Minimization Of Cost Will Be Achieved By Assigning The Products To Plants As Shown Below. Essay Sample

The assignment of products to the plants needs to be done in such a way that the manufacturing costs will be minimized. To determine the plants in which the products will be produced, the formula used involves subtracting the minimum element from all the elements in each row (UNP, 2012). The assignment of the product to a plant is then made using the zero values in each cell. Below is the diagram showing the unit cost of each product in the 8 plants.
After subtracting the lowest element in each row from all the elements in the row, the results are as shown in the table below.
There are some rows that contain multiple zeros meaning that either plant can be assigned the product. Examples of columns with multiple zeros include plant 4, 5, and 8. There were two columns that did not have zero, these include plant 2 and plant 7. Each plant can only be assigned one product so that means that the plants with multiple zeros will only be assigned one product.

C53 Plant 6 $0.06
C81 Plant 3 $0.04
D5 Plant 4 $0.30
D44 Plant 5 $0.10
E2 Plant 8 $0.05
E35 Plant 7 $0.09
G99 Plant 1 $0.55
Total Min Cost $1.19
The assignment of products was based on the zeros that were derived after subtracting the lowest elements in each row. Product E35 was assigned to plant 7 because the cost was lower compared to plant 2. Plant 2 was not assigned any product.

References

UNP, (2012). Transportation and Assignment Problems. Retrieved from: http://www.maths.unp.ac.za/coursework/MATH331/2012/transportation_assignment.pdf