BI-LEVEL MODEL: NEW APPROACH TO DYNAMIC VEHICLE ALLOCATION IN SUPPLY CHAIN

Neves, Júlio César Silva; Lucas, Solange Fortuna; Neves, Gisele Campos; Weissmann, José

doi:10.1590/0101-7438.2023.043.00266695

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ARTICLES • Pesqui. Oper. 43 • 2023 • https://doi.org/10.1590/0101-7438.2023.043.00266695 copy

BI-LEVEL MODEL: NEW APPROACH TO DYNAMIC VEHICLE ALLOCATION IN SUPPLY CHAIN

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

There are different decision levels with distinct decision makers in a decentralized Supply Chain, for example, shippers and carriers. Nevertheless, most studies are conducted considering only one decision-making level. The carrier is the decision-making agent in Dynamic Vehicle Allocation (DVA) problem and allocates vehicles to maximize its profit, usually delaying shipping. It is necessary to respect the partnership principle. This paper presents the DVA problem using bi-level programming. The shipper’s objective is to minimize shipping delays, while the carrier’s objective is to maximize profits. The exact algorithm is used to solve the Bi-level DVA problem. The results show potential applications in logistics, decreasing both transportation delays and costs when synchronizing carrier’s and shippers’ decisions.

Keywords:
supply chain management; transportation; mixed integer linear programming; bi-level optimization; dynamic vehicle allocation; multi-period

Ex.	Region	Cargoes (Period)
Ex.	Region	1	2	3	4
2	1	0	3(3), 3(4),1(5),1(6)	2(2), 2(3),3(4), 3(5)	2(3),2(5)
	2	3(1),1(4),2(5)	0	3(1), 2(2), 3(5)	3(2),2(4),1(5),2(6)
	3	1(2),2(4),1(5),2(6)	2 (1),3(2),3(3), 2(5)	0	1(3), 2 (4), 3(6)
	4	2(2), 2(3),3(6)	1(3), 3(4),2(6)	3(1), 2(2), 1 (4)	0
3	1	0	3(2),2(3),1(4),2(5)	2(2), 2(3),3(4),1(6)	3(5),2(6)
	2	3(1),2(3),3(5)	0	2(1),2(2)	1(4),1(6)
	3	2(1),2(2),1(3),2(6)	1(2),3(3), 1(5),2(6)	0	1(3),1(4),2(5)
	4	1(3),1(5),2(6)	1(3),1(5),2(6)	1(2),3(3), 1(5),2(6)	0
4	1	0	1(3),3(5)	3(1), 2(5),1(6)	1(2),2(3),3(4),1(5)
	2	1(3),3(4),1(5)	0	0	2(1),2(4)
	3	1 (2),1(3), 1(5),2(6)	2(2),1(3),3(4),1(5)	3(4),1(5)	1(3), 1(5),2(6)
	4	1(1),2(3), 1(6)	3(1),1(3),1(6)	3(1),3(2),2(3),3(5)	0
5	1	0	2(2), 3(4)	3(1),2(6)	3(1),1(3)
	2	3(3),3(4),1(5)	0	1(4),1(5)	1(2),2(4),1(5),2(6)
	3	1 (2),1(3), 1(6)	1(3), 3(5),3(6)	0	1(1), 3(4)
	4	3(1),1(3),2(4),2(6)	1(2),3(3),1(4),1(5)	3(1),3(3),2(4),3(6)	0
6	1	0	3(1), 2(2), 2(3),2(6)	3(1),3(2),1(4),3(5)	2(1),2(6)
	2	3(1), 2(2), 3(5),3(6)	0	1(1),1(2), 1(4),2(5)	2(1),3(4)
	3	1 (2),3(3),3(5),1(6)	2(1), 1(3),3(4),2(6)	0	1(2),2(4), 1(5),2(6)
	4	2(1), 2(3),3(4),1(5)	3(1),1(3),2(4),1(5),3(6)	3(1),1(4),2(5),2(6)	0
7	1	0	1(3),3(4), 2(6)	1(3),3(4),1(5)	1(1),1(2),3(5)
	2	3(2),1(3),3(5),1(6)	0	1(1), 1(4), 1(6)	3(2),1(3),2(5),2(6)
	3	1(1),1(2),1(3)	1(1),1(2),1(3),3(4),1(5)	0	1 (2),1(3), 3(4)
	4	1(2),2(4),3(5),2(6)	1(2),2(5),3(6)	1(3),3(5),1(6)	0
8	1	0	l (1),3(2),3(5)	3(1),3(2),3(3),2(5)	2(1),3(2),2(3),2(6)
	2	3(3), 3(4),1(5),1(6)	0	l (2),3(4),3(5)	3(1),2(3),3(4),3(6)
	3	1(1),2(4),1(5)	2(1),1(3),1(4),1(6)	0	2 (2),l (4), 2 (5)
	4	2(2),3(3),l(4)	1(2),2(3),2(5),3(6)	3(2),1(3),3(4),2(6)	0
9	1	0	1(1),2(3),1(4),1(5),1(6)	3(1),3(2),3(3),2(5)	2(1),1(2),2(3),3(4),1(6)
	2	3(1),3(2),2(3),3(6)	0	1(2),1(3),3(4),1(5), 2(6)	3(2), 2(6)
	3	1 (2),1(3),3(4),1(5)	3 (2),l (4), 2 (6)	0	2 (3),l (4), 3 (5)
	4	3(1), 2(2), 3(4),3(5)	2(1),3(2),1(3),1(5)	3(2),1(3),3(4),2(6)	0

