We want to divide N students into M groups of the same size, where each student is a member of exactly one group. The groups are to be simultaneously diverse and compatible based on the following characteristics sets:

Characteristics set K'(k' ∈ K' ) such as personality type, age, sex, grade-point average, years with current employer, income, marital status, employer, current industry, etc.

Characteristics set K'(k' ∈ K' )such as geographic location (i.e., work in same country or area of the city) and work schedule.

To provide diversity, each of the M groups should contain a mixture of personal characteristics in set K'. To provide compatibility, characteristics from set should be as similar as possible within each group.

The following are needed:

1- Mathematical formulation of the model.

2- Solution to a sample problem with N = 20, M = 4, |K'| = 6, & |K| = 2.

3- GAMS model to implement the formulation.

4- Applying the GMAS model to the sample problem.