Appendix A Product Market Combinations 12 APPENDICES

(1)

PRODUCT MARKET COMBINATIONS

12 APPENDICES

Appendix A Product Market Combinations

Customer group _Item group _{KLP B}

(2)

PRODUCT FAMILIES PALEN 9

Appendix B Product families Palen 9

Family # Item G

roup

Item Demand Item Supp

ly Description 1 Description 2 KL P ® M ix ture

9-1 KLP ROND 230112 230112 KLP RONDE PAAL DIA 15 GEEL Geel

9-1 KLP RECHTHOEK 230114 230114 KLP RONDE PAAL DIA 15 GEEL Geel

9-1 KLP RECHTHOEK 231113 231113 KLP BALK 15 X 5 GEEL Geel

9-1 KLP RECHTHOEK 231870 231870 KLP PLANK 10 X 2,5 GEEL Geel

9-1 KLP RECHTHOEK 240080 240080 KLP PLANK 14 X 4 GEEL Geel

9-1 KLP RECHTHOEK 240103 240103 KLP PLANK 10 X 3 GEEL Geel

9-2 KLP ROND 230092 230092 KLP RONDE PAAL DIA 10 Zwart

9-2 KLP VIERKANT 230146 230146 KLP VIERKANTE PAAL 10 X 10 Zwart

9-2 KLP VIERKANT 231002 231002 KLP BALK 7 X 7 Zwart

9-2 KLP RECHTHOEK 231029 231029 KLP BALK 15 X 7 Zwart

9-2 KLP VIERKANT 231830 231830 KLP VIERKANTE PALEN 8 X 8 Zwart

9-2 KLP RECHTHOEK 231880 240714 KLP BALK 12 X 6,0 Zwart

9-2 KLP RECHTHOEK 231894 231894 KLP PLANK 10 X 3 Zwart

9-2 KLP STALLENBOUW 232148 232148 KLP V&G PLANK 14 X 3,2 Zwart

9-2 KLP VIERKANT 232390 232390 KLP BALK 10 X 10 Zwart

9-2 KLP WATERBOUW 233877 233877 KLP STEIGERPLANK 15 X 3 Zwart

9-2 KLP WATERBOUW 233886 233886 KLP STEIGERPLANK 18 X 3,9 Zwart

9-2 KLP WATERBOUW 233889 233889 KLP STEIGERPLANK 20 X 4,7 Zwart

9-2 KLP VIERKANT 240146 240146 KLP VIERKANTE PAAL DIA 15 Zwart

9-2 KLP ROND 240310 240310 KLP RONDE PAAL 10 X 10 BOER Zwart

9-2 KLP RECHTHOEK 240701 240713 KLP BANKPLANK 14 X 6 MET 2 GATEN Zwart

9-2 KLP RECHTHOEK 240702 240713 KLP BANKPLANK 14 X 6 Zwart

9-2 KLP RECHTHOEK 240715 240714 KLP BALK 12 X 6 MET 2 GATEN Zwart

9-2 KLP SPECIALITEITEN 240852 240850 KLP BORSTELBALK KLEIN 11.6 X 4 Zwart

9-2 KLP WATERBOUW 240888 240888 KLP STEIGERPLANK 20 X4.7 Zwart

9-3 KLP ROND 230111 230111 KLP RONDE PAAL DIA 15 Rond 15

9-3 KLP ROND 230113 230113 KLP RONDE PAAL DIA 15 Rond 15

9-3 KLP ROND 240493 240493 KLP RONDE PALEN BOER DIA 15 Rond 15

(3)

DEMAND PRODUCT FAMILIES

Appendix C Demand product families

Item Demand Item Demand Description 1 Description 2 2005 2006 2007 Average Demand

9-1 230112 KLP RONDE PAAL DIA 15 GEEL

9-1 230114 KLP RONDE PAAL DIA 15 GEEL

9-1 231113 KLP BALK 15 X 5 GEEL 9-1 231114 KLP BALK 15 X 5 GEEL 9-1 231870 KLP PLANK 10 X 2,5 GEEL 9-1 240080 KLP PLANK 14 X 4 GEEL 9-1 240103 KLP PLANK 10 X 3 GEEL 9-1 240120 KLP BALK 16 X 8 GEEL

