Operationeel Onderzoek Assignment on Aggregate Production Planning

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Operationeel Onderzoek

Assignment on Aggregate Production Planning

Ben Matth´ e Pieter Wuille April 15, 2007

1 Determine a plan that minimizes all costs.

1.1 Assumptions

• The assignment states that there is a variable inventory cost at the warehouse.

Yet it is not specified at which point during the quarter the demanded forecast will be withdrawn. Therefore we assume the forecast is withdrawn continuously (uniformly) during the quarter, as is the production. Hence the amount of paint in stock changes linearly during a quarter. Our assumption is thus that we can use the average amount in stock during a quarter as variable inventory cost.

• We assume the variable inventory cost is required for both the normal warehouse and the additional warehouse.

• The workers that receive a training have to be paid as well (apart from the EUR 1200 hiring cost); they are included in the total amount of workers, but do not produce anything.

1.2 Variables

c

tot

total cost

c

_i

cost during quarter i

¹

ww

_i

fully employed workers during quarter i wo

i

workers being trained during quarter i ow

_i

workers being fired at the end of quarter i

w

_max

maximum amount of workers of any kind (fixed 380) df

i

demand forecast during quarter i

hu

_i

determines wheather extra warehousespace is rented during quarter i and i + 1 aw

_i

amount of liters stored in additional warehouse at the end of quarter i

vis

i

amount of liters stored in own warehouse at the end of quarter i

sc

_i

amount of liters produced through subcontracting during quarter i

ou

_i

amount of hours overtime during quarter i

(2)

1.3 Solution

To solve this problem in Lindo, we declared the amount of workers to be integers (using GIN), and hu

i

as either zero or one (using INTEGER). The solution requires the steps to be taken in the following table. Hire means: hiring that amount of employees at the beginning of that quarter, so they will be trained during that quarter. Fire means: firing that amount of employees at the beginning of that quarter. Overtime is in total amount of hours; subcontracting is in liters.

Quarter Hire Fire Working Training Overtime Subcontracting

1 0 8 272 0 0 0

2 0 0 272 0 187 0

3 0 78 194 0 0 0

4 14 0 194 14 0 0

5 1 0 208 1 0 0

6 0 0 209 0 233 0

7 0 0 209 0 0 0

8 0 0 209 0 6440 0

At the end of each quarter, we have enough paint in stock. The fires and hires are necessary to get the cost minimal, since in the beforementioned quarters it may be cheaper to fire (and afterwards rehire) them and not having to pay salaries rather than keeping them in service all the time. More working employees would also result in more production, when sometimes new (and expensive!) capacity is needed to store this.

The total cost would be EUR 11 221 900.

2 Determine an optimal production plan to meet ex- actly, at the end of each quarter, the inventory and demand requirements. What is the cost of that plan?

The only changes made here, are stating that the inventory requirements should be met EXACTLY, rather than having at least 50000 liters in stock.

2.1 Solution

These very drastic (and ridiculous) measures have to be taken if we want to get EXACTLY what was demanded, even firing and rehiring employees immediately, so they would not produce during that quarter.

The total cost would be EUR 13 707 533.

1

this includes the cost of firing employees at the end of quarter i

(3)

Quarter Hire Fire Working Training Overtime Subcontracting

1 20 86 194 20 187 0

2 0 0 214 0 38520 80000

3 0 70 144 0 187 0

4 144 72 72 144 93 0

5 14 0 216 14 280 0

6 0 0 230 0 41400 80000

7 0 42 188 0 373 0

8 0 0 188 0 23700 0

3 Determine a compromise plan that minimizes cost with given priorities

3.1 Strategy

For priority 1, we decided to put a limit of 20000 euro per quarter on the expenses in overtime and subcontracting together (since subcontracting is already 1.5 times as expen- sive as overtime per liter, no extra modifier for subcontracting is necessary). Doing this decreased the amount of hours overtime and subcontracting in total significantly (instead of just being spread over more quarters), without influencing the total cost too much.