Example	Profit			Delay			Lost			Fleet
Example	ADV	Bi-level	%	ADV	Bi-level	%	ADV	Bi-level	%	Fleet
2	15	1360	1340	-1%	32	25	-22%	6	3	-50%
	14	1340	1330	-1%	34	31	-9%	5	5	0
	13	1300	1290	-1%	41	38	-7%	9	9	0
	12	1270	1270	0	1270	47	-2%	12	12	0
	11	1220	1220	0	63	63	0	17	17	0
	10	1150	1150	0	84	84	0	23	23	0
3	15	960	920	-4%	23	4	-83%	1	1	0
	14	950	920	-3%	26	7	-73%	2	2	0
	13	940	910	-3%	24	10	-58%	3	3	0
	12	930	900	-3%	25	14	-44%	4	4	0
	11	910	840	-8%	26	14	-46%	6	6	0
	10	870	850	-2%	37	24	-35%	10	9	-10%
4	15	990	940	-5%	24	4	-83%	0	0	0
	14	990	930	-6%	23	4	-83%	0	0	0
	13	990	910	-8%	22	5	-77%	0	0	0
	12	980	860	-12%	23	8	-65%	0	0	0
	11	970	940	-3%	27	16	-41%	2	1	-50%
	10	940	940	0	39	29	-26%	5	4	-20%
5	15	1070	990	-7%	28	8	-71%	0	1	0
	14	1060	1050	-1%	28	17	-39%	1	2	100%
	13	1050	980	-7%	29	13	-55%	2	3	50%
	12	1040	1020	-2%	27	20	-26%	3	3	0
	11	1010	1010	0	26	24	-8%	5	5	0
	10	980	960	-2%	35	29	-17%	9	8	-11%
6	15	1070	1060	-1%	35	18	-49%	8	6	-25%
	14	1040	1010	-3%	41	20	-51%	11	8	-27%
	13	1010	980	-3%	42	22	-48%	12	9	-25%
	12	980	950	-3%	45	28	-38%	15	12	-20%
	11	950	920	-3%	54	34	-37%	18	15	-17%
	10	900	870	-3%	51	42	-18%	20	19	-5%
7	15	1070	1060	-1%	35	18	-49%	8	6	-25%
	14	1040	1010	-3%	41	20	-51%	11	8	-27%
	13	1010	980	-3%	42	22	-48%	13	9	-31%
	12	980	950	-3%	45	28	-38%	15	12	-20%
	11	950	920	-3%	54	34	-37%	18	15	-17%
	10	900	880	-2%	51	42	-18%	20	19	-5%
8	15	1230	1150	-7%	47	25	-47%	6	5	-17%
	14	1220	1160	-5%	51	33	-35%	8	7	-13%
	13	1200	1150	-4%	51	40	-22%	10	10	0
	12	1160	1130	-3%	59	47	-20%	14	13	-7%
	11	1110	1100	-1%	65	55	-15%	18	16	-11%
	10	1060	1060	0	77	70	-9%	22	21	-5%
9	15	1490	1480	-1%	36	29	-19%	4	4	0
	14	1470	1470	0	40	39	-3%	7	7	0
	13	1420	1420	0	55	54	-2%	12	12	0
	12	1370	1370	0	70	70	0%	17	17	0
	11	1310	1310	0	91	91	0%	23	23	0
	10	1250	1250	0	112	112	0%	29	29	0

