Concept explainers
ABC pharmaceutical Company has four factories that ship supplies to four warehouses. The company’s management hires you as a consultant to determine a minimum-cost shipping plan for its monthly output to the warehouses. Factory capacities, warehouse demands, and shipping cost per box are shown below.
Factory |
Supply or capacity (boxes) |
Warehouse |
Demand (boxes) |
Richmond |
60 |
Chicago |
100 |
Santa Fe |
80 |
Jacksonville |
90 |
Austin |
120 |
Huntville |
50 |
Vacaville |
90 |
Fresno |
70 |
|
Shipping Costs per box (In Dollars) |
|||
From |
To Chicago |
To Jacksonville |
To Huntsville |
To Fresno |
Richmond |
35 |
35 |
46 |
60 |
Santa Fe |
65 |
40 |
35 |
25 |
Austin |
50 |
50 |
80 |
90 |
Vacaville |
40 |
40 |
66 |
75 |
- Draw a diagram by showing factories, warehouses, and connecting arcs.
- Define variables, write the objective function and constraints.
The transportation model is used to calculate the minimum cost of the route by selecting different supplies and demands. There are basically the main methods that are used under the transportation model, i.e., the least cost method, VAM, and northwest corners. These methods help in finding the feasibility of the solution but optimally of the solution can be checked the other methods: - The stepping stone method, MODI method, or linear programming method.
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