Solving Capacitated Facility Location Problem Using Lagrangian Decomposition and Volume Algorithm

Table 1

A comparison between the results of the LR and VA and the LD and VA for the small problems sized 100–300.

Problem size	Algorithm	Method	LB	UB	Time	Passes	Error
	LR and VA	LR1	9529.44	11984.03	64.48	650	20.5
		LR2	9529.44	11757.42	359.4	1750	18.9
		LR3	9529.44	11433.22	113.8	571	16.7
		LR4	9529.44	11433.22	41.0	423	16.7
	LD and VA	LR5	11088.854	11717.01	4.35	450	5.43
		LR6	11088.854	11599.43	3.8	397	4.46
		LR7	11088.854	11433.22	4.61	482	3.03
		LR8	11088.854	11433.22	4.12	443	3.02
	Best greedy sol.	Filter 4	11089.6	11634.30	55.19	—	4.68
	LR and VA	LR1	18005.55	20677.407	681.68	1400	12.9
		LR2	18005.75	20447.484	680.48	1450	11.9
		LR3	18005.34	20083.69	822.64	617	10.3
		LR4	18005.75	20083.69	78.10	503	10.3
	LD and VA	LR5	19542.11	19919.04	151.54	1850	1.89
		LR6	19542.02	19919.05	75.06	900	1.89
		LR7	19542.08	19919.05	116.26	1400	1.89
		LR8	19542.07	19792.52	95.01	1150	1.30
	Best greedy sol.	Filter 4	19542.3	19791.608	791.64	—	1.30
	LR and VA	LR1	26428.89	30775.85	1552.28	1000	14.0
		LR2	26428.09	29854.86	774.10	500	11.5
		LR3	26428.85	29092.27	1000.82	647	9.2
		LR4	26428.86	29092.27	644.98	438	9.2
	LD and VA	LR5	28351.01	29197.79	616.77	702	2.9
		LR6	28351.01	29065.70	1469.08	1700	2.5
		LR7	28351.01	28933.05	935.91	1150	2.01
		LR8	28351.01	28933.05	369.46	1150	2.01
	Best greedy sol.	Filter 4	28351.8	29125.771	5403.93	—	2.7