CC3-InventoryManagement

Stanisaw Krzyaniak1

Inventory Management

Inventories today: a curse, a blessing, a must..?

Crash Course on:

Stanisaw Krzyaniak2

1. Why do we keep inventories?

2. Typical demand classifications and analyses helpful in inventory

management.

3. Why high quality forecasting is so important for inventory

management?

4. Cost aspects of inventory management.

5. Material Decoupling Point - dependent and independent demands,

deterministic and stochastic approaches to inventory management.

Course programme:

Stanisaw Krzyaniak3

6. Calculation of safety and cycle stock.

7. Classical stock replenishment systems (Reorder Point and Cycle

Review) and their typical combinations.

8. Safety stock in case of dispersed inventories (square-root law).

9. Information Decoupling Point concept and its role in reduction of

stock levels.

10. Review of selected logistics concepts and solutions oriented on stock

reduction/rationalisation .

Course programme:

Stanisaw Krzyaniak4



management.


management?


5. Material Decoupling Point - dependent and independent demands,


Course programme:

Stanisaw Krzyaniak5

Why do we keep

inventories?

Crash Course on Inventories

Stanisaw Krzyaniak6

Inventory (stock) - materials in a supply chain or in

a segment of a supply chain, expressed in

quantities, locations and/or values, not used at

present, but kept for the future use (consumption/

/sale).

Why do we keep inventories?

Based on ELA Terminology

Stanisaw Krzyaniak7

5% Utility value

?95%

TH

RO

UG

HPU

T T

IME I

N A

SU

PPLY

CH

AIN

Among others, keeping

inventories is also here.


Stanisaw Krzyaniak8


Customer

service

Income Costs Profit

Working

capital

- =Return on

Investment

Inventories

Profit

Stanisaw Krzyaniak9


Customer

service

Income Costs Profit

Working

capital

- =Return on

Investment

Inventories

Profit

Assets

Return on

Assests

Stanisaw Krzyaniak10

Materials stock (raw materials, components)

Work-in-progress stock

Finished products stock

Spare parts and auxiliary materials stock

By type and position in a pipeline

Stock classification



Deliveries Production Distribution

Work-in-progress

Raw materials and components

Finished products

Raw materials and components

Work-in-progress

Consumer goods

Auxillary materials, spare parts



Do you keep a stock of bread in your household?



Cycle stock

Safety stock

Seasonal stock

Speculation stock

Strategic stock

By the reasons for keeping




Fast moving (rotating) stock

Slow moving (rotating) stock

Not moving (rotating) stock

Obsolete stock

Emergency stock

By rotation




SS

SC

Q

Ssp

Cycle stock

Safety stock

Surplus stock


Stock structure


uncertainty of real demand,

uncertainty of real quantity, quality and timing of deliveries,

seasonal access to some materials and goods,

service level required by a customer,

expected difficulties with an access to some goods (expected rise of prices),

discounts offered for purchases of larger quantities,

some technical and/or organisational conditions of deliveries.

Stock maintaining, replenishment and its quantity result from:



Cycle stock:

Lack of possibilities to fully synchronise supplies with consumption,

Technical and/or organisational conditions (limitations),

Economic incentives (discounts).

Safety stock:

Random fluctuations of demand,

Forecast errors,

Long replenishment lead times,

Unpredictable delays,

Required service level.

Surplus stock:

Miscalculation of factors influencing safety stock,

Wrong estimation of the required service level,

Excessive safety measures taken to avoid stock-outs.



Good, because they: Bad, because they: Guarantee a continuous access to all

kinds of goods when supplies are

discontinues,

Guarantee access to goods in periods

when they are not available,

Ensure required service level

compensating random variations of

demand,

Ensure required service level

compensating delays of deliveries

random variations of replenishment

lead time.

Take space (warehouses),

Cost money (space, losses, capital);

carrying stock may cost annually up to

30% of its value.

So, is this good or bad to have inventories?





management.


management?


5. Material Decoupling Point - dependant and independent demands,


Course programme:


Demand analyses



ABC analysis,

XYZ analysis,

Customer and supplier related analyses,

Trends & Seasonality,

Random deviations - demand profile,

Life-cycle analysis,

Identification of wild demand .