For priority 2, we stated that no more than 20 employees should be fired at the same time. (Note: by implementing this rule, no significant changes were introduced in the overtime and subcontracting expenses.) This resulted in 20 employees being fired in each of 4 consecutive quarters, with a total of 87 dismissals.

For priority 3, we set the maximum amount of quarters that were allowed to go over EUR 500 000 to two. After enforcing the two first priorities, only two quarters (quarter 4 and 5; because of extra storage) happened to have a quarterly inventory cost of slightly over EUR 600 000.

By these changes, the total cost rose to EUR 11 981 098.

3.2 Solution

Quarter Hire Fire Working Training Overtime Subcontracting

1 0 0 280 0 867 0

2 0 20 260 0 1000 0

3 0 20 240 0 0 0

4 0 20 220 0 0 0

5 0 20 200 0 0 0

6 0 7 193 0 0 0

7 0 0 193 0 0 0

8 0 0 193 0 0 0

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In quarter 4, we rent the extra storage warehouse (which will be used in quarters 4 and 5).

4 Production plan with uncertain demands

First we calculated the average of the demand forecasts and the variance, and decided to find a solution which was best for three combinations of demand forecasts:

1. df

₅

= 405000, df

₆

= 405000; weight: 0.5 2. df

₅

= 125000, df

₆

= 160000; weight: 0.15 3. df

₅

= 675000, df

₆

= 750000; weight: 0.15 4. df

5

= 125000, df

6

= 750000; weight: 0.1 5. df

₅

= 675000, df

₆

= 160000; weight: 0.1

The average of the given demand forecasts is 405000, so this has been chosen as start value. Afterwards, we chose some combinations of extreme values to see how well the chosen parameters of our model could be used in these cases. Because the average is more likely to occur, we gave this the heighest weighting factor. In real life, these weights could be more carefully chosen using statistical methods.

The value of df

₆

is slightly higher, because in the given demand forecast this was already significantly so. After this, we started a selection procedure where we tried some sequences of fires and hires (reasonable start values for this obtained trough solving the original problem in Lindo). These values did not result in impossibilities in any of the five beforementioned cases. Among these we selected the one that resulted in the best (i.e. lowest) weighted average cost. This results in the following table:

Quarter Hire Fire Working Training

1 0 8 272 0

2 0 0 272 0

3 0 109 163 0

4 0 0 163 0

5 0 0 163 0

6 1 0 163 1

7 0 0 164 0

8 0 0 164 0

Subcontracting, overtime and the rent of additional warehouse space may vary de-

pending on the actual demands, but can easily be adjusted on the spot (whereas employees

must be trained in advance, so it is imperative to know this up front).

(5)

A Lindo question 1

A.1 Input

min ctot st

c0 + c1 + c2 + c3 + c4 + c5 + c6 + c7 + c8 - ctot = 0 ww0 = 280

wo0 = 0 wmax = 380

df1 = 380000 df2 = 630000 df3 = 260000 df4 = 130000 df5 = 390000 df6 = 670000 df7 = 340000 df8 = 440000

ww0 > 0 ww1 > 0 ww2 > 0 ww3 > 0 ww4 > 0 ww5 > 0 ww6 > 0 ww7 > 0 ww8 > 0

ww0 + wo0 - wmax < 0 ww1 + wo1 - wmax < 0 ww2 + wo2 - wmax < 0 ww3 + wo3 - wmax < 0 ww4 + wo4 - wmax < 0 ww5 + wo5 - wmax < 0 ww6 + wo6 - wmax < 0 ww7 + wo7 - wmax < 0 ww8 + wo8 - wmax < 0

ww1 - ww0 - wo0 + ow0 = 0 ww2 - ww1 - wo1 + ow1 = 0 ww3 - ww2 - wo2 + ow2 = 0 ww4 - ww3 - wo3 + ow3 = 0 ww5 - ww4 - wo4 + ow4 = 0 ww6 - ww5 - wo5 + ow5 = 0 ww7 - ww6 - wo6 + ow6 = 0 ww8 - ww7 - wo7 + ow7 = 0

hu2 + hu1 < 1 hu3 + hu2 < 1 hu4 + hu3 < 1 hu5 + hu4 < 1 hu6 + hu5 < 1 hu7 + hu6 < 1 hu8 + hu7 < 1

sc1 > 0 sc2 > 0 sc3 > 0 sc4 > 0 sc5 > 0 sc6 > 0 sc7 > 0 sc8 > 0 sc1 < 80000 sc2 < 80000

