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Production Management I (Prof. Schuh)

Methods and Tools for Materials Management

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Production Management I- Lecture 5 -


Contact:Dipl.-Ing. Tim Hö[email protected] R. 208Tel.: 80-27391

Objectives of the Lecture:

• To calculate requirements using appropriate materials management tools.

• To present the most common methods and tools used in materials management.

• To explain the selection, application and limitations of the methods and tools presented.

• To provide an overview of the options of IT support in materials management.

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Lecture 5



Structure of the Lecture:

5.1 References L5 page III

5.2 Summary of Lecture L5 page 1

5.3 Introduction and Problem L5 page 2

5.4 Deterministic Calculation of Requirements L5 page 5

5.5 Stochastic Calculation of Requirements L5 page 11

5.6 Defining Emergency Stock Level L5 page 15

5.7 Determining Lot Size L5 page 19

5.8 Questions on the Lecture L5 page 23

5.9 Exercise: Methods of Calculating Requirements and Lot Sizes E5 page 1

5.10 Calculation Exercise E5 page 9

5.11 Calculating Requirements Using the Gozintograph A5 page 1

5.12 Derivation of the Andler Formula A5 page 3

5.13 Exponential smoothing of second order A5 page 5

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Lecture 5



5.1 References Lecture 5:

/1/ Wiendahl, H.P. Betriebsorganisation für Ingenieure, Hanser-Verlag,München, 1997

/2/ Grochla, E. Grundlagen der Materialwirtschaft, Gabler Verlag,Wiesbaden, 1992

/3/ REFA Methodenlehre der Planung und Steuerung,Hanser-Verlag, München, 1991

/4/ Hackstein, R. Einführung in die technische Ablauforganisation,Hanser-Verlag, München, 1998

/5/ Hartmann, H. Materialwirtschaft: Organisation, Planung, Durchführung undKontrolle, Deutscher Betriebswirte Verlag, Gernsbach, 1993

/6/ Hahn, D. /Produktionswirtschaft; Controlling industrieller ProduktionLassmann, G. Bd. 1, Physica-Verlag Heidelberg, Wien, 1986

/7/ Hackstein, R. Produktionsplanung und -steuerung (PPS), VDI-Verlag, Düsseldorf, 1989

/8/ Oeldorf, G. / Olfert, K. Materialwirtschaft, Ludwigshafen. Kiehl Verlag, Ludwigshafen (Rhein), 1998

/9/ Eversheim, W. / Betriebshütte, Produktion und Management, Neu bearb.Schuh, G. (Hrsg.) Auflage. Springer-Verlag, Berlin, Heidelberg, New York, 1996

/10/ Dangelmaier, W. Modell der Fertigungssteuerung, Beuth-Verlag, Berlin, 1993

/11/ VDMA Integrierte Materialwirtschaft, Maschinenbau-VerlagFrankfurt, 1990

/12/ Eversheim, W. Organisation in der Produktionstechnik. Band 1: Grundlagen.3. Auflage. VDI-Verlag, Düsseldorf, 1996

/13/ Günther, H.-O. / Produktion und Logistik, 5. Auflage, Tempelmeier, H. Springer-Verlag, Berlin, 2002

/14/ Tempelmeier, H. Material-Logistik; Modelle und Algorithmen für die Produktionsplanung und –steuerung und das Supply Chain

Management, 5. Auflage, Springer-Verlag, Berlin, 2002

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Lecture 5



5.2 Summary of the Lecture:

The large range of parts used in many companies makes the deployment of suitable management tools in the field of materials management essential. The purpose of the tools is to meet what can, in some cases, be contradictory requirements for:

- Higher levels of material availability

- Lower storage space and capital commitment

- Greater flexibility

- More favourable purchase prices.

In research and practice, there is a wide range of methods and tools geared to materials management. There is an extensive range of methods and tools in research and practice. The diversity of their characteristics makes it essential to analyse the function for which they are required precisely before selecting the most suitable one. It is possible, for example, that several different methods, e.g. a deterministic calculation of A and B parts, can exist along with a stochastic calculation of the requirement for C parts.

