit / Sales* Total Asset Turnover = Sales / Total Assets* Return-on-Assets = Net Profit / Total Assets or

Net Profit Margin x Total Asset Turnover* Equity Multiplier = Total Assets / Total Equity* Return-on-Equity = Net Profit / Total Equity

Return-on-Assets * Equity Multiplier

SalesGross $4,212,000Profit

$1,471,600 -COGS

Net $2,740,400Profit

Total Equity Net Profit $198,000 -$964,030 Margin Operating Expenses

4.7% ÷ Total $1,089,100Sales Expenses Interest

$4,212,000 $1,273,600 $82,500Return on Equity Return on Taxes

Equity Multiplier Assets $102,000

20.5% 2.281 9.0% ×Inventory$632,400

Sales

Total Asset $4,212,000 Accounts

Turnover Current Assets Receivables

1.9 ÷ $1,358,160 $405,000

Total Assets

$2,198,740 + Other Current

Fixed Assets Assets$840,580 $320,760

July 2008page 13 /

MARGIN VIA TURNOVER

Different turnover-margin-relations yield the same ROA. Margin and turnover complement each other. A weak margin can be offset by a strong turnover and vice versa.

In this example, because of more competition, the margin dropped from 9% to 3%. But because of better “Asset Management”, turns improved from 2 to 6, yielding the same return-on-investment of 18%.

ProfitMargin

AssetTurns

18%

9%

3%

2 6

Margin X Turnover = ROA9% X 2.00 = 18%8% X 2.25 = 18%7% X 2.57 = 18%6% X 3.00 = 18%5% X 3.60 = 18%4% X 4.50 = 18%3% X 6.00 = 18%2% X 9.00 = 18%

July 2008page 14 /

DUPONT FORMULA DETAILS

Actions to improve ROA (Return-on-Assets):a) Increase sales by increasing volume, sales price or some combination while

maintaining or improving the margin on sales

b) Decrease all kind of expenses, e.g. freight, admin, traveling,

c) Reduce the amount of total assets employed, e.g. reduce the inventory level,

improve collection of accounts receivable, get rid of unneeded fixed assets.

Assets TotalSales

SalesTaxAfter Profit Net

TurnsAsset TotalMarginProfit Assets Total

TaxAfter Profit Net ROA

×=

×=

=

July 2008page 15 /

ROA (RETURN-ON-ASSET) EXAMPLE

For this example, both margin and turnover were increased by getting rid of redundant inventories, reducing so the inventory holding charge and therefore increasing the net profit without increasing sales!

Before Inventory Reduction

%1818.0

209.0000,150000,300

000,300000,27

Assets TotalSales

SalesTaxAfter Profit Net ROA

==

×=

×=

×=

After Inventory Reduction

%201999.0

1429.20933.0000,140000,300

000,300000,28

Assets TotalSales

SalesTaxAfter Profit Net ROA

==

×=

×=

×=

July 2008

CASH CONVERSION CYCLE

July 2008page 17 /

INVENTORY & CASH CONVERSION CYCLE

The Operating Cycle (OC) is the time between purchasing materials from

suppliers and receiving cash from customers after sold as finished products.

OPERATING CYCLE (OC)OPERATING CYCLE (OC)

Inventory (DOH) Receivables (DSO)

Payables (DPO) Cash Conversion Cycle (CCC)Cash Conversion Cycle (CCC)

Cash Outflow

CashInflow

Inventory received

Inventory shipped

July 2008page 18 /

INVENTORY & CASH CONVERSION CYCLE

The Cash Conversion Cycle (CCC), also called Cash Gap, is the time between

paying cash to suppliers for inventory received and collecting cash from

customers from sale as finished product.

When DPO is smaller than DSO the company would act like a bank!

• DOH is Days Inventory On-Hand, average age of inventory

• DSO is Days Sale Outstanding, average collection period

• DPO is Days Payable Outstanding, average payment period

CCC = DOH + DSO - DPOCCC = DOH + DSO - DPO

July 2008page 19 /

MANAGING THE CASH CONVERSION CYCLE

The basic strategy to manage the Cash Conversion Cycle (CCC) is as follows:

1. Turn over inventory as quickly as possible but avoid stock outs that might

result in loss of sales. The Days Inventory On-Hand (DOH) should be as low

as possible. There are two reasons for this: a) Investors do not like to see a

lot of cash tied up in inventory. Low inventory improves profit and frees up

needed capital for investments. b) Inventory held for too long can become

spoiled or obsolete resulting in an additional obsolescence reserve hitting

the EBIT line on the profit & loss statement as an expense.

July 2008page 20 /

MANAGING THE CASH CONVERSION CYCLE

2. Collect Accounts Receivables as quickly as possible into real cash. This

figure should be as low as possible. A low Days Sales Outstanding (DSO)

means that the company collects its outstanding receivables quickly, which

means that it is not giving interest free loans to its customers for long periods

of time.

3. Pay Accounts Payable as late as possible without damaging credit rating

and take advantage of any discount offered. The Days Payable Outstanding

(DPO) should be as high as possible. A high number represents really an

interest-free loan from its suppliers, as long as they are paid under stated

terms.

July 2008page 21 /

CASH CONVERSION CYCLE REDUCTION

Payables 40 days

Receivables 70 days

Cash Conversion Cycle 80 days

OPERATING CYCLE 120 DAYS



Inventory 50 days

Inventory 50 days Receivables 80 days

Payables 40 days Cash Conversion Cycle 90 days

Inventory 70 days Receivables 80 days

Payables 40 days Cash Conversion Cycle 110 days

Inventory reduction

Receivables reduction

1

2

3

July 2008page 22 /

CASH CONVERSION CYCLE FORMULAS

1. Cash Conversion Cycle (CCC)

CCC = DOH + DSO - DPO

2. Days Inventory On-Hand (DOH)

DOH = Inventory / Daily COGS = Inventory / ( COGS / 360 )

3. Days Sales Outstanding (DSO)

DSO = A/C Receivables / Daily Sales = A/C Receivables / ( Sales / 360 )

4. Days Payable Outstanding (DPO)

DPO = A/C Payables / Daily COGS = A/C Payables / ( COGS / 360 )

July 2008page 23 /

SAMPLE CALCULATION PROFIT & CASH

Current Assets Current Liabilities

Cash $243,000 A/C Payables $269,120A/C Receivables $405,000 Accrued Expenses $130,390Inventory $632,400 Income Tax $10,200Prepaid Expenses $77,760 Notes Payable $300,000

Total Current Assets $1,358,160 Total Current Liabilites $709,710

Fixed Assets Long-Term Debt $525,000

Land $200,000Building $500,000 Stockholder's EquityMachines $218,800 Capital/Stock $766,030Depreciation ($78,220) Retained Earnings $198,000

Total Fixed Assets $840,580 Total Stockholder's Equity $964,030

Total Assets $2,198,740 Total Liabilites & Equity $2,198,740

BALANCE SHEET

Sales $4,212,000Cost-of-Goods Sold $2,740,400

Gross-Profit $1,471,600

Operating Expenses $1,089,100

Net-Operating Income $382,500

Interest Expense $82,500

Earnings Before Income Tax $300,000

Income Tax Expense $102,000

Net Profit $198,000

INCOME STATEMENT

For illustration purposes the cash conversion cycle will be calculated on the next slide.

July 2008page 24 /

SAMPLE CALCULATION PROFIT & CASH CONT.

In this example 83 days represents the average length of time a dollar is tied up in current assets. To free-up cash this number must be reduced.

July 2008

CHAPTER B

BASICS OF FORECASTING

July 2008page 26 /

FORECASTING INTRODUCTION

A detailed discussion of forecasting methods is beyond the scope of this presentation. The interested reader should refer to standard text books available from different authors. The focus of this forecasting section is to highlight some general characteristics of good forecasts.

Forecasts will always be wrong.

Forecasts should include an estimate of error.

Forecasts are more accurate for groups of items.

Forecasts are more accurate for shorter periods of time.

George W. Plossl, Production and Inventory Control Applications

July 2008page 27 /

FORECASTING DILEMMA

A “normal” discussion which was forwarded to me in Jan07. Shannon, supplier, has not shipped a product XXX in the last 12 months. There was no usage and no forecast!

The business is in the toilet, let’s move everything to India.Product Management

Why is the factory empty, how the hell will we make our target?

Operations Shannon

No usage and no forecast means no inventory! What do you expect?

Logistics Ottobrunn

You can’t be serious, how the hell will we make our target!Sales to Ottobrunn

Sorry, you have to buy 250 pcs or nothing because no further usage in Ottobrunn.

Ottobrunn to Sales

No stock, impossible to make 10 pcs, absolute minimum we could make are 250 pcs.

Shannon to Ottobrunn

Can you supply 10 pcs of product XXX?Ottobrunn to Shannon (Supplier)

Can my customer have 10 pcs of product XXX?Sales to Ottobrunn (Order point)

July 2008page 28 /

FORECASTING APPROACHES

“You Can Never Plan the Future from the Past”

“I Know No Way of Judging the Future but by the Past”

by Sir Edmund Burke

by Patrick Henry

July 2008page 29 /

WHY TO FORECAST DEMAND

Time

Bac

klog Forecast

Demand

ActualOrders

2 to 4 weeks

Normally the backlog is for the near future. Turn-around orders will come in which must be forecasted to satisfy customer expectations of short lead times. Without forecasting raw materials and/or components have be ordered after receiving orders resulting in long lead times and maybe lost customers!

July 2008page 30 /

MANUFACTURING STRATEGIES

Q

T

Forecast

Production

Q

T

Forecast

Production

Chase StrategyA production planning method that maintains a stable inventory level while varying production to meet demand.

Level StrategyA production planning method that maintains a stable production rate while varying inventory levels to meet demand.

APICS Dictionary, 11th Edition

July 2008page 31 /

REGULAR VIS IRREGULAR DEMAND

Time

D

Dem

and

Time

Dem

and

Items with regular demand can be statistically forecasted compared to

Items with irregular demand, e.g. promotion–driven demand or intermittent demand (=large portion of zero values), which could be forecasted in well understood business scenarios. Better approach might be discrete forecasting (=future demand for known products will repeat) or tender management.

Regular Demand Irregular Demand

July 2008page 32 /

HOW TO DETECT IRREGULAR DEMAND

Irregular demand consists of either both or one of the following two components:

Sporadic Demand

Zero Demand PeriodsZDP > 0.4

ZDP = Zero Periods / Total Periods

High Fluctuating Demand

Noise Level NL > 0.5

NL = MAD / Mean

Legend:• ZDP is Zero-Demand Periods• NL is Noise Level• MAD is mean absolute deviation• Mean is arithmetic mean

July 2008page 33 /

IRREGULAR DEMAND CALCULATION

Month Past Average AbsoluteDemand Demand Deviation

JAN 346 364 18FEB 312 364 52MAR 387 364 23APR 350 364 14MAY 406 364 42JUN 364 364 0JUL 353 364 11AUG 338 364 26SEP 392 364 28OCT 385 364 21NOV 372 364 8DEC 365 364 1TTL 4,370 244

Noise Level

MAD = 244 / 12 = 20.3Mean = 4,370 / 12 = 364NL = MAD / MeanNL = 20.3 / 364 = 0.06

Zero Demand Periods

ZDP = Zero Periods / Total PeriodsZDP = 0 / 12 = 0

Zero-Demand-Periods are not greater 0.4, so the time series has not a sporadic demand and the Noise Level is not greater than 0.5 so we have not a time series with high fluctuating demand.

This item is a proper candidate for statistical forecasting!

July 2008page 34 /

INDEPENDENT VIS DEPENDENT DEMAND

Parent ItemParent Item

Component1

AssemblyA

Component2

Component1

Component3

IndependentDemand

DependentDemand

Items with independent demand(outside of the control of a company, e.g. customer orders) can and should be forecasted.

Demand for items with dependent demand can be calculated from demand from their parent items and is not forecasted.

July 2008page 35 /

INDEPENDENT VIS DEPENDENT DEMANDPLANNING APPROACH

Material Requirements Planning (MRP)

EOQ with ROP and Safety Stock, Forward Planning

Planning Method

Calculated from BOMsStatistical and Discrete Forecasts, Customer Backlog, Frame Orders

Demand Estimation

Raw Materials, Components, Work-in-process (WIP)

Finished Goods, Spare PartsMaterial Type

Parent Items, AssembliesExternal & Internal CustomersDemand Source

DEPENDENT DEMANDINDEPENDENT DEMANDCATEGORY

Legend:•EOQ is Economic Order Quantity, ROP is Reorder-Point, BOM is Bill-of-Material

Items can have independent (customer order) and dependent (component for parent item) demand!

July 2008page 36 /

DEMAND CHARACTERISTICS

Sales Inventories1

• External, independent demand, based on the marketplace

• Demand is random, relatively continuous

• Demand must be forecasted• Safety stock used to attain target

service level

Manufacturing Inventories• Internal, dependent demand, based

on production schedule• Demand is lumpy and discontinuous• Demand can be calculated• Little or no safety stock needed to

ensure a 100% service level

---------------------1) Finish-Goods-Inventory

Independent demand inventory is sometimes called ‘sales inventory’ and dependent demand inventory ‘manufacturing inventory’. In practice it happens very often that items have independent and dependent demand. The independent portion must then be forecasted and the dependent portion must be calculated!

July 2008page 37 /

DILEMMA OF PLANNING/FORECASTING

There is no direct link between a sales forecast in dollar by product line and a discrete product number in unit-of-measure used for manufacturing and/or procurement.

BusinessPlanning

ProductionPlanning

DemandManagement

DetailedMRP & CRP

Plant&SupplierScheduling

Execution

RCCPPlanning

MRPII

Source: Oliver Wight Co.

Disconnection Line

MasterScheduling

July 2008page 38 /

MasterScheduling

LINKING OF FUNCTIONS

BusinessPlanning Production

Planning

• Yearly• Sales Dollars• Plant StdHours• OpIncome, ROCA

etc• Resources

• Monthly• Product Families• UOM• RCCP

• Weekly• Discrete Products• StdHours per Key

Resource• Driving MRP

Production Planning = Sales and Operations Planning

CONTROLLING

LOGISTICS

July 2008page 39 /

BOTTOM-UP VIS TOP-DOWN FORECASTING

In Bottom-Up forecasting, each product item is forecasted independently and the total group forecast is obtained by summing the item forecast. Most appropriate when item histories are stable and the emphasis is on the trends and seasonal patterns of the individual items.

In Top-Down forecasting, the group history is created and forecasted first, and then the total group forecast is distributed down proportionally among the individual items. Top-down is a better choice if some items have very noisy history or the emphasis is on forecasting at the group level.

Source:Smart Software, Inc., SmartForecasts Version 6 User’s Guide, Page 51

Item A B C

Group

Item A B C

Group

July 2008page 40 /

TOP-DOWN DOLLARS TO UOM

One way to convert sales dollars into manufacturing unit of measures is using average unit costs or price per aggregate unit.

PRODUCT LINETO

PART NUMBER

MANUFACTURINGUnit-of-Measure

SALES DOLLAR

July 2008page 41 /

TOP-DOWN CONVERSION

Projected Sales forProduct-Line

XYZ

Projected Salesin Unit-of-Measure

for XYZ

= $ 4,645,000

= $ 367 / unit

= 12,657 units

Conversion to unit-of-measure done via AVERAGE cost or price per unit.

July 2008page 42 /

FAMILY ITEM A = 1,000 ea

PART 1 = 30% ( 300 ea )

PART 2 = 50% ( 500 ea )

PART 3 = 20% ( 200 ea )

TOP-DOWN PLANNING BILLS

Sales Increase by 50%

FAMILY ITEM A = 1,500 ea

PART 1 = 30% ( 450 ea )

PART 2 = 50% ( 750 ea )

PART 3 = 20% ( 300 ea )

Break down into discrete parts via a constant percentage!

Very critical are the planning percentages per part:* How often reviewed?* What parts to include?* Automatic or manual change?

July 2008page 43 /

BOTTOM-UP PLANNING

Part 1 History Forecast



MV J H/S History ForecastIn Bottom-Up forecasting, each product is fore-casted independently and the total group forecast is obtained by summing the item forecast.

WW SALES AND GROSS MARGIN ANALYSIS

AMERICASEMEA AXICOMASIA/PACIFIC

Entities:Ottobrunn

SimelUK

Reporting LinesMV Joints H/SMV Joints C/ALow Voltage H/S

GAP Analysis

July 2008page 44 /

SELECTING KEY ITEMS FOR FORECASTING

Keeping the right items in inventory assures good customer service and an appropriate inventory investment.

But not all items in inventory have the same importance.

Planners should concentrate on the

few important items

instead of

the many trivial ones.

