Discrete Dynamics in Nature and Society

Research Article

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

Table 3

Results of different return rates.


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

P1	0.1	20	5	70	67617	3.22	67617	2.66	0.00
	0.2				67522	3.38	67522	3.48	0.00
	0.3				67423	3.64	67423	3.14	0.00
	0.4				67568	2.73	67320	3.28	−0.37
	0.5				67293	4.69	67211	3.22	−0.12
	0.6				67094	3.26	67094	2.95	0.00
	0.7				66966	3.19	66966	2.77	0.00
	0.8				66904	3.15	66822	3.67	−0.12
	0.9				66646	2.68	66646	3.15	0.00

P2	0.1	20	5	150	42972	2.54	42972	2.87	0.00
	0.2				42969	2.43	42969	2.96	0.00
	0.3				42965	3.07	42965	2.57	0.00
	0.4				42961	3.40	42961	2.66	0.00
	0.5				42955	3.00	42955	3.18	0.00
	0.6				42948	2.63	42948	2.92	0.00
	0.7				42939	2.68	42939	3.08	0.00
	0.8				42927	2.66	42927	3.02	0.00
	0.9				42908	2.47	42908	3.04	0.00

P3	0.1	20	5	70	61544	2.70	61296	2.68	−0.40
	0.2				61175	3.14	61175	3.40	0.00
	0.3				61050	2.68	61050	2.99	0.00
	0.4				61011	3.16	60921	2.91	−0.15
	0.5				60786	2.62	60786	2.98	0.00
	0.6				60733	2.55	60644	2.81	−0.15
	0.7				60492	2.99	60492	3.23	0.00
	0.8				60325	2.87	60325	3.10	0.00
	0.9				60308	3.18	60127	3.19	−0.30

P4	0.1	20	5	150	40396	2.56	40396	2.71	0.00
	0.2				40395	2.58	40395	2.63	0.00
	0.3				40393	2.64	40393	2.94	0.00
	0.4				40390	2.68	40390	2.41	0.00
	0.5				40386	2.66	40386	3.12	0.00
	0.6				40381	2.53	40381	2.46	0.00
	0.7				40373	2.68	40373	2.66	0.00
	0.8				40363	2.46	40363	2.63	0.00
	0.9				40346	2.88	40346	2.61	0.00

P5	0.1	50	5	70	117680	36.19	116409	34.62	−1.08
	0.2				115813	32.65	115115	31.58	−0.60
	0.3				114965	30.64	114542	31.43	−0.37
	0.4				115279	30.7	114927	31.34	−0.31
	0.5				116446	26.22	115078	30.92	−1.17
	0.6				114151	30.48	114039	31.18	−0.10
	0.7				114504	31.34	114190	32.04	−0.27
	0.8				115578	28.66	114239	26.56	−1.16
	0.9				112326	31.31	112310	33.62	−0.01

P6	0.1	50	5	150	87885	20.30	87678	24.04	−0.24
	0.2				87289	23.82	86748	27.87	−0.62
	0.3				88191	23.95	87140	24.59	−1.19
	0.4				89497	20.47	86970	23.87	−2.82
	0.5				87240	21.81	86955	24.84	−0.33
	0.6				87233	24.34	86283	24.26	−1.09
	0.7				86366	24.17	86173	21.05	−0.22
	0.8				85494	22.81	84771	24.78	−0.85
	0.9				84673	23.93	84358	24.24	−0.37

P7	0.1	50	5	70	122232	26.84	121605	22.23	−0.51
	0.2				121038	26.14	120826	26.16	−0.18
	0.3				121147	26.17	120530	26.66	−0.51
	0.4				120239	26.41	119945	26.86	−0.24
	0.5				120223	26.11	119788	26.03	−0.36
	0.6				119636	26.05	119545	28.81	−0.08
	0.7				119795	25.50	119440	32.04	−0.30
	0.8				119994	26.05	119100	27.80	−0.75
	0.9				119728	25.72	118222	27.31	−1.26

P8	0.1	50	5	150	99470	26.38	99178	27.75	−0.29
	0.2				99455	25.21	99319	25.61	−0.14
	0.3				100163	28.65	98682	21.78	−1.48
	0.4				98722	25.14	98642	25.32	−0.08
	0.5				98930	25.27	98617	27.10	−0.32
	0.6				98131	24.90	98056	26.23	−0.08
	0.7				98723	25.60	97815	23.55	−0.92
	0.8				97633	25.78	97296	33.13	−0.35
	0.9				97752	25.43	96882	26.07	−0.89