In addition to the functional characteristics, it is important to consider the work and time required to enter and calculate information. When the task is relatively straightforward, a rule of thumb may well be the most suitable solution. When the problems are more complex and the calculation methods more time consuming, it is advisable to use IT-assisted tools. However, it is important to remember that even the calculating techniques, concealed behind the coloured masks on the monitors, must be suitable for the task in hand and that it is vital to make the optimum selection from what is usually a wide range of parameters, if the result is to be satisfactory.

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Problems in materials management

Target conflicts

Lot size StockLow capital commitmentLow requirement for spaceRational manufactureHigh availability

... ... ...

Requirements Effects

Problem of quantity

- Number of parts

- Number of procurement operations

- Number of suppliers

Uncertain material requirement

Time

Req

uire

men

t

Part 4711old

Part 4712new

techn. modification

Problems in Materials Management

Notes on Figure 1:

5.3 Introduction and problem

The problems facing materials management are characterised particularly by the contradictory requirements for availability of ready materials on one hand, and low stock levels on the other hand. Because of the number of steps involved in the procurement process, it has become essential to use appropriate IT tools..

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Quantity-Related Problems illustrated by Examples from Industrial Practice

Automobile manufacturer

Machine toolmanufacturer

No. of product types:

∅ no. Of parts per product:

Total no. of parts:

No. of orders per week:

No. of suppliers:

~ 20 600

16.000

10

700

5.000 10.000

140.000

10.000

1.050

Anmerkungen zu Bild 2:

Die Anforderungen an die Materialwirtschaft hängen stark vom jeweiligen Produkt- und Unternehmenstyp ab. Eine manuelle Beherrschung der Teilevielfalt ist bei komplexeren, variantenreichen Produkten sowie in der Einzel- und Kleinserienproduktion kaum noch möglich.

Vorlesung 5

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Focus of the Lectures Materials Planning I and IIIntroduction

Methods

Materials procurement planning

Static lot sizes calculationStatic lot sizes calculation

Dynamic lot sizes calculation

Dynamic lot sizes calculation

Materials requirement planning

Stochastic requirement calculation

Stochastic requirement calculation

Deterministic requirement calculation

Deterministic requirement calculation

Materials stock planning

Definition of emergency stock levels

Definition of emergency stock levels

LogisticsLogistics

Legend: = Lecture 4 = Lecture 5

Area of conflict with emergency stock levelArea of conflict with

emergency stock level

Functions and concepts of material storagesFunctions and concepts of material storages

Tasks and objective of materials planningTasks and objective of materials planning

Planning of material sourcingPlanning of material sourcing

Notes on Figure 3:There is already a wide range of methods and tools, some of which are IT-supported for the groups of functions in the areas of material requirement, stock and procurement planning.

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Lecture 5



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According to: Wiendahl

Gross requirementAdditional requirement+

Total requirement=

Stock level-

-

No. earmarked (Reservations)

+

Emergency level+

Net requirement=

- Scrap- Spare parts- Test purposes- etc.

Order inventory(When products are externally manufactured)

- Workshop stock(When products are manufactured in-company)

Available stock

Net Requirement

Notes on Figure 4:

According to REFA, the gross requirement is the period-oriented requirement of material disregarding the inventory. The net requirement is calculated by the difference of gross requirement and the available stock at a certain date. Material requirement planning is based on the net requirement.

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Source: Olfert

Production step method

Production step method

Deterministic calculation of requirements

Deterministic calculation of requirements

Analytical method

Analytical method

Synthetic method

Synthetic method

Re-netting methodRe-netting method

Gozinto methodGozinto method

Disposition step method

Disposition step method

Where-used reportWhere-used report

Deterministic calculation of requirements entails precise determination of material requirements in terms of quantity and date required.

