Plant Opening/Closing |
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| A
company wants to minimize the costs of shipping goods from production plants
to warehouses near |
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demand centers, while not exceeding the supply available from each plant and
meeting |
| the
demand from each metropolitan area. The company has plants in S. Carolina,
Tennessee and |
| Arizona.
It is thinking about opening a plant in Arkansas. |
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Number to ship from plant x to warehouse y (at
intersection): |
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| Plants: |
Total |
San Fran |
Denver |
Chicago |
Dallas |
New York |
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| S. Carolina |
0 |
0 |
0 |
0 |
0 |
0 |
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| Tennessee |
0 |
0 |
0 |
0 |
0 |
0 |
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| Arizona |
0 |
0 |
0 |
0 |
0 |
0 |
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| Arkansas |
0 |
0 |
0 |
0 |
0 |
0 |
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| Totals: |
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0 |
0 |
0 |
0 |
0 |
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Demands by Whse --> |
180 |
80 |
200 |
160 |
220 |
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| Plants: |
Supply |
Shipping costs from plant x to warehouse y (at
intersection): |
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| S. Carolina |
310 |
$10 |
$8 |
$6 |
$5 |
$4 |
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| Tennessee |
260 |
$6 |
$5 |
$4 |
$3 |
$6 |
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| Arizona |
280 |
$3 |
$4 |
$5 |
$5 |
$9 |
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| Arkansas |
0 |
$4 |
$3 |
$6 |
$4 |
$7 |
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| Shipping: |
$0 |
$0 |
$0 |
$0 |
$0 |
$0 |
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Extra shipping cost if opened |
$100 |
Decision to open plant |
0 |
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| Problem |
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| A
company currently distributes products from three plants to five warehouses
in different cities. Management |
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now thinking about opening a new plant to bring down distribution cost.
Should the company decide to |
| open the new
plant or not? |
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| Solution |
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| This
models uses 2 kinds of variables. First, there are the variables that
indicate how many products to ship |
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each plant to each warehouse. Second, we have a decision variable to decide
whether we should |
| open the new
plant. For more information on the decision variables, see the worksheet. |
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| 1) The variables are the number of products to ship from
each plant to each warehouse and the decision to |
| open or close the new plant. These are defined on this
worksheet as Shipments and plant_decision. |
| 2)
First, there are the 'normal' distribution constraints. These are the
constraints that we cannot ship more |
| products from the plants than the supply at these plants.
Also, we don't ship more to the cities than the demand |
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cities. This leads to: |
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Shipped_from_plants <= Supply |
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Shipped_to_warehouses >= Demand |
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| Second, since we can't ship a negative number of products,
we have the logical constraint |
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products_shipped >= 0 via the Assume
Non-Negative option |
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| And third, we must tell the Solver to strictly use 0 or 1
for the 'decision' variable. This gives: |
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plant_decision = binary |
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| 3)
The objective is to minimize cost, defined as Total_cost. This is calculated
by muliplying the distribution |
| cost times the
number of products shipped, plus the extra cost to open the new plant. |
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| Remarks |
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| You might have noticed that this model resembles a pure
transportation model. This is an example of a mix |
| between a transportation model and a pure decision model,
like Lockbox. In real life situations, it is very |
| common
to combine different kind of models to get a better representation of the
problem. |
| Notice
how the decision variable is used to control the supply at the potentially
new plant. If the decision to |
| open is no, the supply is
zero. |
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