Demand analyses


No Item codeNo of used/sold

itemsUnit price

Value of used/sold

items

Cummulated value

of used/sold items

1 10-01 15344 3,5 53 704,00 53 704,00 7,0%

2 10-02 23 76,1 1 750,30 55 454,30 7,2%

3 10-03 557 11 6 127,00 61 581,30 8,0%

4 10-04 1270 5,43 6 896,10 68 477,40 8,9%

5 10-05 7088 2,05 14 530,40 83 007,80 10,8%

6 10-06 278 20,66 5 743,48 88 751,28 11,6%

7 10-07 1513 2,53 3 827,89 92 579,17 12,1%

8 10-08 13 1178 15 314,00 107 893,17 14,1%

9 10-09 997 6,53 6 510,41 114 403,58 14,9%

10 10-10 8724 0,4 3 489,60 117 893,18 15,4%

11 20-01 1245 2,46 3 062,70 120 955,88 15,8%

12 20-02 7688 20,9 160 679,20 281 635,08 36,8%

13 20-03 679 6,2 4 209,80 285 844,88 37,3%

14 20-04 1190 5,14 6 116,60 291 961,48 38,1%

15 20-05 25799 0,89 22 961,11 314 922,59 41,1%

16 20-06 1409 32,6 45 933,40 360 855,99 47,1%

17 20-07 133 74,86 9 956,38 370 812,37 48,4%

18 20-08 799 15,34 12 256,66 383 069,03 50,0%

19 20-09 9887 9,3 91 949,10 475 018,13 62,0%

20 20-10 2234 2,40 5 361,60 480 379,73 62,7%

21 30-01 22 208,9 4 595,80 484 975,53 63,3%

22 30-02 12778 20,4 260 671,20 745 646,73 97,3%

23 30-03 79 63 4 977,00 750 623,73 98,0%

24 30-04 1313 9,92 13 024,96 763 648,69 99,7%

25 30-05 557 4,81 2 679,17 766 327,86 100,0%

Demand analyses - ABC classification


Rules of the ABC analysis:

o establish a criterion,

o rank and sort assortment according to the established

criterion,

o calculate a total sum,

o calculate cumulative sums,

o calculate percentage share of cumulative sums in the

total sum,

o assign to group A items responsible for 80% of the

criterion value, to group B items responsible for further 15%, and the remaining items to group C.



A B C


80:20

20% 30-50%


A B C

Quantity

Price

XY

Z

Demand analyses ABC/XYZ classification

30-04

10-08

20-05

5 20-06 1409 32,6 45 933,40 612 936,90 80,0%

6 20-05 25799 0,89 22 961,11 635 898,01 83,0%

7 10-08 13 1178 15 314,00 651 212,01 85,0%

8 10-05 7088 2,05 14 530,40 665 742,41 86,9%

9 30-04 1313 9,92 13 024,96 678 767,37 88,6%

10 20-08 799 15,34 12 256,66 691 024,03 90,2%


Quantity

Price

XY

Z

Demand analyses - XYZ classification


Quantity

Price

XY

Z




itemsUnit price

Value of used/sold

items

Cummulated value

of used/sold items

Cumm.

[%]

1 10-01 15344 3,5 53 704,00 53 704,00 7,0%

2 10-02 23 76,1 1 750,30 55 454,30 7,2%

3 10-03 557 11 6 127,00 61 581,30 8,0%

4 10-04 1270 5,43 6 896,10 68 477,40 8,9%

5 10-05 7088 2,05 14 530,40 83 007,80 10,8%

6 10-06 278 20,66 5 743,48 88 751,28 11,6%

7 10-07 1513 2,53 3 827,89 92 579,17 12,1%

8 10-08 13 1178 15 314,00 107 893,17 14,1%

9 10-09 997 6,53 6 510,41 114 403,58 14,9%

10 10-10 8724 0,4 3 489,60 117 893,18 15,4%

11 20-01 1245 2,46 3 062,70 120 955,88 15,8%

12 20-02 7688 20,9 160 679,20 281 635,08 36,8%

13 20-03 679 6,2 4 209,80 285 844,88 37,3%

14 20-04 1190 5,14 6 116,60 291 961,48 38,1%

15 20-05 25799 0,89 22 961,11 314 922,59 41,1%

16 20-06 1409 32,6 45 933,40 360 855,99 47,1%

17 20-07 133 74,86 9 956,38 370 812,37 48,4%

18 20-08 799 15,34 12 256,66 383 069,03 50,0%

19 20-09 9887 9,3 91 949,10 475 018,13 62,0%

20 20-10 2234 2,40 5 361,60 480 379,73 62,7%

21 30-01 22 208,9 4 595,80 484 975,53 63,3%

22 30-02 12778 20,4 260 671,20 745 646,73 97,3%

23 30-03 79 63 4 977,00 750 623,73 98,0%

24 30-04 1313 9,92 13 024,96 763 648,69 99,7%

25 30-05 557 4,81 2 679,17 766 327,86 100,0%




itemsUnit price

Value of used/sold

items

Cummulated value

of used/sold items

Cumm.

