Allocation Problem
2 (Multi-period) |
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| Minimize
the cost of operating 3 different types of machines while meeting product
demand over a |
| week's
time. Each machine has a different
cost and capacity. There are a certain number of machines |
| available for each type. |
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| Information on machines |
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Initial
cost per day |
Additional cost per product |
Products per day (Max) |
Number of machines |
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| Alpha-1000 |
$200 |
$1.00 |
40 |
8 |
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| Alpha-2000 |
$275 |
$1.80 |
60 |
5 |
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| Alpha-3000 |
$325 |
$1.90 |
85 |
3 |
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| Number of
machines to use |
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Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
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| Alpha-1000 |
0 |
0 |
0 |
0 |
0 |
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| Alpha-2000 |
0 |
0 |
0 |
0 |
0 |
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| Alpha-3000 |
0 |
0 |
0 |
0 |
0 |
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| Number of products to make per
day |
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Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
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| Alpha-1000 |
0 |
0 |
0 |
0 |
0 |
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| Alpha-2000 |
0 |
0 |
0 |
0 |
0 |
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| Alpha-3000 |
0 |
0 |
0 |
0 |
0 |
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| Made |
0 |
0 |
0 |
0 |
0 |
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| Carry-over |
0 |
-600 |
-1400 |
-2400 |
-3125 |
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| Total |
0 |
-600 |
-1400 |
-2400 |
-3125 |
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| Demand |
600 |
800 |
1000 |
725 |
750 |
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| Maximum number of
products that can be made |
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Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
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| Alpha-1000 |
0 |
0 |
0 |
0 |
0 |
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| Alpha-2000 |
0 |
0 |
0 |
0 |
0 |
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| Alpha-3000 |
0 |
0 |
0 |
0 |
0 |
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Total |
| Cost |
$0.00 |
$0.00 |
$0.00 |
$0.00 |
$0.00 |
$0.00 |
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| Problem |
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| A
company has three different types of machines that all make the same
product. Each machine has |
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different capacity, start-up cost and cost per product. How should the
company produce its |
| product with
the available machines to meet the demand over a week's time? |
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| Solution |
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| The solution
is very similar in structure to the one found on worksheet Alloc1. |
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| 1)
The variables are the number of machines to use and the number of products to
make on each |
| machine. In worksheet Alloc2, these given the names
Products_made and Machines_used. |
| 2) First,
there are the logical constraints. These are |
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Products_made >= 0 via the Assume Non-Negative option |
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Machines_used
>= 0 via the Assume Non-Negative
option |
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Machines_used
= integer. |
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| Second, there
are the demand and capacity constraints. These are: |
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Alpha1000s_used <= Alpha1000s_available |
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Alpha2000s_used <= Alpha2000s_available |
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Alpha3000s_used <= Alpha3000s_available |
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Products_made <= Maximum_products |
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Total_made >= Demand |
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| 3) The
objective is to minimize cost. This is defined on the worksheet as
Total_cost.. |
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| Remarks |
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| Please
see the comments on integer constraints in worksheet Alloc1. In this model we allow for |
| products
made on one day to be carried over to the next. This makes it possible to
meet a demand |
| for one day
that exceeds the capacity of the machines on that particular day. |
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