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

Table 6

Results for first relaxation.

Prob no.	R	QCap	FC	FV	DCs opened ()	DCs closed ()	No. of open DCs	Upper Bound	Lower Bound	% Gap	Lag iter	CPU time (s)
1	1	600	0.7	0.7	10, 11	8, 14	5	2,023,248	2,003,836	0.97	1785	39
4	1	600	0.7	1.0	10, 20	14	6	2,070,318	2,056,800	0.66	1555	34
22	1	600	1.0	0.7	10	14	5	2,161,246	2,131,154	1.41	1011	22
25	1	600	1.0	1.0	2, 3, 5, 8, 14	N/A	5	2,221,538	2,202,020	0.89	1705	37
28	1	600	1.0	1.3	10, 20	14	6	2,282,509	2,263,675	0.83	1343	30
46	1	600	1.3	1.0	None	None	5	2,358,720	2,330,384	1.22	1453	31
49	1	600	1.3	1.3	None	None	5	2,422,577	2,406,503	0.67	1037	23
50	1	900	0.7	0.7	10	14	5	2,022,576	2,002,329	1.01	1906	40
53	1	900	0.7	1.0	10, 20	14	6	2,070,318	2,057,794	0.61	1439	31
71	1	900	1.0	0.7	10	14	5	2,161,246	2,130,454	1.45	1164	24
74	1	900	1.0	1.0	2, 3, 5, 8, 14	N/A	5	2,221,538	2,200,616	0.95	1832	39
77	1	900	1.0	1.3	10, 20	14	6	2,282,509	2,263,675	0.83	1343	30
95	1	900	1.3	1.0	None	None	5	2,358,720	2,330,567	1.21	997	21
98	1	900	1.3	1.3	None	None	5	2,422,577	2,406,503	0.67	1037	23
99	3	600/900	0.7	0.7	12	15,16	11	2,746,539	2,626,621	4.57	1791	51
102	3	600/900	0.7	1.0	None	None	12	2,884,336	2,736,967	5.38	2002	59
120	3	600/900	1.0	0.7	7,12	15,16,19	11	3,063,005	2,910,209	5.25	2707	76
123	3	600/900	1.0	1.0	2,3,5,8,10,11,13, 14,15,16,19,20	N/A	12	3,224,884	3,040,498	6.06	1879	54
126	3	600/900	1.0	1.3	1,12	15	13	3,380,411	3,144,904	7.49	2829	95
144	3	600/900	1.3	1.0	None	None	12	3,565,432	3,340,563	6.73	2372	69
147	3	600/900	1.3	1.3	12	None	13	3,765,373	3,481,191	8.16	1894	57

(): with respect to base case, Prob no 25, 74, and 123, respectively; N/A, not applicable.