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

Table 12

Results for the second relaxation, R=1 and QCap=900.

Prob no.	FC	FV	DCs opened ()	DCs closed ()	No. of open DCs	Upper Bound	Lower Bound	% Gap	Lag iter	CPU time (s)
197	0.7	0.7	11	8	5	2,023,248	2,002,202	1.05	1378	110
198	0.7	0.8	20	None	6	2,041,655	2,024,155	0.86	1588	175
199	0.7	0.9	20	None	6	2,056,095	2,041,989	0.69	1078	122
200	0.7	1.0	14,20	10	6	2,072,384	2,058,187	0.69	1329	188
201	0.7	1.1	20	None	6	2,087,050	2,069,874	0.83	3781	474
202	0.7	1.2	14,20	10	6	2,099,808	2,088,349	0.55	897	106
203	0.7	1.3	20	None	6	2,120,860	2,104,350	0.78	1025	115
204	0.8	0.7	None	None	5	2,068,799	2,050,990	0.87	1017	79
205	0.8	0.8	13,14,20	3,5	6	2,095,860	2,072,179	1.14	1712	173
206	0.8	0.9	14	10	5	2,110,888	2,092,099	0.90	1377	150
207	0.8	1.0	20	None	6	2,126,763	2,110,466	0.77	1465	170
208	0.8	1.1	14,20	10	6	2,140,737	2,126,893	0.65	920	109
209	0.8	1.2	14,20	10	6	2,154,717	2,143,841	0.51	913	123
210	0.8	1.3	20	None	6	2,171,699	2,162,509	0.42	1021	121
211	0.9	0.7	None	None	5	2,115,023	2,087,493	1.32	1693	135
212	0.9	0.8	14	10	5	2,138,537	2,110,820	1.31	886	71
213	0.9	0.9	None	None	5	2,155,285	2,136,130	0.90	881	71
214	0.9	1.0	14	10	5	2,175,811	2,154,123	1.01	806	90
215	0.9	1.1	14,20	10	6	2,195,646	2,179,059	0.76	972	117
216	0.9	1.2	14,20	10	6	2,209,626	2,196,715	0.59	943	110
217	0.9	1.3	20	None	6	2,231,671	2,214,517	0.77	948	106
218	1.0	0.7	None	None	5	2,161,246	2,126,900	1.61	1318	102
219	1.0	0.8	None	None	5	2,190,608	2,153,284	1.73	879	67
220	1.0	0.9	None	None	5	2,201,509	2,175,200	1.21	1139	89
221	1.0	1.0	2, 3, 5, 8, 10	N/A	5	2,222,254	2,197,156	1.14	818	68
222	1.0	1.1	14,20	10	6	2,250,555	2,222,358	1.27	830	93
223	1.0	1.2	14,20	10	6	2,264,535	2,243,913	0.92	882	96
224	1.0	1.3	14	10	5	2,285,395	2,264,942	0.90	867	102
225	1.1	0.7	None	None	5	2,207,470	2,165,608	1.93	1225	96
226	1.1	0.8	14	3	5	2,236,425	2,191,676	2.04	1293	98
227	1.1	0.9	None	None	5	2,247,732	2,214,688	1.49	808	54
228	1.1	1.0	14	10	5	2,267,266	2,241,419	1.15	904	70
229	1.1	1.1	None	None	5	2,300,405	2,259,632	1.80	830	63
230	1.1	1.2	14	10	5	2,319,191	2,283,489	1.56	884	78
231	1.1	1.3	14	10	5	2,331,122	2,308,181	0.99	925	108
232	1.2	0.7	None	None	5	2,253,693	2,203,840	2.26	1004	67
233	1.2	0.8	None	None	5	2,283,055	2,231,213	2.32	1341	104
234	1.2	0.9	None	None	5	2,293,956	2,252,404	1.84	827	53
235	1.2	1.0	None	None	5	2,314,701	2,283,059	1.39	815	63
236	1.2	1.1	None	None	5	2,346,628	2,306,865	1.72	811	65
237	1.2	1.2	14	10	5	2,364,918	2,333,821	1.33	935	100
238	1.2	1.3	14	10	5	2,376,850	2,354,471	0.95	833	115
239	1.3	0.7	14	10	5	2,299,850	2,242,041	2.58	1249	85
240	1.3	0.8	None	None	5	2,329,278	2,270,854	2.57	781	51
241	1.3	0.9	None	None	5	2,340,179	2,298,306	1.82	1211	78
242	1.3	1.0	None	None	5	2,360,924	2,310,342	2.19	773	50
243	1.3	1.1	None	None	5	2,392,852	2,346,581	1.97	797	50
244	1.3	1.2	12	10	5	2,422,495	2,365,429	2.41	786	50
245	1.3	1.3	14	10	5	2,422,577	2,400,707	0.91	855	55

(): with respect to base case, Prob no 221; N/A, not applicable.