Discrete Dynamics in Nature and Society

Research Article

A Location-Inventory-Routing Problem in Forward and Reverse Logistics Network Design

Table 4

Results of different rate between the cost of recovered products and the cost of new products.


Prob. ID					TS		NTS		Gap 1 (%)
Prob. ID					UB	Time	UB	Time	Gap 1 (%)

P1	1	20	5	70	68142	3.00	68142	2.78	0.00
	1.25				67402	2.68	67402	2.39	0.00
	1.5				67211	2.14	66964	2.61	−0.37
	1.75				66898	3.15	66649	2.54	−0.37
	2				66496	2.76	66414	2.79	−0.12

P2	1	20	5	150	43008	3.33	43008	2.35	0.00
	1.25				42964	3.11	42964	2.54	0.00
	1.5				42934	2.49	42934	2.22	0.00
	1.75				42913	2.40	42913	3.15	0.00
	2				42897	3.55	42897	3.19	0.00

P3	1	20	5	70	61680	2.72	61680	2.82	0.00
	1.25				61028	2.46	61028	2.81	0.00
	1.5				60595	2.47	60595	2.54	0.00
	1.75				60367	2.59	60285	2.71	−0.14
	2				60132	2.52	60052	2.50	−0.13

P4	1	20	5	150	40458	2.45	40458	2.05	0.00
	1.25				40391	2.18	40391	2.36	0.00
	1.5				40346	2.86	40346	2.96	0.00
	1.75				40314	2.69	40314	2.32	0.00
	2				40290	1.92	40290	2.28	0.00

P5	1	50	5	70	117832	26.39	116378	25.98	−1.23
	1.25				117029	25.68	114692	26.63	−2.00
	1.5				115617	26.14	114374	25.88	−1.08
	1.75				115126	26.70	114022	26.30	−0.96
	2				113413	25.84	112590	25.75	−0.73

P6	1	50	5	150	90053	22.94	87484	20.19	−2.85
	1.25				88307	24.22	86991	20.15	−1.49
	1.5				87796	23.82	86910	23.21	−1.01
	1.75				86976	20.81	86535	22.24	−0.51
	2				86703	22.88	86394	17.23	−0.36

P7	1	50	5	70	123939	18.23	122295	21.88	−1.33
	1.25				121637	19.25	120958	16.91	−0.56
	1.5				120474	18.75	119532	20.84	−0.78
	1.75				119790	21.88	118308	21.61	−1.24
	2				118183	16.95	117858	21.77	−0.27

P8	1	50	5	150	100524	17.41	100439	25.51	−0.08
	1.25				99371	28.59	99067	29.73	−0.31
	1.5				98231	24.37	97807	29.53	−0.43
	1.75				97514	24.48	96608	22.80	−0.93
	2				96942	25.15	96560	17.95	−0.39

P9	1	50	5	70	117880	27.00	115956	22.17	−1.63
	1.25				116053	30.39	114876	35.22	−1.01
	1.5				114690	24.03	113420	28.06	−1.11
	1.75				113128	19.20	112769	28.95	−0.32
	2				112006	28.62	111756	26.96	−0.22

P10	1	50	5	150	88057	23.26	87883	31.21	−0.20
	1.25				86485	25.83	86222	31.48	−0.30
	1.5				85367	31.62	84589	19.58	−0.91
	1.75				83386	26.10	83478	22.37	0.11
	2				83455	25.45	83235	21.90	−0.26

P11	1	50	5	70	114793	20.04	112544	25.68	−1.96
	1.25				112136	19.99	111395	27.60	−0.66
	1.5				111087	20.16	111062	29.96	−0.02
	1.75				110640	27.13	109472	22.12	−1.06
	2				110405	22.60	108934	26.43	−1.33

P12	1	50	5	150	87232	24.63	86433	29.55	−0.04
	1.25				86410	22.09	86199	18.89	−0.57
	1.5				85173	27.98	83868	19.14	−1.94
	1.75				84523	21.53	83656	15.63	−2.18
	2				83027	18.38	82912	20.22	−1.46

P13	1	100	5	70	364895	155.68	361755	159.32	−0.86
	1.25				363309	160.69	360230	160.93	−0.85
	1.5				362096	163.84	359999	168.78	−0.58
	1.75				359974	157.96	356857	141.78	−0.87
	2				355624	156.57	339404	161.89	−4.56

P14	1	100	5	150	305053	164.11	300033	139.62	−1.65
	1.25				303135	141.89	296364	121.95	−2.23
	1.5				301834	139.24	295118	121.68	−2.23
	1.75				298777	139.76	294442	133.88	−1.45
	2				291740	133.99	276706	135.66	−5.15

P15	1	100	5	70	296619	124.99	258199	125.21	−12.95
	1.25				260317	137.47	254461	128.82	−2.25
	1.5				249922	115.05	247152	183.34	−1.11
	1.75				249195	132.22	244535	154.43	−1.87
	2				247529	149.44	241351	171.13	−2.50