9-2 230092 KLP RONDE PAAL DIA 10

9-2 230146 KLP VIERKANTE PAAL 10 X 10 9-2 230148 KLP VIERKANTE PAAL 10 X 10 9-2 231002 KLP BALK 7 X 7 9-2 231029 KLP BALK 15 X 7 9-2 231030 KLP BALK 16 X 8 9-2 231826 KLP VIERKANTE PAAL 8 X 8 9-2 231830 KLP VIERKANTE PALEN 8 X 8 9-2 231880 KLP BALK 12 X 6,0 9-2 231894 KLP PLANK 10 X 3 9-2 231897 KLP PLANK 10 X 3 9-2 231898 KLP PLANK 14 X 4 9-2 231899 KLP BALK 15 X 5 9-2 231913 KLP BALK 20 X 4 9-2 231940 KLP BALK 12 X 6 9-2 231990 KLP PLANK 15 X 3 9-2 232148 KLP V&G PLANK 14 X 3,2 9-2 232390 KLP BALK 10 X 10 9-2 232398 KLP BALK 15 X 5 9-2 232421 KLP BALK 15 X 5 9-2 232626 KLP BALK 15 X 7 9-2 232680 KLP BALK 7 X 4 9-2 233877 KLP STEIGERPLANK 15 X 3 9-2 233886 KLP STEIGERPLANK 18 X 3,9 9-2 233889 KLP STEIGERPLANK 20 X 4,7

9-2 240146 KLP VIERKANTE PAAL DIA 15

9-2 240310 KLP RONDE PAAL 10 X 10 BOER

9-2 240701 KLP BANKPLANK 14 X 6 MET 2 GATEN

9-2 240702 KLP BANKPLANK 14 X 6

9-2 240715 KLP BALK 12 X 6 MET 2 GATEN

9-2 240852 KLP BORSTELBALK KLEIN 11.6 X 4

9-2 240888 KLP STEIGERPLANK 20 X4.7

9-3 240493 KLP RONDE PALEN BOER DIA 15 9-3 240494 KLP RONDE PALEN BOER DIA 15

(4)

DEMAND CHARACTERISTICS

Appendix D Demand characteristics

Data

# Orders Total demand Average order size Standard deviation

Month (units) (units) (units)

(5)

INTERNAL BENCHMARKING

Appendix E Internal benchmarking

The estimates of capacity in the process boxes in the current state map, which give the throughput TH

p

process cycle time CT

p1

, and WIP are required to conduct a performance evaluation. The process

parameters are averages, which account for different types of products (e.g. poles, planks, beams).

They also account for detractors. The throughput and process cycle time help to determine the key

parameters for describing Palen 9; the bottleneck rate (r

b

), raw process time (T

0

), and the critical WIP

(W

0

). These are shown at the bottom of Appendix Table E-1.

Appendix Table E-1: Performance cases (Hopp & Spearman, 2000)

Case Throughput performance law Cycle time performance law

Best-Case 0

T

w

if w ≤ W0

T

₀ if w ≤ W0 b

r

otherwise b

r

w

otherwise Worst-Case 0

1 T

wT

0 Practical Worst-Case

r

_b

w

W

w

1

0

+

−

r

b

w

T

₀

+

−

1

T0 = 6.5 sec; rb = 16.5 parts/hr; W0 = 108 parts

Throughput. The best possible rate for a given WIP level w is determined by the critical WIP W

0

of

the line. W

0

of Palen 9 is 108. If w is smaller or equal to this value, maximum throughput TH

max

is

defined by the ratio of w and the T

0

. When w is larger than 108, TH

max

is equal to the bottleneck rate r

b

,

16.5. The lowest possible rate TH

worst

for a given w is given by the inverse of T

0

, 1/16.5 = 0.15 parts

per hour. There two ways to compute the rate of practical worst-case. One way is to compute the TH

that would be achieved by a PWC line with the same r

b

, T

0

, and WIP level as Palen 9 and to compare

it to actual throughput. Using the practical worst-case law in Appendix Table E-1:

( )

16 .