[%]

1 10-01 15344 3,5 53 704,00 53 704,00 7,0%

2 10-02 23 76,1 1 750,30 55 454,30 7,2%

3 10-03 557 11 6 127,00 61 581,30 8,0%

4 10-04 1270 5,43 6 896,10 68 477,40 8,9%

5 10-05 7088 2,05 14 530,40 83 007,80 10,8%

6 10-06 278 20,66 5 743,48 88 751,28 11,6%

7 10-07 1513 2,53 3 827,89 92 579,17 12,1%

8 10-08 13 1178 15 314,00 107 893,17 14,1%

9 10-09 997 6,53 6 510,41 114 403,58 14,9%

10 10-10 8724 0,4 3 489,60 117 893,18 15,4%

11 20-01 1245 2,46 3 062,70 120 955,88 15,8%

12 20-02 7688 20,9 160 679,20 281 635,08 36,8%

13 20-03 679 6,2 4 209,80 285 844,88 37,3%

14 20-04 1190 5,14 6 116,60 291 961,48 38,1%

15 20-05 25799 0,89 22 961,11 314 922,59 41,1%

16 20-06 1409 32,6 45 933,40 360 855,99 47,1%

17 20-07 133 74,86 9 956,38 370 812,37 48,4%

18 20-08 799 15,34 12 256,66 383 069,03 50,0%

19 20-09 9887 9,3 91 949,10 475 018,13 62,0%

20 20-10 1554 3,45 5 361,30 480 379,43 62,7%

21 30-01 22 208,9 4 595,80 484 975,23 63,3%

22 30-02 12778 20,4 260 671,20 745 646,43 97,3%

23 30-03 79 63 4 977,00 750 623,43 98,0%

24 30-04 1313 9,92 13 024,96 763 648,39 99,7%

25 30-05 557 4,81 2 679,17 766 327,56 100,0%


itemsUnit price

Value of used/sold

items

Cummulated value

of used/sold items

Cumm.

[%]

1 20-05 25799 0,89 22 961,11 53 704,00 7,0%

2 10-01 15344 3,5 53 704,00 55 454,30 7,2%

3 30-02 12778 20,4 260 671,20 61 581,30 8,0%

4 20-09 9887 9,3 91 949,10 68 477,40 8,9%

5 10-10 8724 0,4 3 489,60 83 007,80 10,8%

6 20-02 7688 20,9 160 679,20 88 751,28 11,6%

7 10-05 7088 2,05 14 530,40 92 579,17 12,1%

8 20-10 2234 2,40 5 361,60 107 893,17 14,1%

9 10-07 1513 2,53 3 827,89 114 403,58 14,9%

10 20-06 1409 32,6 45 933,40 117 893,18 15,4%

11 30-04 1313 9,92 13 024,96 120 955,88 15,8%

12 10-04 1270 5,43 6 896,10 281 635,08 36,8%

13 20-01 1245 2,46 3 062,70 285 844,88 37,3%

14 20-04 1190 5,14 6 116,60 291 961,48 38,1%

15 10-09 997 6,53 6 510,41 314 922,59 41,1%

16 20-08 799 15,34 12 256,66 360 855,99 47,1%

17 20-03 679 6,2 4 209,80 370 812,37 48,4%

18 10-03 557 11 6 127,00 383 069,03 50,0%

19 30-05 557 4,81 2 679,17 475 018,13 62,0%

20 10-06 278 20,66 5 743,48 480 379,43 62,7%

21 20-07 133 74,86 9 956,38 484 975,23 63,3%

22 30-03 79 63 4 977,00 745 646,43 97,3%

23 10-02 23 76,1 1 750,30 750 623,43 98,0%

24 30-01 22 208,9 4 595,80 763 648,39 99,7%

25 10-08 13 1178 15 314,00 766 327,56 100,0%



Basic parameters describing demand variability

n

D.........DDD n21

1n

)DD(......)DD()DD( 2n2

2

2

1D

DD

D

Mean (average) demand

Standard deviation

Coefficient of variation



D = 82,7

D = 4,5

D=0,055



D = 40,9

D = 9,4

D=0,23



D = 4,21

D = 2,07

D=0,49



D = 0,0417

D = 0,201

D=4,82



Coefficient of variation as a criterion for the XYZ classification

DD

D


2,0D 6,02,0 D 6,0D

X Y Z


A B C

XAX Group

High turnover in terms of value,

high and even periodical

consumption (daily, weekly

demand). Highly reliable

forecasts.