	Ananthapur	Chittoor	Ichapur	Khammam	Srikakulam
Ananthapur	0	1 - 1.8	2 - 3.6	2 - 3.6	2 - 3.6
Chittoor	1 - 1.8	0	2 - 3.6	2 - 3.6	2 - 3.6
Ichapur	2 - 3.6	2 - 3.6	0	2	1 - 1.8
Khammam	2 - 3.6	2 - 3.6	2 - 3.6	0	2 - 3.6
Srikakulam	2 - 3.6	2 - 3.6	1 - 1.8	2 - 3.6	0

Ex.	Region	Cargoes (Period)
Ex.	Region	1	2	3	4	5
11	1	0	1(2), 2(3), 3(4),1(5)	2(1),1(2),2(3),2(4),3(5)	2(4)	3(2), 1(3), 1(4), 3(5)
	2	2(1), 1(2), 1(3), 1(4)	0	(1)	2(1)	1(2), 2(5)
	3			0	2(5)	1(1), 1(3),
	4	2(1), 2(2),	1(3),	1(1), 3(3),	0	1(1), 2(2), 1(3), 1(5)
	5	1(1), 2(3), 3(4)	1(1), 1(2), 1(4), 2(5)	1(1), 1(2), 1(4), 1(5)	2(3)	0
12	1	0	3(1)	1(1), 2(2), 2(4)	3(1), 3(2), 3(3)	3(1), 3(3)
	2	2(3), 2(4)	0	2(4)	1(1), 3(3), 2(4), 2(5)	1(1), 3(3), 1(5)
	3	3(5)	1(3)	0	3(2)	3(2), 3(2), 3(5)
	4	2(5)	1(1), 1(2), 2(4)	3(1), 1(3), 3(4)	0	3(1), 1(5)
	5	1(1), 3(3), 2(4), 2(5)	3(2), 3(4), 3(5)	3(4)	1(3)	0
13	1	0	3(1), 3(2), 1(4)	3(2), 2(3)	1(1), 2(2), 1(4)	3(2), 3(3), 3(5)
	2	3(2)	0	3(4), 3(5)	1(1), 2(3)	3(2), 2(4), 2(4), 2(5)
	3	2(1), 1(3), 2(4), 1(5)	2(1), 3(3), 2(4), 1(5)	0	3(3)	2(2)
	4	3(3), 2(4), 2(5)	2(1), 1(3), 1(4), 2(5)	2(5)	0	1(1), 2(2), 2(4)
	5	3(2), 3(5)	1(2), 1(4)	2(3), 2(5)	2(1), 3(2), 1(4), 2(5)	0
14	1	0	2(2), 3(3), 1(5)	3(2), 1(5)	3(1), 3(4), 3(5)	1(2), 1(3), 1(4)
	2	1(2), 3(3), 3(5)	0	2(1), 3(4), 2(5)	2(3), 3(5)	1(2), 1(3), 1(5)
	3	1(3), 1(4)	1(2), 2(3), 2(4)	0	3(4), 1(5)	2(2), 3(5)
	4	2(1),3(2),2(3),3(4),3(5)	3(2), 3(3), 1(4)	2(1)	0	1(1), 1(4), 3(5)
	5	2(1), 3(2), 1(5)	3(2), 3(4)	2(2), 1(3), 2(5)	1(1), 2(1), 1(4), 3(5)	0
15	1	0	3(1), 3(2), 1(4)	3(2), 2(3)	1(1), 2(2), 1(4)	3(2), 3(3), 3(5)
	2	3(2), 1(3)		3(4), 3(5)	1(1), 2(3)	3(2), 2(4), 2(5)
	3	2(1), 1(3), 2(4), 1(5)	2(1), 3(3), 2(4), 1(5)	0	3(3)	2(2)
	4	3(3), 2(5)	2(1), 1(4), 2(5)	2(5)	0	1(1), 2(2), 2(4)
	5	3(2), 3(5)	1(2), 2(3), 1(4)	2(5)	2(1), 3(2), 1(4), 2(5)	0

