Inventory policy using the Multi-Echelon Closed-Loop Supply Chain in the Acquisition Market

Sassaki, Rafael Pereira; Rodríguez, Elias Carlos Aguirre; Marins, Fernando Augusto Silva; Chaves, Antônio Augusto

doi:10.1590/1806-9649-2024v31e0624

person Rafael Pereira Sassaki

conceptualization · theoretical-methodological approach · theoretical review · data collection coordination · data analysis · writing and final revision

schoolUniversidade Estadual Paulista "Júlio de Mesquita Filho" - UNESP, Faculdade de Engenharia e Ciências, Guaratinguetá, SP, Brasil. E-mail: rafaelpsgv@gmail.com; elias.aguirre@unesp.br; fernando.marins@unesp.br

0009-0009-6447-9843

person Elias Carlos Aguirre Rodríguez

conceptualization · theoretical-methodological approachwriting and final

schoolUniversidade Estadual Paulista "Júlio de Mesquita Filho" - UNESP, Faculdade de Engenharia e Ciências, Guaratinguetá, SP, Brasil. E-mail: rafaelpsgv@gmail.com; elias.aguirre@unesp.br; fernando.marins@unesp.br

0000-0003-1120-1708

person Fernando Augusto Silva Marins

conceptualization · theoretical-methodological approachtheoretical review · data collection coordination · data analysis · writing and final revision

schoolUniversidade Estadual Paulista "Júlio de Mesquita Filho" - UNESP, Faculdade de Engenharia e Ciências, Guaratinguetá, SP, Brasil. E-mail: rafaelpsgv@gmail.com; elias.aguirre@unesp.br; fernando.marins@unesp.br

0000-0001-6510-9187

person Antônio Augusto Chaves

conceptualizationtheoretical-methodological approach · data collection coordination · data analysis · writing and final revision

schoolUniversidade Federal de São Paulo - UNIFESP, Instituto de Ciência e Tecnologia, São José dos Campos, SP, Brasil. E-mail: antonio.chaves@unifesp.br

0000-0001-5767-6798

Recovery Systems	Definition
Reused	No components or materials are replaced
Repair	Fix or replace a few slightly damaged parts of the product
Remanufacturing	Products are completely disassembled and parts in usable condition are cleaned, refurbished and placed in repaired inventory

Source	Keywords	NP	NC
Scopus	Inventory Control	6,890	142,896
	Inventory Management	4,461	75,341
	Inventory policy	1,146	20,634
	Inventory Control and closed-loop supply chain	81	2,039
	Inventory Management and closed-loop supply chain	40	1,118
	Inventory Policy and closed-loop supply chain	15	292
	Inventory Control and Multi-echelon	239	5,591
WOS	Inventory Control	2,790
	Inventory Management	3,805
	Inventory policy	661
	Inventory Control and closed-loop supply chain	51
	Inventory Management and closed-loop supply chain	46
	Inventory Policy and closed-loop supply chain	8
	Inventory Control and Multi-echelon	87

$z_{11}$	${C B}_{11}$	${C F}_{11}$	${C S}_{11}$	Cost at CDC
85%	R$ 57,826	R$ 110,814	R$ 14,515	R$ 183,156
90%	R$ 59,015	R$ 110,814	R$ 9,677	R$ 179,506
95%	R$ 60,778	R$ 110,814	R$ 4,838	R$ 176,430
99%	R$ 64,082	R$ 110,814	R$ 968	R$ 175,864

Quantity to be produced	Distribution Center	Inventory composition	Lead time	Production deviation
195,864	DC1	DC1	2	0.3
102,526		Repair Center 1	20	8.0
131,099		Supplier 1	5	1.0
43,940		Repair Center 2	15	5.0
14,567		Supplier 2	3	1.0

	%	D.O.A.
	%	5.0%	10.0%	15.0%
Installation Failure	10.0%	R$13,640,576	R$13,680,767	R$13,721,721
	15.0%	R$13,715,222	R$13,757,240	R$13,800,055
	20.0%	R$13,789,868	R$13,833,712	R$13,878,389

Indicators/States in Brazil	AC	AL	AM	AP	BA
Technology	1	1	1	1	1
Daily Demand	4.73	18.90	4.73	4.73	108.68
Demand Deviation	1.32	6.43	1.04	0.95	28.26
CDC Capacity	255	340	85	170	1,445
Lead Time - LT	10	6	3	10	5
LT Deviation	2.00	0.78	0.60	1.70	0.80
factor k	2.03	2.24	2.21	2.09	2.24
Periodic Check	5	5	5	5	5
D.O.A.	5%	5%	5%	5%	5%
Installation Failure	20%	20%	20%	20%	20%
Safety Inventory	26	59	9	22	298
Cycle Inventory	24	95	24	24	543
Inventory at CDC	50	154	33	46	841
Inventory in Transit	47	113	14	47	543
Target Inventory at CDC	97	267	47	93	1,385
Annual Cost - POS devices	R$19,425	R$53,471	R$9,407	R$18,660	R$276,905
Quantity - Transportation	1,217	4,822	1,200	1,213	27,684
Annual Cost of Freight	R$21,247	R$32,938	R$6,995	R$17,861	R$183,524
Shortage Cost	R$592	R$1,002	R$210	R$463	R$5,329
Total Cost	R$41,264	R$87,412	R$16,612	R$36,985	R$465,759

