Assigning people to jobs is a common application of the assignment problem. However, the assignees need not be people. They also could be machines, or vehicles, or plants, or even time slots to be assigned tasks.
Let us understand this using a problem.
A company has three offices in Hong Kong, London and New York with 3, 4 and 2 Sales Representatives respectively. These sales representatives have to bring in new business in four locations Sydney, Johannesburg, Miami and Dubai with a demand of 2, 2, 2 and 3 representatives respectively. The following table gives the information about the flight cost from each of these locations to other. Let us understand how to assign these sales representatives from three different office locations to four new locations so that the airfare is kept minimum.
The problem set up is the same as the Transportation Problem discussed previously.
The only change is that we have to add one parameter under “Subject to the Constraints” as shown below (highlighted in blue).
The final answer is as shown below.