5

14 .

5

1

780

108

780

1

0

=

−

+

=

−

+

=

_b pwc

_W

_w

r

w

TH

Actual throughput of 14.3 per hour is just a bit lower, but still indicating a performance that lies in the

‘bad’ region between the rate of the worst- and practical worst case. Alternatively, the WIP level

required in a PWC line can be computed with the same r

b

and T

0

as the Palen 9 line, to achieve the

observed level of throughput. That is,

b b

r

w

W

w

TH

⋅

=

⋅

−

+

=

14 .

3

0 .

87

1

0

which yields,

(6)

INTERNAL BENCHMARKING

87 .

0

1

0

=

−

+ w

W

w

or

(

108

1 )

716

13 .

0

87 .

0 ₋

₌

=

w

Actual WIP is 780, 64 parts more than two times this level, indicating that Palen 9 is less efficient than

the PWC line.

Cycle time. The best possible cycle time CT

max

for a given w is determined by the critical WIP level

W

0

of the line, 108. If w is smaller or equal to W

0

, CT

max

is equal to the raw process time T

0

. When w is

larger than 108, CT

max

is defined by the ratio of w with the bottleneck r

b

, 16.5. The largest possible

cycle time of the line is given by the product of w and T

0

, 6.5 hour. The CT

pwc

is defined by the time

the parts spend waiting for other parts to complete processing plus the time for the part to be

processed. The practical worst-case cycle time is given by the CT that would be achieved by a PWC

line with the same r

b

, T

0

, and WIP level as Palen 9 and to compare it to actual CT. Using the practical

worst-case law in Appendix Table E-1:

7 .

53

5 .

16

1

780

5 .

6

1

0

=

−

+

=

−

+

=

b pwc

r

w

T

CT

(7)

ATKINS & IYOGUN’S (1988) PROCEDURE

Appendix F Atkins & Iyogun’s (1988) procedure

The Atkins and Iyogun’s procedure consists of the following steps (Strijbosch et al., 2002):

1. Calculate the EOQ and the time supply for each item without taking into account the major setup

cost. The EOQ is given by the formula of Camp [1]:

j j j

rv

aD

Q

=

2 [1]

where,

j

D

= expected yearly demand for item j

a

= minor setup cost to produce an item

A

= major setup cost to produce a family

r

= inventory charge

j

v

= unit cost price of item j

The time supply in years is [2]:

j j j

D

Q

T

=

[2]

2. The result is a set of time supplies for each item in the family. Sort the time supplies from small to

large. Denote the item with the smallest time supply as item 1, the next smallest as item 2, etc.

Initialize

m

=

0 and

α

_j

=

0 for all j

3. Increase m by 1. Recalculate

α

_j

for j = 1, …, m such that the time supply of end item j increases

to T

m+1

, the time supply of end item m+1. Allocate a proportion α

j

A of the major setup cost to item

m. To determine to what level the α

j

(j = 1, …, m) have to be increased to reach time supply T

m+1

,

it is useful to write α

j

as a function of T

j

. In total α

j

A+a

j

is allocated to item j, so adapted EOQ of j

follows from [3]:

j j j j

rv

D

a

A

EOQ

=

2 (

α

+

)

[3]

Dividing left and right side by D

j

, and using

T

j

=

(

EOQ

/

D

j

)

, it follows [4]:

A

a

A

D

rv

T

D

rv

a

A

T

j j j j j j j

⇒

=

−

+

=

2 )

(

2

α

[4]

To reach a time supply quantity of T

m+1

α

j

has to be increased to [5]:

.

,...,

1 ,

2

m

j

A

a

A

D

rv

T

_j _j j

=

−

=

α

[5]

4. Check if

1 .