BX Group

Medium turnover in terms of

value, high and even periodical



forecasts.

CX Group

Low turnover in terms of value,




forecasts.

YAY Group




demand). Less reliable forecasts

(significant forecast errors).

BY Group






CY Group






ZAZ Group




demand). Very poor reliability

of forecasts.

BZ Group





of forecasts.

CZ Group





of forecasts.



AZ BZ CZ

AY BY CY

AX BX CX



General pattern of a time series seasonality with a trend

Year I Year II Year III Year IV

Seasonality

Trend

Dem

and

Time

Demand analyses trends and seasonality


Analysis of a demand variability and profiles

Demand analyses


Demand analyses variability and profiles

D = 82,1

D = 4,5

D=0,055


50

40

30

20

10

0



0 10 20 30 40 50 Demand

Frequency

0,40

0,30

0,20

0,10



Demand analyses variability and profilesD = 82,1

D = 4,5

D=0,055


D = 40,9

D = 9,4

D=0,23




Normal distribution can be applied in the case of fast moving goods (groups X and Y)

D = 40,9

D = 9,4

D=0,23



D = 0,0385

D = 0,197

D=5,03



Poisson distribution can be applied in the

case of slow moving goods, where

calculated average demand (for a chosen

time unit) D is equal to the square of the

standard deviation D D2.

D = 0,0385

D = 0,197

D=5,03


Poisson distribution


D = 0,5D = 0,0385 D = 1,0

D = 2,0 D = 3,0 D = 4,21


TIME

DEMAND

Phases:

Introduction

Development

Saturation

Decline

Withdrawal

Inventory management v. life cycle



D = 38,4; D = 5,84 D = 42,5; D = 15,0





management.


management?




Course programme:


Why high quality forecasting

is so important

for inventory management?



Inventory planning requires foreseeing future events,

influencing processes which determine stock level:

demand and its variability (trends, seasonality, random nature),

changes of replenishment lead time and its variability,

cost relationships.

Foreseeing future events means:

forecasting (based on formal procedures, formulas and algorithms),

prediction (expert analysis).

Basic forecasting models and techniques


Forecasting can be based on:

internal data (e.g. historical data about sales of nutrients for infants),

external data (e.g. demographical data regarding increase or decrease of births).



Year I Year II Year III Year IV

Seasonality

Trend

Demand D

time t

Random factor



Shortterm forecasts Longterm forcests

Exponential smoothing Winters model

Seasonal coefficients model

Analytical models

Exponential smoothing Holts model

Exponential smoothing Brown model

Weighted moving average

Moving average

Arithmetical average

Econometric models

Heuristic models

Analog models

Scenarios

Simulations

Selected forecasting metods



Exponential smoothing

= 0 constant forecast model= 1 naive forecast

all data considered in a forecast

selection of the smoothing constant (0 < < 1)

calculation of a forecast:

)1(DDD kk1k

kkk1k DDDD



0

2

4

6

8

10

12

64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

Exponential smoothing

7,00

kkk1k DDDD

0,0



0

2

4

6

8

10

12

64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

7,11

1,0Exponential smoothing

kkk1k DDDD



0

2

4

6

8

10

12

64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

6,83


kkk1k DDDD



0

2

4

6

8

10

12

64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

6,68


kkk1k DDDD



0

2

4

6

8

10

12

64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

6,84


kkk1k DDDD



0

2

4

6

8

10

12

64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

7,00


kkk1k DDDD



68

Three areas of assessment:

Quality of a forecast model

Forecast accuracy

Forecast acceptance

How to assess forecast quality?



69



Forecast accuracy

Forecast acceptance




t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Demand 120 132 141 150 159 166 173 181 184 190 195 199 206 210 215 220 223 230 233 236




Determination coefficient

n

1t

2

t

n

1t

2

t

2

yy

yy

R

1,0R 2

- real, historical value of the considered variable for the period t,

- theoretical (model) value of the considered variable for the period t,

- mean value of the considered variable for n periods.

ty

ty

y



t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Demand 120 132 141 150 159 166 173 181 184 190 195 199 206 210 215 220 223 230 233 236




73



Forecast accuracy

Forecast acceptance




Forecast accuracy

t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Forecast 50 49 48 50 52 53 52 54 54 54 54 54 50 46 48 47 44 43 46 47