July 2008page 45 /

DOING FORECASTING RIGHT

Doing forecasting right, it must be understood that each forecast consists of two key components:

Science

component, which describes the forecasting method, e.g. single-exponential smoothing and

Art

component, which includes the marketing and/or sales adjustment.

July 2008page 46 /

STEPS IN FORECASTING

Determine the objective of the forecast, e.g. sales forecast.

Determine which items to forecast, all or key items.

Determine the forecast horizon, monthly, quarterly or yearly.

Determine the forecast frequency, e.g. daily, weekly or monthly.

Plot and clean historical data, e.g detect outliers or adjust missing data.

Automatic selection of forecasting model, e.g. use computer software.

Make forecasts.

Validate results, e.g. adjust results where necessary.

Implement results and make decisions, e.g. load into MRP.

July 2008page 47 /

FORECASTIG ERROR OVER TIME

Future period

PositiveError

NegativeError

To minimize the forecast error , a monthly forecasting approach should be chosen!

Time at forecasting

July 2008page 48 /

ROLLING MONTHLY FORECAST

The Planning horizon should cover at least the next six months. If monthly forecasts are placed, the planning lead time is 4 weeks although the total lead time (from placing an order till goods received in the warehouse) might be 12 weeks.

JUL

JAN

FEB

MAR

AUG SEP OCT NOV DEC

AUG SEP OCT NOV DEC

JANSEP OCT NOV DEC

FEBJANOCT NOV DEC

Planning HorizonRolling 6 Months

CurrentMonth

+ 1 Mth

+ 2 Mth

etc.

July 2008page 49 /

FORECAST BREAKDOWN TO MRP

GROSS-FORECASTMTH JAN FEB MAR APRDAYS 20 19 24 20PLAN 20000 19000 24000 20000

NET-FORECASTWEEK 14 15 16 17Product A 750 500Product B 300....Product X 200 600TOTAL 5000 5000 5000 5000

Product A

SUB PUR

ITEM

RAW

12

3

1. Gross-Forecast by Month

2. Net-Forecast by Week

3. MRP Schedule

MRP SCHEDULEWEEK 17 500

WEEK 16 500

WEEK 15 500

WEEK 14 500

July 2008page 50 /

FORECAST ORDERS FROM MRP TO CRP

Part A

Fiscal Period 1 2 3 4 5 6 7 8Planned Order 100 200 300

Workcenter 4: Detailed Load Period 6Routing Set-up Run-Time TotalWC 4 (min) (min) (100h) Manufacturing hours part A 7Cutting 18 0.5 2.8 Manufacturing hours part B 15H-Coating 24 0.4 2.4 Manufacturing hours part C 5J-Coating --- 0.2 1.0 Planned hours for other parts 158Inspection --- 0.8 0.8

1857.0

Workcenter Summary Report

Period 1 2 3 4 5 6 7Workcenter 4 185Workcenter 5Workcenter 6

1 2 3 4 5 6 7 8Workcenter 4: Load Profile

Planned orders based on forecasted demand

50

250

150

Capacity

Load

Load Hours

MRP is Material Requirements Planning and CRP is Capacity Requirements Planning

1) Cutting: 18’ + 0.5 * 300 = 168’ = 2h48’ 48’/60’=x/100 x=(48/60)*100=80 2.8 hours

1)

July 2008page 51 /

SHOULD ALL ITEMS BE FORECASTED?

Sales pro Year Parts % Trade Sales % Order Lines %(000)

<= $1,200 15,738 42% 6,168 1% 38,080 7%

>$1,200 AND <=$12,000 13,875 37% 61,691 10% 116,188 21%

>$12,000 AND <= $120,000 6,819 18% 255,427 41% 248,137 45%

> $120,000 1,048 3% 293,916 48% 145,305 27%

WORLDWIDE 37,480 100% 617,202 100% 547,710 100%

Legend:* Only competency 13005; CLP installation service exluded

42%

37%

18%

3%

1%

10%

41%

48%

7%

21%

45%

27%

0% 10% 20% 30% 40% 50% 60%

<= $1,200

>$1,200 AND <=$12,000

>$12,000 AND <= $120,000

> $120,000

Parts Trade Sales Order Lines

X Y ZABC

$5,143KInventory

July 2008page 52 /

FORECAST SIMULATION

Items to forecast Forecasted Demand

SmartForecast

AMAPSSimulation

Item Master

Bill ofMaterial

Process &Routing

MRPSeparate AMAPS MRP simulation run from production environment

PurchaseOrders

ProductionOrders

ResultsOkayImplement

No

Yes

Time

Hou

rs

July 2008page 53 /

SAMPLE PROCEDURE

ABC/XYZ

SMOE815

EXRM 1213502K016EPKJ-5210

EPKT-1212MWTM 25/8

Yearly sold items~ 17,000

Planned Items~ 3,700

MAMA Tables

FG = Forecast and safety stockSS = Only safety stockEE = Forecast 10-digit kits EERA = Frames not included in FG & SSZZ = Items using combination of above

JUL

JAN

FEB

MAR

AUG SEP OCT NOV DEC

AUG SEP OCT NOV DEC

JANSEP OCT NOV DEC

FEBJANOCT NOV DEC

Planning HorizonRolling 6 Months

CurrentMonth+ 1 Mth

+ 2 Mth

etc.

Daily/Weekly/Monthly* Items per MAMA table* Inventory value* Safety stock value* Planning parameters

Ottobrunn

TEDWeekly/Monthly* Lead time (=Median)* Early and on time

July 2008page 54 /

PARETO OR ABC ANALYSIS

Pareto Analysis, also called 80/20 rule or ABC analysis, is a method to classify data according to their importance. It was invented by Vilfredo Pareto (1848-1923), an Italian economist and sociologist. He discovered that 80% of the wealth in Italy was held by only 20% of the population, hence called 80/20 rule.

Separate the Important Few from the Trivial Many!

This method is frequently used in inventory management to group items according to their yearly usage value. Close control is important for fast moving items with a high usage value. For slow moving items with a low usage value simple control is applied.

In Inventory Management ABC Analysis is the more common term.

July 2008page 55 /

XYZ ANALYSIS

ABC analysis alone can generate very misleading results. Focusing on A-Items (high yearly usage value) as forecasts for coming periods could be wrong because values might be completely overstated.

ABC analysis is a static method, describing historical data and represents the value component. In inventory management we are more concerned about the future. Will the past repeat?

XYZ analysis is a dynamic method and complements ABC analysis. It represents the time component. How often was an item used and how good can it be forecasted?

July 2008page 56 /

ABC / XYZ BASICS

ABC analysis – value component, static - alone gives misleading results. It must be complemented by a XYZ analysis – time component, dynamic!

ABC / XYZ X Y Z

A High Usage Value High Usage Value High Usage ValueHigh Forecastability Medium Forecastability Low Forecastability

B Medium Usage Value Medium Usage Value Medium Usage ValueHigh Forecastability Medium Forecastability Low Forecastability

C Low Usage Value Low Usage Value Low Usage ValueHigh Forecastability Medium Forecastability Low Forecastability

July 2008page 57 /

ABC / XYZ OVERVIEW

X Y Z

A

B

C

Q

T

XYZ

$%

#%A

ABC

Make-to-order, TenderManagement, Discrete Forecasting

Reorder-Point

Make-To Order,cumulative lead time

XYZ is TIME Component

ABC is VALUEComponent

50%

30%

20%

Items

5%C

15%B

80%A

UsageClass

0 to 5 timesZ

6 to 10 timesY

11, 12 timesX

FrequencyClass

July 2008page 58 /

ABC / XYZ CALCULATION

xx

n

ii

n

= =∑

1

( )sn

x xii

n

=−

−=∑1

12

1

cv sx

=

Calculate the arithmetic mean.Calculate the standard deviation.Divide the standard deviation by the arithmetic mean getting the coefficient of variance.Classify your items into ABC and XYZ, see next slide for rules of thumb.

The steps for determining XYZ are simple and are described below. It is assumed that ABC is known and can be applied.

July 2008page 59 /

ABC / XYZ RULES OF THUMB

• ABCA: 80% of usage value and 20% of items.B: 15% of usage value and 30% of items.C: 5% of usage value and 50% of items.

• XYZ (exact method)X: CV <= 40%Y: CV > 40% and <= 80%Z: CV > 80%

• XYZ (based on frequency)X: FREQ 11, 12Y: FREQ 6 to 10Z: FREQ 0 to 5

The frequency is an integer value counting how often there was a usage greater than zero in the active periods. Max 12 and min 0!

July 2008page 60 /

ABC / XYZ WITH MS EXCEL I

USAGE-USD % Cum% ABC FREQ XYZ CLASS1,412,252 2.00% 2.00% A 11 X AX1,287,090 1.83% 3.83% A 9 Y AY1,152,782 1.64% 5.47% A 10 Y AY1,080,560 1.53% 7.00% A 11 X AX

986,931 1.40% 8.40% A 11 X AX972,563 1.38% 9.78% A 11 X AX

0 0.00% 100.00% C 2 Z CZ0 0.00% 100.00% C 0 Z CZ0 0.00% 100.00% C 0 Z CZ0 0.00% 100.00% C 2 Z CZ0 0.00% 100.00% C 0 Z CZ

70,438,129

=IF([FREQ]<=5,"Z",IF([FREQ]<=10,"Y","X"))=COUNTIF([Usage],">0")

From column [Cum%]:A-items 0 to 80%B-items >80% to 95%C-items >95%

Legend:* [Usage] refers to usage range

July 2008page 61 /

ABC / XYZ WITH MS EXCEL IIUSAGE-USD % Cum% ABC FREQ XYZ CLASS

1,412,252 2.00% 2.00% A 11 X AX1,287,090 1.83% 3.83% A 9 Y AY1,152,782 1.64% 5.47% A 10 Y AY1,080,560 1.53% 7.00% A 11 X AX

986,931 1.40% 8.40% A 11 X AX972,563 1.38% 9.78% A 11 X AX


70,438,129

1. Calculate USAGE-USD per item, e.g. YTD usage quantity multiplied by unit costs.

2. Sort USAGE-USD by descending value and add Total Usage Value, here $70,438,129, at bottom of column.

3. Divide each item’s USAGE-USD by Total Usage Value in column [%].

4. Add cumulative percentages in column [Cum%].

5. From column [Cum%] determine ABC in column [ABC]. Rule-of-thumb: 80% of cumulative percentage A-items, >80% to 95% B-items and balance C-items.

6. Calculate the frequency (How often was the monthly usage greater than Zero?) per item in column [FREQ] with forumula:=Countif([Usage-Range], “>0”)!

July 2008page 62 /

ABC / XYZ WITH MS EXCEL IIIUSAGE-USD % Cum% ABC FREQ XYZ CLASS

1,412,252 2.00% 2.00% A 11 X AX1,287,090 1.83% 3.83% A 9 Y AY1,152,782 1.64% 5.47% A 10 Y AY1,080,560 1.53% 7.00% A 11 X AX

986,931 1.40% 8.40% A 11 X AX972,563 1.38% 9.78% A 11 X AX


70,438,129

7. Calculate XYZ category in Column [XYZ] with a nested if-formula.=If([XYZ]<=5,”Z”,If([XYZ]<=10,”Y”,”X”))

8. Determine CLASS category in column [CLASS] with formula:=[ABC] & [XYZ]

9. Prepare ABC / XYZ analysis overview.

July 2008page 63 /

ABC / XYZ EXCEL RESULTS

ABC Data X Y Z Grand TotalA Items 69 134 93 296

Items% 2.50% 4.86% 3.37% 10.74%Usage 19,083,592 26,752,108 10,475,689 56,311,389Usage% 27.11% 38.01% 14.88% 80.00%Inventory 1,596,775 1,948,628 954,298 4,499,700Inv% 16.06% 19.60% 9.60% 45.26%Res25% 34,564 16,520 2,011 53,095Res100% 0 0 0 0

B Items 31 173 313 517Items% 1.12% 6.27% 11.35% 18.75%Usage 667,003 3,952,292 5,945,577 10,564,872Usage% 0.95% 5.61% 8.45% 15.01%Inventory 172,619 748,739 1,326,590 2,247,948Inv% 1.74% 7.53% 13.34% 22.61%Res25% 7,056 28,843 101,115 137,013Res100% 0 0 38,925 38,925

C Items 75 199 1,670 1,944Items% 2.72% 7.22% 60.57% 70.51%Usage 166,513 621,558 2,726,583 3,514,654Usage% 0.24% 0.88% 3.87% 4.99%Inventory 98,749 331,880 2,764,252 3,194,881Inv% 0.99% 3.34% 27.80% 32.13%Res25% 8,687 33,754 135,687 178,129Res100% 0 881 1,187,916 1,188,796

Total Items 175 506 2,076 2,757Total Items% 6.35% 18.35% 75.30% 100.00%Total Usage 19,917,108 31,325,958 19,147,849 70,390,915Total Usage% 28.29% 44.50% 27.20% 100.00%Total Inventory 1,868,143 3,029,246 5,045,139 9,942,529Total Inv% 18.79% 30.47% 50.74% 100.00%Total Res25% 50,307 79,116 238,813 368,236Total Res100% 0 881 1,226,840 1,227,721

ABC

XYZ

Items

InventoryUsage

ObsolescenceReserve

July 2008page 64 /

ABC/XYZ INVENTORY POLICY RULES

No forecasting and safety stock, make-to-order policy, order quantity LFL (lot-for-lot), cumulative lead times

CZ

No forecasting due to low usage and/or sales value, safety stock policy should be used only, economic order quantity can be applied

CX, CY

Tender management or discrete forecasting if applicable, make-to-order policy, long lead times

AZ, BZ

Can be statistically forecasted, make-to-stock or assemble-to-order policy, medium lead times

BY

Statistically forecasted, make-to-stock policy, short lead times, safety stock policy should be used

AX, AY, BX

July 2008page 65 /

PRACTICAL FORECAST EXAMPLE

• The next slides show detailed steps converting historical sales data into forecasts. MRP screens are shown as well.

• Cognos Query is used to extract historical sales data from TED (Tyco Electronics Data Warehouse).

• Microsoft Access is used to change vertical historical data into horizontal time periods.

• Software used for forecasting SmartForecasts for Windows, Version 6, Commercial Edition, from Smart Software, Inc.

July 2008page 66 /

COGNOS QUERYData & Filter

The query data contain all fields of interest and the filter definition downloads only selected historical data records from TED. Save into a comma separated file!

July 2008page 67 /

HISTORY AND FORECASTS

History Current

Current month forecast values will NOT be loaded into AMAPS!

36 months historical values

AMAPS MRP relevant months with forecast values always total forecasted months minus current month.

12 months forecasted with Smart Forecast for Windows

July 2008page 68 /

FORECAST FILTER

The Crosstab query filters from historical sales data only items which should be forecasted (=Finished Goods, Quick-Ship, Off-the-shelve). Vertical time periods are changed to horizontal ones for easier forecasting.

July 2008page 69 /

COPY FILTERED DATA

Copy query content from Microsoft Access into Smart Forecast for Windows. If needed sort periods in right sequence.

July 2008page 70 /

FILL BLANKS WITH ZERO

Fill blank cells with zero. Zeros are valid historical values but blanks are treated as gaps in the time series and forecasts will start at blank cells.

July 2008page 71 /

FORECAST TOURNAMENT

1) Configure ---> Files; Variable Labels = 62) Forecast tournament with Smart Forecast

for Windows. Automatic selection of forecasting method

3) Forecast horizon = 12

July 2008page 72 /

BASIC FORECASTING STEPSSmart Forecast for Windows

1) Adjust forecast as needed; review manual for more details.2) Save forecasts results; press button “Save All … “3) Export final forecast into Microsoft Excel.4) Load into MRP system; AMAPS in Ottobrunn.

July 2008page 73 /

FORECASTS IN MRP SYSTEMSample screen from Ottobrunn’s AMAPS

Demand generated by Forecasting is identified by an order type M/S.

July 2008page 74 /

PERIOD ORDER QUANTITYSample screen from Ottobrunn’s AMAPS

A dynamic Order Policy is used, here POS (=Periods of Supply).

July 2008

SAP CLASSIFICATION OF MATERIAL

July 2008page 76 /

The following criteria are aimed for a stock material:

• At least 5 months demand in the last 6 months.• At least 3 customers in last 6 months• No customer greater than 75% share in last 6 months• A ratio of the last 2 months demand compared to the avg. demand in last 6

months.• Supply MOQ < 3 months forecast• At least 1 PPQ per weeks forecast• At least 12 ship lines (hits) in last 6 months• The X Distribution Chain status must be E2 (released).• Material must not be included on the “do not change to stock” file.

