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

Table 11

Results for the second relaxation, R=1 and QCap=600.

Prob no.	FC	FV	DCs opened ()	DCs closed ()	No. of open DCs	Upper Bound	Lower Bound	% Gap	Lag iter	CPU time (s)
148	0.7	0.7	11	8	5	2,023,248	2,004,405	0.94	1330	103
149	0.7	0.8	20	None	6	2,041,897	2,024,218	0.87	1344	138
150	0.7	0.9	20	None	6	2,056,136	2,041,853	0.70	999	106
151	0.7	1.0	20	None	6	2,070,318	2,058,653	0.57	1372	206
152	0.7	1.1	14,20	10	6	2,093,276	2,070,168	1.12	3156	375
153	0.7	1.2	12,14,20	3	7	2,113,500	2,086,609	1.29	1680	198
154	0.7	1.3	20	None	6	2,120,860	2,104,350	0.78	1025	124
155	0.8	0.7	None	None	5	2,068,799	2,051,220	0.86	1017	79
156	0.8	0.8	13,14,20	3,5	6	2,096,264	2,072,203	1.16	1186	110
157	0.8	0.9	None	None	5	2,109,062	2,091,920	0.82	859	92
158	0.8	1.0	20	None	6	2,126,971	2,108,184	0.89	1283	145
159	0.8	1.1	14,20	10	6	2,140,929	2,125,481	0.73	895	105
160	0.8	1.2	14,20	10	6	2,154,840	2,144,731	0.47	907	112
161	0.8	1.3	20	None	6	2,171,699	2,162,440	0.43	1071	123
162	0.9	0.7	None	None	5	2,115,023	2,087,493	1.32	1693	133
163	0.9	0.8	14	10	5	2,138,568	2,110,547	1.33	1105	86
164	0.9	0.9	None	None	5	2,155,285	2,136,130	0.90	881	69
165	0.9	1.0	14	10	5	2,175,811	2,155,991	0.92	890	97
166	0.9	1.1	14,20	10	6	2,195,839	2,178,961	0.77	1759	194
167	0.9	1.2	14,20	10	6	2,209,749	2,194,826	0.68	865	93
168	0.9	1.3	20	None	6	2,231,671	2,214,517	0.77	948	100
169	1.0	0.7	None	None	5	2,161,246	2,126,896	1.62	1071	83
170	1.0	0.8	14	10	5	2,184,295	2,151,423	1.53	1092	83
171	1.0	0.9	None	None	5	2,201,509	2,175,341	1.20	984	76
172	1.0	1.0	2, 3, 5, 8, 10	N/A	5	2,222,254	2,197,156	1.14	818	65
173	1.0	1.1	14	10	5	2,257,526	2,219,496	1.71	818	86
174	1.0	1.2	14,20	10	6	2,264,658	2,241,920	1.01	823	91
175	1.0	1.3	14	10	5	2,285,395	2,264,942	0.90	867	97
176	1.1	0.7	None	None	5	2,207,470	2,165,608	1.93	1225	98
177	1.1	0.8	14	10	5	2,230,023	2,191,819	1.74	831	66
178	1.1	0.9	None	None	5	2,247,732	2,214,688	1.49	808	54
179	1.1	1.0	14	10	5	2,267,266	2,244,320	1.02	1060	85
180	1.1	1.1	14	10	5	2,303,254	2,264,255	1.72	806	83
181	1.1	1.2	14	10	5	2,319,191	2,292,148	1.18	877	106
182	1.1	1.3	14	10	5	2,331,122	2,308,181	0.99	925	108
183	1.2	0.7	None	None	5	2,253,693	2,203,834	2.26	1314	88
184	1.2	0.8	None	None	5	2,283,055	2,231,213	2.32	1341	102
185	1.2	0.9	None	None	5	2,293,956	2,252,404	1.84	827	54
186	1.2	1.0	None	None	5	2,314,701	2,283,059	1.39	815	64
187	1.2	1.1	None	None	5	2,346,628	2,307,932	1.68	809	70
188	1.2	1.2	12, 14	3,10	5	2,363,777	2,336,492	1.17	845	90
189	1.2	1.3	14	10	5	2,376,850	2,354,471	0.95	833	113
190	1.3	0.7	14	10	5	2,299,884	2,242,034	2.58	1277	84
191	1.3	0.8	None	None	5	2,329,278	2,270,847	2.57	781	50
192	1.3	0.9	None	None	5	2,340,179	2,298,306	1.82	1211	76
193	1.3	1.0	None	None	5	2,360,924	2,310,342	2.19	773	49
194	1.3	1.1	None	None	5	2,392,852	2,346,581	1.97	797	50
195	1.3	1.2	14	10	5	2,410,646	2,371,311	1.66	839	53
196	1.3	1.3	14	10	5	2,422,577	2,400,707	0.91	855	54

(): with respect to base case, Prob no 172; N/A, not applicable.