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

Table 13

Results for the second 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)
246	0.7	0.7	None	12	11	2,762,632	2,624,245	5.27	813	51
247	0.7	0.8	1	16	12	2,821,579	2,667,098	5.79	1700	102
248	0.7	0.9	1	19	12	2,852,741	2,699,063	5.69	1800	109
249	0.7	1.0	1	12	12	2,902,314	2,738,089	6.00	1653	102
250	0.7	1.1	1	11	12	2,924,387	2,767,645	5.66	1674	101
251	0.7	1.2	15	None	13	2,988,536	2,808,140	6.42	1526	94
252	0.7	1.3	15	None	13	3,028,174	2,839,398	6.65	1534	94
253	0.8	0.7	7	12,16	11	2,860,498	2,719,105	5.20	851	54
254	0.8	0.8	None	19	11	2,919,636	2,764,674	5.61	2577	153
255	0.8	0.9	1	19	12	2,965,225	2,797,354	6.00	1691	101
256	0.8	1.0	1	12	12	3,017,797	2,839,010	6.30	1703	102
257	0.8	1.1	1	11	12	3,038,856	2,869,832	5.89	1917	123
258	0.8	1.2	15	None	13	3,111,402	2,913,305	6.80	1436	86
259	0.8	1.3	7,15	16	13	3,136,899	2,946,396	6.47	1599	95
260	0.9	0.7	None	12	11	2,972,986	2,814,084	5.65	1240	79
261	0.9	0.8	None	19	11	3,021,814	2,862,296	5.57	1713	107
262	0.9	0.9	1	19	12	3,077,708	2,895,100	6.31	2142	134
263	0.9	1.0	1	12	12	3,133,280	2,939,919	6.58	1595	105
264	0.9	1.1	1	11	12	3,153,325	2,972,015	6.10	1771	119
265	0.9	1.2	15	None	13	3,234,269	3,018,470	7.15	1491	97
266	0.9	1.3	15	None	13	3,273,907	3,053,394	7.22	1687	108
267	1.0	0.7	7	12,16	11	3,071,115	2,908,436	5.59	1463	94
268	1.0	0.8	15	10,16	11	3,122,842	2,956,507	5.63	2108	129
269	1.0	0.9	1	19	12	3,190,192	2,993,937	6.56	1776	113
270	1.0	1.0	2,3,5,8,10,11,12 13,14,16,19,20	N/A	12	3,241,325	3,040,813	6.59	1574	98
271	1.0	1.1	1	11	12	3,267,793	3,074,195	6.30	1497	90
272	1.0	1.2	15	None	13	3,357,135	3,123,635	7.48	1793	106
273	1.0	1.3	15	None	13	3,396,774	3,160,391	7.48	1428	83
274	1.1	0.7	7	12,16	11	3,176,424	3,006,561	5.65	1631	102
275	1.1	0.8	None	12	11	3,243,314	3,054,626	6.18	2187	134
276	1.1	0.9	1	19	12	3,302,676	3,092,207	6.81	1806	110
277	1.1	1.0	1	12	12	3,364,246	3,141,710	7.08	1610	97
278	1.1	1.1	15	3	12	3,377,059	3,176,389	6.32	1350	83
279	1.1	1.2	1,15	19	13	3,479,214	3,228,800	7.76	1691	100
280	1.1	1.3	15	None	13	3,519,640	3,267,390	7.72	1667	100
281	1.2	0.7	None	16	11	3,268,978	3,101,566	5.40	1734	107
282	1.2	0.8	None	19	11	3,328,346	3,152,607	5.57	1645	99
283	1.2	0.9	1	19	12	3,415,160	3,190,419	7.04	1772	110
284	1.2	1.0	1	12	12	3,479,729	3,242,618	7.31	1715	107
285	1.2	1.1	15	3	12	3,489,521	3,278,575	6.43	1542	97
286	1.2	1.2	1,15	19	13	3,600,037	3,333,966	7.98	1428	83
287	1.2	1.3	15	None	13	3,642,507	3,374,388	7.95	1491	86
288	1.3	0.7	1	3,19	11	3,389,315	3,194,564	6.10	1805	108
289	1.3	0.8	None	19	11	3,430,524	3,248,659	5.60	1706	101
290	1.3	0.9	1	19	12	3,527,644	3,288,238	7.28	1589	94
291	1.3	1.0	15	16	12	3,592,914	3,343,519	7.46	1539	91
292	1.3	1.1	15	11	12	3,618,080	3,380,594	7.02	1630	97
293	1.3	1.2	1,15	19	13	3,720,860	3,439,130	8.19	1549	88
294	1.3	1.3	1,15	19	13	3,761,791	3,481,305	8.06	1666	101

(): with respect to base case, Prob no 270; N/A, not applicable.