TYCO’S GIC SAP STOCK POLICY Z100

Paul McCullagh, GIC EMEA

AX, AY, BX

July 2008page 77 /

This is firstly a transitional MRP Group with a view to changing to Z100.

• When a new Stock material has been identified and agreed with the relevant PM it will be changed to a Z110 for an initial 3 month period. This then allows the Xelus forecast to be active in MRP. At the end of this period and if thematerial still meets the required criteria, it is then changed to a Z100. Any failed materials are reviewed on a individual basis with the PM to either change to Z120 or Z200.

• Z110 can also be used for a manual forecast provided by the PM to initiate supply for a new or strategic product.



BY

July 2008page 78 /

• A Z120 strategic material is Sales/Product Management initiated.These are materials that do not qualify to be Stock. These materials are effectively Make to Order with a replenishment lead time as a Z200.

There are 4 reasons why a material can be a Z120 :

• Customer Order with supporting schedule agreement for the MOQ.• A buffer stock• A forecasted part for specific customers in the form of schedule agreements• Agreement to sell in PPQ’s.



AZ, BZ

July 2008page 79 /

• Back to Back ordering Logic only.• No Xelus forecasts.• No EDI forecasts.• No Schedule agreements• No Buffer stocks.



CZ

July 2008

INVENTORY QUALITY RATIO (IQR)

July 2008page 81 /

INVENTORY QUALITY RATIO (IQR)

The IQR logic divides inventory into three groups: items with future requirements, items with no future requirements but with recent past usage, and items with neither. The items in these groups are then stratified into typical ABC-type classifications using their future dollar requirements, their past dollar usage, or their current balances on hand. A rule or target inventory level is set for each item based on its classification. The balance on hand of each item is compared to the rule and the dollars of each item are categorized as either active (A1 or A2), excess (E1, E2 or E3), slow moving (SM) or no moving (NM). These are called the seven quality categories.

Gary Gossard, Improving Inventory Performance and Bottom-Line Profits

The IQR is the ratio of active inventory dollars to total inventory dollars.

In a theoretically perfect situation (i.e., with no excess, slow moving or no moving inventories), the IQR would be 100 percent. Using nominal target inventory levels of 4-12-24 weeks’ supply for A-B-C items, respectively, the IQR for most companies surveyed is in the 30-45 percent range.

July 2008page 82 /

OVERVIEW INVENTORY QUALITY RATIO

6

A1A1 A2A2

NMNM

SMSM

E1E1

E3E3

12

BB

R H

D E F A B C

E2E2

MRP / ERP

Extract

A B C

GHK

DataBOHV

80 - 15 - 5 %4 - 12 - 24

AWWUV

© 1992-2004 IQR International

AWWRV

July 2008page 83 /

INVENTORY QUALITY RATIO

IQRIQR ==A1 + A2A1 + A2

IQR =IQR =Active Inventory DollarsActive Inventory Dollars

Total Inventory DollarsTotal Inventory Dollars

Perfect Perfect IQRIQR = 100%= 100%

A1 + A2A1 + A2 + E1 + E2 + E3+ E1 + E2 + E3 + SM + NM+ SM + NM


July 2008page 84 /

AVERAGE INVENTORY QUALITY RATIO


IQRIQR ==A1 + A2A1 + A2

IQR =IQR =Active Inventory DollarsActive Inventory Dollars

Total Inventory DollarsTotal Inventory Dollars

Average Average IQRIQR = 30= 30--45%45%

10%10%3030--50%50%

A1 + A2A1 + A2 + E1 + + E1 + E2E2 + E3+ E3 + + SM + NMSM + NM

July 2008page 85 /

INVENTORY QUALITY RATIO LOGIC


• Analyzes inventory using:- Balance on hand and unit cost- Past usage and future requirements- Dynamic ABC and user-defined parameters

• Develops inventory quality categories:- Active: reqmt/use, balance within limits- Excess: reqmt/use, balance over user’s limits- Slow Moving: no reqmt, no use in 6 months- No Moving: no reqmt, no use in 12 months

• Measures overall inventory performance.

July 2008page 86 /

INVENTORY QUALITY RATIO SAMPLE


Quick Look Dollars ($1000) by Purch / Manuf and Quality Category

Purch Active Active Excess Excess Excess Slow No Total IQRManuf 1 2 1 2 3 Moving Moving Value Ratio

P 351 16,994 4,097 26,879 0 1,738 3,400 53,458 32.4%

M 21 695 121 385 18 267 1,507 47.5%

Total 372 17,689 4,218 27,264 0 1,756 3,667 54,965 32.9%

0

July 2008

ABC / XYZ CLASSIFICATIONExamples

July 2008page 88 /

EXERCISE 1 A

Description: SOME-1094-102K049-126/89Unit-Cost: €6.10Qty on-hand: 3,800Inventory Value: €23,161Usage Value: €22,552Months with Usage: 7 (=Frequency)

What quantity will be forecasted?

July 2008page 89 /

EXERCISE 1 B

Classification = BY

July 2008page 90 /

CONCLUSION EXERCISE 1

The Arithmetic Mean is an in-appropriate tool to use as an order quantity and/or monthly forecast for items with irregular demand.

In this situation the Median ( = the middle value! ) should be used instead, because it excludes extreme high and/or low values!

Stock is normally available for components going into parent items. Lead times could be 2 to 3 weeks.

These items are normally purchased and/or manufactured with an assemble-to-order policy.

July 2008page 91 /

EXERCISE 2 A

Description: RICS-5043-30-1Unit-Cost: €20.67Qty on-hand: 1,106Inventory Value: €22,864Usage Value: €364,734Months with Usage: 12 (=Frequency)


July 2008page 92 /

EXERCISE 2 B

Classification = AX

July 2008page 93 /


For items with regular demand, either the Arithmetic Mean or the Median could be the proper tool for calculating monthly order quantities and/or forecasts.

A good practice in forecasting is, to eliminate extreme values. One method could be excluding the highest and lowest value!

Stock is normally available and lead times are short and predictable.

These items are purchased and/or manufactured with a make-to-stock policy.

July 2008page 94 /

EXERCISE 3 A

Description: 603W035-53/239(S5)Unit-Cost: €8.58Qty on-hand: 1,400Inventory Value: €12,006Usage Value: €5,146Months with Usage: 2 (=Frequency)


July 2008page 95 /

EXERCISE 3 B

Classification = CZ

July 2008page 96 /


For items with one-time or very irregular demand, either the Arithmetic Mean or the Median are in-proper tools for monthly order quantities and/or forecasts.

These items should be treated with discrete and not with statistical forecasting. Could build stock in anticipation of a known (=discrete) potential order with a high probability.

In nearly all cases, this items are purchased and manufactured with a make-to-order policy.

Stock is normally not available and lead times are long!

July 2008

CHAPTER C

MISLEADING INVENTORY TURNS

July 2008page 98 /

MISLEADING INVENTORY TURNS INTRODUCTION

Adam Hinton, controller UK, wrote me an E-Mail on the 10th of July 2006 with the following content regarding the inventory performance for Dulmison UK for June 2006:

“Erwin, Q3 Dulmison COS (cost-of-sales) was $1,146K; annualized COS equals $4,582K; current inventory $447K; stock turns 10.25.”

He concluded, that inventory turns is a misleading figure because much of the Dulmison UK inventory was slow moving and most of the sales were from drop shipped projects [from Thailand]. The UK got a credit for the cost-of-sales although there was no inventory activity because of the drop-shipments. The next slide illustrates the unfavorable month-of-supply distribution and why inventory turns or DOH (days on-hand) were misleading.

July 2008page 99 /

MISLEADING INVENTORY TURNS INTRODUCTION CHART

July 2008page 100 /

MISLEADING INVENTORY TURNS 1A

Ottobrunn, Jordan Products, July 2004

Gross-Inv: $450,054

3 COS: $1,625,663

(Jul04: $502,659, Jun04: $480,792,May04: 642,212)

Daily COS: $1,625,663 / 90 ~ $18,063

Days: $450,054 / $18,063 ~ 25

Inv Turns: 360 / 25 ~ 14.4

Based on inventory turns pretty good performance. But is there a further potential for inventory reduction?

July 2008page 101 /

MISLEADING INVENTORY TURNS 1B

Although inventory turns were pretty high with 14.4 there is another inventory reduction potential of at least $74K!

July 2008page 102 /

MISLEADING INVENTORY TURNS 2A

Shannon, Cable Accessories, July 2004

Gross-Inv: $1,527,221

3 COS: $5,882,663

(Jul04: $1,922K, Jun04: $1,623K,May04: $2,338K)

Daily COS: $5,882,663 / 90 ~ $65,363

Days: $1,527,221 / $65,363 ~ 23

Inv Turns: 360 / 23 ~ 16

Based on inventory turns pretty good performance. But is there a further potential for inventory reduction?

July 2008page 103 /

MISLEADING INVENTORY TURNS 2B

Inventory turns of 16 were misleading. In fact we have a big obsolescence reserve problem of around $500K!

July 2008

CHAPTER D

PRACTICAL APPLICATION OF INVENTORY MANAGEMENT

July 2008page 105 /

INVENTORY REDUCTION APPROACH

Management Input

Classification of Sites

Inventory Control Tools

3-Years Inventory Targets:50-Days-Reach Inventory or

7.2 WW Inventory Turns

Manufacturing Sites: 4+ TurnsDistribution Sites: 6 – 8 TurnsSales Inventory Sites: 12 Turns

• ABC/XYZ Analysis• Month-of-Supply• Obs Reserve Procedure• Push / Pull Strategy• Inventory Ratios

Sites classified as 'Distribution Inventory' must have a kitting operation and sites classified as 'Sales Inventory' have no kitting operation – only pick & pack!

July 2008page 106 /

INVENTORY POLICY for Global EnergyPublished 6th February, 2008

Tony Gatt / Joe Lane / Olaf Happe

Further to our e-mail in June 2007, it has become necessary to issue a further reminder and re-statement of the Inventory Policy for Global Energy Division as follows:

• No supplying site is allowed to ship more than 2 MOS (months-of-supply) to ordering sites based on minimum order quantities for purchased and manufactured parts. Supplying sites producing or purchasing minimum lot sizes over 2 MOS have to keep the excess inventory if this does not affect negatively their inventory targets.

• As of December 2007 CZ parts (no usage and no demand in the last 12 months) accounted for [3.2%] of our usage and [19.6%] of worldwide gross-inventory. This has to be reversed. Ordering sites should refuse receipts over 2 MOS if this will hurt their inventory targets. To avoid unnecessary inventory build-up in our supply-chain, orders have to be placed directly to supplying sites.

• No inventory build is allowed for potential projects with questionable accounts. It is mandatory to have an order before. The key objective is to cut our worldwide shipping inventory (not released due to customer inflicted reasons) by half down to $2.5M to $3M.

Urgent action is needed now. We expect all sites and functions to fully support these measures. Energy management will consider taking appropriate disciplinary action against anyone who fails to comply with this policy. Any business requirements which need to deviate from this policy will be approved by Olaf Happe on an exception basis.

July 2008page 107 /

INVENTORY CYCLE I

RM WIP

M&P

FG

GIT

COGS

Intercos RevenueRecognition

Net-Inventory and DOH

Obsolescence Reserve

1.Accounting View of Inventory

2. Approximated DOH

3. Month-of-Supply Analysis

X Y Z

A

B

C

Make-to-order, TenderManagement, Discrete Forecasting

Reorder-Point

Make-To Order,cumulative lead time

Q

T

XYZQ

T

XYZ

$%

#%A

ABC

$%

#%A

ABC

XYZ is TIME Component

ABC is VALUEComponent

4. ABC / XYZ Analysis

July 2008page 108 /

INVENTORY CYCLE II

1. The „Accounting View of Inventory“ splits inventory into raw material, work-in-process, and finished goods. The focus here is „added-value“ from receiving material into the warehouse till the shipment to the customer as finished goods. For inventory control this view is not sufficient for corrective actions.

2. Calculating „Approximated DOH“ breaks down inventory into product lines and/or groups separating the good from the bad performers. The bad performers have to be broken down further.

3. A „Month-of-supply Analysis“ of inventory (=aging!) should be done to detect the scope of the problem for the bad performers. A good inventory distribution must be right-skewed.

4. Last but not least a combined „ABC/XYZ Analysis“ is needed to find the items representing the „bread-and-butter“ business also called standard products. Here we determine our inventory strategy, e.g. make-to-order or make-to-stock, safety stock, lot sizes etc.

July 2008page 109 /

Trade Sales FY 2006

XYZABC Data X Y Z Grand TotalA Parts 2,103 1,526 1,329 4,958

Parts % 5.5% 4.0% 3.4% 12.9%Sales 310,208,124 154,469,291 97,954,126 562,631,541Sales % 44.1% 22.0% 13.9% 80.0%Margin 148,498,509 60,404,177 35,165,566 244,068,252Margin% 49.2% 20.0% 11.6% 80.8%

B Parts 1,195 2,386 4,416 7,997Parts % 3.1% 6.2% 11.5% 20.8%Sales 18,226,298 32,236,584 55,049,545 105,512,427Sales % 2.6% 4.6% 7.8% 15.0%Margin 7,783,244 14,366,248 22,182,658 44,332,150Margin% 2.6% 4.8% 7.3% 14.7%

C Parts 489 2,569 22,519 25,577Parts % 1.3% 6.7% 58.4% 66.4%Sales 1,501,919 6,215,043 27,448,623 35,165,586Sales % 0.2% 0.9% 3.9% 5.0%Margin 552,783 2,461,219 10,568,462 13,582,464Margin% 0.2% 0.8% 3.5% 4.5%

Total Parts 3,787 6,481 28,264 38,532Total Parts % 9.8% 16.8% 73.4% 100.0%Total Sales 329,936,340 192,920,919 180,452,294 703,309,553Total Sales % 46.9% 27.4% 25.7% 100.0%Total Margin 156,834,535 77,231,644 67,916,686 301,982,866Total Margin% 51.9% 25.6% 22.5% 100.0%

• TED trade sales of $703M in USD TBR06 in FY2006 for competency 13005 (only Energy).

• We sold around 40K discrete products but around 60% of our products in class CZ generated only 3.9% of sales with only 3.5% of margin.

• For our repetitive business in class AX, AY, BX, and BY we only needed ~20% items but generating ~75% of sales.

July 2008page 110 /

Trade Sales FY 2006 – C Items

Looking at C-items from an inventory point of view it can be shown that these items account for the majority of slow-moving and/or dead-stock inventory. Most fo these items have a low inventory value but the cumulative impact goes into the millions!

July 2008page 111 /

FY2007 Inventory Reduction Approach

ADR-049 December 2006:Purchased outside Vendor $48,129 43%Manufactured in-house $33,801 31%Purchased within Tyco $28,500 26%

July 2008page 112 /

MONTHLY INVENTORY REPORTING

1. All reported inventory is based on Hyperion and valued in USD TBR (Tyco-Budget-Rate) for FY2007.

2. Reported inventory represents Net-Inventory.

3. Net-Inventory consists of raw-material plus work-in-progress plus finished goods plus goods in-transit minus obsolescence reserve.

4. Inventory turns or DOH (days on-hand) are based on Hyperion total trade COS (other and standard cost-of-sales) and are used as corporate performance measure.

5. Depending on the Interco shipments per site DOH for worldwide benchmarking might be based on total shipments – Interco and Trade shipments at cost – from TED (Tyco Electronics Data warehouse).

6. Total cost-of-sales for Zibo is based on feedback from local controllers.

July 2008page 113 /

WW Inventory by Region Jan07

$19,23113.8%

$4,4273.2%

$12,2438.8%

$89,02364.1% $13,984

10.1%TOP10 $138,908 107Ottobrunn $30,173 56U.K. $15,429 126USA $15,070 107Shannon $13,911 131Gevrey $11,254 68Wyong $11,504 126Axicom $5,587 55Canada $3,261 53Corp-India $1,978 116

July 2008page 114 /

MONTHLY HYPERION INVENTORY REPORTING

Monthly Hyperion inventory reporting (=accounting view!)

July 2008page 115 /

MONTHLY INVENTORY REPORTING TOP 10

July 2008page 116 /

MONTHLY INVENTORY BY COMPETENCY

July 2008page 117 /

MONTHLY INVENTORY PROJECTION

Monthly inventory reduction action meetings.