(6)

sc3 < 80000 sc4 < 80000 sc5 < 80000 sc6 < 80000 sc7 < 80000 sc8 < 80000

ou1 > 0 ou2 > 0 ou3 > 0 ou4 > 0 ou5 > 0 ou6 > 0 ou7 > 0 ou8 > 0

ou1 - 180ww1 < 0 ou2 - 180ww2 < 0 ou3 - 180ww3 < 0 ou4 - 180ww4 < 0 ou5 - 180ww5 < 0 ou6 - 180ww6 < 0 ou7 - 180ww7 < 0 ou8 - 180ww8 < 0

aw0 = 0 aw1 > 0 aw2 > 0 aw3 > 0 aw4 > 0 aw5 > 0 aw6 > 0 aw7 > 0 aw8 > 0

aw1 - 400000hu1 < 0

aw2 - 400000hu2 - 400000hu1< 0 aw3 - 400000hu3 - 400000hu2< 0 aw4 - 400000hu4 - 400000hu3< 0 aw5 - 400000hu5 - 400000hu4< 0 aw6 - 400000hu6 - 400000hu5< 0 aw7 - 400000hu7 - 400000hu6< 0 aw8 - 400000hu8 - 400000hu7< 0

vis0 = 80000 vis1 + aw1 > 50000 vis2 + aw2 > 50000 vis3 + aw3 > 50000 vis4 + aw4 > 50000 vis5 + aw5 > 50000 vis6 + aw6 > 50000 vis7 + aw7 > 50000 vis8 + aw8 > 50000

vis1 < 360000 vis2 < 360000 vis3 < 360000 vis4 < 360000 vis5 < 360000 vis6 < 360000 vis7 < 360000 vis8 < 360000

c0 - 5000ow0 = 0

c1 - 5250ww1 - 5250wo1 - 1200wo1 - 5000ow1 - 20ou1 - 7sc1 - 0.5vis0 - 0.5vis1 - 0.375aw0 - 0.375aw1 - 600000hu1 = 0 c2 - 5250ww2 - 5250wo2 - 1200wo2 - 5000ow2 - 20ou2 - 7sc2 - 0.5vis1 - 0.5vis2 - 0.375aw1 - 0.375aw2 - 600000hu2 = 0 c3 - 5250ww3 - 5250wo3 - 1200wo3 - 5000ow3 - 20ou3 - 7sc3 - 0.5vis2 - 0.5vis3 - 0.375aw2 - 0.375aw3 - 600000hu3 = 0 c4 - 5250ww4 - 5250wo4 - 1200wo4 - 5000ow4 - 20ou4 - 7sc4 - 0.5vis3 - 0.5vis4 - 0.375aw3 - 0.375aw4 - 600000hu4 = 0 c5 - 5250ww5 - 5250wo5 - 1200wo5 - 5000ow5 - 20ou5 - 7sc5 - 0.5vis4 - 0.5vis5 - 0.375aw4 - 0.375aw5 - 600000hu5 = 0 c6 - 5250ww6 - 5250wo6 - 1200wo6 - 5000ow6 - 20ou6 - 7sc6 - 0.5vis5 - 0.5vis6 - 0.375aw5 - 0.375aw6 - 600000hu6 = 0

