A professor will assign research papers to his students as a partial fulfilment of the requirements of a graduate course. There are six students enrolled in the course and each student will be assigned exactly two research papers. The professor has selected twelve research papers and also determined the expected workload (in hours) required to read,understand and present each of these papers.
An important concern of the professor in organizing the assignments is to be fair to all students by keeping the variance of student workloads as small as possible. Let $v_n$ be the workload associated with the $n$'th research paper,and suppose that a student's workload is the sum of the workloads associated with the research papers he/she is responsible for.
For instance, the total workload of a student responsible for the 1'st and 5'th paper is equal to $v_1+v_5$. Formulate an IP to determine how to assign papers to students to minimize the variance of students workloads. Note that, for a given set of values $\{x_1,x_2,..,x_n\}$ the variance is a non-linear expression defined as
$\operatorname{Variance}=\sum_{i=1}^n (x_i - \overline x)$
where $\overline x$ is the arithmetic mean.