Oct07 Nov07 Dec07 Feb08 Mar08 Apr08 Feb08 Mar08 Apr08 Sep08Act Act Act Fcst Fcst Fcst Plan Plan Plan Plan

NET-INVENTORY BASE 133,333 81 136,171 144,014 142,416 144,467 99 145,510 145,550 144,000 138,937 138,002 139,611 132,790Ottobrunn 0973 M. Kessler TED 31,740 50 33,305 34,102 33,977 35,111 63 35,000 36,000 35,000 31,694 31,903 32,037 30,756Gevrey 0436 C. Djane TED 11,356 59 12,105 12,491 12,586 12,328 75 12,200 12,200 12,200 11,545 11,774 12,298 10,883UK All T. Burgess TED 12,622 62 12,937 12,825 12,519 12,898 79 13,000 12,600 12,400 11,536 11,487 11,662 11,000Shannon 0964 R. MacDonnell TED 10,766 94 10,691 10,934 10,864 11,159 126 11,500 11,500 11,500 11,700 11,700 11,700 10,000Axicom 1294 D. Stenz TED 6,061 49 7,084 8,225 8,225 7,863 58 8,000 8,000 7,000 6,350 6,350 6,500 6,700India All H. Dave TED 3,742 128 4,165 3,795 4,021 4,143 156 4,200 4,100 4,350 5,663 5,700 5,658 5,161Saudi 0993 H. Dave HYP 984 50 1,193 1,113 1,131 1,226 104 1,250 1,200 1,450 2,730 2,580 2,430 2,200Dubai 1369 A. Wadhwa HYP 2,666 70 2,838 3,351 3,114 2,995 66 3,100 3,200 3,200 3,400 3,400 3,100 2,900USA FV 1083 M. Dominguez HYP 11,589 83 12,152 13,827 13,859 15,305 124 14,700 14,300 14,300 14,000 13,500 14,000 11,036Canada 0392 M. Dominguez TED 2,798 50 3,211 3,259 2,656 2,138 32 2,200 2,200 2,200 3,180 2,379 2,461 2,800Brazil 1300 R. Leme TED 1,797 63 1,896 1,658 1,769 1,977 90 2,230 2,000 2,100 2,100 2,000 1,900 1,650Mexico 0399 R. Leme HYP 1,143 74 861 867 966 1,048 59 1,200 1,350 1,250 1,450 1,200 1,250 1,100Wyong 1147 A. Morris HYP 10,557 106 10,719 11,414 11,230 11,254 95 10,900 11,000 10,900 9,100 9,000 9,000 9,000Thailand 1148 Nok TED 6,076 137 5,501 5,184 5,143 5,166 114 5,700 5,500 5,500 4,900 4,900 5,200 7,000Hong Kong 0451 J. Wong HYP 1,014 32 1,194 1,490 1,385 985 28 1,200 1,200 1,300 1,393 1,681 1,680 1,450Shanghai 1006 H. Qiu HYP 2,323 73 2,753 3,749 3,230 3,754 97 3,800 3,800 3,800 3,576 3,680 3,732 3,732Zibo 1149 H. Qiu TED 1,114 64 1,242 1,294 1,477 1,419 82 1,500 1,500 1,500 2,177 2,229 2,488 2,851Indonesia 1143 A. Glennharto TED 758 50 1,025 1,231 1,158 1,194 53 1,200 1,300 1,400 1,164 1,172 1,216 1,356Singapore 1,014 R. Tan HYP 762 53 999 940 977 1,028 71 1,100 1,100 1,100 950 980 900 780Dul Malay ??? S. Wan Yusuf HYP 713 60 675 834 728 728 141 750 750 750 750 800 750 600Rayenergo ??? D. Kryukov HYP 1,647 81 1,574 1,912 1,658 1,747 87 1,780 1,750 1,800 1,577 1,588 1,648 1,837Other Sites XXXX E. Opalla 8,517 8,051 9,519 9,743 9,001 9,000 9,000 9,000 8,000 8,000 8,000 8,000

Legend: Fcst DOH* Fy2008 recost impact on inventory $2,588K!

3COS = $131,000 100

3COS = $140,000 94

Sep07 Jan08Act Act

Actual Inventory FY2008FY 2007 Inventory Forecast Inventory Plan FY 2008

July 2008page 118 /

INVENTORY FORMULAS

1. Daily Cost-of-sales = COS last three months divided by 90

2. Days-Reach (DOH) = Net-Inventory divided by daily cost-of-sales

3. Inventory-Turns = 360 / Days-Reach

The following formulas are used for Inventory Days-Reach and Turns.

COSDaily INV

90) / (3COS / INV3COS4

INV 360INV) / 3COS) ((4 / 360

INV) / (COS / 360Turns / 360DOH

=

=××

=

×===

Derivation:

July 2008page 119 /

MONTH-OF-SUPPLY CALCULATION I

A good starting point for analyzing manufacturing inventory is a simple month-of-supply calculation. This ratio gives a good insight into the “aging”of inventory and highlights items where urgent review of order parameter is needed.

1. Dead-stock is all inventory with no usage in the last 12 months and no demand.

2. 1st Demand has as well no usage in the last 12 months but for the first time demand has been recorded.

July 2008page 120 /

MONTH-OF-SUPPLY CALCULATION II

1. Divide per item the last 12-month usage by the number of active usage periods.

2. Divide the current free qty on-hand by the monthly usage from point “1”.3. Classify the inventory in meaningful terms, see next slide for an example.

Example:Usage last 12 months = 600 pcs, Active periods = 6, and Qty OH = 500 pcs

Month of Supply QtyOHUsage last 12 months

Active Periods= 500

6006

5 months

− − = ÷

÷=

The calculation is done in three steps:

July 2008page 121 /

Quality of Inventory Percentage (QIP)% of Inventory < 3 MOS

( ) ( ) ( )

43%$104,652

$11,767$18,447$14,803InventoryGrossTotal

3M22M11M0QIP

=

++=

−+−+−=

QIP should be between 60 to 70%!

July 2008page 122 /

FY 2008 Inventory Reduction PlanQuality of Inventory Percentage (QIP)

The QOI percentage must be around 70%.

July 2008page 123 /

Approximated DOH

Approximated DOH by competency will be used to detect inventory reduction potential during monthly inventory reviews. A good inventory performance is right-skewed using month-of-supply and has a QIP between 60 to 70%!

July 2008page 124 /

MONTH-OF-SUPPLY APPLICATION I

• Dead-Stock items had Zero Usage and Zero Demand and were active in the last 12 months.

• 1st Demand are all items with Zero Usage but First Time Demand.

Competency Code 5 0-1 M 1-2 M 2-3 M 3-6 M 6-12 M 12-24 M 24-99 M 1st Demand Dead Stock Total %Bowthorpe (13155) 108,688 131,253 73,274 447,932 432,947 988,310 1,020,085 62,482 466,451 3,731,422 37.53%ENERGY CABLE ACCS (13041) 445,180 436,146 324,951 483,692 109,360 47,555 258,256 190,305 2,295,446 23.09%INSULATORS (13040) 214,742 50,101 152,916 228,350 620,104 300,248 461,200 184,685 2,212,347 22.25%SURGE ARRESTER (13037) 114,659 372 28,646 111,320 102,848 40,930 176,476 31,983 607,233 6.11%COMPOUNDS (13054) 14,845 192,682 66,122 153,957 69,645 42,459 29,118 24,261 593,090 5.97%COPPER (13061) 16,621 30,137 81,711 11,965 38,994 13,902 25,361 218,692 2.20%RAYSULATE (13039) 3,758 19,164 26,513 41,760 4,657 25,059 33,685 6,562 161,157 1.62%Dulmison Insulators (13074) 4,173 360 9,731 12,411 23,034 20,145 36,492 106,346 1.07%MATERIALS (13055) 9,393 9,393 0.09%B&H Products (13150) 3,973 3,973 0.04%HARNESS COMPONENTS (13048) 0 739 1,161 1,901 0.02%DULMISON FITTINGS (13072) 0 492 257 748 0.01%HV Products (13234) 623 623 0.01%HARNESSES (13049) 89 89 0.00%SINGLE WALL TUBING (13043) 0 69 69 0.00%Utilux (13181) 0 0 0.00%SUCOFIT PRODUCTS (13149) 0 0 0.00%Corrosion Protection (13007) 0 0 0.00%

Total 932,772 860,954 682,153 1,562,363 1,374,560 1,503,700 1,997,189 62,482 966,357 9,942,529 100%% 9.38% 8.66% 6.86% 15.71% 13.83% 15.12% 20.09% 0.63% 9.72% 100%

July 2008page 125 /

932,772860,954

682,153

1,562,363

1,374,560

1,503,700

1,997,189

62,482

966,357

0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

0-1 M 1-2 M 2-3 M 3-6 M 6-12 M 12-24 M 24-99 M 1st Demand Dead Stock

MONTH-OF-SUPPLY APPLICATION II

Target

July 2008page 126 /

TYCO’S OBSOLESCENCE RESERVE POLICY

Each site has to report their obsolescence reserve. This is normally done by finance quarterly. It's important to understand the impact of changing the obsolescence reserve. An increase of obs reserve from $500 to $1,000 has an immediate income impact because our operating income will be reduced by the resulting obs expense.

July 2008page 127 /

OBSOLESCENCE RESERVE EXAMPLE

Usage per year is 300 pcs; Quantity on-hand is 500 pcs.

1. Transactions in the last 6 months

500 pcs minus 300 pcs is 200 pcs.Obs Res is 200 pcs * 25%

2. Transactions in month 7 to 12

500 pcs minus 300 pcs is 200 pcsObsRes is 200 pcs * 100%

3. No Transactions in the last 12 months

500 pcs minus 0 is 500 pcsObs Res is 500 pcs * 100%

July 2008page 128 /

ORDER QUANTITIES GUIDELINES

Worldwide Controller and/or Global Logistics Manager

Greater than 6 months-of-supply

Local group leader, authorized by local Logistics Manager

Between 2 to 6 month-of-supply

Local planner/buyerUp to 2 month-of-supply

July 2008page 129 /

STOCK BUILD APPROVALWhen to Apply• Stock Builds should be used for items having irregular demand or for new product launches.

For items with regular demand a stock build is only needed if violating our inventory policy not ordering and/or producing more than 2 months-of-supply of inventory. All values must be entered in K USD!

• The Requester of the stock build is normally a person from sales and/or product management.

• The Issuer of the stock build is the person filling out the form. It can be the same person as the requester but this depends on the decision of the local Supply-Chain-Manager granting access to this application. The issuer sends the stock build to the approver with the status Initialized. The issuer has the responsibility to maintain “current” stock builds. Old or completed stock builds should be closed as explained in the training.

• The Approver is the local supply-chain manager being accountable for the inventory performance. Depending on the total value (see as well approval level policy) the approver can approve/authorize the stock build if it does not violate his approval level policy. If the value for the stock build is higher than his approval limit the stock build is send to EMT members for authorization. As the time of writing this mail we identified the following approvers

• The Authorizers are Geert Quaegebeur and Olaf Happe.

July 2008page 130 /

STOCK BUILD APPROVALList of Approvers – February 2008

1147 Wyong Australia Ashley Morris [email protected]

1300 Braganza Brazil Ruy Leme [email protected]

0451 Hong Kong Jassica Wong [email protected]

1006 Shanghai China Heidi Qiu [email protected]

1149 Zibo China Heidi Qiu [email protected]

0436 Gevrey France Fabrice Chazee [email protected]

0973 Ottobrunn Germany Michael Kessler [email protected]

0464 India-Corp India Himanshu Dave [email protected]

1144 India-Sys India Himanshu Dave [email protected]

1143 Djakarta Indonesia Agus Glennharto [email protected]

0964 Shannon Ireland Randal McDonnell [email protected]

0468 Auckland New Zealand Murray Green [email protected]

9999 Moscow Russia Dmitry Kryukov [email protected]

0993 Damman Saudi Arabia Himanshu Dave [email protected]

1014 Singapore Ridhwan Tan [email protected]

1151-0862 Wohlen CH Daniel Stenz [email protected]

1148 Bangkok Thailand Nutchanat Permpool [email protected]

1369 Dubai UAE Akash Wadhwa [email protected]

0962 Witham UK Troy Burgess [email protected]

1441 Witham UK Troy Burgess [email protected]

1325 Aldrige UK Troy Burgess [email protected]

1083 Fuquay-Varina US Marco Dominguez [email protected]

0392 Markham CA Marco Dominguez marco.dominguez@tycoelectronics

July 2008page 131 /

• You can enter/request a new SBA (Stock Build Approval) at

http://deoworld1/energy-sba/sba-new.asp

• You can find an overview of all requested SBAs at

http://deoworld1/energy-sba-masterlist.asp

STOCK BUILD APPROVALIntranet Link

July 2008page 132 /

STOCK BUILD APPROVALTotals by Entity

Click on Org-ID to see a list of all Stock-Builds.

July 2008

TED INVENTORY AND USAGE

July 2008page 134 /

WW INVENTORY AND USAGE REPORTING

III.

II.

I.Power-Cubes

Intranet Reports

TED CatalogLeve

l of D

etai

l

Screen on-line drill down for last completed month by region, competency, GPL, product code, Item number, measures in HTML format.

Separate IWR request for competency, GPL, product code. Worldwide items search. Site usage report for last completed month.

TED details as above plus 12 month historical usage reports by site. Total 2 year’s history.

July 2008page 135 /

WW INVENTORY REPORTING SET-UP

BKK

TED

NCIRL

Otto

AUS

ADR-049 Data feed

Codes

• Common front-end for worldwide inventory planning and control independent from current used systems, e.g. AMPICS, SAP, Mfg/Pro, or any Legacy Systems.

• Link between item-numbers and competency biz codes.• Availability of 12 monthly usage data, quantity on-hand and unit-costs from

Global-Cost-System for the last 2 years.• Total outstanding customer requirements and supplies.• Month-of-supply and weeks-of-supply ratios, calculated obsolescence

reserve, stock on-hand etc.

July 2008page 136 /

WW INVENTORY HYPERION VIA USAGE REPORT

The Intranet usage report includes obsolescence reserve and represents gross inventory minus work-in-process plus manufactured & purchased components!

July 2008page 137 /

GAP HYPERION TO ADR-049

Gross-Inventory $75,753K ADR-049

WIP excl M & P $16,892K Hyperion

GIT $1,924K Hyperion

Sub-Total $94,569K

Obs Reserve $10,112K Hyperion

Net-Inventory $84,457K ADR-049

Net-Inventory $86,138K Hyperion

S E P T EM B E R 2 0 0 5

GAP $1,681Kor 2%

July 2008page 138 /

IWR REPORT SELECTION

Intranet web reports can be requested by competency, GPL, product code and part number. All worldwide usage reports can be downloaded into Excel as comma-separated format.

July 2008page 139 /

IWR REPORT NUMBER 1 SELECTION

With this report you can request a worldwide inventory/usage overview per discrete item number. All sites will be shown having either inventory and/or usage. To get results for all entities will enter Tyco’s product number (TCPN).

July 2008page 140 /

IWR REPORT NUMBER 10 SELECTION

Select inventory and usage information for ALL items per reporting organization and/or plant. In this case TELAG, entity 1151, is selected with plant code 0862 to get results for Axicom in Wohlen.

July 2008page 141 /

ADR-049 RESULTS I

July 2008page 142 /

ADR-049 RESULTS II

July 2008page 143 /

ADR-049 RESULTS III

• AX, AY and BX items account for around 66% of total usage. Represent typical candidates for statistical forecasting.

• CZ inventory (3.9% usage) make up 28% of total gross-inventory.

• Calculated obsolescence for CZ inventory $1,324K. Fully reserved $1,188K.

???

ABC Data X Y Z Grand TotalA Items 69 134 93 296

Items% 2.50% 4.86% 3.37% 10.74%Usage 19,083,592 26,752,108 10,475,689 56,311,389Usage% 27.11% 38.01% 14.88% 80.00%Inventory 1,596,775 1,948,628 954,298 4,499,700Inv% 16.06% 19.60% 9.60% 45.26%Res25% 34,564 16,520 2,011 53,095Res100% 0 0 0 0

B Items 31 173 313 517Items% 1.12% 6.27% 11.35% 18.75%Usage 667,003 3,952,292 5,945,577 10,564,872Usage% 0.95% 5.61% 8.45% 15.01%Inventory 172,619 748,739 1,326,590 2,247,948Inv% 1.74% 7.53% 13.34% 22.61%Res25% 7,056 28,843 101,115 137,013Res100% 0 0 38,925 38,925

C Items 75 199 1,670 1,944Items% 2.72% 7.22% 60.57% 70.51%Usage 166,513 621,558 2,726,583 3,514,654Usage% 0.24% 0.88% 3.87% 4.99%Inventory 98,749 331,880 2,764,252 3,194,881Inv% 0.99% 3.34% 27.80% 32.13%Res25% 8,687 33,754 135,687 178,129Res100% 0 881 1,187,916 1,188,796

Total Items 175 506 2,076 2,757Total Items% 6.35% 18.35% 75.30% 100.00%Total Usage 19,917,108 31,325,958 19,147,849 70,390,915Total Usage% 28.29% 44.50% 27.20% 100.00%Total Inventory 1,868,143 3,029,246 5,045,139 9,942,529Total Inv% 18.79% 30.47% 50.74% 100.00%Total Res25% 50,307 79,116 238,813 368,236Total Res100% 0 881 1,226,840 1,227,721

July 2008page 144 /

ADR-049 RESULTS IV

Only competency 13005 (Energy products) is shown!