(7)

c7 - 5250ww7 - 5250wo7 - 1200wo7 - 5000ow7 - 20ou7 - 7sc7 - 0.5vis6 - 0.5vis7 - 0.375aw6 - 0.375aw7 - 600000hu7 = 0 c8 - 5250ww8 - 5250wo8 - 1200wo8 - 20ou8 - 7sc8 - 0.5vis7 - 0.5vis8 - 0.375aw7 - 0.375aw8 - 600000hu8 = 0

vis1 + aw1 - vis0 - aw0 - sc1 - 1800ww1 - 4.2857143ou1 + df1 = 0 vis2 + aw2 - vis1 - aw1 - sc2 - 1800ww2 - 4.2857143ou2 + df2 = 0 vis3 + aw3 - vis2 - aw2 - sc3 - 1800ww3 - 4.2857143ou3 + df3 = 0 vis4 + aw4 - vis3 - aw3 - sc4 - 1800ww4 - 4.2857143ou4 + df4 = 0 vis5 + aw5 - vis4 - aw4 - sc5 - 1800ww5 - 4.2857143ou5 + df5 = 0 vis6 + aw6 - vis5 - aw5 - sc6 - 1800ww6 - 4.2857143ou6 + df6 = 0 vis7 + aw7 - vis6 - aw6 - sc7 - 1800ww7 - 4.2857143ou7 + df7 = 0 vis8 + aw8 - vis7 - aw7 - sc8 - 1800ww8 - 4.2857143ou8 + df8 = 0 end

gin ww0 gin ww1 gin ww2 gin ww3 gin ww4 gin ww5 gin ww6 gin ww7 gin ww8

gin ow0 gin ow1 gin ow2 gin ow3 gin ow4 gin ow5 gin ow6 gin ow7

gin wo0 gin wo1 gin wo2 gin wo3 gin wo4 gin wo5 gin wo6 gin wo7 gin wo8

integer hu1 integer hu2 integer hu3 integer hu4 integer hu5 integer hu6 integer hu7 integer hu8

A.2 Output

OBJECTIVE FUNCTION VALUE 1) 0.1122190E+08

VARIABLE VALUE REDUCED COST

WW0 280.000000 -1.000000

WW1 272.000000 -1350.000244 WW2 272.000000 -3150.000244 WW3 194.000000 2250.999756

WW4 194.000000 449.999725

WW5 208.000000 -1350.000244 WW6 209.000000 -3150.000244 WW7 209.000000 -1351.000244 WW8 209.000000 -3149.000244

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OW0 8.000000 5001.000000

OW1 0.000000 5001.000000

OW2 78.000000 5001.000000

OW3 0.000000 5000.000000

OW4 0.000000 5000.000000

OW5 0.000000 5000.000000

OW6 0.000000 5000.000000

OW7 0.000000 5001.000000

WO0 0.000000 -1.000000

WO1 0.000000 6449.000000

WO2 0.000000 6449.000000

WO3 0.000000 6450.000000

WO4 14.000000 6450.000000

WO5 1.000000 6450.000000

WO6 0.000000 6450.000000

WO7 0.000000 6449.000000

WO8 0.000000 6450.000000

HU1 0.000000 400000.000000 HU2 0.000000 400000.000000 HU3 0.000000 400000.000000 HU4 0.000000 400000.000000 HU5 0.000000 400000.000000 HU6 0.000000 400000.000000 HU7 0.000000 450000.000000 HU8 0.000000 550000.000000 CTOT 11221900.000000 0.000000

C0 40000.000000 0.000000

C1 1562800.000000 0.000000 C2 1941533.375000 0.000000 C3 1113100.000000 0.000000 C4 1357600.000000 0.000000 C5 1449050.000000 0.000000 C6 1298316.625000 0.000000 C7 1165350.000000 0.000000 C8 1294150.000000 0.000000

WMAX 380.000000 0.000000

DF1 380000.000000 0.000000 DF2 630000.000000 0.000000 DF3 260000.000000 0.000000 DF4 130000.000000 0.000000 DF5 390000.000000 0.000000 DF6 670000.000000 0.000000 DF7 340000.000000 0.000000 DF8 440000.000000 0.000000