P16	1	100	5	150	233346	120.31	223398	126.11	−4.26
	1.25				229687	129.75	220760	114.91	−3.89
	1.5				226932	127.63	218861	117.39	−3.56
	1.75				216624	137.42	214174	115.09	−1.13
	2				211223	128.79	205238	122.39	−2.83

P17	1	100	5	70	267713	134.93	265309	110.60	−0.90
	1.25				266067	132.17	262547	122.34	−1.32
	1.5				263994	130.92	260267	110.49	−1.41
	1.75				261711	116.78	259735	150.61	−0.76
	2				260804	170.99	252673	124.40	−3.12

P18	1	100	5	150	226178	124.86	224348	139.70	−0.81
	1.25				223053	127.08	219578	134.79	−1.56
	1.5				220970	115.28	218823	184.85	−0.97
	1.75				219154	158.19	216341	129.00	−1.28
	2				217751	159.37	209257	182.73	−3.90

P19	1	100	10	70	412240	135.46	409643	141.11	−0.63
	1.25				406518	139.13	403969	173.98	−0.63
	1.5				404199	137.06	401006	167.12	−0.79
	1.75				403475	136.64	400046	178.88	−0.85
	2				401608	136.54	394231	149.81	−1.84

P20	1	100	10	150	366576	105.10	364188	166.50	−0.65
	1.25				364342	123.15	362564	100.25	−0.49
	1.5				360397	153.27	358732	143.08	−0.46
	1.75				357502	158.04	356178	114.59	−0.37
	2				350419	100.43	345948	154.21	−1.28

P21	1	100	10	70	337749	113.31	334240	100.11	−1.04
	1.25				333248	114.45	330768	112.04	−0.74
	1.5				330981	127.66	329900	133.01	−0.33
	1.75				329982	143.46	325218	139.32	−1.44
	2				327911	189.02	322382	150.34	−1.69

P22	1	100	10	150	300245	112.22	297406	94.24	−0.95
	1.25				293642	127.66	291212	119.95	−0.83
	1.5				290938	186.05	287471	192.95	−1.19
	1.75				288716	183.72	285885	127.07	−0.98
	2				286473	132.29	281933	125.07	−1.58

P23	1	100	10	70	369343	127.38	364871	132.22	−1.21
	1.25				364871	152.70	359677	141.96	−1.42
	1.5				359613	147.70	355286	152.78	−1.20
	1.75				358094	155.05	354980	142.97	−0.87
	2				341610	146.96	320343	172.26	−6.23

P24	1	100	10	150	328663	124.91	299018	132.71	−9.02
	1.25				325042	125.13	295553	137.29	−9.07
	1.5				323847	156.83	291860	135.43	−9.88
	1.75				299214	135.60	288433	157.16	−3.60
	2				294706	121.22	281938	168.67	−4.33

P25	1	200	10	70	665281	829.11	653633	1026.07	−1.75
	1.25				657935	834.27	652114	1061.26	−0.88
	1.5				655818	823.79	651574	984.23	−0.65
	1.75				649604	820.10	646761	1055.81	−0.44
	2				642489	820.87	641864	1139.61	−0.10

P26	1	200	10	150	581623	611.52	580270	618.26	−0.23
	1.25				579961	608.25	569283	626.20	−1.84
	1.5				574684	604.60	536008	613.79	−6.73
	1.75				556955	621.66	535570	623.55	−3.84
	2				554052	621.92	528999	622.53	−4.52

P27	1	200	10	70	773781	793.09	662523	778.08	−14.38
	1.25				713012	819.64	655573	803.25	−8.06
	1.5				681260	804.27	642081	739.51	−5.75
	1.75				635834	770.17	632602	723.11	−0.51
	2				632061	739.14	623493	704.85	−1.36

P28	1	200	10	150	576983	666.69	555923	987.24	−3.65
	1.25				568736	675.82	546433	859.83	−3.92
	1.5				564064	674.70	543330	859.83	−3.68
	1.75				560726	914.60	535818	761.02	−4.44
	2				534830	977.03	522356	795.76	−2.33

P29	1	200	10	70	666957	790.82	636582	820.80	−4.55
	1.25				658832	832.47	633813	1119.70	−3.80
	1.5				653454	1149.63	621988	965.82	−4.82
	1.75				622078	801.89	619907	825.17	−0.35
	2				616051	863.47	608644	1080.37	−1.20

P30	1	200	10	150	542071	734.01	540384	705.36	−0.31
	1.25				525159	727.55	524172	786.56	−0.19
	1.5				521758	716.37	510933	763.03	−2.07
	1.75				518474	787.04	506479	752.31	−2.31
	2				515142	755.66	502884	698.85	−2.38