Contract Awards 2 |
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| A
large software company with 4 separate buildings in different states, has
offers from 3 different |
| floppy
disk manufacturers to supply their monthly need of new diskettes. To whom
should the |
| contracts be
awarded to minimize cost? |
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| Bids per 1000
diskettes |
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Building 1 |
Building 2 |
Building 3 |
Building 4 |
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| Manufacturer
1 |
$50 |
$45 |
$48 |
$52 |
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| Manufacturer
2 |
$52 |
$48 |
$51 |
$54 |
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| Manufacturer
3 |
$49 |
$51 |
$50 |
$52 |
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| Contracts awarded per 1000
diskettes |
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Building 1 |
Building 2 |
Building 3 |
Building 4 |
Total |
Available |
| Manufacturer
1 |
5 |
5 |
5 |
5 |
20 |
25 |
| Manufacturer
2 |
5 |
5 |
5 |
5 |
20 |
30 |
| Manufacturer
3 |
5 |
5 |
5 |
5 |
20 |
25 |
| Total |
15 |
15 |
15 |
15 |
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| Required |
20 |
25 |
15 |
15 |
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| Manufacturer
1 is only interested in contracts of 15000
diskettes or more. |
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| Decisions |
0 |
0 |
0 |
0 |
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0 |
0 |
0 |
0 |
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0 |
0 |
0 |
0 |
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| Total Cost |
$3,010 |
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| Problem |
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| A
large software company with 4 different buildings in different states, needs
a large supply |
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diskettes on a monthly basis in each of those buildings. The company has 3
different offers |
| from
several floppy disk manufacturers. However, Manufacturer 1 is only interested
in |
| contracts
of 15,000 diskettes or more. Which offer or combination of offers should the |
| company accept
to minimize cost? |
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| Solution |
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| On
the surface this problem seems to be no different from the one in Award1.
However, we |
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the problem that the number of diskettes bought from Manufacturer 1 should
either be 0 |
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greater than 15000. This is a frequently occurring constraint and Award2
shows us how to |
| handle
this type of condition. The key is to introduce 4 new binary integer
variables that tell us |
| whether a
contract is bought from manufacturer 1 or not, for each building. |
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| 1)
The variables are the contracts to be awarded, and the binary integer
variables as discussed |
| above. In worksheet Award2 these are given the
names Contracts and Contract_decisions. |
| 2) First, we
still have the constraints used in Award1: |
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Contracts_given >= Contracts_required |
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Total_contracts <= Contracts_available |
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Contracts >= 0 via the Assume Non-Negative option |
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| Second, we
have the logical constraints for the binary integer variables: |
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Contract_decisions = binary |
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| The 15000
diskettes constraint is now handled by: |
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Awarded_to_1 <= Maximum_diskettes |
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Awarded_to_1 >= Minimum_diskettes |
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| 3) The objective is still to minimize total cost, defined
on this worksheet as Total_Cost. |
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| Remarks |
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| The
introduction of binary integer variables often allows us to express the
effect of more |
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conditions as seen in this model. It would also be possible to handle other
types of |
| constraints.
For example, if Manufacturer 2 only distributes diskettes in multiples of
5000, |
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could model this constraint with binary integer variables. |
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