Deterministic calculation of requirements entails precise determination of material requirements in terms of quantity and date required.

Methods of Deterministic Calculation of Requirements

Notes on Figure 5:

5.4 Deterministic calculation of requirements

The deterministic calculation of requirements is based on the planned requirement for products or product components (primary requirement). The exact requirement for assemblies, single parts and raw materials (secondary requirement) is determined over all levels of the product structure in an analytical process by breaking down the product step-by-step on the basis of the parts list. In contrast to this, the synthetic method is based not on the whole product but on single components, examined in isolation. In this case the where-used report is used as a tool.

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According to: Wiendahl

Structuring Products According to Production and Planning Steps

R 1

T 3 T 4

Production steps technique Disposition steps techniqueStep

0

1

2

3

4Exact determination of requirement datesDecomposition of the components on several structural levelsStraightforward products without repeated use of components

Decomposition of requirement on only one structural level eachMore difficult to determine exact requirement datesComplex products

+-

+-

E 1

R 2

R 1 T 2

T 3

G 2

T 4

G 1

T 1T 2G 2

T 1

R 1

R 1

E 1

R 2 R 1 T 2

T 3

G 2

T 4

R 1

G 1

T 1T 2G 2

T 3 T 4

T 1

R 1R 1

Legend: E = Product (German: Erzeugnis); G = Assembly Part (Gruppe); T = Single part(Teil); R = Raw material (Rohmaterial)

Notes on Figure 6:

The production steps method is based on a product structure broken down into the chronological sequence. In contrast to this, the components which are used in a number of several applications are combined on the lowest structural level in the disposition step method. This eliminates the need for multiple breakdowns.

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Calculating date required

W 26

- 3 W

= W 23

Date higher order components requiredLead time

Date required

Calculating net requirement

85

x 3= 255- 110

= 145

Net requirement of higher order componentsUse

Gross requirementAvailable stock

Net requirement

G1Engine

1001585

T2Cog wheel

255110145

G2Transm.17060

110

2 33 W

W 26

G1

G2 T2

Example of How to Calculate Net Requirements

Legend: W = Week; G = Assembly Part (German: Gruppe); T = Single part (Teil)

Notes on Figure 7:

The requirement deadline for a component is calculated on the basis of the requirement deadline for the higher-ranking components minus lead time. In the disposition step method, the requirement dates calculated are sometimes too early. However, more time-consuming calculation operations permit the actual data of requirement to be calculated accurately.

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1 11

32 1

1 2 21

1 1 1 1

Compo-nents

Available stock

Net Re-quirement

Require-ment date

E1 --- 100 W 34

G1 15 85 W 26

G2 60 210 W 23

T1 25 160 W 23

T2 110 145 W 23

T3 210 100 W 21

T4 160 260 W 21

R1 --- 260 W 19

R2 100 160 W 19

2 W

2 W

3 W

8 W

Lead time

Total requirementComponentGross requirementAvailable stockNet requirementUse

16010010060------40---------60---2001001006060---R2R1R1R1R2R1

20010060---------160110

200100220110T4T3T4T3

10010060145110------2511060

10010085255170G2T1T1T2G2

8515100G1

100---

100E1

Using the Disposition Step Method to Determine Net Requirements

Legend: W = Week; E = Product (German: Erzeugnis); G = Assembly Part (Gruppe); T = Single part (Teil); R = Raw material (Rohmaterial)

11

Notes on Figure 8:

The information needed to structure the products is contained in the parts lists. The gross requirement for a component is calculated by multiplying the net requirement for the higher-ranking components by the number of times it is used (see Fig. 7). The net requirement is obtained by subtracting the available stock. In the disposition step method, the available stock is allocated to each component on only one structural level. This avoids errors.