1

<

∑

= m j j

α

If this is true, go back to 3. If not, the base cycle in T

*

_{in years is can be}

(8)

ATKINS & IYOGUN’S (1988) PROCEDURE

∑

= =

⎟

⎠

⎞

⎜

⎝

⎛

+

=

m j j j m j

D

rv

a

A

T

1 1 *

₂

_/

₍

₎

_[6]

5. Recalculate the α

j

(j = 1, …, m) for time supply T

*

[7]:

A

a

A

D

rv

T

_j _j j

=

−

2 )

(

* 2

α

[7]

6. The end items that after sorting got the numbering 1 up till m, have time supply T

*

_{. The rest of the}

end items keep their original time supply. Note that the major setup cost is allocated completely to

the end items 1 up till m.

7. Rounding the base cycle T

*

_{to an integer number of weeks (or another time unit) might in practice}

be useful. Use powers-of-two of the base cycle, so that each end item is either the base cycle

period or 2, 2

2

_{, 2}

3

_{, and so on, times the base cycle.}

8. Repeat the process to establish a common base length across families, so that each family is a

powers-of-two-multiple of the common period. Compute and compare to find a length that

minimizes overall costs (e.g. setup and holding costs).

Appendix Table F-1 gives an overview of the relevant data per item for Palen 9. The item’s family and

article number are in columns A and B. Columns C, D, and E list the required data to compute the

EOQ of an item (not considering major setups). For simplicity, it is assumed that the minor setup time

(m) is similar for all products (0.5 hour). The major setup time (M) depends on the production

sequence of the families. Even though the sequence has yet to be determined, the major setup time is

set at 16 hours. It is recorded in the parameters at the bottom of the table. Recall that we assumed a

setup cost of €40 per hour. Using this setup cost and only minor setup times for each part, the EOQ is

computed (column F) with the required carrying charge (column E) and unit cost price (column C),

and translated into a time supply (in weeks) in column G. The Atkins & Iyogun’s (1988) procedure is

used to find values for the target time supply T (column H), and calculated alpha α (column I). A new*

EOQ

j

(including major setups) is then computed for each item in column J, and again translated into a

time supply T

j

(column K). To lend order to the schedule, the time supplies are rounded to

powers-of-two multiples of the minimum time supply, in column L. Column L is what we call the item cycle time

(9)

ATKINS & IYOGUN’S (1988) PROCEDURE

Appendix Table F-1: Family base cycles Palen 9

A B C C D E F G H I J K L Family N r Item Nr M anuf actur ing str ategy vj _Dj rj _EO Qj (only mino r setup costs) T (j w eeks) T* (weeks) αj _EO Qj ( m in or + ma jo r setup costs ) Tj (weeks) Tj rounded ( w eek s) 9-1 230112 MTS 20 7,75 30,48 0,4519 79 30,48 32,00 9-1 230114 MTS 17 11,73 30,48 0,1798 43 30,48 32,00 9-1 231113 MTO 9-1 231114 MTS 41 9,39 30,48 0,2979 133 30,48 32,00 9-1 231870 MTO 9-1 240080 MTS 33 16,90 30,48 0,0704 60 30,48 32,00 9-1 240103 MTS 34 31,05 0,00 34 31,05 32,00 9-1 240120 MTO 9-2 230092 MTS 76 6,29 0,00 76 6,29 8,00 9-2 230146 MTS 106 3,10 4,05 0,0221 138 4,05 4,00 9-2 230148 MTS 68 6,39 0,00 68 6,39 8,00 9-2 231002 MTS 208 3,88 4,05 0,0029 217 4,05 4,00 9-2 231029 MTS 135 2,92 4,05 0,0288 187 4,05 4,00 9-2 231030 MTS 60 3,60 4,05 0,0083 67 4,05 4,00 9-2 231826 MTS 97 5,75 0,00 97 5,75 4,00 9-2 231880 MTS 132 4,20 0,00 132 4,20 4,00 9-2 231894 MTS 430 3,06 4,05 0,0234 568 4,05 4,00 9-2 231897 MTS 379 2,96 4,05 0,0275 519 4,05 4,00 9-2 231898 MTS 191 3,21 4,05 0,0185 241 4,05 4,00 9-2 231899 MTS 128 3,28 4,05 0,0163 158 4,05 4,00 9-2 231913 MTS 196 2,01 4,05 0,0954 394 4,05 4,00 9-2 231940 MTS 65 6,70 0,00 65 6,70 8,00 9-2 231990 MTS 266 2,85 4,05 0,0321 379 4,05 4,00 9-2 232148 MTS 318 2,72 4,05 0,0381 473 4,05 4,00 9-2 232390 MTS 110 3,19 4,05 0,0192 139 4,05 4,00 9-2 232398 MTS 147 3,58 4,05 0,0088 167 4,05 4,00 9-2 232421 MTS 135 4,75 0,00 135 4,75 4,00 9-2 232626 MTS 93 3,85 4,05 0,0034 98 4,05 4,00 9-2 232680 MTS 209 6,79 0,00 209 6,79 8,00 9-2 233877 MTS 368 1,98 4,05 0,1002 755 4,05 4,00 9-2 233886 MTS 229 1,92 4,05 0,1082 484 4,05 4,00 9-2 233889 MTS 220 1,39 4,05 0,2348 642 4,05 4,00 9-2 240146 MTS 172 2,03 4,05 0,0937 343 4,05 4,00 9-2 240701 MTS 138 4,01 4,05 0,0007 139 4,05 4,00 9-2 240702 MTS 19 29,40 0,00 19 29,40 32,00 9-2 240715 MTS 124 4,45 0,00 124 4,45 4,00 9-2 240852 MTS 338 3,16 4,05 0,0200 433 4,05 4,00 9-2 240888 MTS 165 2,00 4,05 0,0973 334 4,05 4,00 9-3 230111 MTS 58 2,36 9,80 0,5067 240 9,80 8,00 9-3 230113 MTS 51 3,21 9,80 0,2593 154 9,80 8,00 9-3 240493 MTS 67 3,36 9,80 0,2341 196 9,80 8,00 9-3 240494 MTS 28 9,98 0,00 28 9,98 8,00

