|
Solver.com
From Frontline Systems, developers of the Excel Solver.
|
|
|
|
|
Transportation Problem 1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| Minimize
the costs of shipping goods from factories to customers, while not
exceeding |
|
|
|
| the
supply available from each factory and meeting the demand of each customer. |
|
|
|
|
|
|
|
|
|
|
|
|
| Cost of shipping ($ per product) |
|
|
|
|
|
|
| |
Destinations |
|
|
|
|
| |
Customer 1 |
Customer 2 |
Customer 3 |
Customer 4 |
Customer 5 |
|
|
|
| Factory 1 |
$1.75 |
$2.25 |
$1.50 |
$2.00 |
$1.50 |
|
|
|
| Factory 2 |
$2.00 |
$2.50 |
$2.50 |
$1.50 |
$1.00 |
|
|
|
|
|
|
|
|
|
|
|
|
| Number of
products shipped |
|
|
|
|
|
|
| |
Customer 1 |
Customer 2 |
Customer 3 |
Customer 4 |
Customer 5 |
Total |
Capacity |
|
| Factory 1 |
0 |
0 |
0 |
0 |
0 |
0 |
60,000 |
|
| Factory 2 |
0 |
0 |
0 |
0 |
0 |
0 |
60,000 |
|
| Total |
0 |
0 |
0 |
0 |
0 |
|
|
|
| Demand |
30,000 |
23,000 |
15,000 |
32,000 |
16,000 |
|
|
|
| |
|
|
|
|
|
|
|
|
| Total cost of
shipping |
$0 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| Problem |
|
|
|
|
|
|
|
|
| A
company wants to minimize the cost of shipping a product from 2 different
factories to 5 different customers. |
|
| Each
factory has a limited supply and each customer a certain demand. How should
the company distribute the |
|
| product? |
|
|
|
|
|
|
|
|
| |
|
|
|
|
|
|
|
|
| Solution |
|
|
|
|
|
|
|
|
| 1)
The variables are the number of products to ship from each factory to the
customers. These are given the |
|
| name Products_shipped
in worksheet Transport1. |
|
|
|
|
|
| 2) The logical
constraint is |
|
|
|
|
|
|
|
| |
Products_shipped >= 0 via the Assume Non-Negative option |
|
|
|
| The other two
constraints are |
|
|
|
|
|
|
| |
Total_received >= Demand |
|
|
|
|
|
|
| |
Total_shipped <= Capacity |
|
|
|
|
|
|
| 3) The
objective is to minimize cost. This is given the name Total_cost. |
|
|
|
|
| |
|
|
|
|
|
|
|
|
| Remarks |
|
|
|
|
|
|
|
|
| This
is a transportation problem in its simplest form. Still, this type of model
is widely used to save many |
|
| housands of
dollars each year. |
|
|
|
|
|
|
| In
worksheet Transport2 we will consider a 2-level transportation, and in
worksheet Transport3 we expand this to |
|
| a
multi-product, 2-level transportation problem. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