Demand 51 51 56 52 53 48 63 56 49 52 49 45 36 57 48 36 38 49 62 57

Forecast

Real demand

Today



Forecast accuracy ex post measures Formula

1 Absolute forecast error ex post

2 Mean absloute forecast error ex post

3 Relative forecast error ex post

4 Mean relative forecast error ex post

*

ttt yyq

n

)yy(

e

n

1t

*

tt

0e

100y

yy

t

*

tt

t


- forcast value of the considered variable for the period t,

ty

ty

100y

yy

n

1 n

1t t

*

tt



Forecast accuracy ex post measures Formula

5 Mean square error

6 Mean absolute error (deviation)


- forecast value of the considered variable for the period t,

ty

ty

n

1t

2*

tt

* )yy(n

1s

n

1i

*

tt

n

yyd


mind*,s



Quality of the forecast model

Forecast accuracy

Forecast acceptance




Forecast acceptance

t 1 2 3 4 5 6 7 8 9 10 11 12 13

Forecast/model 37 38,8 40,6 42,4 44,2 46 47,8 49,6 51,4 53,2 55 56,8 58,6

Demand 37 38 42 39 46 49 49 44 55 52 ? ? ?

Today

1n

1

)tt(

)tT(*s

n

1t

2

2

T 100y*t

t

t

Absolute forecast error ex ante Relative forecast error ex ante



What are the consequences of wrong forecasts (wrong forecast models)? Wrong safety stock levels: too high or too low,


What are the consequences of high forecast errors? High safety stock levels.

It has to be distinguished between

a wrong forecast and a forecast error.


1. Why do we keep inventory?


management.


management?




Course programme:


Cost aspects

of inventory management



Replenishment costs (Cr)

Carrying costs (Cc)

Stock-out costs (Co)

We can distinguish

Fixed (independent) costs (Crf, Ccf, Cof)

Variable (dependant) costs (Crv, Ccv, Cov)

Cost aspects


Replenishment costs (Cr) fixed (independent) costs (Crf)

fixed costs of a purchasing department and other departments responsible for

receipts (rooms, media, salaries,

overheads)

fixed transport costs (fleet depreciation, salaries, overheads)

Cost aspects



variable costs (dependent on a number of orders) (Crv) Order preparation costs,

Quality control costs,

Transport costs (fuel, maintenance),

Custom clearance fees.

Cost aspects



variable costs (dependent on a number of orders) over a given period (Crv) can be

calculated by multiplying a unit cost related

to a single order/delivery (cr) and a number

of deliveries (nd) realised in the period.

ndcCr rv

Cost aspects


Carrying costs (Cc)

fixed (independent) costs (Ccf)

Depreciation and exploitation costs of a warehouse (building)

Depreciation costs of a warehouse equipment

Salaries plus overheads

Cost aspects


Carrying costs (Cc)

variable costs (dependent on stock quantity) Ccv Cost of maintaining special storing conditions,

Stock insurance costs,

Cost of losses and stock depreciation,

Cost of a tied-up capital (cost of credit or lost incomes from a deposit).

Cost aspects


Carrying costs (Cc)

variable costs (dependent on stock quantity) (Ccv ) over a given period depends on a storing period (time) and stock value (eg.

purchase price).

ucv pcCc

A unit inventory carrying cost can be calculated as:

cc coefficient of periodical inventory carrying cost (cc = 0.050.20 per year)pu unit price

Cost aspects


Stock-out costs (Co)

fixed (independent costs (Cof):

Additional transport cost for emergency purchase,

Fixed penalty fee paid to the customer,

Permanent loss of a customer (loss of future incomes),

Loss of the market reputation (temporary or permanent loss of a group of customers),

Cost of stopping a production line.

Cost aspects


Stock-out costs (Co) Variable costs (dependant on the shortage

quantity) Cov Higher price for emergency purchase, Penalty fee based on number of missing items, Lost margin income due to particular transaction, Less margin income due to selling a substitute product, Cost of the postponement (transaction and payment

postponed), Cost of lost production.

Cost aspects




management.

3. Why high quality forecasting is so important for inventory management?

4. Cost aspects of inventory management..



Course programme:


Material Decoupling Point dependent and independent demand



Delivery Production Distribution

Customer order lead time

Reaction time

Customer order lead time

Customer order lead timeLead time gap

Lead time gap

Lead time gap

Material Decoupling Point

Source: M. Christopher. Logistics and Supply Chain Management. Startegies for Reducing Costs and Improving Services. 1st edition. Financial Times. Prentice Hall


Information (orders)

Delivery

Inventory




Delivery

Inventory



12

34

5

Dependent demand



Independent demand


2



Dependent demand

Independent demand

ForecastsCalculationsMaterial Requirements Planning

Cycle and safety stockof finished goodsResidual stock


6. Service level and safety stock.

7. Classical optimisation of the cycle stock.



9. Safety stock in case of dispersed inventories (square-root law),


stock levels.


reduction/rationalisation.