July 2008page 145 /

ADR-049 RESULTS V

July 2008page 146 /

ADR-049 RESULTS VI

July 2008page 147 /

ADR-049 RESULTS VII

This is a snapshot of the results of the new worldwide web-report. It shows per product line all entities carrying active parts (=usage and/or stock is greater zero!) with month-of-supply, total usage, stock submitted etc. Here the first item is dead-stock in Dubai but could be used up in the UK!

July 2008page 148 /

ADR-049 MONTHLY CUBE

This ADR-049 cube shows only data for the current month!

July 2008page 149 /

ADR-021 WEEKLY CUBE

The ADR-021 data feeds shows weekly gross-inventory (excluding WIP & GIT) by entity. Several weekly values are available.

July 2008page 150 /

ADR-049 FEBRUARY 2007KEY ENERGY ENTITIES

July 2008page 151 /

ADR-049 IMPLEMENTATION STATUSFebruary 2008

As of February 2008 nearly all Energy sites report their gross-inventory and usage via the ADR-049 data feed. Missing sites is

Rayenergo with $1.8M inventory.

Total net-inventory as of February 2008 $145M with DOH=99!

July 2008

CHAPTER E

PROBLEMS WITH MINIMUM ORDER QUANTITIES

July 2008page 153 /

MISUSE OF MINIMUM ORDER QTY’S

An ordering site needs only 1 pc of an item from a supplying site. The supplying site‘s answer is that the mimimum order quantity for this item is 300 pcs. If the ordering site would accept this minimum order quantity it would have to create a reserve for the receiced quantity in excess of a yearly usage if it would follow strictly financial procedures. What is the apporach?

I need one piece!

You have to order 300 pcs!

July 2008page 154 /

PROBLEM OF MINIMUM ORDER QTY’S

The typical purpose of a minimum manufacturing or purchase order quantity is to find an optimal level between set-up or order costs and inventory carrying costs.

Advocats of mimimum order quantities normally claim that it doesn't make sense setting up a machine in order to produce only a few meters or pieces because the set-up time would be much greater than the run-time. Set-up time is regarded as a fixed element which is not modifiable.

On the purchasing side quantities are bought taking advantage of discounts leading to lower unit costs, but at the same time the quantity ordered represents much more than the yearly demand. Financially, if followed strictly, a provison for an obs reserve must be done for all quantities in excess of a yearly demand.

July 2008page 155 /

CURRENT PUSH SYSTEM

In our existing push system, ordering sites have to procure minimum order qtys although their customer demand is much lower. This approach 'optimizes' the supplying site but sup-optimizes the worldwide supply chain. This system results as well in slow-moving and/or obsolete inventory at ordering sites and leads to irregular demand at supplying sites although demand could be stable at source.

TargetTurns MFG INV C/O P/O INV C/O P/O INV

1 Customer places order --- 0 0 0 0 0 5 5 02 Hub places min order qty --- 0 0 500 500 0 5 5 03 Supplying Site produces min order qty --- 500 0 500 500 0 5 5 04 Supplying site delivers min order qty --- 0 500 0 0 500 5 5 05 Hub ships to end customer --- 0 0 0 0 495 0 0 5

Legend:P/O Purchase orderC/O Customer OrderMFG Manufacturing orderINV Inventory

TE Supplying Site TE Regional Hub Customer

July 2008page 156 /

EXAMPLE DATA PUSH SYSTEM

SupplyingSite

OrderingSite 1

OrderingSite 2

OrderingSite N

WorldwideYearly Demand: 1,200 pcsMinOrdQty: 500 pcsInv Turns: 2.4

Regional/TerritoryYearly Demand: 120 pcsMinOrdQty: 500 pcsInv Turns: 0.24

....

....Legend:MinOrdQty = EOQ etc.

July 2008page 157 /

PUSH SYSTEM AND IRREGULAR DEMAND

Although the demand at the ordering site is quite regular demand at the supply site is showing an irregular demand pattern because of min order qtys.

OrderingSite

ROP ROP ROP

TimeSupply EOQ EOQ EOQ

Site

Time

Legend:* ROP is Reorder-Point* EOQ is Economic-Order-Quantity

July 2008page 158 /

EXAMPLE DATA PULL SYSTEM

SupplyingSite

OrderingSite 1

OrderingSite 2

OrderingSite N

WorldwideYearly Demand: 1,200 pcsMinOrdQty: 300 pcsTarget Turns: 4

Regional/TerritoryYearly Demand: 120 pcsMinOrdQty: 10 pcsTarget Turns: 12

....

.... Legend:MinOrdQty = WW Demand / Target Turns

July 2008page 159 /

FUTURE PULL SYSTEM

TargetTurns MFG INV C/O P/O INV C/O P/O INV

1 Customer places order --- 0 0 0 0 0 5 5 02 Hub places min order qty based on target turn 12 0 0 10 10 0 5 5 03 Supplying Site produces min order qty 4 300 0 10 10 0 5 5 04 Supplying site delivers purchase order 4 0 290 0 0 10 5 5 05 Hub ships to end customer 12 0 290 0 0 5 0 0 5

Legend:P/O Purchase orderC/O Customer OrderMFG Manufacturing orderINV Inventory

TE Supplying Site TE Regional Hub Customer

The new modified supply chain, pull system, tries to optimize the worldwide supply chain. Minimum order quantities at both, the supplying and ordering site, are set-up in relation to inventory target turns. This approach avoids slow-moving and/or obsolete inventory at ordering and supplying sites. Remnants of min order qtys remain at supplying sites. Capacity is better utilized.

July 2008page 160 /

PUSH / PULL FUNDAMENTALS

• Each minimum order quantity must be evaluated in relation to the yearly (=worldwide) usage.

• If the yearly (=worldwide) usage is 500 pc and the minimum order quantity is 100 pc then the resulting inventory turns would be 500/100=5!

• No minimum order quantity should be greater than the yearly (=worldwide) usage because the excess has to be put into obsolescence reserve.

• Supplying sites have worldwide visibility about total demand.

• Each order quantity must be evaluated in relation to their yearly (=regional) usage.

• If the yearly (=regional) usage is 120 pc and the target inventory turns are 4 the order quantity should be equal to 30 pc.

• No minimum order quantity should be greater than the yearly (=regional) usage because the excess has to be put into obsolescence reserve.

• Ordering sites have only visibility about their regional demand.

Supplying Site Ordering Site

July 2008

INVENTORY CONSOLIDATION

July 2008page 162 /

CENTRALIZATION OF INVENTORY

It is not a good inventory strategy to have the same stock of inventory at different warehouses just in case for a future possible sale. It makes more sense to stock the fast-moving items decentralized near customers and slow-moving items at central warehouses.

Offering the same lead time for the whole product portfolio is also too costly as described in the previous section because normally minimum order quantities are pushed to ordering sites for slow-moving parts.

The approximated savings for centralization can be approximated by the same approach used for warehouse consolidation, e.g. going from 5 warehouses to 1.

The formula used is known as the Square Root Law of Inventory. This law was proved mathematically by D. H. Maister in his 1975 article “Centralization of Inventories and The Square Root Law” in the International Journal of Physical Distribution.

July 2008page 163 /

THE SQUARE ROOT LAW OF INVENTORY

The square root law of inventory states that the total inventory can be approximated by multiplying the total inventory by the square root of future warehouses divided by the current number of warehouses.

This formula can be used if an equal amount of inventory is kept in each warehouse and inventory control at each warehouse is based on EOQ principles.

Old

NewOldNew Whse

WhseII ×=

INew is centralized inventory in one or several locationsIOld is total de-centralized inventoryWhseNew is number of new centralized warehousesWhseOld is number of de-centralized warehouses

Notation:

July 2008page 164 /

THE SQUARE ROOT LAW OF INVENTORYMultiple Warehouses ExampleExample:

* $5M total inventory in de-centralized warehouses * Total number of de-centralized warehouses is 5* Total number of centralized warehouses is 2

$3.16M52$5M

WhseWhseII

Old

NewOldNew

=

×=

×=

The total new inventory in 2 warehouses will be $3.16M or 37% less inventory!

July 2008page 165 /

THE SQUARE ROOT LAW OF INVENTORYSingle Warehouses DerivationThe square root formula1) can be simplified if consolidation of inventory is done into one single warehouse.

OldAverage

OldOld

Old

Old

Old

OldOld

OldOld

Old

NewOldNew

WhseI

WhseWhse

IWhseWhse

Whse1I

Whse1I

WhseWhseII

×=

×=

××=

×=

×= Take care that in the simplified version of this formula the average inventory is now used instead of the total inventory!

To get the average inventory you have to divide the total inventory by the number of existing warehouses.

1) See Ronald H. Ballou, “Business Logistics Management”, 3rd Edition, 1992, Prentice Hall. He covers on pages 447 to 449 the square root formula for one single warehouse.

July 2008page 166 /

THE SQUARE ROOT LAW OF INVENTORYSingle Warehouses Example

$2.236M2.236$1M

5$1M

WhseII OldAverageNew

=×=×=

×= At first the total inventory of $5M in 5 warehouses has to be divided by the total number of warehouses to get the average inventory of $1M per warehouse.

Example:* $5M total inventory in de-centralized warehouses * Total number of de-centralized warehouses is 5* Total number of centralized warehouses is 1

The total new inventory in ONE warehouse will be $2.236M or 55% less inventory!

July 2008page 167 /

CONSOLIDATION OF INVENTORYNon Average InventoryThe previous examples were applicable if average inventory per warehouse was nearly equal. If we relax this assumption the inventory impact for centralization of warehouses has to be modified. We now have to apply basic statistics for joint (independent) random variables.

The variance of the sum of several independent random variables is equal to the sum of variances of the individual items!

For two random independent variables the variance and standard deviation can be calculated as:

222YXYX σσσ +=+

22YXYX σσσ +=+

Variance: Standard Deviation:

July 2008page 168 /

CONSOLIDATION OF INVENTORYNon Average Inventory – Example I

( )( )

1.6595%NORMSINVPNORMSINVscorez

===−

What is the reduction on safety stock if inventory is centralized. The table below shows the base data. Assume a lead time of 6 weeks. The service level should be 95%. Demand distribution is normal N(0,1).

a) Using Microsoft-Excel we get the z-score.

3001,0006002,5001,000Standard Deviation

5001,5001,0003,0002,000Average Demand

IDMYHKSPTHCountry Code

b) Weekly data from decentralized warehouses:

July 2008page 169 /

CONSOLIDATION OF INVENTORYNon Average Inventory – Example IIc) Decentralized safety stock

21,826isStockSafetyTotal4,04263001.65ID

4,04261,0001.65MY

2,04266001.65HK

10,10462,5001.65SP

4,04261,0001.65TH

LTzS/S

=××=

=××=

=××=

=××=

=××=

××= σ

d) Centralized Standard Deviation

950,2000,700,8

000,700,8000,90000,000,1000,360000,250,6000,000,1

300000,1600500,2000,1

2

2

222222

222222

==

=

++++=

++++=

++++=

σσ

σ

σ

σ

σσσσσσ IDMYHKSPTH

e) Centralized Safety Stock

11,92362,9501.65

LTσzS/S

=××=

××=

f) Safety Stock Reduction

45.4%9,903Reduction11,923StockSafetyNew21,826StockSafetyOld

≈===

July 2008page 170 /

CENTRALIZATION OF WAREHOUSESBenchmarking

July 2008

CHAPTER F

LOT SIZING MODELS

July 2008page 172 /

INVENTORY CONTROLBasics

Inventory Control comprises all activities and techniques of maintaining the desired levels of items, whether raw material, work in process, or finished goods (APICS Dictionary, 11th Edition).

The objective is to minimize total variable cost of a cost function over a specified time period; e.g. a year, month, week etc.

The cost function may be represented by

CosttionTransporta

CostShortage

CostHolding

CostSetup

CostPurchasing

CostInventoryTotal

++++=

July 2008page 173 /

INVENTORY COSTSDefinition• Purchasing / Manufacturing costs represent the actual price of the item.

• Setup / Ordering costs occur regardless of the of the quantity ordered. Ordering costs are salaries and expenses of processing and order and setup (changeover) costs are for start-up scrap, calibration, downtime etc.

• Holding costs is the cost of holding inventory, usually defined as a percentage of the dollar value of inventory per unit of time (generally one year). It includes finance costs and costs maintaining the inventory as taxes, insurance, obsolescence, spoilage, and space occupied.

• Shortage costs is the marginal profit that is lost when a customer orders an item that is not available.

• Transportation cost is caused by inventory that is in transit between locations.

APICS Dictionary, 11th Edition, 2005

July 2008page 174 /

INVENTORY COSTSHolding Cost and Average Inventory

1) L.A. Johnson, D. C. Montgomery, Operations Research in Production Planning, Scheduling, and Inventory Control, Wiley, 1974

Johnson1) described that inventory holding costs is assumed to be proportional to average inventory. If I(t) is the inventory at time t, the average inventory over a period (0,T) is defined as

( )∫=T

0dttI

T1I

Inve

ntor

y I(t

)

Time T

The average inventory is now the shaded area under the inventory curve divided by T.

If h is the holding cost for one unit of time, then the average holding cost over the interval (0,T) is h x AvgInv. The total holding inventory cost is of courseT x h x AvgInv.

It is crucial to understand time units, e.g. does h refer to one unit of time or to the total period T!

July 2008page 175 /

INVENTORY COSTSExample 1

120

1,200

T

Q

Avg Inv

Total (=Area)Inventory

7,20061,200

121,20021

InvTotal

=×=

××=

6007,200/12

TInvTotal

InvAvg

==

=

21,600123600

ThInvAvgYear

CostInv

=××=

××=

1,8003600

hInvAvgTimeUnitCostInv

=×=

×=

The holding cost per unit of time h is normally calculated by multiplying the inventory carrying rate in percent by the product unit cost. The average holding cost per unit of time is then h=i*c and total holding cost H=h*T!

Calculate with h=3 a) Total inventory, b) Average inventory, c) Holding cost per unit of time, and d) Total inventory cost for period T (here 1 year!)

July 2008page 176 /


3,6009004

3600214

InvTotal

=×=

×××=

30012

3,600T

InvTotalInvAvg

=

=

=

800,01123300

ThInvAvgYear

CostInv

=××=

××=

0093300


=×=

×=

600

T

Q

120 3 6 9


July 2008page 177 /


7,2001,8006003,6001,200

4900212600

2132,400

213800

21

InvTotal

=+++=

××+××+××+××=

60012

7,200T

InvTotalInvAvg

=

=

=

600,21123600

ThInvAvgYear

CostInv

=××=

××=

800,13600


=×=

×=


600

T

Q

120 3 6 8

800900

2,400

July 2008page 178 /

INVENTORY CONTROLQuantity and Timing

Rules have to be defined of

1. How much of an inventory item has to be ordered?

2. When an order should be placed?

Two standard systems are in use

1. Fixed Order Quantity, Continuous Review, or Order Point System

2. Fixed-Time Period System or Periodic Review System.

July 2008page 179 /

INVENTORY SYSTEMSOverview

(variable)( fixed )

t, st, s, St, s, qfixedCombined

tt, St, qfixedOrder Cycle

ss, Ss, qvariableOrder Point

Triggered

by

Order QuantityReview

Period

Inventory

Systems

Notation:

q is Fixed-Order Quantitys is Reorder-PointS is Fixed order up inventory levelt is Fixed review period

July 2008page 180 /

ORDER-POINT SYSTEMSs,q and s,S

Time

Stoc

k

q1

q2

s, q

Stoc

kTime

s, S

s s

S

q2 q3q1

t1 t2 t3 t1 t2 t3

q1 = q2 = qn and t1<> t2 <> t3 <> tn q1 <> q2 <> qn and t1<> t2 <> t3 <> tn

Inventory position checked continuously. At or below s (=reorder-point) constant quantity will be ordered.

Inventory position checked continuously. At or below s (=reorder-point) variable quantity to fill target inventory S will be ordered.

July 2008page 181 /

ORDER-CYCLE SYSTEMSt,q and t,S

Time

Stoc

k

q1 q3

t, q t, S

t1 t2 t3

q2

TimeSt

ock

t1 t2 t3

S

q1

q2

q3

q1 = q2 = qn and t1= t2 = t3 = tn q1 <> q2 <> qn and t1= t2 = t3 = tn

At constant intervals t a constant quantity q will be ordered. Irregular demand leads to strong fluctuating inventory.

