Salvaging College Registrations During COVID-19 via Integer Programming

Figures & data

Table 1: Computational data reported by Mosek after a timed termination of 8.5 hours working on (9). Instances A and B did not perturb the objective function.

	Random	Cutting	Branches	Relaxations	Simplex	Optimality
	Perturb.	Planes	Created	Solved	Iterations	Gap (%)
A	No	2	1,348,205	1,266,138	409,986,094	14.62
B	No	4	1,417,327	1,325,648	409,435,633	14.41
C	Yes	5	2,380,516	2,242,821	769,773,065	11.97
D	Yes	8	2,532,475	2,376,589	778,706,493	12.02

Table 2: Four near optimal solutions: Number of sections assigned to each term, percentage of seats saved, percentage of students who do not need to make any changes to their registration, and number of two course faculty constraints violated. (No solutions had a three course faculty violation.)

	# Sections	# Sections	Seats	Students	Faculty
	${\mathcal{T}}_{\mathit{1}}$	${\mathcal{T}}_{\mathit{2}}$	Saved (%)	Unchanged (%)	Violations
A	195	163	90.66	69.93	5
B	192	166	90.82	70.62	4
C	192	166	91.00	71.24	6
D	196	162	90.62	70.39	3

Table 3: Time slots: within each general time slot of morning, afternoon, or evening were full time period laboratory time slots conflicting with shorter time slots; the morning and afternoon included two nonconflicting 110 minute time slots.

Morning		Afternoon		Evening
(110 min.)	(230 min.)	(110 min.)	(230 min.)	(110 min.)	(230 min.)
$t_1$	$t_3$	$t_4$	$t_6$	$t_7$
$t_2$		$t_5$

Table 4: Computational Data reported by Mosek on the Time Slot Problem (12). The optimal solution was found for each problem in less than 30 seconds.

	Cutting	Branches	Relaxations	Simplex	Time	Seats
	Planes	Created	Solved	Iterations	(sec.)	Lost
${\mathcal{T}}_{\mathbf{1}}$	21	11,493	8,585	354,513	26.04	71
${\mathcal{T}}_{\mathbf{2}}$	34	4,396	3,424	176,680	14.25	106