Course programme:


Service level

and safety stock



D = 40,9

D = 9,4

D=0,23

Service level and safety stock


Knowledge of a demand distribution over a selected

time unit (e.g. a day, a week) is very important. But this

is not enough to manage inventories in a proper way.

Stock replenishment is realised over a defined time

period, called a replenishment lead time.

It is very important to know this time.

The key issue is the demand distribution over the

replenishment lead time



Demand distribution within

replenishment cycle



Replenishment lead time the period of time between the moment the decision is made that a product is to

be replenished and the moment the product is

available for use.

Delivery lead time is the time between the receipt of the

customer order and the delivery of the product to the customer

and is always shorter then the replenishment lead time.

Replenishment lead time



Decision on replenishment

Placing an order

Receipt of the order

Starting production or picking the order

Preparation for loading

Loading

Arrival to the customer (receiver)

Approval of the delivery (quality control)

Unloading

Availability for use

Deliverycycle

Replenishmentcycle




LT

The need for replenishment occurs

The need is recognized

Decision on replenishment

Placing an order

Receipt of the order

Starting production or picking the order

Preparation for loading

Loading

Arrival to the customer (receiver)

Approval of the delivery (quality control)

Unloading

Availability for use




D = 40,9

D = 9,4

D=0,23

D = 163,6

D = 18,8

D=0,121


LT=4


0 20 40 60 80 100 120 140 160 180 200 220 240 260 280

D;D

LT;LTDD DDLT LT

Probability density functions



0 20 40 60 80 100 120 140 160 180 200 220 240

Probability density function

Distribution function

Probability that demand over the replenishment cycle will not exceed the given level



0 20 40 60 80 100 120 140 160 180 200 220 240

185 190 195 200 205

p(DLT195) 0,953



50 100 150

f(T)

P

Normal distribution

340 500 660 DLT

f(D)

LT50 100 150 D

f(LT)

f(DLT)


Service level



Row materials and

componentsFinished goods

Time to inform about emergency situation,

Relaibilty of deliveris (quality, quanitity, time),

Flexiblity of deliveries (time, quantity)

Avalibility of ordered raw materials and components

Suppliers Sevice Level indicators

Customer oriented Sevice Level indicators

Avalibility of goods

Responsiveness to customer needs (flexibility).



Customer service level

(Probability that a stock-out situation will not

occur over a replenishment lead time)

Probability of not getting out of stock


SL1


220

200

180

160

140

120

100

80

60

40

20

0

DLT

How often?



0

0,005

0,01

0,015

0,02

0,025

0,03

0,035

0,04

0,045

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Stock-out probability

within a replenishment cycle

Stock level at the beginning of a replenishment cycle

DLT

Service levelProbability of serving demand

within replenishment cycle



0

0,005

0,01

0,015

0,02

0,025

0,03

0,035

0,04

0,045

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

50%

DLT


within replenishment cycleStock-out probability


Stock level at the

beginning of a

replenishment cycle



0

0,005

0,01

0,015

0,02

0,025

0,03

0,035

0,04

0,045

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

DLT

SSSafety stock

LTDsS

nd

ndnd1SL outstock


within replenishment cycle

Stock-out probability


Stock level at the

beginning of the

replenishment cycle



)SL(f

SL



LT LT LT

[t]

Stock level

Variable demand


Constant replenishment cycle lead time LTDDLT

SS


LT

LT1

LT

[t]

Stock level


Constant demand

Variable replenishment cycle lead time

DLTDLT

SS


LT

LT1

LT

[t]

LT

SS


Variable demand

Variable replenishment cycle lead time

Stock level

22

LT

2

DD DLTLT


Customer service level

(Probability of meeting the expected demand in terms of quantity)

Fill rate for customer orders


SL2


0

0,005

0,01

0,015

0,02

0,025

0,03

0,035

0,04

0,045

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

DLT

How many units can be

missing? What is the

expected number of shorteges

nsh?

Stock level at the beginning of the replenishment cycle

Q

nQFR sh



50 100 150

f(T)f(D)

D LT

Normalndistribution

340 500 660 DLT

Expectedservicelevel

Real service level resulting from the assumtion that the

demand distribution is compatible with the normal

distribution.

f(LT)


Safety stock (SS)

Average demand DDemand variability D(forecast std. deviation)

Replenishment lead time TLead time variability LT

Service level:

probability of a no stock-out situation over a replenishment cycle (probability

measure),

demand (order) fulfilment (quantity measure).