Example	Fleet	Profit			Delay			Lost
Example	Fleet	ADV	ADVBL	%	ADV	ADVBL	%	ADV	ADVBL	%
11	20	195.6	180.4	-7.77%	68	41	-39.71%	17	15	-11.76%
	19	189.4	176.8	-6.65%	74	46	-37.84%	19	16	-15.79%
	18	182.8	173.2	-5.25%	71	51	-28.17%	20	17	-15.00%
	17	176	167.8	-4.66%	72	57	-20.83%	20	19	-5.00%
	16	168.6	161.2	-4.39%	76	63	-17.11%	21	20	-4.76%
	15	160	153.4	-4.13%	79	69	-12.66%	24	23	-4.17%
12	20	233.4	230.2	-1.37%	136	115	-15.44%	36	31	-13.89%
	19	224.2	219.4	-2.14%	140	123	-12.14%	38	34	-10.53%
	18	220.8	214.8	-2.72%	143	132	-7.69%	37	35	-5.41%
	17	210.4	205.8	-2.19%	149	141	-5.37%	40	38	-5.00%
	16	202	195	-3.47%	155	150	-3.23%	41	41	0.00%
	15	191.2	184.2	-3.66%	168	159	-5.36%	45	44	-2.22%
13	20	240	232.2	-3.25%	109	100	-8.26%	27	29	7.41%
	19	230.8	222.4	-3.64%	113	107	-5.31%	29	32	10.34%
	18	221.2	211.6	-4.34%	118	114	-3.39%	32	35	9.38%
	17	211.6	200.8	-5.10%	125	121	-3.20%	36	38	5.56%
	16	200.8	188.4	-6.18%	134	129	-3.73%	39	42	7.69%
	15	190	177.6	-6.53%	146	138	-5.48%	43	45	4.65%
14	20	222	215.4	-2.97%	133	116	-12.78%	42	42	0.00%
	19	212.8	195.2	-8.27%	139	122	-12.23%	45	49	8.89%
	18	203.6	194.2	-4.62%	141	129	-8.51%	46	49	6.52%
	17	194.4	186	-4.32%	145	136	-6.21%	48	51	6.25%
	16	185.2	176.2	-4.86%	153	143	-6.54%	51	54	5.88%
	15	175.6	166.4	-5.24%	161	150	-6.83%	56	57	1.79%
15	20	240	232.2	-3.25%	109	100	-8.26%	27	29	7.41%
	19	230.8	222.4	-3.64%	113	107	-5.31%	29	32	10.34%
	18	221.2	211.6	-4.34%	118	114	-3.39%	32	35	9.38%
	17	211.6	200.8	-5.10%	125	121	-3.20%	36	38	5.56%
	16	200.8	188.4	-6.18%	134	129	-3.73%	39	42	7.69%
	15	190	177.6	-6.53%	146	138	-5.48%	43	45	4.65%

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