# Assignment problem with divisible tasks and hours

A general assignment problem is assigning a set of tasks(Ti) to a set of workers (Wi). Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment. It is required to perform all tasks by assigning exactly one agent to each task and exactly one task to each agent in such a way that the total cost of the assignment is minimized.

Assignment problem table

For instance, Worker A can do Job1 in 9 hours, Job2 in 2 hours, Job3 in 7 hours and so on.

In my case, say Worker A has a total of 8 hours, can do 1/2 of Job1 in 3 hours, 1/4 of Job1 in 1/8 hours and so on, Worker B can do 1/3 of Job1 in 2 hours, 1/4 of Job2 in 5 hours similarly for other workers and job combinations. We need to assign fractional tasks to each of the workers so as to minimize the cost and maximize the task assignment.

• What to solve for? What is asked? – idea Sep 14 '18 at 7:59
• Minimize the cost (number of hours), while maximizing the matching of persons with tasks – Roh Codeur Sep 14 '18 at 8:37
• still appears unclear... – idea Sep 14 '18 at 8:41
• My apologies, I have updated the problem description – Roh Codeur Sep 14 '18 at 9:25