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Alternative Presentation of Product Structure Using Gozinto-Graph

Product, assembly part, single part, raw materialRequirement

Gozinto-Graph

Straightforward mathematical requirement

Unclear presentation, takes time to get used to

+

-

E1100

G1-

G220

T4-

T1-

R1-

T2-

T3-

R2-

1 1

1 2 2

31 1

1

1

Legend: E = Product (German: Erzeugnis); G = Assembly Part (Gruppe); T = Single part (Teil); R = Raw material (Rohmaterial)

1

Notes on Figure 9:

Alternatively, the composition of a product can be shown by a Gozinto-Graph. Since this presents each component only once, this form of presentation permits the requirement to be worked out on the basis of a very straightforward algorithmic resolution. This form of categorising products is therefore used by many IT systems to organise the material needed for internal data structures.

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Consumption Models as Basis for Stochastic Determination of Requirement

Con

sum

ptio

n

Time

Con

sum

ptio

n

Time

Con

sum

ptio

n

Time

Consumption model

Without trend With trend

Con

sum

ptio

n

Time

Pure constant model

Seasonal constant model

Pure trend model

Seasonal trend model

Without seasonal fluctuation

With seasonal fluctuation

Without seasonal fluctuation

With seasonal fluctuation

Source: REFA

Notes on Figure 10:

5.5 Stochastic Calculation of Requirements

The stochastic calculation of requirements differs from the deterministic mode in that it is based on historical data, which is extrapolated for the future using stochastic methods and which therefore carries a degree of statistical uncertainty. The consumption pattern must first be interpreted before a suitable technique can be selected. The consumption models suggested by REFA /3/, for example, are useful in this context.

Lecture 5

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Common Techniques of Stochastic Determination of Requirement

According to: REFA/ Zeigermann/Tempelmeier

Exponential smoothing of first order

Timet t+1

V1V-V1

V1 = Exp. smoothed value 1st order

α = Smoothing factor

( )VVVVP ttttt

1

1

1

1

1

1 −−+−+== α

Exponential smoothing with trend correction at

1 = corrected estimate value of the trends‘ axis intercept

bt1 = exponential smoothed value of the

trends‘ gradient

baP ttt

11

1 +=+

Con

sum

ptio

n V

Timea

)1(*1 ++=+

tbaPt

Pt+1 = Forecast valuea = Axis interceptb = Gradient

Regression analysis

Floating mean valueVi = Requirement in period i

Time

n ∑−+=

+=

t

ntiit VP n 1

1

1

Ver

brau

ch

Perioden05

1015202530354045

7 8 9 10

V

V1

Pt+1

VV1

Pt+1

Con

sum

ptio

n V

Con

sum

ptio

n V

Con

sum

ptio

n V

Time

Notes on Figure 11:

While the regression analysis for a given set of value couples determines a mean straight line, the other operations shown in the figure adapt the forecast value flexibly to the changes in consumption. The characteristics of the forecasting method can be influenced by changing the parameters (number of periods considered “n”, smoothing factor “α”).

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Comparison of Forecasting Methods

0

5

10

15

20

25

30

35

40

45

1 2 3 4 5 6 7 8 9 10Period t

Req

uire

men

t

Actual RequirementFloating mean Value (n = 5)Exp. smoothing of f irst orderExp. smoothing w ith trend correctionRegression analysis for period 7

Notes on Figure 12:

The floating mean value is very suitable for pure constant models, since its reaction is sluggish, particularly when the number of periods taken into account “n” is high. The sensitivity of the technique must be increased when trend models are required. However, when this is done, the operation reacts very strongly to any random peaks in requirement. Similar considerations apply to the exponential smoothing method in relation to the definition of the α-factor. When the α-factor is high, the operation reacts very swiftly to any changes in requirement, causing the current requirement values to be heavily weighted when they are included in the forecast. In contrast, when the α-factor is low, the predicted value reacts slowly.