Same as t,p policy but variable quantity q will be ordered to fill target inventory level S.

July 2008page 182 /

COMBINED SYSTEMSt,s,q and t,s,S

Time

Stoc

k t, s, q

Stoc

kTime

t, s, S

t1 t2 t3

q1

q2

t1 t2 t3

q1 q1

s

S

s

q1 = q2 = qn and t1= t2 = t3 = tn q1 <> q2 <> qn and t1= t2 = t3 = tn

Similar to t,q policy but reorder point s is used to place order quantity q.

Similar to t,s,q policy. Inventory position is checked at constant intervals. Depending on s inventory filled up to target level S.

July 2008page 183 /

NOTATION

Time indexest, j

Economic Order QuantityEOQ

Lot size in units.Q

Holding cost per unit per time.h

Constant setup (ordering) cost to produce (purchase) a batch in

dollars.

K

Unit production or purchasing cost not including setup or inventory

carrying costs in dollar per unit.

c

Demand rate in units per period, e.g. week, month.d

Demand rate in units per year.D

July 2008page 184 /

CLASSIFICATION OF LOT SIZING MODELSDeterministic via Probabilistic

StaticLot Sizing

Simple

Optimum

Heuristic

Lot SizingModels

• Economic Order Quantity EOQ• Economic Production Quantity EPQ• EOQ with Shortage• Resource Constraints• Fixed Order Quantity

• Fixed Period• Period Order Quantity• Lot for Lot

• Wagner-Whitin

• Silver- Meal• Least Unit Cost• Part Period Balancing• Groff

Deterministic Probabilistic

DynamicLot Sizing

• Single Period or News Boy model

• Reorder-Point Models• Periodic Review Models

Some lot size models will be described on the next slides.

July 2008page 185 /

CHARACTERISTICS OF LOT SIZES

• For Deterministic lot sizes demand is constant and known. There is no uncertainty. Probabilistic (Stochastic) lot sizes can only be described by probability distribution, e.g. Normal or Poisson, because demand is uncertain and not constant.

• Static / Fixed order quantities (demand rates are fixed at all times) remain the same each time they are ordered unless the factors used in determining the quantity change.

• Dynamic (Discrete) lot sizing models change with each order because they deal with lumpy demand (known but allowed to vary over time!); not regular or continuous. The advantage in using them is that there will be no remnants from one order cycle to the next as with fixed or economic order quantities.

• Heuristic models achieve a low-cost solution which is not necessarily optimal.

July 2008page 186 /

VARIABILITY COEFFICIENTFormula

Dynamic lot sizes should be used if the variability of demand exceeds some threshold value, see Peterson-Silver (1979). “A useful measure of the variability of a demand pattern is the variability coefficient VC”. It is calculated by dividing the “Variance of demand per period” by the “Square of average demand per period”.

1

D

DNVC 2

N

1jj

N

1j

2j

−

⎟⎟⎠

⎞⎜⎜⎝

⎛

×=

∑

∑

=

=

1. If VC < 0.2, use a simple EOQ with average demand as demand estimate.

2. If VC ≥ 0.2, use the Silver-Meal heuristic.

July 2008page 187 /

VARIABILITY COEFFICIENTExample

VC ≥ 0.2, use the Silver-Meal heuristic instead of the EOQ.

205030102040dj

654321t / j

23.0

128,90035,400

1170

900,56VC 2

=

−=

−×

=

1

D

DNVC 2

N

1jj

N

1j

2j

−

⎟⎟⎠

⎞⎜⎜⎝

⎛

×=

∑

∑

=

=

July 2008page 188 /

ECONOMIC ORDER QUANTITYTrail-and-Error Approach

D = 2,700 units per yearK = $50 per orderc = $10 unit costi = 30% carrying chargeh = $3 per unit per yearOne order per year results

in lowest ordering but highest inventory costs!

July 2008page 189 /

ECONOMIC ORDER QUANTITYIncremental Analysis

( )( )

( )

KQD

ΔQQΔQ

KΔQQQ

DQΔQDDQ

KΔQQQ

DQΔQQD

KΔQQ

DQDIC UpSet

×⎟⎟⎠

⎞⎜⎜⎝

⎛×⎟⎟⎠

⎞⎜⎜⎝

⎛+

=

×⎟⎟⎠

⎞⎜⎜⎝

⎛+

−×+=

×⎟⎟⎠

⎞⎜⎜⎝

⎛+

−+=

×⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=−

h2ΔQ

h2

QΔQQ

h2Q

2ΔQQICInv

×⎟⎠⎞

⎜⎝⎛=

×⎟⎠⎞

⎜⎝⎛ −+

=

×⎟⎠⎞

⎜⎝⎛ −

+=Inventory carrying charge is a function

of average inventory Q/2. Incremental increase in inventory carrying cost (regarded as a loss!) is then

Larger order quantities result in less set-up cost. Producing or ordering once per year results in lowest ordering costs but is offset by additional inventory carrying costs. The incremental gain in set-up reduction can be calculated as

July 2008page 190 /

ECONOMIC ORDER QUANTITYCost Elements Analysis

At the optimal order quantity the absolute values for setup and inventory (holding) cost of the first derivative (= slope of total cost curve) are equal to average order and inventory (holding) cost.

July 2008page 191 /

ECONOMIC ORDER QUANTITYSlope of total cost

At the optimal order quantity the absolute values for setup and inventory (holding) cost of the first derivative (= slope of total cost curve) are equal to average order and inventory (holding) cost.

Cos

t

QtyEOQ

TotalCost

Total 1stDerivative

July 2008page 192 /

ECONOMIC ORDER QUANTITYAssumptions

The simplest, oldest, and most widely used order quantity was developed 1913 by F. W. Harris. This formula is applicable if all decision parameters are known with certainty:

1. Demand is known and constant per period, see picture below.2. Lead time is instantaneous or zero.3. Unit price is constant. There is no discount.4. Inventory holding costs are based on average inventory.5. Ordering or setup cost are constant and can be expressed as K+c*q6. No backorders are allowed. All demand will be satisfied.

Time

- dIn

vent

ory

Time

d

Dem

and

July 2008page 193 /

ECONOMIC ORDER QUANTITYBasic Sawtooth Model

Time

Qty

t 2t

q-d

0

At time zero an order quantity of q arrives and will be consumed during t with d units per unit of time. As inventory reaches t a new order of q is received immediately (lead time is zero) and will be consumed in the next cycle and so forth.

Cycle length:t = q / d

July 2008page 194 /

ECONOMIC ORDER QUANTITYCosts per Cycle / Unit of Time

1. Inventory per cycle

2dq

dqq

21

q/dttq21IC

2

=

××=

=××=

2. Holding cost per cycle

2dqh2dqhH

2

2

×=

×=

3. Total cost per cycle

2dqhqcK

CostHoldingCostOrderTC2×

+×+=

+=

4. Total cost per unit of time

h2qdc

qdK

q/dt2dtqh

tqc

tK

tbydivided2d

qhqcKC

2

2

×+×+×=

=××

+×

+=

×+×+=

July 2008page 195 /

ECONOMIC ORDER QUANTITYDerivation of EOQ

5. Minimal cost with respect to q

hdK2q

02h

qdK

dqdC

h2qdc

qdKC

*

2

××=

=+×

−=

×+×+×=

hdK2q* ××

=

6. Economic Order Quantity (EOQ)

• Take the first derivative of C with respect to q and set it equal to zero.

• Because the second derivative of C is positive we reached a minimum.

• Note as well that q does not depend on the purchase/unit cost because they are constant for each quantity.

Minimum!0q

Kd2dq

Cd2h

qdK

dqdC

32

2

2

>××

=

+×

−=

July 2008page 196 /

ECONOMIC ORDER QUANTITYOptimal Cycle Length7. Optimal cycle length

2d1

hdK2t

dh

dK2

t

dqt

tdq

×××

=

××

=

=

×=

∗

∗

∗∗

dhK2t××

=∗

July 2008page 197 /

ECONOMIC ORDER QUANTITYMinimum Cost per Unit of Time8. Minimum cost per unit of time

dchdK221hdK2

21C

dchhdK2

21

hhdK2

21C

2d/hK2hdc

2d/hK2hC

2d/hK2hdc

d/hK2d/hK2dKC

2d/hK2hdc

d/hK2d/hK2

d/hK2dKC

d/hK2qh2qdc

qdKC

h2qdc

qdKC

22

×+××××+××××=

×+××××+××××=

×××+×+

×××=

×××+×+

××××××

=

×××+×+

××××

××××

=

××=×+×+×=

×+×+×=

∗

∗

∗

∗

∗

∗∗

∗∗

dchdK2C ×+×××=∗

July 2008page 198 /

ECONOMIC ORDER QUANTITYSensitivity Analysis9. Sensitivity Analysis

∗

∗

∗

∗

∗

∗

∗

×+×=

×+×=

×+

××=

×+

××××

=

××

+×

×=

×+×=

×+×

×+×=

qq

21

qq

21

q2q

h2Kdh

2q1

q2q

hq22Kdh

h2Kdh2

q2Kdh2Kdhq

2KdhKd

2Kdh2hq

2KdhqKd

2Kdh

h2q

qdK

h2q

qdK

h2q

qdK

CC

2

2

⎟⎟⎠

⎞⎜⎜⎝

⎛+×= ∗

∗

∗ qq

qq

21

CC

For this analysis we can skip the factor c * d (=total purchasing or manufacturing cost per cycle), because it is independent of the lot size q!

July 2008page 199 /

ECONOMIC ORDER QUANTITYExample - EOQ

pcs3003

2,700502h

dK2q*

=

××=

××=

weeks6weeks5.8weeks/year52years0.111

2,7003502

dhK2t

≈=×=

××

=

××

=∗

D = 2,700 units per year; K = $50 per order; c = $10 unit cost; i = 30% carrying charge per year;h = $3 = c * i = $10 * 0.30 per unit per year

yearper$27,90027,000810,000

2,7001032,700502

dchdK2C

=+=

×+×××=

×+×××=∗

Calculate the optimal quantity q, cycle time t, and total cost.

July 2008page 200 /

ECONOMIC ORDER QUANTITYExample - Sensitivity

( )

3.5%1.0346

1.300.769221

11.30

1.301

21

qq

qq

21

CC

≈=

+×=

⎟⎠⎞

⎜⎝⎛ +×=

⎟⎟⎠

⎞⎜⎜⎝

⎛+×= ∗

∗

∗

What cost impact does it have if the actual purchased/manufactured quantity is 30% higher or 30% lower than the EOQ (Economic Order Quantity)?

Plus 30%

( )

6.4%1.0643

0.701.428621

10.70

0.701

21

qq

qq

21

CC

≈=

+×=

⎟⎠⎞

⎜⎝⎛ +×=

⎟⎟⎠

⎞⎜⎜⎝

⎛+×= ∗

∗

∗

Minus 30%

Although the deviation (plus/minus) of the order quantity compared to the EOQ is quite big the cost impact is much lower. Due to the flatness of the total cost curve around the EOQ it is more cost effective to produce bigger lot sizes than smaller ones.

July 2008page 201 /

ECONOMIC PRODUCTION QUANTITYInventory over Time

Time

Qty

2t

q

Invmax

t1 t2t

p-d-d

( )

( )

dInvttdInv

qpd1

pqdp

tdpInvd

q t dtq

pqttpq

max22max

1max

11

=⇒×=

×⎟⎟⎠

⎞⎜⎜⎝

⎛−=

×−=

×−=

=⇒×=

=⇒×=

For this model inventory builds up during the production cycle t1 but is consumed by d. The maximum inventory level is reduced by the factor (p-d) during production cycle t1.

July 2008page 202 /

ECONOMIC PRODUCTION QUANTITYCosts per Cycle / Unit of Time1. Inventory per cycle

dq

pd1

21

dqq

pd-1

21

q/dttInv21IC

2

max

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

××⎟⎟⎠

⎞⎜⎜⎝

⎛×=

=××=

2. Holding cost per cycle


dhq

pd1

21qcK

CostHoldingCostOrderTC2

⎟⎟⎠

⎞⎜⎜⎝

⎛−+×+=

+=

4. Total cost per unit of time

hqpd1

21dc

qdKC

q/dttdhq

pd1

21

tqc

tKC

tbydividedhq

pd1

21qcKTC

2

2

××⎟⎟⎠

⎞⎜⎜⎝

⎛−+×+×=

=××

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

×+=

⎟⎟⎠

⎞⎜⎜⎝

⎛−+×+=

dhq

pd1

21

hdq

pd1

21H

2

2

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

×⎟⎟⎠

⎞⎜⎜⎝

⎛−=

July 2008page 203 /

ECONOMIC PRODUCTION QUANTITYDerivation of EPQ

hpd1

dK2q

hpd1

21

dKq

hpd1

21

qdK

0hpd1

21

qdK

dqdC

hqpd1

21dc

dqKC

2

2

2

2

×⎟⎟⎠

⎞⎜⎜⎝

⎛−

××=

×⎟⎟⎠

⎞⎜⎜⎝

⎛−

×=

×⎟⎟⎠

⎞⎜⎜⎝

⎛−=

×

=×⎟⎟⎠

⎞⎜⎜⎝

⎛−+

×−=

××⎟⎟⎠

⎞⎜⎜⎝

⎛−+×+×=

5. Minimal cost with respect to q

hpd-1

dK2q*

×⎟⎟⎠

⎞⎜⎜⎝

⎛××

=

6. Economic Production Quantity (EPQ)

• Take the first derivative of C with respect to q and set it equal to zero.

• Because the second derivative of C is positivewe reached a minimum.

• Note as well that q does not depend on the purchase/unit cost because they are constant for each quantity.

Minimum!0q

Kd2dq

Cd

hpd1

21

qdK-

dqdC

32

2

2

>××

=

×⎟⎟⎠

⎞⎜⎜⎝

⎛−×+

×=

July 2008page 204 /

ECONOMIC PRODUCTION QUANTITYOptimal Cycle Length

( )

( )

( ) 2dhd/p1Kd2

dhd/p1

Kd2

hd/p1Kd2q/dqt

××−××

=

×−××

=

×−××

== ∗∗∗

7. Optimal cycle length t*

( ) dhd/p1K2t

××−×

=∗

Keep in mind that the production period t1 = q / p (time to produce the lot size) is different to the (production) cycle time t = q / d (time between production runs)!

July 2008page 205 /

ECONOMIC PRODUCTION QUANTITYMinimum Cost per Unit of Time

( ) ( )

( )

( ) ( )

( ) ( )( )

( )( )

( )( )

( )( )

( )( ) dc

d/p1d/p1

hKd2hKd2

dchd/p12dKhd/p1Kd2

dchd/p1Kd2

Kd22

hd/p1hd/p12dK

hd/p1Kd

dchhd/p1

Kd2d/p121

Kd2hd/p1Kd

dchhd/p1

Kd2d/p121

hd/p1Kd2

Kd

hd/p1Kd2qdchqd/p1

21K

qdC

22222

×+−−

×××××××

=

×+×−××−×××

=

×+×−×××

×××

×−+

×−××−××

=

×+××−

×××−+

×××−××

=

×+××−

×××−+

×−××

×=

×−××

=×+××−+×= ∗∗∗

∗

8. Minimum cost per unit of time

dcpd1hKd2C ×+⎟⎟⎠

⎞⎜⎜⎝

⎛−××××=∗

July 2008page 206 /

ECONOMIC PRODUCTION QUANTITYExample

2,0000.10.5

200,000

0.108,0004,0001

4,000252

hpd-1

dK2q*

=×

=

×⎟⎠

⎞⎜⎝

⎛ −

××=

×⎟⎟⎠

⎞⎜⎜⎝

⎛××

=

A heat-shrink tube has a yearly usage of 4,000 meters. The production capacity is 8,000 meters per year. Each setup requires cleaning of the equipment and inspection and calibration costs $25 per run. The cost to produce the tubing is $0.25 per meter and inventory holding cost is estimated as 40% annually. What should be the optimum production size?

K=$25 /order; c=$0.25; h=i x c = 40% x $0.25 = $0.10 per meter/year; d=4,000 meters per year;p=8,000 meters per year

Production time is 0.25 years or 3 months.(t1=q/p=2,000/8,000=0.25)

Cycle time is 0.5 years or 6 months.(t=q/d=2,000/4,000=0.5)

July 2008page 207 /

EOQ with ShortageBasics

Time

Qty

tt1 t2

mm

M

q

Mqmd

MqdM

dq

tttM/dtq/dt

12

1

−=

−=

−=

−===

-d

Inventory/cycle

Backorders/cycle

In this scenario backorders are now allowed (=no lost sales!) but a shortage cost s must be paid proportional to the waiting time t2 till the order can be delivered.