SC1 0.000000 3.333333

SC2 0.000000 2.333333

SC3 0.000000 5.333333

SC4 0.000000 4.333333

SC5 0.000000 3.333333

SC6 0.000000 2.333333

SC7 0.000000 3.333333

SC8 0.000000 2.333333

OU1 0.000000 4.285714

OU2 186.666672 0.000000

OU3 0.000000 12.857142

OU4 0.000000 8.571428

OU5 0.000000 4.285714

OU6 233.333344 0.000000

OU7 0.000000 4.285714

OU8 6440.000000 0.000000

AW0 0.000000 0.000000

AW1 0.000000 0.000000

AW2 0.000000 0.000000

AW3 0.000000 0.000000

AW4 0.000000 0.000000

AW5 0.000000 0.000000

AW6 0.000000 0.000000

AW7 0.000000 0.000000

AW8 0.000000 0.000000

VIS0 80000.000000 0.000000

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VIS1 189600.000000 0.000000 VIS2 50000.000000 0.000000 VIS3 139200.000000 0.000000 VIS4 358400.000000 0.000000 VIS5 342800.000000 0.000000 VIS6 50000.000000 0.000000 VIS7 86200.000000 0.000000 VIS8 50000.000000 0.000000

B Lindo question 2

B.1 Input

min ctot st

c0 + c1 + c2 + c3 + c4 + c5 + c6 + c7 + c8 - ctot = 0 ww0 = 280

wo0 = 0 wmax = 380

df1 = 380000 df2 = 630000 df3 = 260000 df4 = 130000 df5 = 390000 df6 = 670000 df7 = 340000 df8 = 440000

ww0 > 0 ww1 > 0 ww2 > 0 ww3 > 0 ww4 > 0 ww5 > 0 ww6 > 0 ww7 > 0 ww8 > 0

ww0 + wo0 - wmax < 0 ww1 + wo1 - wmax < 0 ww2 + wo2 - wmax < 0 ww3 + wo3 - wmax < 0 ww4 + wo4 - wmax < 0 ww5 + wo5 - wmax < 0 ww6 + wo6 - wmax < 0 ww7 + wo7 - wmax < 0 ww8 + wo8 - wmax < 0

ww1 - ww0 - wo0 + ow0 = 0 ww2 - ww1 - wo1 + ow1 = 0 ww3 - ww2 - wo2 + ow2 = 0 ww4 - ww3 - wo3 + ow3 = 0 ww5 - ww4 - wo4 + ow4 = 0 ww6 - ww5 - wo5 + ow5 = 0 ww7 - ww6 - wo6 + ow6 = 0 ww8 - ww7 - wo7 + ow7 = 0

hu2 + hu1 < 1 hu3 + hu2 < 1 hu4 + hu3 < 1 hu5 + hu4 < 1 hu6 + hu5 < 1 hu7 + hu6 < 1

(10)

hu8 + hu7 < 1

sc1 > 0 sc2 > 0 sc3 > 0 sc4 > 0 sc5 > 0 sc6 > 0 sc7 > 0 sc8 > 0

sc1 < 80000 sc2 < 80000 sc3 < 80000 sc4 < 80000 sc5 < 80000 sc6 < 80000 sc7 < 80000 sc8 < 80000

ou1 > 0 ou2 > 0 ou3 > 0 ou4 > 0 ou5 > 0 ou6 > 0 ou7 > 0 ou8 > 0

ou1 - 180ww1 < 0 ou2 - 180ww2 < 0 ou3 - 180ww3 < 0 ou4 - 180ww4 < 0 ou5 - 180ww5 < 0 ou6 - 180ww6 < 0 ou7 - 180ww7 < 0 ou8 - 180ww8 < 0

