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 ε K) like personality type, age, sex, grade-point average, years with current employer, income, marital status, employer, current industry, etc. Characteristics set K (k ε 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 K should be as similar as possible within each group.

The following are required:

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 formulation.
4- Pertaining the GMAS model to the sample problem.