Integrated recycling-integrated production - distribution planning for decentralized closed-loop supply chain

Yi Jing; Wenchuan Li

doi:10.3934/jimo.2017058

Article Contents

2018, Volume 14, Issue 2: 511-539. Doi: 10.3934/jimo.2017058

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Integrated recycling-integrated production - distribution planning for decentralized closed-loop supply chain

Yi Jing^1, , and
Wenchuan Li^2,

1.
College of Management, Chongqing University of Technology, NO.69, Hongguang Road, Banan District, Chongqing 400054, China
2.
School of Economics and Management, Nanchang Hangkong University, NO.696, Fenghenan Road, Honggutan District, Nanchang 330063, China

* Corresponding authorr: Yi Jing
* Corresponding authorr: Yi Jing

Received: April 30, 2015

Early access: May 2017

Published: March 2018

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Abstract

Integrated integrated production - distribution planning in traditional forward supply chain has attracted a lot of attention in recent years and its economic advantages are particularly noticeable. However, for closed-loop supply chain, recycling and remanufacturing processes should be taken further into account to the integrated planning. In this paper, we address a planning problem of a multi - echelon decentralized closed-loop supply chain system, which consists of a joint recycling center, multiple manufacturing/remanufacturing factories and multiple distributors decentralized to different regions. For this problem, an integrated recycling-integrated production - distribution multi - level planning model is developed, which considers material flows and decision interactions among members at different echelons in the system, as well as their own operation objectives. And the local interests of members at every echelon would be balanced in order to coordinate the operation of the whole system. According to the characteristics of the planning model, the solution approach is designed by hierarchical iteration strategy based on Self-Adaptive Genetic Algorithm (SAGA). Hierarchical iteration processes, in which SAGA is used to solve every single level model, are corresponding to repeated negotiation behaviors among members at different echelons in closed-loop supply chain. Finally, a numerical example is suggested to demonstrate the applicability and effectiveness of the proposed model and solution approach.

Keywords:

Recycling-production-distribution planning,
closed-loop supply chain,
multi-level program,
SAGA,
hierarchical iteration.

Mathematics Subject Classification: Primary: 90B50; Secondary: 90C10.

Citation:

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Figure 1. Diagrammatic sketch for the two - point crossover

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Figure 2. Diagrammatic sketch for the inverted sequence mutation

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Figure 3. The changes of computational results with the values of $M$ and $N$

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Table 1. The generation intervals of decision variables in encoding

Variables	Generation interval	Variables	Generation interval
$x_{pit} $	$[0, MA_{pi}/ab_{pi}]$	$fdn_{pijt} $	$\displaystyle \left[0, \left(MT_{i}^{f} -\sum\limits_{N_{p} =1}^{p-1}{\sum\limits_{N_{j} =1}^J {fdn_{pijt} \cdot tpb_{p}}} \right. \right. $ $\displaystyle \left. \left. -\sum\limits_{N_{j} =1}^{j-1}{fdn_{pijt} \cdot tpb_{p}} \right)\Bigg/tpb_{p} \right]$
$y_{pit} $	$[0, MRA_{pi}/rab_{pi}]$	$fdr_{pijt} $	$\displaystyle \left[0, \left(MT_{i}^{f} -\sum\limits_{N_{p} =1}^P {\sum\limits_{N_{j} =1}^J {fdn_{pijt} \cdot tpb_{p}}} \right. \right. $ $\displaystyle -\sum\limits_{N_{p} =1}^{p-1}{\sum\limits_{N_{j} =1}^J {fdr_{pijt} \cdot tpb_{p}}} $ $\displaystyle \left. \left.-\sum\limits_{N_{j} =1}^{j-1} {fdr_{pijt} \cdot tpb_{p}} \right)\Bigg/tpb_{p} \right]$
$v_{cit} $	$[0, MP_{ci}/pb_{ci}]$	$subc_{cit} $	$\displaystyle \left[0, {v_{cit} \cdot pb_{c}} -\sum\limits_{p=1}^P {BOC_{pc} \cdot x_{pit} \cdot ab_{p} +\overline \zeta_{ci}^{f}}\right]$
$z_{cit} $	$[0, MRP_{ci}/rpb_{ci}]$

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Table 2. The bill of each kind of core component to each type of product

	A	B-1	B-2	C-1	C-2	D
Ⅰ	1	1	0	4	0	1
Ⅱ	1	0	1	0	4	1
Ⅲ	1	0	1	0	4	1

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Table 3. The demand data for new products in market of each distributor

$j=$	1			2			3			4			5
$p=$	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3
$t=1$	378	384	400	394	395	396	365	367	389	370	391	405	398	408	423
$t=2$	387	407	402	380	387	394	376	395	399	368	378	393	409	416	416
$t=3$	380	397	393	376	391	409	384	389	384	374	397	393	365	367	389
$t=4$	393	395	390	381	388	391	370	395	383	393	395	390	376	395	399
$t=5$	398	408	423	370	391	405	381	387	394	394	395	396	374	389	384
$t=6$	409	416	416	368	378	393	385	386	397	380	387	394	370	395	383