P9	0.1	50	5	70	86438	25.22	86398	29.74	−0.05
	0.2				86031	22.20	85926	28.47	−0.12
	0.3				86300	25.01	85635	21.50	−0.77
	0.4				85292	21.61	85283	22.87	−0.01
	0.5				85084	24.46	84834	28.05	−0.29
	0.6				84628	23.10	84495	28.72	−0.16
	0.7				84358	24.98	84116	22.87	−0.29
	0.8				83239	21.88	83103	21.64	−0.16
	0.9				83386	22.48	82806	25.97	−0.70

P10	0.1	50	5	150	115321	25.76	115143	28.26	−0.15
	0.2				114968	26.16	114609	21.55	−0.31
	0.3				114628	27.12	114347	24.59	−0.25
	0.4				114620	26.62	113993	27.86	−0.55
	0.5				114243	25.93	113821	27.95	−0.37
	0.6				113720	26.05	113461	29.29	−0.23
	0.7				113367	22.95	113204	28.36	−0.14
	0.8				113157	26.73	112657	28.41	−0.44
	0.9				112518	32.52	111908	26.90	−0.54

P11	0.1	50	5	70	112376	26.82	111843	32.35	−0.47
	0.2				111582	25.94	111286	27.18	−0.27
	0.3				111920	23.13	111054	29.51	−0.77
	0.4				111642	24.91	110986	28.05	−0.59
	0.5				111345	23.08	110891	27.75	−0.41
	0.6				110712	26.11	110203	28.93	−0.46
	0.7				110789	25.79	109949	29.03	−0.76
	0.8				110232	25.79	109923	28.18	−0.28
	0.9				109797	24.80	109042	32.89	−0.69

P12	0.1	50	5	150	85505	24.69	85246	27.45	−0.30
	0.2				85187	24.25	85019	23.92	−0.20
	0.3				84879	24.73	84757	24.78	−0.14
	0.4				84797	28.33	84337	30.83	−0.54
	0.5				84312	25.84	83955	28.38	−0.42
	0.6				84053	26.65	83933	21.82	−0.14
	0.7				83933	26.31	83358	31.33	−0.69
	0.8				83651	26.92	82897	29.92	−0.90
	0.9				82655	23.22	82439	26.95	−0.26

P13	0.1	100	5	70	343359	189.12	341812	146.89	−0.45
	0.2				346569	187.44	343870	187.75	−0.78
	0.3				345210	169.49	342124	141.65	−0.89
	0.4				348100	180.08	345668	190.9	−0.70
	0.5				349269	159.25	343318	184.88	−1.70
	0.6				347719	182.23	343891	162.19	−1.10
	0.7				349525	182.84	342643	169.88	−1.97
	0.8				349171	160.17	341151	158.68	−2.30
	0.9				351251	182.08	349382	186.92	−0.53

P14	0.1	100	5	150	282054	135.84	281389	190.02	−0.24
	0.2				281199	128.94	279541	151.39	−0.59
	0.3				279903	155.98	279153	160.32	−0.27
	0.4				278748	161.52	277988	130.87	−0.27
	0.5				279806	152.32	278460	162.29	−0.48
	0.6				280003	188.32	279155	127.99	−0.30
	0.7				280823	126.66	278542	171.61	−0.81
	0.8				276206	136.94	275974	138.12	−0.08
	0.9				276528	157.65	275917	163.14	−0.22

P15	0.1	100	5	70	246010	156.28	245337	148.54	−0.27
	0.2				245120	175.84	244537	172.42	−0.24
	0.3				244563	154.52	243754	154.32	−0.33
	0.4				243537	154.53	243124	133.88	−0.17
	0.5				242570	120.21	241529	192.88	−0.43
	0.6				241778	171.75	241435	150.70	−0.14
	0.7				240726	153.04	240237	138.58	−0.20
	0.8				239819	149.01	239716	153.79	−0.04
	0.9				238793	145.75	238624	144.34	−0.07