Cost based optimisation:

safety stock carrying cost stock-out cost

Strategic (tactical) decisions Intuitive, Casual.



TC = Crf + Ccf + Crv + Cc(Sr)v + Cc(Ss)v + Cso

CsoCc(Ss)v

SsSL opt

Ss opt

CrvSrCc(Sr)v

Q Q opt

Sr opt

Cost relationships in optimisation of safety stock



0,0

200,0

400,0

600,0

800,0

1000,0

1200,0

1400,0

90 91 92 93 94 95 96 97 98 99

Stock-out cost

Stock carrying cost

A sum of stock carrying and stock-out costs

Optimal serice levelSL [%]

Cost


Opitmal safety stock






9. Safety stock in case of dispersed inventories (square-root law),


stock levels.



Course programme:


Cycle stock optimisation



SS

CS

SS

CS

Q

Q



TC = Crf + Ccf + Crv + Cc(Sr)v + Cc(Ss)v + Cso

CsoCc(Ss)v

SsSL opt

Ss opt

CrvSrCc(Sr)v

Q Q opt

Sr opt

Cost relationships in optimisation of cycle stock



A principle of calculating the Economic Order Quantity

Variable cost of replenishment and carrying the cycle stock:

Dp forecast (planned) demand over a period p (eg. a year annual demand,Q order quantitycr - replenishment cost related to a single order/delivery

pu unit price (or production cost per unit),ccp inventory cost carrying coefficient for a period p.

pcur

p

vv cpQ5,0cQ

DCcCr



Q

C

O

S

TCcv

Crv

EOQEconomic Order Quantity



Economic Order Quantity

pcu

rp

cp

cD2EOQ





8. Classical stock replenishment systems (Reorder Point and

Cycle Review) and their typical combinations.



stock levels.



Course programme:


Basic replenishment

systems



C

U

S

T

O

M

E

R

Demand fluctuations

Demand distribution

S

U

P

P

L

I

E

R

Orders

Lead time distribution

Stock

Decisions

Basic replenishment systems


There are two basic replenishment (ordering)

systems:

Replenishment system based on a reorder level (BQ) variable replenishment periods safety stock: when to order? fixed order quantity

Replenishment system based on a periodic review (ST) variable order quantity safety stock: how many (how much) to order? fixed replenishment periods



Replenishment system

based on a reorder level(when to order?)



Basic principles and rules:

fixed quantity of orders and deliveries (Q = const)

variable replenishment period (t)

current knowledge of the economic stock (Se)

calculated reorder level (order point B)

B = D LT + SS (SS = D(LT))

an order is placed whenever the economic stock falls below

the reorder level: SeB

Replenishment system based on a reorder level



Economic stock =

= Physical stock

+ quantity of that product ordered but

not yet received

quantity of that product already reserved




Safety stock:


LT:then0and0If.I DDLTD LT

D:then0and0If.II LTDDLT LT

22

LT

2

DD

LTD

DLT

:then0and0If.III

LT

LTDs)SL(S



LT

LT1

LT

[t]

S

T

O

C

K

LT

Variable demand

Variable replenishment

lead timeSs

B




Replenishment system

based on periodic review(how much to order?)



Basic principles and rules:

fixed review and replenishment period (To=const)

variable quantity of orders and deliveries (Q)

current knowledge of the economic stock (Se)

calculated maximum level S

S = D LT+To) + SS (SS = D(LT))

an order quantity is calculated as: Q= S-Se

Replenishment system based on a periodic review



Safety stock:

0DDLTD TLT:then0and0If.I LT

D:then0and0If.II LTDDLT LT

22

LT0

2

DD

LTD

D)TLT(

:then0and0If.III

LT

LTDs)SL(S




[t]

LT

T0

LT

T0

LT

T0

S

Ss

STOCK

Variable demand




Alternative (hybrid)

replenishment systems



Review

period

(Tr)

Order

period (T0)

Order

quantity

(Q)

Reorder

level

(B/s)

Maximum

level

(S)

(A) BQ fixed fixed

(B) ST fixed fixed fixed

(C) BS fixed fixed

(D) sQ fixed fixed fixed

(E) sS fixed fixed fixed



Reorder level based system (a lot of small orders)

LT LT LT

Q Q

B

Q

Basic replenishment systemsBQ


LT

T0 T0 T0 T0

LT LT LT LT

S

Periodic review

T0

Basic replenishment systemsST


LT

B

S

LT LT

Recommended in the case of relatively small number of big orders (MIN-MAX)

Basic replenishment systemsBS


LT

s

T0

LT

T0 T0

LT

QQ

Fixed cycle of possible orders of fixed quantity

T0 T0

Q

Basic replenishment systemssQ


LT

s

S

LT

T0

LT

T0 T0

Small number of big orders fixed review cycle

T0T0

Basic replenishment systemssS








stock levels.