aw0 = 0 aw1 > 0 aw2 > 0 aw3 > 0 aw4 > 0 aw5 > 0 aw6 > 0 aw7 > 0 aw8 > 0

aw1 - 400000hu1 < 0

aw2 - 400000hu2 - 400000hu1< 0 aw3 - 400000hu3 - 400000hu2< 0 aw4 - 400000hu4 - 400000hu3< 0 aw5 - 400000hu5 - 400000hu4< 0 aw6 - 400000hu6 - 400000hu5< 0 aw7 - 400000hu7 - 400000hu6< 0 aw8 - 400000hu8 - 400000hu7< 0

vis0 = 80000 vis1 + aw1 = 50000 vis2 + aw2 = 50000 vis3 + aw3 = 50000 vis4 + aw4 = 50000 vis5 + aw5 = 50000 vis6 + aw6 = 50000 vis7 + aw7 = 50000 vis8 + aw8 = 50000

vis1 < 360000 vis2 < 360000 vis3 < 360000

(11)

vis4 < 360000 vis5 < 360000 vis6 < 360000 vis7 < 360000 vis8 < 360000

c0 - 5000ow0 = 0

c1 - 5250ww1 - 5250wo1 - 1200wo1 - 5000ow1 - 20ou1 - 7sc1 - 0.5vis0 - 0.5vis1 - 0.375aw0 - 0.375aw1 - 600000hu1 = 0 c2 - 5250ww2 - 5250wo2 - 1200wo2 - 5000ow2 - 20ou2 - 7sc2 - 0.5vis1 - 0.5vis2 - 0.375aw1 - 0.375aw2 - 600000hu2 = 0 c3 - 5250ww3 - 5250wo3 - 1200wo3 - 5000ow3 - 20ou3 - 7sc3 - 0.5vis2 - 0.5vis3 - 0.375aw2 - 0.375aw3 - 600000hu3 = 0 c4 - 5250ww4 - 5250wo4 - 1200wo4 - 5000ow4 - 20ou4 - 7sc4 - 0.5vis3 - 0.5vis4 - 0.375aw3 - 0.375aw4 - 600000hu4 = 0 c5 - 5250ww5 - 5250wo5 - 1200wo5 - 5000ow5 - 20ou5 - 7sc5 - 0.5vis4 - 0.5vis5 - 0.375aw4 - 0.375aw5 - 600000hu5 = 0 c6 - 5250ww6 - 5250wo6 - 1200wo6 - 5000ow6 - 20ou6 - 7sc6 - 0.5vis5 - 0.5vis6 - 0.375aw5 - 0.375aw6 - 600000hu6 = 0 c7 - 5250ww7 - 5250wo7 - 1200wo7 - 5000ow7 - 20ou7 - 7sc7 - 0.5vis6 - 0.5vis7 - 0.375aw6 - 0.375aw7 - 600000hu7 = 0 c8 - 5250ww8 - 5250wo8 - 1200wo8 - 20ou8 - 7sc8 - 0.5vis7 - 0.5vis8 - 0.375aw7 - 0.375aw8 - 600000hu8 = 0

vis1 + aw1 - vis0 - aw0 - sc1 - 1800ww1 - 4.2857143ou1 + df1 = 0 vis2 + aw2 - vis1 - aw1 - sc2 - 1800ww2 - 4.2857143ou2 + df2 = 0 vis3 + aw3 - vis2 - aw2 - sc3 - 1800ww3 - 4.2857143ou3 + df3 = 0 vis4 + aw4 - vis3 - aw3 - sc4 - 1800ww4 - 4.2857143ou4 + df4 = 0 vis5 + aw5 - vis4 - aw4 - sc5 - 1800ww5 - 4.2857143ou5 + df5 = 0 vis6 + aw6 - vis5 - aw5 - sc6 - 1800ww6 - 4.2857143ou6 + df6 = 0 vis7 + aw7 - vis6 - aw6 - sc7 - 1800ww7 - 4.2857143ou7 + df7 = 0 vis8 + aw8 - vis7 - aw7 - sc8 - 1800ww8 - 4.2857143ou8 + df8 = 0 end

gin ww0 gin ww1 gin ww2 gin ww3 gin ww4 gin ww5 gin ww6 gin ww7 gin ww8

gin ow0 gin ow1 gin ow2 gin ow3 gin ow4 gin ow5 gin ow6 gin ow7

gin wo0 gin wo1 gin wo2 gin wo3 gin wo4 gin wo5 gin wo6 gin wo7 gin wo8

integer hu1 integer hu2 integer hu3 integer hu4 integer hu5 integer hu6 integer hu7 integer hu8