(10)

ORDER-UP-TO LEVEL PROCEDURE

Appendix G Order-up-to level procedure

The order-up-to level is equal to the demand until the review moment plus lead time (R+L), where

lead time is defined as the average time from the production start of an item at the beginning of the

routing until it is available in FGI. Safety stock is required to protect against demand uncertainty. The

safety stock level depends on the delivery performance. The delivery performance is defined by the

desired probability of not running out of stock during the review plus lead time. This desired

probability can be expressed by a performance measure such as the fill rate or service level. The fill

rate is a reasonable measure for LRP. The safety stock level depends on the forecast error over the

review plus lead time (R+L). LRP does not collect demand information for a time interval that is

exactly the same as R+L. The error in the forecast σ

t

of demand during review plus lead time is than

expressed by [8]:

L R+

σ

=

σ

_t

(

R

+

L

)

[8]

When demand is assumed to be normally distributed, the safety stock level can be found by

multiplying the number of standard deviations from the mean (z) needed to implement the fill rate.

The value of z can be looked up in a standard normal table. For example, the closest number in the

table to a fill rate of 0.9 is 0.8997, which correspond with a value of 1.2 in the row heading and 0.08 in

the column heading. Adding these values gives a z of 1.28. The safety stock [9] and the order-up-to

level [10] of an item are than computed by:

SS

=

z

σ

_R₊_L

[9]

S

=

μ

R+L

+

z

σ

R+L

[10]

The mean physical stock is calculated by simple approximation. The approximation of Silver and

Peterson (1985) is accurate for high fill rates (Van der Heijden & De Kok, 1998) Therefore, the mean

on-hand inventory level with their approximation [11]:

OH =

S

−

(

μ

_L

+

1₂

R

)

μ

_t

_[11]

where,

t

μ

= mean expected demand during a time interval with length t

L

μ

= mean expected demand during a time interval with length L

(11)

ORDER-UP-TO LEVEL PROCEDURE

Appendix Table G-1: Order-up-to levels Palen 9

(12)

SETUPS AND INVENTORY

Appendix H Setups and inventory

A B C D E F G H I J K L

Family N

r

Article N

r

rj _Expected # Setups _{Average # Setups} _Δ Se

tups Time in setups Pr ocessing hr s

Capacity used up Exptected OH Average OH Δ OH