Process Selection |
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| A planing mill uses 3 different types of planers. What
planers should the company use |
| to minimize
cost? The total job has to be finished in |
3 |
hours. |
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| Characteristics
of planers |
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Speed (ft/min) |
Cost ($/hour) |
Maximum wood thickness (inches) |
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| Planer 1 |
5 |
$150 |
6 |
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| Planer 2 |
7 |
$190 |
4 |
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| Planer 3 |
8 |
$225 |
2 |
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| Wood to be
planed (ft) |
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1" |
2" |
3" |
5" |
Hours |
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Cost |
| Planer 1 |
0 |
0 |
0 |
0 |
0.00 |
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$0.00 |
| Planer 2 |
0 |
0 |
0 |
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0.00 |
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$0.00 |
| Planer 3 |
0 |
0 |
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0.00 |
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$0.00 |
| Total |
0 |
0 |
0 |
0 |
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$0.00 |
| Demand |
500 |
800 |
600 |
300 |
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| Problem |
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| A
planing mill has three different planers. Each planer has a different speed,
cost to operate and |
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thickness of wood it can handle. What planers should the mill use to minimize
cost, given |
| an amount of
wood and no more than 3 hours to do the job? |
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| Solution |
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| The solution
is structurally very similar to the one found on worksheet Alloc1. |
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| 1)
The variables are the amounts of wood that go through the different planers.
In worksheet |
| Process,
these are given the names Wood_through_planer1, Wood_through_planer2 and |
| Wood_through_planer3. |
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| 2) The logical
constraints are all defined via the Assume Non-Negative option: |
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Wood_through_planer1
>= 0 |
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Wood_through_planer2
>= 0 |
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Wood_through_planer3
>= 0 |
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| The time and
demand constraints give |
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Total_hours <= Hours_available |
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Total_planed >= Demand |
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| 3) The objective is to minimize cost and this is defined on
the worksheet as Total_cost. |
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| Remarks |
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| This
is only a small example of a process selection. An example where process
selection is very |
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is the oil industry. A process selection model is often used to decide what
method to use |
| to create a
product. |
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