States in Brazil/Indicators	k	Annual Cost	Annual Freight Cost	Shortage Cost
AC	2.0315	47.1%	51.5%	1.4%
AL	2.2444	61.2%	37.7%	1.1%
AM	2.2125	56.6%	42.1%	1.3%
AP	2.0887	50.5%	48.3%	1.3%
BA	2.2352	59.5%	39.4%	1.1%

Month	DC	Repair Center	Producer	$Y_{p j}$ (days)	$Y_{p i}$ (days)	Finished Product Target Inventory (days)
M0	39%	18%	43%	5.60	9.67	15.27
M+1	41%	27%	32%	6.75	9.67	16.41
M+2	68%	32%	0%	6.78	9.67	16.45
M+3	66%	34%	0%	7.08	9.67	16.74
M+4	46%	48%	5%	9.53	9.67	19.20
M+5	43%	45%	12%	9.15	9.67	18.82
M+6	16%	16%	68%	5.95	9.67	15.62
M+7	45%	46%	9%	9.25	9.67	18.92
M+8	44%	46%	9%	9.33	9.67	18.99
M+9	43%	31%	27%	7.22	9.67	16.89
M+10	48%	25%	27%	6.40	9.67	16.06
M+11	38%	22%	40%	6.12	9.67	15.79

		Representativeness of the repair centers
		0.0%	3.0%	6.0%	9.0%	12.0%	15.0%	18.0%	21.0%	24.0%	27.0%	30.0%	33.0%
DC	67.0%	2.56	2.95	3.35	3.75	4.15	4.55	4.95	5.36	5.76	6.16	6.57	6.97
	64.0%	2.63	3.02	3.42	3.82	4.22	4.62	5.03	5.43	5.83	6.23	6.64	7.04
	61.0%	2.70	3.09	3.49	3.89	4.29	4.69	5.10	550	5,90	6.31	6.71	7.11
	58.0%	2.77	3.16	3.56	3.96	4.36	4.76	5.17	5,57	5.97	6.38	6.78	7.18
	55.0%	2.84	3.23	3.63	4.03	4.43	4.83	5.24	5,64	6.04	6.45	6.85	7.25
	52.0%	2.91	3.30	3.70	4.10	4.50	4.91	5.31	5.71	6.11	6.52	6.92	7.33
	49.0%	2.98	3.37	3.77	4.17	4.57	4.98	5.38	5.78	6.18	6.59	6.99	7.40
	46.0%	3.05	3.44	3.84	4.24	4.64	5.05	5.45	5.85	6.26	6.66	7.06	7.47
	43.0%	3.12	3.51	3.91	4.31	4.71	5.12	5.52	5.92	6.33	6.73	7.13	7.54
	40.0%	3.18	3.58	3.98	4.38	4.79	5.19	5.59	5.99	6.40	6.80	7.20	7.61
	37.0%	3.25	3.65	4.05	4.45	4.86	5.26	5.66	6.06	6.47	6.87	7.28	7.68
	34.0%	3.32	3.72	4.12	4.52	4.93	5.33	5.73	6.14	6.54	6.94	7.35	7.75

\min \sum_{p \in P} \sum_{i ϵ I} {{(C B}_{p i} + C F}_{p i} + {C S}_{p i}) + \sum_{p ϵ P} \sum_{r ϵ R} \sum_{j ϵ J} \sum_{f ϵ F} ({C R}_{j} w_{p j}) + ({C L}_{j r} w_{p r}) + ({C A}_{p f} w_{p f})

\sum_{p \in P} (w_{p j} + w_{p r} + w_{p f}) \geq \sum_{i \in I} \sum_{j \in J} {(Y}_{p j} {+ Y}_{p i} - E_{p j} - E_{p i} + {((d}_{p i} . 30) (1 + α_{p i}))) j ϵ J, r ϵ R, f ϵ F, i ϵ I

S_{p i} = z_{p i} . \sqrt{L_{i} {σ_{p i}}^{2} + {(d_{p i} . (1 + α_{p i}))}^{2} . {σ_{i}}^{2}} . (1 + λ_{p i}) i ϵ I, p ϵ P

L_{j p} = \frac{\sum_{j \in J} L_{p j} w_{p j}}{\sum_{j \in J} w_{p j}} + \frac{\sum_{r \in R} L_{p r} w_{p r}}{\sum_{r \in R} w_{p r}} + \frac{\sum_{f \in F} L_{p f} w_{p f}}{\sum_{f \in F} w_{p f}} p ϵ P

σ_{j p} = \frac{\sum_{j \in J} σ_{p j} w_{p j}}{\sum_{j \in J} w_{p j}} + \frac{\sum_{r \in R} σ_{p r} w_{p r}}{\sum_{r \in R} w_{p r}} + \frac{\sum_{f \in F} σ_{p f} w_{p f}}{\sum_{f \in F} w_{p f}} p ϵ P

[1] Source: Adapted from Dev et al. (2017).

Inventory policy using the Multi-Echelon Closed-Loop Supply Chain in the Acquisition Market

Política de estoque utilizando a Cadeia de Suprimentos Multinível Fechada no Mercado de Aquisição

Abstract