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Suitability of Forecasting Methods for Various Consumption Models

Regression analysis

Exponentional floating of the first orderExponentional floating with trend correction

Exponential smoothing given seasonal demand *

Multiple regression *

Floating mean value

Pur

e co

nsta

nt

mod

el

Pur

e tre

nd

mod

el

Sea

sona

l co

nsta

nt

mod

el

Sea

sona

l tre

nd

mod

el

Method

Consumption model

Suitable Suitable in some cases Suitable in principle, but not always useful

Source: Dangelmaier * Not further explained in this lecture

Notes on Figure 13:

The methods used in order to take explicit account of seasonal influences are based on the values recorded in the same period of the previous year. When seasonal trend models are used, a further component which reflects the trend can be added to this technique. These techniques are explained in greater detail in literature /6/.

Lecture 5

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Reasons for Storing Emergency Stocks

Time

Sto

ck le

vel

Stock emergency level

Actual requirement

Requirement forecast

Time


Target delivery dateActual delivery date

Time


Stock level assumed

Actual stock level

Source: FIR

Sto

ck le

vel

Sto

ck le

vel

Uncertainties in procurement

Uncertainties in determining stock level

Uncertainties in determining requirements

Notes on Figure 14:

5.6 Defining Emergency Stock Level

The purpose of emergency stocks is to avoid bottlenecks in the material supply from occurring when the requirements and stock levels differ from those planned. However, there are conflicting aims even in defining the emergency stock levels. Any increase in the emergency stock level, in an attempt to improve the capacity to supply, is at the expense of increasing storage and stock costs (see Fig. 15).

Lecture 5

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Impact of Emergency Stock on Cost

Source: Wiendahl

FMK = Cost incurred as a result of incorrect quantities (German: Fehlmengenkosten)

SBK = Cost of emergency stock (German: Sicherheitsbestands-kosten)

Level of service = x 100%No. of requests satisfied immediately

Total no. of requests

FMK + SBK

SBK

80% 100%

FMK

Level of service

minimale Kapitalbindung

Minimum storagecosts

Maximum readiness to supply

Objectives

Notes on Figure 15:

The progressive course of emergency stock costs is the result of the additional costs (e.g. for renting or building additional warehouses) when the available storage capacity is exceeded and from the steep increase in handling, transport, and administrative expenditure incurred when a warehouse is filled to capacity. The excess quantity costs result, for example, from loss of production caused by incorrect parts.

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Techniques of Determining Emergency Stock Levels

According to: Riggs

Ultra-conservative method

Ultra-conservative method

Percentage methodPercentage method

Heuristic functionHeuristic function

Emergency stock

Maximum daily con-sumptionto date

Maximum poss.

procurement time in days

Emergency level

∅removal

from stock

∅procure-

menttime

Factor(25-

40%)

Emergency level

- ∅ removal from stock- Standard deviation- Replacement procurement time- etc.

f

=

=

x

x x

=

Notes on Figure 16:

The “ultra-conservative method” of defining the emergency stock level estimates the “worst case” scenario. This normally results in unnecessarily high stock levels. The percentage method, which uses average values for stock removal and for procurement time as well as a factor which can be set individually, is usually more suitable for determining useful emergency stock levels. The heuristic method explained in Fig. 17 is outstanding in that it provides the option of specifying a required service level.

Lecture 5

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Heuristic Method of Determining Emergency Stock Level

According to: REFA

Emergency stock level: BS = b x s = 4,3 x 10,29 = 44,25 units

(Given 99% level of service)

Emergency stock level: BS = b x s = 4,3 x 10,29 = 44,25 units

(Given 99% level of service)

Quantity removed from stock Determining factor “b”87654321n

10294105127104116100109Removal

[units]

Replacement procurement time

∅ removal from stock:

Standard deviation:

unitsxn i 1,1071x =∑=

( )units

xn

xn

s ii

29,10

11

1 22

=

⎥⎦⎤

⎢⎣⎡ −

−= ∑ ∑

(Probability of correctness 95%)

Factor „b“

Number of removals n

1

2

3

4

5

6

7

5 10 20 50 100 200 400

4,3

8

Level of service:99%95%90%

Notes on Figure 17:

This method is explained in greater detail in REFA /3/.