P16	0.1	100	5	150	209027	131.28	208711	153.17	−0.15
	0.2				208060	149.78	207229	157.39	−0.40
	0.3				206328	167.99	205454	200.44	−0.42
	0.4				207220	154.39	205877	195.70	−0.65
	0.5				206676	163.29	205654	172.25	−0.49
	0.6				204833	137.78	204547	168.87	−0.14
	0.7				204402	137.86	204284	153.95	−0.06
	0.8				203509	173.04	203068	191.72	−0.22
	0.9				203695	153.95	201648	146.62	−1.00

P17	0.1	100	5	70	259816	195.04	258025	149.48	−0.69
	0.2				258004	164.99	256937	193.31	−0.41
	0.3				256120	124.51	256057	123.60	−0.02
	0.4				254658	130.21	254594	150.79	−0.03
	0.5				254764	133.42	253722	165.32	−0.41
	0.6				255047	155.20	252587	151.01	−0.96
	0.7				250732	153.72	249812	149.22	−0.37
	0.8				253732	182.23	249612	167.72	−1.62
	0.9				252906	168.49	249337	157.79	−1.41

P18	0.1	100	5	150	204826	145.28	204678	191.50	−0.07
	0.2				205474	172.75	204621	193.28	−0.42
	0.3				203254	167.53	202691	155.11	−0.28
	0.4				203120	148.82	201380	121.34	−0.86
	0.5				202003	122.00	201329	145.70	−0.33
	0.6				200401	145.62	199858	151.80	−0.27
	0.7				199032	147.58	198618	155.51	−0.21
	0.8				198858	153.76	197776	145.95	−0.54
	0.9				199502	134.57	197513	150.85	−1.00

P19	0.1	100	10	70	414613	171.01	401365	198.5	−3.20
	0.2				413680	164.18	400546	204.34	−3.17
	0.3				420538	167.47	399896	195.42	−4.91
	0.4				414460	154.11	394054	202.68	−4.92
	0.5				411688	158.96	395828	211.36	−3.85
	0.6				412339	162.17	394750	213.73	−4.27
	0.7				410641	163.97	394617	210.72	−3.90
	0.8				409561	181.48	394513	218.27	−3.67
	0.9				408967	178.1	394294	201.13	−3.59

P20	0.1	100	10	150	365982	113.65	362144	114.33	−1.05
	0.2				365164	111.79	361157	142.29	−1.10
	0.3				365868	117.97	349578	113.22	−4.45
	0.4				365307	145.30	349277	144.62	−4.39
	0.5				366266	115.01	348378	158.55	−4.88
	0.6				363989	151.05	348198	117.37	−4.34
	0.7				113367	22.95	113204	28.36	−0.14
	0.8				113157	26.73	112657	28.41	−0.44
	0.9				112518	32.52	111908	26.90	−0.54

P21	0.1	100	10	70	330001	132.05	323564	131.91	−1.95
	0.2				329657	155.75	322848	178.39	−2.07
	0.3				329303	166.30	322162	176.31	−2.17
	0.4				328939	160.91	321756	167.07	−2.18
	0.5				328561	167.71	321589	152.01	−2.12
	0.6				328166	166.06	321183	182.85	−2.13
	0.7				327744	132.12	321102	174.83	−2.03
	0.8				327281	133.30	320160	179.93	−2.18
	0.9				326742	134.59	319244	188.47	−2.29

P22	0.1	100	10	150	281700	140.71	278464	129.13	−1.15
	0.2				285498	140.01	278181	179.95	−2.56
	0.3				285035	128.87	277760	184.58	−2.55
	0.4				282821	157.09	277349	159.42	−1.93
	0.5				284563	129.31	277133	181.07	−2.61
	0.6				284057	152.07	276776	183.34	−2.56
	0.7				280960	129.57	276530	172.01	−1.58
	0.8				282955	157.32	276208	181.27	−2.38
	0.9				278306	132.02	273261	178.52	−1.81

P23	0.1	100	10	70	399113	125.10	375576	164.77	−5.90
	0.2				396761	146.84	371533	160.97	−6.36
	0.3				397280	168.97	360348	155.58	−9.30
	0.4				396341	139.25	347788	175.99	−12.25
	0.5				393942	143.91	346723	183.96	−11.99
	0.6				392957	153.30	344273	145.58	−12.39
	0.7				393378	159.10	325508	172.95	−17.25
	0.8				390858	130.43	325392	172.15	−16.75
	0.9				391111	140.30	322910	167.81	−17.44