July 2008page 208 /

EOQ with ShortageCycle Costs1. Inventory cost per cycle

h2dM

hdM

2M

M/dth2

tMIC

2

11

×=

××=

=××

=

2. Shortage cost per cycle

( )

( ) s2d

Mq

sd

MqMq21

Mqm;d

Mqts2

tmBC

2

22

×−

=

×−

×−×=

−=−

=××

=


( )2d

Mqs2dMhcqK

CostShortageCostHoldingCostOrderTC22 −×

+×

++=

++=

July 2008page 209 /

EOQ with ShortageTotal Cost per Unit of Time4. Total cost per unit of time

( )

( )

( )

Ms2sq

2qMsMhcdK

qd

2qsM

2q2Mqs

2qsq

2qMhcdK

qd

2qM2MqqsMhcdK

qd

2qMqs

2qMhcdK

qd

2dqdMqs

2dqdMh

qcqdK

qd

q/dtt

TCC

22

222

222

22

22

−+×+×

++=

+−+×

++=

+−×+×++=

−×+

×++=

×−×+

××++=

==

( ) sM2sq

2qshMcdK

qdC

2

−++

++=

July 2008page 210 /

EOQ with ShortagePartial Derivation of M

5. Partial derivation for M

( )

( )

( )

qsh

sM

2qshM2s

0s2q

shM2MC

sM2sq

2qshMcdK

qdC

2

×+

=

+××=

=−+××

=∂∂

−++

++=

6. Modifying M-term for q derivation

( )22

2

2

shs

qM

shs

qM

qsh

sM

+=

+=

×+

=

July 2008page 211 /

EOQ with ShortagePartial Derivation of q7. Partial derivation for q

( )

( )( )

( )( )

( )

ssh

h2dKq

shsh2dKq

shsssh

qKd2

shsshs

qKd2

shss

qKd2

sh2shs

2s

qKd

shs

qM0

2s

2qshM

qKd

qC

sM2sq

2qshMcdK

qdC

2

2

22

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

+×=

+×=

+−+

=××

+−+×

=××

+−=

××

+×+×

−=×

+==+

+−

×−=

∂∂

−++

++=

ssh

hKd2q +×

××=∗

July 2008page 212 /

EOQ with ShortageSolution for M8. Solution for M

shs

hKd2M

+×

××=∗

( )

( )

( )1/21/2

1/2

1/2

1/2

1/2

sh1s

h2dK

shsh

h2dK

ss

ssh

h2dK

shs

ssh

h2dKqq

shsM

+××=

++

××=

+××

+=

+×=×

+=

M is the up-to inventory level after receiving the order quantity.

July 2008page 213 /

EOQ with ShortageCycle Length9. Optimal Cycle Length

ssh

dhKd2d

ssh

hKd2

dqt

2

+×

×××

=

+×

××

=

∗=∗

ssh

dhK2t +×

××

=∗

July 2008page 214 /

EOQ with ShortageMaximum Shortage Quantity10. Maximum Shortage Quantity

( ) ( )( ) ( )

( )( ) ( )

( ) ( )

( ) ( )[ ]

( )

( )shhh

s2dK

hshsh

2dK

sshshsh

2dK

sshshsh

2dK

sshs

h2dK

shssh

h2dK

sshss

h2dK

shsshsh

h2dK

shs

h2dK

ssh

h2dK

Mqm

2

22

22

+×=

×+××

=

−+×+××

=

⎥⎦⎤

⎢⎣⎡ −+×

+××=

×+−

+×+

=

×+×

−+×+×+

=

+−

+=

−= ∗∗∗

shh

sKd2m

+×

××=∗

Multiply the 1st square root by (h+s)/(h+s) and the 2nd square root by s/s and simplify further!

Because m represents backorders it is actually a negative value!

July 2008page 215 /

EOQ with ShortageMaximal Shortage Time

Because of the difficulties to calculate shortage costs Neumann (Produktions- und Operations Management, Springer-Verlag, 1996) recommends to use the maximal shortage time Θ instead. This shortage time determines how many days a customer must wait till goods are delivered.

11. Maximal Shortage Time

shh

sdK2

shh

dsKd2

/dsh

hs

Kd2d

MqΘ

2

+××

=

+×××

=

⎟⎟⎠

⎞⎜⎜⎝

⎛

+××

=

−∗=

∗

12. Shortage Cost Derivation

( )

( )

22

2

2

ΘdhK2hss0

ΘdhK2shs

shsdhK2Θ

shh

sdK2Θ

×××

−×+=

×××

=+×

+××××

=

+××

=

July 2008page 216 /

EOQ with ShortageShortage Cost

The shortage cost is now the positive part of the quadratic equation!

2

2

ΘdKh2

2h

2hs

×××

+⎟⎠⎞

⎜⎝⎛+−=

0Θd

hK2hss 22 =

×××

−×+

Note:The standard quadratic equationin normal form is shown on the right

p=h andq=-2hK/dΘ2

q2p

2px

0qpxx2

1,2

2

−⎟⎠⎞

⎜⎝⎛±−=

=++

July 2008page 217 /

EOQ with ShortageExample I

4200.250.5

2520012

21

21

ΘdKh2

2h

2hs

2

2

2

2

=++−=

×××

+⎟⎠⎞

⎜⎝⎛+−=

×××

+⎟⎠⎞

⎜⎝⎛+−=

We deliver to a key account customer a special type of HV connectors. In order not to loose this customer management decided that in case of shortage the maximum waiting time is 2 days. Order cost are $200 and the unit-cost is $30. Holding cost is $1 /unit/day.Yearly usage with 250 working days is 1,000 units.

K=$200 /order; c=$30; h=$1 /unit/day ; Θ=2 days; Daily usage d=5 units (1,250/250)

1. Shortage Cost s:

Shortage cost s is$4 per unit per day.

501.252,000

441

120052

ssh

hKd2q

=×=

+×

××=

+×

××=∗

2. Optimal Order quantity q:

Optimal order quantity q is 50 units per order.

Example taken from Neumann, Produktions- und Operations Management, 1996, Springer

July 2008page 218 /

EOQ with ShortageExample II

400.82,000

414

120052

shs

hKd2M

=×=

+×

××=

+×

××=∗

3. Optimal Inventory Level M:

Optimal up-to inventory levelM* = 40 units.

100.2500

411

420052

shh

sKd2m

=×=

+×

××=

+×

××=∗

4. Optimal Order Point m:

A new order should be placed if backorders reach minus m* = 10.

July 2008page 219 /

EOQ with ShortageExample III

5. Optimal Cycle Length t:

Each 10 days, after reaching (minus) 10 units backorders, a new order for 50 units should be placed filling inventory up to 40 units. If the lead time would be for example 7 days the reorder-point would be

m* + LT x d = -10 + 7 x 5 = 25 units.

More details for reorder points will follow in later sessions.

101.2580

441

512002

ssh

dhK2t

=×=

+×

××

=

+×

××

=∗

July 2008

LOT SIZING TOURNAMENT

July 2008page 221 /

ECONOMIC QRDER QUANTITY (EOQ)

hKD2

Cost HoldingOrderCostDemand2EOQ

××=

××=

The most popular order quantities in practice is the ‘Economic Order Quantity’ or EOQ because of its simplicity. Optimal results can only be reached if following assumptions are met.

1. Item demand is constant.2. Lead time is constant.3. Cost per unit is constant, no discounts.4. Holding cost is based on average inventory.5. Ordering cost is constant.6. No shortages are allowed.

Time

- DIn

vent

ory

Time

D

Dem

and

July 2008page 222 /

EOQ Example

5485.531

50292EOQ ≈=××

=

Average Demand d = 40+20+10+30+50+20 = 170 / 6 = 28.3 ~ 29

205030102040dj

654321t / j

K=$50; h=$1/unit/period

46128384814End Inv54545454EOQ205030102040dj

654321t / j

hKD2EOQ ××

=

For holding costs only ending inventory is considered!

July 2008page 223 /

EOQ Example Results

54 545454

0

10

20

30

40

50

60

1 2 3 4 5 6

Demand Lot size

64145054Q(1)

62125054Q(5)

366166200Total Cost96465054Q(6)

144945054Q(2)

CostHoldingSetupQtyLot

July 2008page 224 /

SILVER-MEAL HEURISTIC (SM)

( )

j1)hd(j...2hdhdK

C(j)

32hdhdKC(3)

2hdKC(2)

K1C

j32

32

2

−++++=

++=

+=

=

This method is quite similar to the least unit cost approach, but instead of minimizing the unit cost for a lot it minimizes the cost per period over the number of periods the lot will cover.

If Cj ≥ Cj-1 stop and set lot Q = d1+d2+d3+…+dj-1. Start calculation again at period j.

July 2008page 225 /

SILVER-MEAL Example

t=1; j=1: C(1) = (50+0*1*40)/1 = 50t=2; j=2: C(2) = (50+0*1*40+1*1*20)/2 = 35t=3; j=3: C(3) = (50+0*1*40+1*1*20+2*1*10)/3 = 30t=4; j=4: C(4) = (50+0*1*40+1*1*20+2*1*10+3*1*30)/4 = 45 STOP!

C(4) ≥ C(3) , Q(1) = d1+d2+d3 = 70

t=4; j=1: C(1) = (50+0*1*30)/1 = 50t=5; j=2: C(2) = (50+0*1*30+1*1*50)/2 = 50 STOP!

C(2) ≥ C(1), Q(4) = d4 = 30

t=5; j=1: C(1) = (50+0*1*50)/1 = 50t=6; j=2: C(2) = (50+0*1*50+1*1*20)/2 = 35 End of horizon, STOP!

Q(5) = d5+d6 = 70

205030102040dj

654321t / j


Cj ≥ Cj-1 Stop!

July 2008page 226 /

SILVER-MEAL Example Results

90405070Q(1)

21060150Total Cost70205070Q(5)5005030Q(4)


70

30

70

0

10

20

30

40

50

60

7080

90

100

1 2 3 4 5 6

Demand Lot size

July 2008page 227 /

LEAST UNIT COST (LUC)

( )

j321

j32

321

32

21

2

1

d...ddd1)hd(j...2hdhdK

C(j)

ddd2hdhdKC(3)

ddhdKC(2)

dK1C

++++

−++++=

++++

=

++

=

=

This method is similar to the Silver-Meal method but instead of dividing the cost over j periods it is divided by the total number of units d1+d2+d3+…+dj.

If Cj ≥ Cj-1 stop and set lot Q = d1+d2+d3+…+dj-1. Start calculation again at period j.

July 2008page 228 /

LEAST-UNIT COST (LUC) Example

t=1; j=1: C(1) = (50+0*1*40)/40 = 1.25t=2; j=2: C(2) = (50+0*1*40+1*1*20)/60 = 1.17t=3; j=3: C(3) = (50+0*1*40+1*1*20+2*1*10)/70 = 1.29 STOP!

C(3) ≥ C(2) , Q(1) = d1+d2 = 60

t=3; j=1: C(1) = (50+0*1*10)/10 = 5t=4; j=2: C(2) = (50+0*1*10+1*1*30)/40 = 2t=5; j=3: C(3) = (50+0*1*10+1*1*30+2*1*50)/90 = 2 STOP!

C(3) ≥ C(2), Q(3) = d3+d4 = 40

t=5; j=1: C(1) = (50+0*1*50)/50 = 1t=6; j=2: C(2) = (50+0*1*50+1*1*20)/70 = 1 STOP!

C(2) ≥ C(1), Q(5) = d5 = 50Q(6) = d6 = 20 End of horizon!

205030102040dj

654321t / j


Cj ≥ Cj-1 Stop!

July 2008page 229 /

LEAST-UNIT COST (LUC) Example Results

70205060Q(1)

5005050Q(5)

25050200Total Cost5005020Q(6)

80305040Q(3)


50

20

40

60

0

10

20

30

40

50

60

70

80

1 2 3 4 5 6

Demand Lot size

July 2008page 230 /

This method, sometimes called the Least Total Cost (LTC) method , chooses a lot size which makes the holding and set-up costs as nearly equal as possible. It’s derived from the fact that for the economic order quantity the set-up cost is equal to the holding cost for that lot size!

( ) K1jdhj

1jj ≈−∑

=

For each step compare holding cost with set-up cost.

PART PERIOD BALANCING (PPB)

( )∑=

−j

1jj 1jd is called part-periods!

( )hK1jd

j

1jj ≈−∑

=

July 2008page 231 /

PART PERIOD BALANCING (PPB)Example

t=1; j=1: $1*0*40 = 0 < Kt=2; j=2: $1*0*40+$1*1*20 = 20 < Kt=3; j=3: $1*0*40+$1*1*20+$1*2*10 = 40 < Kt=4; j=4: $1*0*40+$1*1*20+$1*2*10+$1*3*30 = 130 > K STOP!

40 is closer to K=50 than 130! Q(1) = d1+d2+d3 = 70

t=4; j=1: $1*0*30 = 0 < Kt=5; j=2: $1*0*30+$1*1*50 = 50 = K STOP!

50 is equal to K=50! Q(4) = d4+d5 = 80

Q(6) = d6 = 20 End of horizon!

205030102040dj

654321t / j


( ) K1tdhj

1jj ≈−∑

=

July 2008page 232 /

PART PERIOD BALANCING (PPB)Example Results

90405070Q(1)

5005020Q(6)24090150Total Cost

100505080Q(4)


20

8070

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6

Demand Lot size

July 2008page 233 /

GROFF HEURISTIC I

It is based on the feature of the economic order quantity that at the optimal lot size the incremental reduction of set-up costs per period equals the incremental increase of holding costs per period.

1)j(jK

1)j(jKjKKj

1)j(jKj1)K(j

1jK

jKΔK

+=

+−+

=+−+

=

+−=

The incremental reduction of set-up or order cost per period can be shown by comparing average costs per period.

554

100)14(4

1001)j(j

K

5202514

1004

100ΔK

=×

=+

=

+=

=−=+

−=

or

Example:K=$100; h=$1/unit/period

July 2008page 234 /

GROFF HEURISTIC II

The lot size is increased by the requirement of another period till the increased holding costs equals roughly the decreased set up cost.

2dh 1j+×

( )1jjK+×( )1jj

K2dh 1j

+×≈

× +

( ) STOP!1jj

K2dh 1j ⇒

+×>

× +

Increasedholding cost

Decreasedset up cost

If in period j the incremental increase of holding costs is greater than the incremental decrease of set-up costs then choose order qty Q as d1+d2…+dj-1!

July 2008page 235 /

GROFF HEURISTIC Example

205030102040dj

654321t / j


t=1; j=1: ($1*20)/2 = 10 < $50/(1*[1+1]) = 25t=1; j=2: ($1*10)/2 = 5 < $50/(2*[2+1]) = 8.33t=1; j=3: ($1*30)/2 = 15 > $50/(3*[3+1]) = 4.17 STOP!

Q(1) = d1+d2 = 60

t=3; j=1: ($1*30)/2 = 15 < $50/(1*[1+1]) = 25t=3; j=2: ($1*50)/2 = 25 > $50/(2*[2+1]) = 8.33 STOP!

Q(3) = d3 = 10

t=4; j=1: ($1*50)/2 = 25 > $50/(1*[1+1]) = 25t=4; j=2: ($1*20)/2 = 10 > $50/(2*[2+1]) = 8.33 STOP!

Q(4) = d4 = 30

t=5; j=1: ($1*20)/2 = 10 < $50/(1*[1+1]) = 25Q(5) = d5+d6= 70 End of horizon!

( ) STOP!1jj

K2dh 1j ⇒

+×>

× +

July 2008page 236 /

GROFF HEURISTIC Example Results

70205060Q(1)

5005030Q(4)

24040200Total Cost70205070Q(5)

5005010Q(3)


70

10

30

60

0

10

20

30

40

50

60

70

80

1 2 3 4 5 6

Demand Lot size

July 2008page 237 /

WAGNER-WHITIN

This method analyzes all possible combinations to find the optimal lot sizes. For example it is possible to produce lot-for-lot or produce 1 lot for period 1 and a second lot in period 2 covering requirements from period 2 to period 6.

Wagner-Whitin is included because it is common to use it for benchmarking!

To start with a matrix is calculated showing the cost impact of all different lot sizes.

( ) t

j

1τtτj dτthKc ×−×+= ∑

+=

Be aware that a sum from a higher index to a smaller, e.g. from 2 to 1 is defined as zero!

1 2 63 4 5

July 2008page 238 /

WAGNER-WHITIN Example I

50670505

14010050424018080503350270120605024803801809070501654321t\τ

205030102040dj

654321t / j


1. Calculate cost matrix 2. Determine minimum cost per period

For example, in period 3 add minimum cost of $70 from period 2 and in period 5 add minimum cost of $140 from period 4.

