Corner Working Challenge!

For all you techno-weenies out there (I resemble that remark!):
How about a nice linear programming challenge for the holidays?
Assume you have six colored run groups (Red, White, Blue, Orange, Green, and Yellow).
Each group must do corner working while three other groups drive.
Further assume that all Instructors are in either the Red, White, or Orange groups, and all students are in the Blue, Green, or Yellow groups - for simplicity, assume only one student per instructor and that the Instructor-Student pairings are:
Red Instructor = Green Student
Orange Instructor = Blue Student
White Instructor = Yellow Student
The instructor and student run groups must not conflict when corner working (i.e., an instructor cannot be corner working while the student is driving, or vice-versa). EXCEPT that for the timed runs (last two sets of run groups), instructors and students can drive separately.
The instructor should drive in their run group (with the student riding) prior to the student driving with the instructor. (*** This is a key change we would like to implement - many students have commented that the track/line became much clearer after they rode with their instructor.)
Assume that students need their instructors while corner working - but instructors do NOT need to have their students while corner working.
Corner workers CANNOT be scheduled to drive in the run group immediately after their corner working session.
Corner workers (and/or their instructors/students) SHOULD NOT be scheduled to drive immediately before their corner working session.
Ok - find the optimum distribution of run groups and corner working that minimizes the above conflicts.
The best I have been able to come up with is:
Session 1 -
Blue corner workers (with Orange instructors as needed)
Red, Green, White run groups
Session 2 -
Green corner workers (with Red instructors as needed)
Yellow, Orange, Blue run groups
Session 3 -
Orange corner workers
White, Yellow, Red run groups
Session 4 -
Yellow corner workers (with White instructors as needed)
Green, Orange, Blue run groups
Session 5 (timed runs)
Red corner workers
White, Green, Yellow run groups
Session 6 (timed runs)
White corner workers
Blue, Orange, Red run groups
The only problem I can see with the order above is that at the end of Session 2, the Blue drivers will be out with their Orange instructors, which means that the Orange instructors aren't available to "hot swap" to their corners for Session 3. Ergo, we have to shut down the track between 2 and 3 or leave the Session 2 workers out on the track longer...
Can any mathematical geniuses out there come up with a better solution (or prove that such a solution isn't possible).
I am trying to get around the persistent problems of hot swapping while having students and/or instructors in cars immediately before/after corner working switches. (How many of you have had to jump out of cars recently to show up for corner working?)
I will provide a prize to anyone who provides a better solution that meets all the criteria above.
How about a nice linear programming challenge for the holidays?
Assume you have six colored run groups (Red, White, Blue, Orange, Green, and Yellow).
Each group must do corner working while three other groups drive.
Further assume that all Instructors are in either the Red, White, or Orange groups, and all students are in the Blue, Green, or Yellow groups - for simplicity, assume only one student per instructor and that the Instructor-Student pairings are:
Red Instructor = Green Student
Orange Instructor = Blue Student
White Instructor = Yellow Student
The instructor and student run groups must not conflict when corner working (i.e., an instructor cannot be corner working while the student is driving, or vice-versa). EXCEPT that for the timed runs (last two sets of run groups), instructors and students can drive separately.
The instructor should drive in their run group (with the student riding) prior to the student driving with the instructor. (*** This is a key change we would like to implement - many students have commented that the track/line became much clearer after they rode with their instructor.)
Assume that students need their instructors while corner working - but instructors do NOT need to have their students while corner working.
Corner workers CANNOT be scheduled to drive in the run group immediately after their corner working session.
Corner workers (and/or their instructors/students) SHOULD NOT be scheduled to drive immediately before their corner working session.
Ok - find the optimum distribution of run groups and corner working that minimizes the above conflicts.
The best I have been able to come up with is:
Session 1 -
Blue corner workers (with Orange instructors as needed)
Red, Green, White run groups
Session 2 -
Green corner workers (with Red instructors as needed)
Yellow, Orange, Blue run groups
Session 3 -
Orange corner workers
White, Yellow, Red run groups
Session 4 -
Yellow corner workers (with White instructors as needed)
Green, Orange, Blue run groups
Session 5 (timed runs)
Red corner workers
White, Green, Yellow run groups
Session 6 (timed runs)
White corner workers
Blue, Orange, Red run groups
The only problem I can see with the order above is that at the end of Session 2, the Blue drivers will be out with their Orange instructors, which means that the Orange instructors aren't available to "hot swap" to their corners for Session 3. Ergo, we have to shut down the track between 2 and 3 or leave the Session 2 workers out on the track longer...
Can any mathematical geniuses out there come up with a better solution (or prove that such a solution isn't possible).
I am trying to get around the persistent problems of hot swapping while having students and/or instructors in cars immediately before/after corner working switches. (How many of you have had to jump out of cars recently to show up for corner working?)
I will provide a prize to anyone who provides a better solution that meets all the criteria above.