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Conventional Techniques of Determining Lot Size

Source: Wiendahl

Techniques of determining lot size

Techniques of determining lot size

DeterministicDeterministic StochasticStochastic

Static(constant lot size)

Static(constant lot size)

Dynamic(variable lot size)

Dynamic(variable lot size)

Basic model (according to Andler)

Extended basic models

Floating economic lot size

Part period technique

WAGNER-WITHIN technique

SILVER-MEAL technique

Order point technique

Order rhythm technique

Notes on Figure 18:

5.7 Determining Lot Sizes

The deterministic methods of determining lot sizes strive to reduce lot size-dependent costs to an arithmetic minimum. The static methods assume a constant removal rate from the stores whilst the dynamic methods are based on the planned variable requirement values. The stochastic methods were explained in Lecture 4.

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Determining the Optimum Lot Size according to Andler

Source: REFA

Total cost

Storage costManufacturing cost

Cos

t

Quantityxopt

Quantity

Cos

ts

Quantity

- Order processing cost

- Set-up cost- Material cost- Additional cost with unfavourable manufacturing quantity

- Order processing cost

- Set-up cost- Material cost- Additional cost with unfavourable manufacturing quantity

- Storage cost- capital commitment

- interest cost(external capital)

- Opportunity cost(equity capital)

- Storage cost- capital commitment

- interest cost(external capital)

- Opportunity cost(equity capital)

Legend:xopt = Optimum lot size [units]iL = Storage cost rate [%]xkes = Total requirement per

period [units]KR = Set-up cost [€]Kh = Manufacturing cost per unit

of quantity [€/Unit]

„Andler Formula“„Andler Formula“

Cos

tsLh

gesRopt iK

xKx

⋅⋅⋅

=%200

Notes on Figure 19:

The cost-optimised lot size according to Andler is given by the sum of all fixed costs per lot (set-up efforts, etc.) and variable costs per lot (storage). The original Andler formula assumes an infinite production speed, i.e. stock levels in the production area are not taken into account. However, when the Andler formula is expanded, the production phase can also be included on the basis of the throughput time involved. A derivative of the Andler formula is given in the Appendix (Chapter 5.12).

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Calculating Floating Economically Efficient Lot Size

Period1 2 3

Kges, n = Unit cost (for n periods)A = Fixed lot costKL = Storage costs per unit and periodBmi = mean stock level in period “i”xges,n = cumulated lot size (n periods)

Formula

• Single product manufacturing

• Production speed infinitely high

• Stock removal rate variable (actual requirement for period)

Boundary conditions

Summary of the requirement per period up to minimisation of costs per unit.

Summary of the requirement per period up to minimisation of costs per unit.

Stock level

170

3060

n=2

n=1

n=3

1

2

3

4

60

30

80

50

n=2

n=1

n=3

Lot size 170Lot size 90Lot size 60

Requirement[units]

Period

4,17

3,38

3,41

Unit cost [€]

nges

n

imiL

nges x

BKAK

,

1,

∑=

⋅+=

Notes on Figure 20:

In this method, the planned requirements for future periods are condensed until the sum of the lot and storage costs per unit are reduced to a minimum. When the requirement fluctuates substantially, this method has considerable advantages over the Andler formula.

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Additional Factors which Impact on the Determination of Lot Size

Source: REFA

General Outsourcing• Available storage space• Liquidity• Storage life of the products

In-company manufacture• Capacity use of manufacturing facilities

• Flexibility required of manufacturing facilities

• Manufacturing sequence (throughput times, set-up times)

• Supply capability of supplier

• Pricing• Transport facilities/ packaging units

Uni

t cos

ts

xopt½ xopt 2 xopt

Advisable spread

• Better utilisation of capacity

• Lower prices

• Capacity use of transport facilities

• Better utilisation of capacity

• Lower prices

• Capacity use of transport facilities

• Higher flexibility

• Less requirement for space

• Shorter throughput time

• Higher flexibility

• Less requirement for space

• Shorter throughput time

Lot size

Additional relevant criteria in determining lot size

Notes on Figure 21:

In addition to the methods previously discussed, in practice, there are diverse additional criteria which are used to determine lot size. When, for example, the machining time for a lot is long in relation to the available capacity, bottlenecks can occur, which lead to delays in processing subsequent orders. Since the overall cost curve is generally very flat in the area around the minimum, permissible tolerance limits can be given for the optimum lot size, without causing the unit costs to rise too steeply.

