Question

(Before anyone asks, this is not homework.)

I have a set of workers with interests, i.e.:

• Bob: Java, XML, Ruby

• Susan: Java, HTML, Python

• Fred: Python, Ruby

• Sam: Java, Ruby

• etc.

(There are actually somewhere in the range of 10-25 “interests” for each worker, and I have around 40-50 workers)

At the same time, I have a very large set of tasks that need to be distributed among the workers. Each task has to be assigned to at least 3 workers, and the workers must match at least one of the tasks’ interests:

Task 1: Ruby, XML
Task 2: XHTML, Python

and so on. So Bob, Fred, or Sam could get Task 1; Susan or Fred could get Task 2.

This is all stored in a database thusly:

Task
    id integer primary key
    name varchar

TaskInterests
    task_id integer
    interest_id integer

Workers
    id integer primary key
    name varchar
    max_assignments integer

WorkerInterests
    worker_id
    interest_id

Assignments
    task_id
    worker_id
    date_assigned

Each worker has a maximum number of assignments they will do, around 10. Some interests are more rare than others (i.e. only 1 or 2 workers have listed them as a interest), some interests are more common (i.e. half of the workers list them).

The algorithm must:

• Assign every task to 3 workers (it is
  assumed that at least 3 of the
  workers are interested in one of the
  interests of the task).
• Assign every worker 1 or more tasks

Ideally, the algorithm will:

• Assign each worker a number of tasks proportional to their maximum assignments and the total number of tasks. For example, if Susan says she will do 20 tasks and most people will only do 10 tasks and there are 50 workers and 300 tasks, she should be assigned 12 tasks (20/10*(300/50)).
• Assign a variety of tasks to each worker, so if Susan lists 4 interests she gets tasks that include 4 interests (rather than getting 10 tasks all with the same interest)

The most difficult aspect so far has been dealing with theses issues:

• tasks having interests with few corresponding workers
• workers who have few interests, especially
• workers who have a few interests, for which there are relatively few tasks

Answer 1

Try mapping your task to the stable marriage problem. Tasks become prospective wives `, and your staff become suitors.

You might want to add some extra algorithm for assigning preferences of each task to the staff, and vice-versa – you could assign some ideal proficiency neccessary for the components of each task, and then allow your staff to rank each task. You could assign a proficiency for each component that each staff member posses and use that to get each tasks preference in staff members.

Once you have the preferences then run the algorithm, post the results, then allow people to apply in pairs to you to swap assignments – after all this is a people problem and people work better when they have a degree of control.