Lagrangian Relaxation for an Inventory Location Problem with Periodic Inventory Control and Stochastic Capacity Constraints

Table 10

Results for the first relaxation, R=3 and QCap=600; QCap=900.

Prob no.	FC	FV	DCs opened ()	DCs closed ()	No. of open DCs	Upper Bound	Lower Bound	% Gap	Lag iter	CPU time (s)
99	0.7	0.7	12	15,16	11	2,746,539	2,626,621	4.57	1791	51
100	0.7	0.8	1,12	15,16	12	2,821,579	2,668,238	5.75	1516	43
101	0.7	0.9	12	16	12	2,851,136	2,698,879	5.64	2071	59
102	0.7	1.0	None	None	12	2,884,336	2,736,967	5.38	2002	59
103	0.7	1.1	1,12	11,15	12	2,924,387	2,767,487	5.67	1652	49
104	0.7	1.2	12	None	13	2,988,536	2,804,060	6.58	1764	53
105	0.7	1.3	1,12	15	13	3,005,910	2,839,190	5.87	1904	59
106	0.8	0.7	1,12	15,16,19	11	2,855,967	2,722,479	4.90	1860	53
107	0.8	0.8	None	15	11	2,927,783	2,764,501	5.91	2232	64
108	0.8	0.9	1,12	15,19	12	2,965,225	2,796,807	6.02	1931	55
109	0.8	1.0	None	None	12	2,997,852	2,838,973	5.60	1625	48
110	0.8	1.1	1,12	11,15	12	3,033,260	2,867,744	5.77	2254	67
111	0.8	1.2	12	None	13	3,111,402	2,910,038	6.92	1814	54
112	0.8	1.3	1,12	15	13	3,130,744	2,946,207	6.26	1783	54
113	0.9	0.7	7	15,16	11	2,965,807	2,817,936	5.25	1645	46
114	0.9	0.8	1	11,15	11	3,027,515	2,862,289	5.77	1798	51
115	0.9	0.9	1,12	15,19	12	3,077,708	2,893,453	6.37	1905	54
116	0.9	1.0	None	None	12	3,111,368	2,939,921	5.83	1789	52
117	0.9	1.1	1,12	11,15	12	3,147,729	2,972,010	5.91	1991	59
118	0.9	1.2	12	None	13	3,234,269	3,017,179	7.20	1793	53
119	0.9	1.3	1,12	15	13	3,255,577	3,048,281	6.80	2170	65
120	1.0	0.7	7,12	15,16,19	11	3,063,005	2,910,209	5.25	2707	76
121	1.0	0.8	None	15	11	3,138,137	2,958,396	6.08	1838	52
122	1.0	0.9	1,12	15,19	12	3,190,192	2,992,886	6.59	1964	55
123	1.0	1.0	2,3,5,8,10,11,13,	N/A	12	3,224,884	3,040,498	6.06	1879	54
			14,15,16,19,20
124	1.0	1.1	1,12	11,15	12	3,267,793	3,074,058	6.30	1797	53
125	1.0	1.2	12	None	13	3,357,135	3,122,780	7.50	1882	56
126	1.0	1.3	1,12	15	13	3,380,411	3,144,904	7.49	2829	95
127	1.1	0.7	7	15,16	11	3,176,424	3,007,463	5.62	2633	74
128	1.1	0.8	12	15,19	11	3,226,169	3,055,590	5.58	2583	74
129	1.1	0.9	1,12	15,19	12	3,302,676	3,092,201	6.81	1647	47
130	1.1	1.0	None	None	12	3,338,400	3,141,701	6.26	2035	61
131	1.1	1.1	7,12	11,16	12	3,380,893	3,173,092	6.55	2466	81
132	1.1	1.2	1,12	19	13	3,479,214	3,228,727	7.76	1706	59
133	1.1	1.3	12	None	13	3,519,640	3,263,281	7.86	2507	80
134	1.2	0.7	1,12	15,16,19	11	3,265,744	3,098,273	5.41	2484	71
135	1.2	0.8	1,7,12	11,15,16,19	11	3,347,472	3,151,445	6.22	2130	61
136	1.2	0.9	1,12	15,19	12	3,415,160	3,190,416	7.04	2025	58
137	1.2	1.0	None	None	12	3,451,916	3,242,612	6.45	1981	58
138	1.2	1.1	7,12	11,16	12	3,493,527	3,275,587	6.65	2420	71
139	1.2	1.2	1,12	19	13	3,600,037	3,331,035	8.08	2534	76
140	1.2	1.3	1,12	15	13	3,630,078	3,374,142	7.59	2022	61
141	1.3	0.7	1	11,15	11	3,386,827	3,191,709	6.11	3215	91
142	1.3	0.8	1,7,12	11,15,16,19	11	3,449,723	3,243,352	6.36	2728	77
143	1.3	0.9	1,12	15,19	12	3,527,644	3,288,221	7.28	1698	49
144	1.3	1.0	None	None	12	3,565,432	3,340,563	6.73	2372	69
145	1.3	1.1	7,12	11,16	12	3,606,160	3,376,022	6.82	2576	76
146	1.3	1.2	1,12	19	13	3,720,860	3,423,069	8.70	2089	73
147	1.3	1.3	12	None	13	3,765,373	3,481,191	8.16	1894	57

(): with respect to base case, Prob no 123; N/A, not applicable.