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5.8 Questions on the Lecture

1. How do the analytical techniques differ from the synthetic techniques in deterministic calculations of requirements?

2. Explain the difference between the production step method and the disposition step method.

3. List a suitable forecasting technique for each of the four consumption models (in accordance with REFA) and explain under what circumstances each of the techniques is suitable.

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4. Explain briefly some reasons for keeping emergency stocks.

5. Explain the impact of the emergency stock on cost.

6. Discuss briefly the advantages and disadvantages of the techniques of defining the emergency stock levels.

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7. List the boundary conditions which apply to the application of the Andler technique.

8. Explain briefly the advantage of the technique of the floating economic lot size over the Andler technique.

9. List relevant criteria used to determine lot sizes in addition to the cost variables used in the Andler formula.

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Presentation of Product Structure in a Gozinto-Graph

E1

100

G1

-

G2

20

T4

-

T1

-

R1

-

T2

-T3

-

R2

-

1 1

1 2 2

3

1 1

1

1

Product, assembly, part, raw material

Requirement

Legend: E = Product (German: Erzeugnis); G = Assembly Part (Gruppe); T = Single part (Teil); R = Raw material (Rohmaterial)

Notes on Figure A-1:

5.11 Calculating Requirements Using the Gozinto-Graph

The principle of calculating gross requirement using the Gozinto technique is explained in greater detail in the following, on the basis of the product structure shown in the so-called Gozinto-Graph (Fig. A-1).

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Appendix 5



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Gozinto-Graph Calculation Plan

Z Quantity Z Quantity Z Quantity Z Quantity1 E1 0 100 1002 G1 1 0 100 1003 G2 2 1 100+20 0 200 3204 T1 2 1 100 0 100 2005 T2 1 0 300 3006 T3 1 0 320 3207 T4 1 0 640 6408 R1 2 1 200 0 320 5209 R2 1 0 640 640

Run 3 Gross requirement

Product, assembly, single part

Arithmetic step

Run 0 Run 1 Run 2

z = Arrow counter

(According to: Hahn, Laßmann)

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The stop criterion in this type of gross requirement calculation is the number of arrows starting from one nodal point, which describe the use of a part or of an assembly within a product. The secondary requirements of the assemblies, single parts, etc. are determined in the individual runs on the basis of the elements, whose arrow numerator is a “z” or an “o”. In the case of the assembly G2, account must also be taken of the primary requirement. Fig. A-2 shows the arithmetic development of the Gozinto technique /8/.

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Determining the Optimum Order Quantity according to Andler

Optimum order quantity when products are manufactured externally

Gives the optimum procurement quantity.

Legend:x = Order quantityxges = Total quantity per periodxopt = Optimum procurement quantityKB = Order cost per order KB,ges = Order cost per periodKB,zus,ges = Additional cost per periodKx = Additional cost per unit of quantityKL = Storage cost per orderKE = Cost per unit of quantity when products are

manufactured externallyiL = Interest rate for storage [%]

Order cost:

Additional cost:

Storage cost:

Total cost:

Bges

gesB Kx

xK ⋅=,

gesxgeszusB xKK ⋅=,,

LfL iKxK ⋅⋅=200

LfgesxBges

LgeszusBgesB

iKxxKKx

xKKKK

⋅⋅+⋅+⋅=

++=

200

,,,

0)( =xK I

Lf

Bgesopt iK

Kxx

⋅⋅⋅

=200

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5.12 Derivation of the Andler Formula

ANDLER derives the economic lot size or order quantity both for in-company manufacture and for external manufacture. Only the cost categories which vary with the procurement quantity need to be considered, since these are the only ones which influence the decision in favour of one or the other alternative. The sum of all costs which influence the order quantity or the lot size is minimised. Fig. A-3 shows the calculation of the optimum order quantity when the products are purchased externally and the cost categories which must be taken into account /3/.