210190140907050f240621019052301901404310250150120340032017011010024803801809070501654321t\τ

t

( ) t

j


+=

July 2008page 239 /

WAGNER-WHITIN Example II

205030102040dj

654321t / j


210190140907050f240621019052301901404310250150120340032017011010024803801809070501654321t\τ

t

3. Derive optimal order quantities

Q(1) = d1+d2+d3 = 70; Q(4) = d4 = 30; Q(5) = d5+d6 = 70

Start

( ) t

j


+=

July 2008page 240 /

WAGNER-WHITIN Example Results

90405070Q(1)

21060150Total Cost70205070Q(5)5005030Q(4)


70

30

70

0

10

20

30

40

50

60

70

80

1 2 3 4 5 6

Demand Lot size

July 2008page 241 /

LOT SIZE Benchmarking

366166200Q(1)=Q(2)=Q(5)=Q(6)=54EOQ25050200Q(1)=60, Q(3)=40, Q(5)=50, Q(6)=20Least-Unit24090150Q(1)=70, Q(4)=80, Q(6)=20Part-Period

21060150Q(1)=70, Q(4)=30, Q(5)=70Wagner-Whitin

24040200Q(1)=60, Q(3)=10, Q(4)=30, Q(5)=70Groff21060150Q(1)=70, Q(4)=30, Q(5)=70Silver-Meal

CostHoldingSetupQtyMethod

Comparing the different dynamic lot sizing methods with each other and with the EOQ the worked-out examples match with different simulations in textbooks. Wagner-Whitin, although tedious to calculate, shows normally the lowest costs, followed by Silver-Meal. Here both methods generate the same costs!

For time-varying demand Silver-Meal and Groff are normally used. It is obvious as well from this simulation that the EOQ should not be used for time-varying demand.

July 2008

CHAPTER G

SAFETY STOCK CALCULATION

July 2008page 243 /

REASONS FOR SAFETY STOCK

One of the biggest problems in inventory management is random variability in the demand rate and/or lead time because it is unpredictable. Running out of stock has a very negative impact on customer service: Loss of goodwill, expediting costs from vendors, special set-up costs in manufacturing etc. To absorb shortages companies maintain safety stock. The objective is to balance the additional costs of holding safety stock with the expected cost of shortages.

Obtaining accurate shortage costs is very difficult. Therefore management accepts a reasonable service level in the form of safety stock. Two major forms of safety stock are common: cycle-service level and unit-service level. Both will be covered in detail.

Safety stock is all inventory held in excess of average, expected demand during lead time to reduce the risk of stock outs because of random variation of either lead time and/or demand.

July 2008page 244 /

DETERMINISTIC INVENTORY SYSTEMS

Quantity

Time

Lead Time

Ord

er Q

uant

ity DemandRate

In a deterministic inventory system all parameters are predictable, e.g. demand rate or usage per period, lead time, no shortages etc. No safety stock is needed!

July 2008page 245 /

PROBABILISTIC INVENTORY SYSTEMS

OrderQuantity

Time

ROP

Lead Time

RelativeFrequencyDistribution50

100150

250300

200

%

SafetyStock

Stock out

July 2008page 246 /

PROBABILISTIC INVENTORY SIMULATION

Period 0 1 2 3 4 5 6 7 8 9 10 AVG

Demand 0 100 100 100 100 100 100 100 100 100 100 100INV Avg 1,000 900 800 700 600 500 400 300 200 100 0

Demand 0 100 150 50 200 0 120 0 50 50 70 79INV <Avg 1,000 900 750 700 500 500 380 380 330 280 210

Demand 0 0 200 150 50 250 50 150 200 150 50 120INV >Avg 1,000 1,000 800 650 600 350 300 150 -50 -200 -250

-250

-50

150

350

550

750

950

1,150

0 1 2 3 4 5 6 7 8 9 10

=Avg <Avg >Avg

-50

0

50

100

150

200

250

300

Avg Fcst < Fcst > Fcst

Projected Inventory Average Forecast Error

July 2008page 247 /

SAFETY STOCK DEFINITION

In deterministic inventory models the reorder point is equal to lead time demand or ROP = d * LT. If, however, demand during lead-time is ‘normally distributed’, demand will be greater than the mean 50% and less than the mean 50% of the time. To provide for a service level greater than 50% a safety stock must be added, see the picture on the right.One popular method relates safety stock to “usage rates or time supply”, e.g. “Two weeks of Supply”. But the variability of supply and demand, not the average rate, should determine the amount of safety stock. Both methods will be described on the next slides.

July 2008page 248 /

SAFETY STOCK BASICS I

How safety stock is calculated is important to discover excess inventory. If safety stock is based on “time supply”, e.g. one monthly usage as safety stock, there is room for improvement because a “time supply” calculation could be misleading.

Let’s consider two items, A and B, both with an average monthly usage of 1,000 pcs a month. Item A has a standard deviation of 100 pcs and B of 300 pcs. The safety stock is set on “time supply” with 250 pcs ( = one week! ), the service level should be 95% (is equal to a z-score of 1.65) and demand during lead-time is normally distributed.

Statistically, safety stock is a function of a safety factor, which reflects the desired service level, and the variability of the forecast error during lead-time.

Safety Stock = Std Deviation * z-score

July 2008page 249 /

SAFETY STOCK BASICS II

For part A we would carry too much safety stock of 85 pcs (250 minus 165) and for part B too less safety stock minus 245 pcs (250 minus 495) for a target service level of 95%.

250 250

100

300

165

495

0

100

200

300

400

500

600

Part A Part B

2 weeks-of-supply Standard deviation Statistical safety stock

Part A Part BMonthly usage 1,000 1,0002 weeks-of-supply 250 250Standard deviation 100 300Statistical safety stock 165 495

StatisticalSafetyStock StdDev z score= × −

July 2008page 250 /

SAFETY STOCK BASICS III

With the statistically calculated safety stock we not only avoid excess inventory, we can shift inventory from items with low variable demand to items with higher variable demand with the same investment. If done properly, this could increase service and decrease investment.

The figure below illustrates the statistical approach for item A.

Time

1,000

1,250

ActualUsage

“Statistical”Safety Stock

July 2008page 251 /

SAFETY STOCK INVESTMENT

There is a trade-off between desired customer service level and inventory investment. Increasing safety stock in a way to achieve a 100% service level has disastrous results on the cash-flow of a company. The figure below shows the relation between desired service level and inventory investment.

To increase the service level from 90% to 96% by only 6%, the incremental investment in safety stock will be (1.75-1.28)/1.28 = 36.7%!!!

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

90% 92% 94% 96% 98% 99%Desired Service Level

Per

cent

Incr

ease

S/S

Inve

stm

e Compared to 90%

Service Z-Factor Safety StockLevel Increase90% 1.28 0.0%92% 1.41 10.2%94% 1.56 21.9%96% 1.75 36.7%98% 2.06 60.9%99% 2.33 82.0%

July 2008page 252 /

SAFETY STOCK INVESTMENT EXAMPLE

StdDev 100 Order Qty 200

z-score Service Safety Avg Q Average Invlevel SL stock Inv Inc

0.00 50% 0 100 100 --- --- ---0.84 80% 84 100 184 50% to 80% 30% 84%1.28 90% 128 100 228 80% to 90% 10% 24%1.64 95% 164 100 264 90% to 95% 5% 16%2.33 99% 233 100 333 95% to 99% 4% 26%

Service Level

100

184

228264

333

0

50

100

150

200

250

300

350

50% 80% 90% 95% 99%

Service Level

Aver

age

Inve

ntor

y

SFMADQ

MADzQ

zQAvgInv

×+=

××+=

×+=

2

25.12

2σ

Service Level SL in %:= NORMSDIST(z); N(0,1)

Z-Score:= NORMSINV(P); N(0,1)

July 2008page 253 /

DETERMINING SAFETY STOCK LEVELS

In practice there are two common methods how to calculate a safety stock for providing a desired customer service level. They are

a) The ‘cycle service level’ andb) The ‘unit service level’.

Because of the simpler calculation the cycle service level is very popular.

The ‘cycle service level’ determines the probability of not running out of inventory during an order cycle. The ‘unit service level or fill-rate’ determines the amount of stock which can be immediately satisfied.

Cycle Demand Backorder1 1002 120 203 804 1505 170 56 140

760 25

In this example the ‘cycle service level’ would be 67 % because there was a stockout during two cycles. The ‘unit service level’ would be 97 % because only 25 units were backordered.

July 2008page 254 /

CYCLE-SERVICE-LEVEL VIA UNIT-SERVICE-LEVEL

• Also called alpha or Type I service level.

• Represents an event oriented ratio. • Probability of not incurring a stockout

during an inventory cycle, e.g received orders can be completely filled from available stock.

• Applied when the likelihood of a stockout in percent and not its magnitude in pieces is important for the company.

• Also called beta or Type II service level.• Represents a quantity oriented ratio.• Percentage of demand that are filled

without incurring any stock-out, e.g. 100 short of 1,000 ordered means 90% service level.

• Applied when the percentage of unsatisfied demand should be under control.

Cycle-Service-Level Unit-Service-Level

July 2008page 255 /

CYCLE SERVICE LEVEL I

For a ‘cycle service level’ the safety stock is calculated as depicted below:

SS Z S LT / FP

SS Z 1.25 MAD LT / FP

SS MAD SF LT / FP

= × ×

= × × ×

= × ×

Legend:SS Safety stockZ Z-score from standard normal distribution tableS Standard deviation during lead-timeSF Safety factorLT lead-time in weeks, months etc.FP Forecast period in weeks, months etc.MAD Mean absolute deviation

Table of Safety Factors:

Service Value Safety FactorLevel Z SF = Z x 1.25

50.00% 0.00 0.0075.00% 0.67 0.8480.00% 0.84 1.0584.13% 1.00 1.2585.00% 1.04 1.3090.00% 1.28 1.6094.52% 1.60 2.0095.00% 1.65 2.0697.72% 2.00 2.5098.00% 2.05 2.56

July 2008page 256 /

CYCLE SERVICE LEVEL II

SS MAD SF LT/ FP

SS 20.3 2.06 4/ 4SS 42

= × ×

= × ×=

Month Past Average AbsoluteDemand Demand Deviation

JAN 346 364 18FEB 312 364 52MAR 387 364 23APR 350 364 14MAY 406 364 42JUN 364 364 0JUL 353 364 11AUG 338 364 26SEP 392 364 28OCT 385 364 21NOV 372 364 8DEC 365 364 1TTL 4,370 244

LT = 4 weeks, FP = 4 weeksService Level = 95%Average Demand = 4,370 / 12 ~ 364MAD = 244 / 12 = 20.3

July 2008page 257 /

CYCLE SERVICE LEVEL WITH MS EXCEL

Jan-04 Feb-04 Mar-04 Apr-04 May-04 Jun-04 Jul-04 Aug-04 Sep-04 Oct-04 Nov-04 Dec-04346 312 387 350 406 364 353 338 392 385 372 365

MAD = AVEDEV(Usage Jan04 to Dec04) SF = z score * 1.25 = 1.65 * 1.25 = 2.06

MAD SF=95% LT FP S/S20.3 2.06 4 4 42

S/S = Safety Factor SF * Mean Absolute Deviation MAD *SQRT(Lead Time LT / Forecast Period FP)

July 2008page 258 /

EXPECTED NUMBERS SHORT I

The ‘cycle service level’ only considers the probability of running out of stock, but doesn’t answer how many units will be short. Let’s assume that demand per month was estimated with the following probabilities, see sample data below:

Demand/ ProbabilityMonth

12 0.1013 0.1514 0.1515 0.2016 0.2017 0.1018 0.0519 0.05

0.00

0.05

0.10

0.15

0.20

0.25

12 13 14 15 16 17 18 19Monthly Demand

Prob

abilit

y of

Dem

and

units35EOQ7.50/2512152EOQ

CostHolding/CostOrderDemandYearly2EOQ

=

×××=

××=Order Cost = $25Carrying Rate = 25% per yearItem Cost = $30Holding Cost = $7.50 per unit per year

July 2008page 259 /

EXPECTED NUMBERS SHORT II

Expected monthly demand is, see previous slide:12 x 0.10 + 13 x 0.15 + 14 x 0.15 + 15 x 0.20 + 16 x 0.20 + 17 x 0.10 + 18 x 0.05 + 19 x 0.05 = 15

∑+=

−×MAXD

ROPD

ROPDDP1

)()(

ShortNumbersExpectedROP SS P(D)=ROP Numbers Service

Short Level15 0 0.20 0.75 97.9%16 1 0.20 0.35 99.0%17 2 0.10 0.15 99.6%18 3 0.05 0.05 99.9%19 4 0.05 0.00 100.0%

ROP = 15; SS = 0;E(Short) = (16-15) x 0.20 + (17-15) x 0.10 + (18-15) x 0.05 + (19-15) x 0.05 = 0.75Service Level = 1 - E(Short)/Q = 1 - 0.75 / 35 = 1 - 0.021 = 0.979 = 97.9%

ROP = 17; SS = 2;E(Short) = (18-17) x 0.05 + (19-17) x 0.05 = 0.15Service Level = 1 - E(Short)/Q = 1 - 0.15 / 35 = 1 - 0.004 = 0.996 = 99.6%

It is very tedious to calculate the ‘expected numbers short’ for a discrete distribution.

July 2008page 260 /

UNIT SERVICE LEVEL I

It’s more convenient to approximate a discrete distribution with a continuous distribution to simplify the safety stock and reorder point calculations.

If demand during lead time is normally distributed the expected numbers short for an average of zero and a standard deviation of one can be taken from a table, see the attachment and R.G. Brown, Decision Rules for Inventory Management, pp 95 - 103.

If the unit-service level is P then there would be a shortage of (1-P) x D units, where D is the annual demand.

If Q is the order quantity there would be D/Q orders per year. Because the table in the attachment is based on a standard deviation of one, E(z) must be multiplied by the standard deviation during lead time to get the expected numbers short per order.

July 2008page 261 /

UNIT SERVICE LEVEL II

( ) ( )

( ) ( )LT

LT

QPzE

QDzEDP

σ

σ

×−=

××=×−

×=×

1

1

yearperordersofNumber

orderpershortNumber

demandAnnual

shortPercentage

July 2008page 262 /

UNIT SERVICE LEVEL III

Example:Annual demand D = 1,000 units; Q = 200 units; Service Level P needed = 95%;Standard deviation during lead time = 25 and lead time LT = 15 daysDetermine the reorder point.

( ) ( ) ( )

( )60250154ROP

04.0

4.025

20095.01125154

zLTdROP

day/units4year/days250year/units1,000d

LT

=×+×==⇒=

=×−

=×−

=

×+×=×+×=

==

zzE

QPzE

z

LTσ

σ

( ) ( )( )

101020095.014.025

1

orderper Shortage

LT

=×−=××−=× QPzEσ

The shortage per order is 10 and there are 5 orders per year ( 1,000 / 200 ) then the total shortage per year is 50 units. The service level is SL = ( 1,000 - 50 ) / 1,000 = 95 %

July 2008page 263 /

UNIT SERVICE LEVEL IV

E(z) z E(z) z E(z) z E(z) z2.9005 -2.90 1.4367 -1.40 0.3509 0.10 0.0232 1.602.8008 -2.80 1.3455 -1.30 0.3069 0.20 0.0183 1.702.7011 -2.70 1.2561 -1.20 0.2668 0.30 0.0143 1.802.6015 -2.60 1.1686 -1.10 0.2304 0.40 0.0111 1.902.5020 -2.50 1.0833 -1.00 0.1978 0.50 0.0085 2.002.4027 -2.40 1.0004 -0.90 0.1687 0.60 0.0065 2.102.3037 -2.30 0.9202 -0.80 0.1429 0.70 0.0049 2.202.2049 -2.20 0.8429 -0.70 0.1202 0.80 0.0037 2.302.1065 -2.10 0.7687 -0.60 0.1004 0.90 0.0027 2.402.0085 -2.00 0.6978 -0.50 0.0833 1.00 0.0020 2.501.9110 -1.90 0.6304 -0.40 0.0686 1.10 0.0015 2.601.8143 -1.80 0.5668 -0.30 0.0561 1.20 0.0011 2.701.7183 -1.70 0.5069 -0.20 0.0455 1.30 0.0008 2.801.6232 -1.60 0.4509 -0.10 0.0367 1.40 0.0005 2.901.5293 -1.50 0.3989 0.00 0.0293 1.50

z = Number of standard deviations of safety stockE(z) = Expected number of units short for

Source:John A. Lawrence & Barry A. Pasternack, Applied Management Science, 1998

July 2008page 264 /

Thanks for your attention!

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Inv How-To Manual v Erwin Opalla

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