An Approximation Algorithm for the Facility Location Problem with Lexicographic Minimax Objective

Table 1

Computational results for the algorithm A-LEX: small instances.

Instance	|𝐼|	𝑝	𝑘max	O-LEX		A-LEX^𝑋
				Time [s]	𝑘𝑠	Time [s]	𝑘𝑠	Δ
𝑝𝑚𝑒𝑑𝑐𝑎𝑝1	50	5	30	1.88	11	0.64	11	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝2	50	5	42	3.23	8	0.67	7	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝3	50	5	28	1.60	9	0.46	7	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝4	50	5	43	2.97	15	0.91	15	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝5	50	5	33	2.11	13	0.74	10	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝6	50	5	38	2.51	11	1.21	12	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝7	50	5	40	3.15	13	0.98	13	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝8	50	5	39	2.75	7	0.80	6	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝9	50	5	36	2.80	9	0.80	8	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝10	100	10	30	1.98	10	0.59	10	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝11	100	10	21	4.29	2	1.04	1	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝12	100	10	26	5.21	4	1.74	3	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝13	100	10	30	5.65	2	1.76	1	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝14	100	10	24	4.89	3	1.91	2	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝15	100	10	27	6.21	2	1.89	1	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝16	100	10	23	4.59	1	1.20	0	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝17	100	10	25	6.83	2	1.50	1	2
𝑝𝑚𝑒𝑑𝑐𝑎𝑝18	100	10	25	4.67	2	1.70	1	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝19	100	10	30	6.83	2	2.46	1	0
𝑝𝑚𝑒𝑑𝑐𝑎𝑝20	100	10	20	5.95	3	0.90	2	0
𝑆𝐽𝐶1	100	5	732	47.90	588	28.54	569	0
𝑆𝐽𝐶1	100	10	426	22.99	283	10.82	282	0
𝑆𝐽𝐶1	100	15	427	24.51	261	10.65	269	0
𝑆𝐽𝐶1	100	20	150	5.31	64	2.91	65	0