B.2 Output

OBJECTIVE FUNCTION VALUE

(12)

1) 0.1370753E+08

VARIABLE VALUE REDUCED COST

WW0 280.000000 -4.291667

WW1 194.000000 -3150.000244 WW2 214.000000 -9150.000000 WW3 144.000000 -3151.000244 WW4 72.000000 -3150.000244 WW5 216.000000 -3149.000244 WW6 230.000000 -9150.000000 WW7 188.000000 -3150.000244 WW8 188.000000 -3150.000244

OW0 86.000000 5000.000000

OW1 0.000000 5000.000000

OW2 70.000000 5000.000000

OW3 72.000000 5001.000000

OW4 0.000000 5001.000000

OW5 0.000000 5000.000000

OW6 42.000000 5000.000000

OW7 0.000000 5000.000000

WO0 0.000000 0.000000

WO1 20.000000 6450.000000

WO2 0.000000 6450.000000

WO3 0.000000 6449.000000

WO4 144.000000 6449.000000

WO5 14.000000 6450.000000

WO6 0.000000 6450.000000

WO7 0.000000 6450.000000

WO8 0.000000 6450.000000

HU1 0.000000 400000.000000 HU2 0.000000 400000.000000 HU3 0.000000 400000.000000 HU4 0.000000 400000.000000 HU5 0.000000 400000.000000 HU6 0.000000 400000.000000 HU7 0.000000 450000.000000 HU8 0.000000 550000.000000 CTOT 13707533.000000 0.000000 C0 430000.000000 0.000000 C1 1216233.375000 0.000000 C2 2851900.000000 0.000000 C3 1169733.375000 0.000000 C4 1358666.625000 0.000000 C5 1279900.000000 0.000000 C6 2845500.000000 0.000000 C7 1044466.687500 0.000000 C8 1511133.375000 0.000000

WMAX 380.000000 0.000000

DF1 380000.000000 0.000000 DF2 630000.000000 0.000000 DF3 260000.000000 0.000000 DF4 130000.000000 0.000000 DF5 390000.000000 0.000000 DF6 670000.000000 0.000000 DF7 340000.000000 0.000000 DF8 440000.000000 0.000000

SC1 0.000000 2.333333

SC2 79714.289062 0.000000

SC3 0.000000 2.333333

SC4 0.000000 2.333333

SC5 0.000000 2.333333

SC6 78571.437500 0.000000

SC7 0.000000 2.333333

SC8 0.000000 2.333333

OU1 186.666672 0.000000

OU2 38520.000000 0.000000

OU3 186.666672 0.000000

OU4 93.333336 0.000000

OU5 280.000000 0.000000

(13)

OU6 41400.000000 0.000000

OU7 373.333344 0.000000

OU8 23706.667969 0.000000

AW0 0.000000 0.000000

AW1 0.000000 0.000000

AW2 0.000000 0.000000

AW3 0.000000 0.000000

AW4 0.000000 0.000000

AW5 0.000000 0.000000

AW6 0.000000 0.000000

AW7 0.000000 0.000000

AW8 0.000000 0.000000

VIS0 80000.000000 0.000000 VIS1 50000.000000 0.000000 VIS2 50000.000000 0.000000 VIS3 50000.000000 0.000000 VIS4 50000.000000 0.000000 VIS5 50000.000000 0.000000 VIS6 50000.000000 0.000000 VIS7 50000.000000 0.000000 VIS8 50000.000000 0.000000