Appendix 5



WZL©

Economic lot size when goods are manufactured in-company

Determining Economic Lot Size When Goods Are Manufactured In-Company

Gives the economically efficient lot size.

Legend:x = Order quantity xges = Total quantity per periodxopt = Optimum procurement quantityKR = Setting up costs per order KB,ges = Setting up costs per periodKA = Order processing costKL = Storage cost per orderKh = Manufacturing cost per unit of quantity iL = Interest rate for storage [%]

Order processing costs:

(Operations planning/ administration etc.)

Setting up costs:

Storage cost:

Total cost:

Rges

gesR Kx

xK ⋅=,

.constK A =

LhL iKxK ⋅⋅=200

LhARges

LAgesR

iKxKKx

x

KKKK

⋅⋅++⋅=

++=

200

,

0)( =xK I

Lh

Rgesopt iK

Kxx

⋅

⋅⋅=

200

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The most economically efficient lot size when the products are manufactured in-company can be calculated in the same way (Fig. A-4).

The calculation of the optimum procurement quantity, when other cost factors (such as staggered discounts and tax considerations) or restrictions (such as delivery periods, minimum stock levels, etc.) are involved, is considerably more complex. The cost progressions are then uneven and can no longer be shown by a straightforward equation.

Appendix 5



5.13 Exponential smoothing of second order

Initial point: Fluctuation of the time series about a linear trend

tbaVt ⋅+= for t = 1...T

Forecast equation with exponential smoothing of second order:

rbarbtbarbVP ttttrt ⋅+⋅+⋅+=⋅+= =+ )(

Objective: Determining and with the information available at time point t at bt

If a straight line (a+b*t) is smoothed with exponential smoothing of first order, then it is

displaced by the absolute value of .

describes the average age of the considered values:αα−

⋅1b

t=−αα1

αα

ααα

αα

αααα

αα

−⋅−⋅+=

−⋅⋅−⋅⋅+⋅=

−⋅⋅⋅−−⋅⋅+⋅=

−⋅+⋅−⋅=

∑∑

∑∞

=

∞

=

∞

=

1)(

11)(

)1()1()(

))(()1(

2

00

0

btba

btba

rbtba

rtba

r

r

r

r

r

r)(1 1tbaV t ⋅+=

With the consumption smoothed with exponential smoothing of first and second order:

VVV ttt1

11 )1( −⋅−+⋅= αα

VVV ttt2

112 )1( −⋅−+⋅= αα

there is the correlation:

tbVtbtbatbaV tt ⋅−=⋅−⋅+=⋅+= )()( 11

tbVtbtbatbtbatbaV tt ⋅⋅−=⋅⋅−⋅+=⋅−⋅+=⋅+= 22)()()( 122

tbVV tt ⋅=−⇒ 21

which is put into graphs in fig. 1.

Appendix 5

A5 Page 5



and can be determined with the smoothing factor α and the value of the exponential smoothed time series of second order :

Period

Vt

Vt

t

αα−1

Fig. 1

at bt

VVVVVbVa

VVVVb

tttttttt

tttt

t

212111

2121

211

)(1

1)(1

−⋅=−

⋅−

⋅−+=−

⋅+=

−⋅−=

−−

=

αα

αα

αα

αα

αα

V t2

Vt1

Vt2

rVVVVrbaP ttttttrt ⋅−⋅−

+−⋅=⋅+=+ )(1

2 2121

αα

Appendix 5

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production management i - rwth aachen university · production management i (prof. schuh) methods...

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