P24	0.1	100	10	150	297873	126.28	296530	138.04	−0.45
	0.2				295735	139.68	294394	164.50	−0.45
	0.3				334584	138.60	292118	173.75	−12.69
	0.4				334011	152.64	288251	183.57	−13.70
	0.5				345871	130.23	287245	142.65	−16.95
	0.6				343622	150.07	286258	149.21	−16.69
	0.7				344063	132.18	285833	132.30	−16.92
	0.8				343388	151.00	285505	145.31	−16.86
	0.9				342624	161.02	276622	165.18	−19.26

P25	0.1	200	10	70	665405	1003.37	646837	1358.56	−2.79
	0.2				663368	1022.24	646011	1275.81	−2.62
	0.3				662357	840.78	645933	1052.16	−2.48
	0.4				660795	819.73	643790	900.59	−2.57
	0.5				660155	819.55	641200	1170.31	−2.87
	0.6				657577	835.74	640619	1172.54	−2.58
	0.7				655423	831.23	640582	851.98	−2.26
	0.8				654409	830.95	637338	858.12	−2.61
	0.9				653286	792.33	622908	836.45	−4.65

P26	0.1	200	10	150	573667	753.47	553421	1069.24	−3.53
	0.2				570023	765.06	551891	1297.82	−3.18
	0.3				569666	776.15	537807	1069.80	−5.59
	0.4				567939	797.95	535782	1163.39	−5.66
	0.5				564777	900.56	535225	1108.99	−5.23
	0.6				564413	887.18	535083	1195.13	−5.20
	0.7				562167	849.13	531505	1236.66	−5.45
	0.8				560098	799.95	514584	1157.03	−8.13
	0.9				557554	864.90	513652	1023.90	−7.87

P27	0.1	200	10	70	661785	1384.45	631700	1228.42	−4.55
	0.2				662602	1317.90	630853	969.39	−4.79
	0.3				647333	1144.41	630036	1119.12	−2.67
	0.4				647377	1238.22	625782	1060.19	−3.34
	0.5				647837	955.81	625659	1159.76	−3.42
	0.6				651234	972.11	624175	1104.26	−4.16
	0.7				643657	994.18	623635	1203.08	−3.11
	0.8				648507	1007.51	618926	1251.66	−4.56
	0.9				640631	974.55	617253	1352.17	−3.65

P28	0.1	200	10	150	560151	1039.68	554838	901.12	−0.95
	0.2				567066	805.96	552250	1205.61	−2.61
	0.3				565177	1107.27	551150	1429.66	−2.48
	0.4				551554	1150.46	546455	1283.46	−0.92
	0.5				550006	845.09	546211	901.12	−0.69
	0.6				548151	679.59	543161	850.63	−0.91
	0.7				546181	835.08	539990	965.50	−1.13
	0.8				545049	869.30	538293	1444.22	−1.24
	0.9				543203	937.76	522946	1065.27	−3.73

P29	0.1	200	10	70	621423	1031.98	619749	810.58	−0.27
	0.2				624921	755.35	618833	817.09	−0.97
	0.3				620040	711.57	617782	991.29	−0.36
	0.4				617601	867.88	615738	958.45	−0.30
	0.5				623408	1135.24	614301	1168.53	−1.46
	0.6				614480	799.56	612048	1337.13	−0.40
	0.7				612960	1095.73	611365	948.58	−0.26
	0.8				611261	1126.74	609791	969.75	−0.24
	0.9				609581	846.60	608927	712.33	−0.11

P30	0.1	200	10	150	522946	935.56	520709	1214.20	−0.43
	0.2				521952	696.92	518710	871.10	−0.62
	0.3				520505	730.31	516812	1182.22	−0.71
	0.4				519262	780.89	516352	1289.81	−0.56
	0.5				517999	707.29	516019	1335.97	−0.38
	0.6				516930	1052.88	515388	1212.71	−0.30
	0.7				515604	954.61	513938	1054.47	−0.32
	0.8				514221	687.26	511705	1073.18	−0.49
	0.9				497335	1020.75	492080	1113.48	−1.06