Continuous Time Formulation and Lagrangian Relaxation Algorithm for the Gate Assignment Problem

Table 1

Comparison between linearized model and quadratic model.

Problem			Avg. CPU time (s)		MIP gap (%)
|N|	|M|	T	Linearized	Quadratic	Linearized	Quadratic
10	3	360	0.28	469.87^{8}	0.00	0.53
12	5	360	3.87	600.00^{10}	0.01	28.28
14	5	360	27.37	600.00^{10}	0.01	36.93
16	5	360	125.65^{1}	600.00^{10}	0.11	16.43
18	5	360	153.73^{1}	600.00^{10}	0.43	11.62
20	5	360	83.39^{1}	542.85^{9}	0.01	5.72

^{•}The number of instances not optimally solved in 600 s, and CPU time is set to 600 s.