Modeling the logistics design of a multi-commodity industry

Farias, Everton da Silveira; Borenstein, Denis

doi:10.1590/0104-530X842-16

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Articles • Gest. Prod. 24 (1) • Jan-Apr 2017 • https://doi.org/10.1590/0104-530X842-16 copy

Modeling the logistics design of a multi-commodity industry

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract:

This paper presents two different mathematical formulations for the Supply Chain Network Design of a company responsible for producing and distributing multi-commodity products. Investments in a new manufacturing plant required the readjustment of the company’s logistics project, with a necessary re-structuring of the raw materials and finished product flows and the possibility of opening new distribution centers (DCs). The supply chain was modeled using a formulation in mixed linear integer programming, in which the facilities are represented by nodes and the links by the arcs. The computer implementations were performed using OPL and results obtained by CPLEX© solver. The implemented models was validated by a series of computational experiments. We incorporated studies to identify the market demands (market shares) and transportation costs in order to enable the application of models to the company's problem. The application of the models allowed several decisions concerning the initial project of the company to be performed by the project team.

Keywords:
Logistics project; Multicommodity; Supply chain network design; Single-source; Operational research

Instances	Suppliers	Raw Materials	Plants	DCs	Products (Groups)	Customer Zones	Quantity of Products	Arc-based model			Single-source model
Instances	Suppliers	Raw Materials	Plants	DCs	Products (Groups)	Customer Zones	Quantity of Products	DCs opened	Cost $	Time (s)	DCs opened	Cost $	Time (s)	% var. Cost $
Instance 1	5	5	3	10	5	150	1,000,000	7	16,616,300	2.80	7	16,970,300	2.07	2.13%
Instance 2	5	5	3	20	5	150	1,000,000	9	16,165,200	7.17	9	16,541,500	2.42	2.33%
Instancea 3	5	5	3	30	5	150	1,000,000	3	17,249,000	10.81	4	17,484,800	4.06	1.37%
Instance 4	5	5	3	40	5	150	1,000,000	12	15,003,100	32.34	13	15,453,300	7.65	3.00%
Instance 5	5	5	3	50	5	150	1,000,000	10	14,666,600	81.14	10	15,051,100	4.86	2.62%
Instance 6	5	5	3	10	10	150	1,575,000	4	29,129,000	4.69	4	31,098,000	2.45	6.76%
Instance 7	5	5	3	10	50	150	1,576,200	8	27,078,168	62.36	8	30,755,440	3.97	13.58%
Instance 8	5	5	3	10	100	150	1,583,100	7	25,788,806	152.03	7	29,169,246	9.61	13.11%
Instance 9	5	5	3	20	10	150	1,575,000	12	24,636,000	8.21	12	28,816,500	3.93	16.97%
Instance 10	5	5	3	20	50	150	1,576,200	14	25,683,340	138.60	13	30,880,456	10.97	20.24%
Instance 11	5	5	3	20	100	150	1,583,100	13	26,051,168	1062.33	13	31,226,678	39.62	19.87%
Instance 12	5	5	3	30	10	150	1,575,000	15	23,423,500	37.57	14	27,681,500	4.39	18.18%
Instance 13	5	5	3	30	50	150	1,576,200	15	24,571,496	945.34	13	29,728,252	13.54	20.99%
Instance 14	5	5	3	30	100	150	1,583,100	Out	of	Memory	13	27,813,526	36.44	-
Instance 15	5	5	3	40	10	150	1,575,000	19	24,047,600	127.76	17	28,525,950	10.74	18.62%
Instance 16	5	5	3	40	50	150	1,576,200	16	24,767,588	2687.56	14	29,947,862	15.03	20.92%
Instance 17	5	5	3	40	100	150	1,583,100	Out	of	Memory	15	28,943,138	54.42	-
Instance 18	5	5	3	50	10	150	1,575,000	15	23,248,000	177.77	14	27,532,500	4.96	18.43%
Instance 19	5	5	3	50	50	150	1,576,200	15	23,067,188	3743.47	14	27,763,300	17.45	20.36%
Instance 20	5	5	3	50	100	150	1,583,100	Out	of	Memory	15	27,935,264	38.47	-
Instance 21	5	5	3	20	10	150	3,000,600	18	48,963,496	6.79	15	60,940,660	7.12	24.46%
Instance 22	5	5	3	20	50	150	3,152,400	20	52,678,632	72.15	18	63,771,168	13.23	21.06%

Market	Commodity 1		Commodity 2		Commodity 3		TOTAL
Market	Areas	Demands	Areas	Demands	Areas	Demands	Common areas	Demands
Retail-market	181	556,951	107	36,180,162	105	6,781,554	229	43,518,667
Original-market	8	658,996	16	6,366,042	8	3,405,523	32	10,430,561
Total	189	1,215,947	123	42,546,204	113	10,187,077	261	53,949,228

Scenarios	Market	Commodity 1	Commodity 2	Commodity 3
Market Share 1	Retail-market	10%	10%	10%
	Original-market	10%	10%	10%
	Original State	10%	10%	10%
Market Share 2	Retail-market	20%	10%	15%
	Original-market	20%	10%	15%
	Original State	25%	10%	15%
Market Share 3	Retail-market	20%	10%	15%
	Original-market	20%	10%	15%
	Original State	35%	10%	15%

Scenario	Model (approach)	Demand (products)	DCs (open)	Total Cost $ (operation)	Time (seconds)	Iterations
Market share 1	Single-source 1	5,391,881	1, 2 and 5	$56,882,604	32.32	4,868
	Single-source 2	5,391,881	1 and 5	$66,020,663	10.32	767
	Arc-based 1	5,391,881	1, 2 and 5	$55,678,012	13.04	656
	Arc-based 2	5,391,882	1 e 5	$62,553,128	10.22	1,044
Market share 2	Single-source 3	6,037,604	1, 2 and 5	$68,474,638	13.05	1,016
	Single-source 4	6,037,604	1 and 5	$83,386,676	8.30	874
	Arc-based 3	6,037,604	1, 2 and 5	$65,171,209	11.47	635
	Arc-based 4	6,037,604	1 and 5	$78,109,464	8.35	1,139
Market share 3	Single-source 5	6,070,660	1 and 5	$83,920,572	6.41	15
	Single-source 6	6,070,660	3 and 5	$93,663,497	6.10	21
	Single-source 7	6,070,660	4 and 5	$104,956,316	5.57	12
	Arc-based 5	6,070,660	1 and 5	$80,031,564	6.05	450
	Arc-based 6	6,070,660	3 and 5	$88,414,182	6.14	457
	Arc-based 7	6,070,660	4 and 5	$95,278,179	6.12	487

Universidade Federal de São Carlos Departamento de Engenharia de Produção , Caixa Postal 676 , 13.565-905 São Carlos SP Brazil, Tel.: +55 16 3351 8471 - São Carlos - SP - Brazil
E-mail: gp@dep.ufscar.br

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