Facility Location |
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| A
company currently ships its product from 5 plants to 4 warehouses. It is
considering closing |
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or more plants to reduce cost. What plant(s) should the company close, in
order to |
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fixed costs? |
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| Transportation Costs (per
1000 products) |
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Plant 1 |
Plant 2 |
Plant 3 |
Plant 4 |
Plant 5 |
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| Warehouse 1 |
$4,000 |
$2,000 |
$3,000 |
$2,500 |
$4,500 |
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| Warehouse 2 |
$2,500 |
$2,600 |
$3,400 |
$3,000 |
$4,000 |
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| Warehouse 3 |
$1,200 |
$1,800 |
$2,600 |
$4,100 |
$3,000 |
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| Warehouse 4 |
$2,200 |
$2,600 |
$3,100 |
$3,700 |
$3,200 |
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| Open/close
decision variables |
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Plant 1 |
Plant 2 |
Plant 3 |
Plant 4 |
Plant 5 |
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| Decision |
0 |
0 |
0 |
0 |
0 |
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| Number of products to ship
(per 1000) |
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Plant 1 |
Plant 2 |
Plant 3 |
Plant 4 |
Plant 5 |
Total |
Demand |
| Warehouse 1 |
0 |
0 |
0 |
0 |
0 |
0 |
15 |
| Warehouse 2 |
0 |
0 |
0 |
0 |
0 |
0 |
18 |
| Warehouse 3 |
0 |
0 |
0 |
0 |
0 |
0 |
14 |
| Warehouse 4 |
0 |
0 |
0 |
0 |
0 |
0 |
20 |
| Total |
0 |
0 |
0 |
0 |
0 |
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| Capacity |
0 |
0 |
0 |
0 |
0 |
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| Distr.
Cost |
$0 |
$0 |
$0 |
$0 |
$0 |
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| Fixed Cost |
$0 |
$0 |
$0 |
$0 |
$0 |
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| Total Cost |
$0 |
$0 |
$0 |
$0 |
$0 |
$0 |
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| Problem |
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| A
company currently ships products from 5 plants to 4 warehouses. The company
is considering the option of |
| closing
down one or more plants. This would increase distribution cost but perhaps
lower overall cost. What |
| plants, if
any, should the company close? |
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| Solution |
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| 1)
The variables are the decisions to open or close the plants, and the number
of products that should be |
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from the plants that are open to the warehouses. In worksheet Facility these are given the names |
| Open_or_close
and Products_shipped. |
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| 2) The logical
constraints are |
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Products_shipped >= 0 via the Assume Non-Negative option |
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Open_or_close = binary |
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products made can not exceed the capacity of the plants and the number
shipped should meet the |
| demand. This gives |
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Products_made <= Capacity |
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Total_shipped >= Demand |
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| 3) The
objective is to minimize cost. This is given the name Total_cost on the
worksheet. |
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| Remarks |
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| It
is often possible to increase the capacity of a plant. This could be worked
into the model with additional 0-1 |
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binary integer variables. The Solver would find out if it would be profitable
to extend the capacity of a plant. |
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could also be interesting to see if it would be profitable to open another
warehouse. An example of this can |
| be found, in somewhat modified form, in the capacity
planning model in the Finance Examples workbook. |
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