Outsource or Train: A team formation problem

Many large projects in organizations need to be broken down into manageable tasks for their completion, yet such tasks still demand a diverse set of skills to be completed. Team formation is a way of acquiring workers with different set of skills to complete the tasks and minimizing the cost of assigned workers for the benefit of the organization. It is also found that workers work effectively when they are happy with the task they are working on. In this project, we are given a set of tasks that need to be completed and a set of workers who can be assigned to the tasks. Each task will require a set of skills to be completed. Each worker will possess a set of skills. Each worker has some cost of working on a task. This cost can also be seen as a dissatisfaction factor. And this cost might be different for different tasks. We want to find an assignment of workers to tasks, while making sure that all the skills required to complete a task are covered. In addition to that, we also have to minimize the cost (dissatisfaction) of the workers assigned to the tasks. In real world applications, not all tasks can be completely covered by the available workers. This is because, not all the required skills to complete the tasks are possessed by the workers. In this project, we propose two approaches to overcome these downfalls. One approach is to outsource the entire task for a cheaper cost. And the other approach is to train the workers. We provide algorithmic solutions for both the approaches. We first prove that this team formation problem is NP-Complete. And then we propose and analyze different algorithms for both the approaches. These algorithms are inspired from solutions to matching and set cover problems. We used the data from stackexchange Q \& A discussion forum and bibsonomy social bookmarking and publication-sharing website to model workers and tasks for our experiments. From the results we found that the difference in the performance of the algorithms was very lit