Course programme:


Safety stock in case of dispersed

inventories (square-root law)



Dispersed inventories

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

Regional Warehouse 1 Regional Warehouse 2

Regional Warehouse 3 Regional Warehouse 4

units20;units100DDDD 1D1D1D1D4321

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40


0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40


Central warehouse


2

D

2

D

2

D

2

D

2

DNRW3RW2RW1RWMC

.....

N321 RWRWRWRWMC D.........DDDD

Dispersed inventories0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40


then:RWCW DND

2

D

2

D RWCWN

RWMC DDN

RWRWRWRWRW DD.........DDD N3212

D

2

D

2

D

2

D

2

D

2

D RWNRW3RW2RW1RWMC.....

If:Dispersed inventories


2

D

2

D

2

D

2

DD1RW1RW1RW1RWCW

....

2

S

2

S

2

S

2

SCWS RWN3RW2RW1RWS......SSSS

? LTS DDs LT








10. Information Decoupling Point concept and its role in reduction

of stock levels.


reduction/rationalisation .

Course programme:


Information Decoupling Point




Delivery

Inventory



D = 38,4; D = 5,84 D = 42,5; D = 15,0




Delivery

Inventory









stock levels.

11. Review of selected logistics concepts and solutions oriented on

stock reduction/rationalisation.

Solutions oriented on stock reduction


SS

SC

Q

Ssp

Cycle stock

Safety stock

Surplus stock

Stock structure



22

LT

2

DS DLTS

Centralised stock

Shorter replenishment

cycles

Fewer delays

Revision of service levels

ABC/XYZ/CAV analysis

Solutions oriented on stock reductionSafety stock

Forecats


ocu

roS

cp

cD2

2

1EOQ

2

1C

Forecats

Cycle stock


Reduction of replenishment costs. Improvements ofordering process.

Reduction of inventory carrying costs.


22

LT

2

DS DLTS

ocu

roS

cp

cD2

2

1

2

EOQC

SS

SC

EOQ



Just-in Time JiT

Quick Response QR

Efficient Consumer Response ECR

Vendor Managed Inventory VMI

Co-managed Inventory CMI

Collaborative Planning, Forecasting and Replenishment CPFR



22

LT

2

DS DLTS

ocu

roS

cp

cD2

2

1

2

EOQC

Just-in-Time



22

LT

2

DS DLTS

Qiuck Response


ocu

roS

cp

cD2

2

1

2

EOQC


22

LT

2

DS DLTS

Collaborative Planning, Forecasting and Replenishment


ocu

roS

cp

cD2

2

1

2

EOQC


22

LT

2

DS DLTS

Continous replenishemnt


ocu

roS

cp

cD2

2

1

2

EOQC


ocu

roS

cp

cD2

2

1

2

EOQC

22

LT

2

DS DLTS

Vendor Managed Inventory

Co-Managed Inventory



D

SSTO

S

DSCO


Stock turnover: Stock cover:

Performance measures stock controll


Last year This year

Sales (demand) - D 475 560

Average stock level - S 31 35

13,952

475D 39,3

13,9

31

D

SSCO 3,15

31

475

S

DSTO

25,377,10

35

D

SSCO 16

35

560

S

DSTO77,10

52

560D



Inventories Today

Inventories today: a curse, a blessing, a must..?

In a way INEVITIBILITY, but ..

. dont let them get out of control!

Thank you for your attention!

Crash Course on inventorises.


Summary of the questionnarie

1. Do you keep in your household a stock of:



1. In case of permanent stock is it high or low level stock?



2. Please indicate three most important reasons for keeping inventories in your company:



3. Which, in your opinion, would be the most effective ways to reduce stock levels in your company?



4. What are the most critical barriers for implementation of solutions leading to stock reduction in your company?


Contact:

[email protected]

[email protected]

Instytut Logistyki i Magazynowania(Institute of Logistics and Warehouisng)Pozna - POLAND

www.ilim.poznan.pl

Tel. +48-61-852-98-98

Documents

CC3-InventoryManagement