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Table 4. The demand data for remanufactured products in market of each distributor

$j=$	1			2			3			4			5
$p=$	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3
$t=1$	157	163	165	158	166	170	168	172	172	158	160	162	158	167	171
$t=2$	160	162	169	160	162	173	162	163	165	163	169	171	167	170	172
$t=3$	155	156	160	162	168	175	158	167	171	162	168	175	152	159	166
$t=4$	162	163	165	156	159	168	167	170	172	156	159	168	158	163	170
$t=5$	158	160	162	152	159	166	167	174	174	157	163	165	155	156	160
$t=6$	163	169	171	158	163	170	151	163	166	160	162	169	162	163	165

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Table 5. The quantity of EOL products available in market of each distributor

$j=$	1			2			3			4			5
$p=$	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3
$t=1$	186	188	189	186	191	197	191	192	187	184	184	190	187	198	202
$t=2$	190	198	199	184	195	198	198	193	195	192	195	198	199	207	205
$t=3$	184	184	190	181	195	195	187	198	202	181	195	195	196	198	205
$t=4$	192	195	198	197	190	199	199	204	204	197	190	199	182	190	191
$t=5$	174	198	204	187	179	195	189	184	198	186	191	197	198	193	195
$t=6$	182	190	191	188	189	191	180	193	194	184	195	198	187	179	195

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Table 6. The parameters data about joint recycling center

	$c$							$p$
	1	2	3	4	5	6		1	2	3
$UDC_{ct} $	35	30	30	25	25	30	$SDT_{pt} $	1000	1200	1200
$ICQC_{ct}^{a} $	10	10	10	5	5	5	$UDTC_{pt} $	100	100	100
$\theta_{ct} $	0.95	0.92	0.92	0.90	0.90	0.85	$ICRP_{pt}^{a} $	10	10	10

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Table 7. The parameters data about products in manufacturing/remanufacturing factories

$i=$	1			2			3
$p=$	1	2	3	1	2	3	1	2	3
$SA_{pit} $	25000	30000	35000	25000	30000	35000	25000	30000	35000
$SRA_{pit} $	25000	30000	35000	25000	30000	35000	25000	30000	35000
$UAC_{pit} $	5900	7400	7900	6000	7500	8000	6050	7550	8050
$URAC_{pit} $	5900	7400	7900	6000	7500	8000	6050	7550	8050
$ICNP_{pit}^{f} $	20	20	20	20	20	20	20	20	20
$ICRMP_{pit}^{f} $	20	20	20	20	20	20	20	20	20

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Table 8. The parameters data about components in manufacturing/remanufacturing factories

i=	1						2						3
c=	1	2	3	4	5	6	1	2	3	4	5	6	1	2	3	4	5	6
SP_cit	25000	20000	24000	15000	18000	18000	25000	20000	24000	15000	18000	18000	25000	20000	24000	15000	18000	18000
SRP_cit	10000	6000	7000	5000	6000	5000	10000	6000	7000	5000	6000	5000	10000	6000	7000	5000	6000	5000
UPC_cit	3900	2400	2700	70	95	950	4000	2500	2800	75	100	1000	4100	2600	2900	80	105	1050
URPC_cit	950	550	650	22	28	325	1000	600	700	25	30	350	1050	650	750	28	32	375
ICQC_cit^f	10	10	10	5	5	5	10	10	10	5	5	5	10	10	10	5	5	5
ICNC_cit^f	15	15	15	10	10	10	15	15	15	10	10	10	15	15	15	10	10	10
ICRC_cit^f	15	15	15	10	10	10	15	15	15	10	10	10	15	15	15	10	10	10
UTCa_cit^f	40	30	30	15	15	25	45	35	35	15	15	30	40	30	30	15	15	25
PPC_cit	820	520	540	135	135	355	820	520	540	135	135	355	800	500	520	120	120	345
MP_ci	2400	800	1600	3200	6400	2400	2400	800	1600	3200	6400	2400	2400	800	1600	3200	6400	2400
MRP_ci	1050	350	700	1400	2800	1050	1050	350	700	1400	2800	1050	1050	350	700	1400	2800	1050

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Table 9. The parameters data about distributors

j=	1			2			3			4			5
p=	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3
URCC_pjt	1000	1150	1150	1000	1150	1150	1050	1200	1200	1050	1200	1200	1100	1250	1250
URCD_pjt	900	1050	1050	900	1050	1050	950	1100	1100	950	1100	1100	1000	1150	1150
SPN_pjt	18160	20670	21340	18160	20665	21340	18150	20680	21345	18150	20680	21345	18170	20690	21365
SPR_pjt	12570	14740	15400	12570	14740	15400	12580	14740	15410	12580	14740	15410	12590	14760	15430
USNP_pjt	4120	4690	4840	4120	4690	4840	4110	4690	4840	4110	4690	4840	4120	4690	4850
USRP_pjt	2850	3340	3490	2850	3340	3490	2850	3340	3500	2850	3340	3500	2860	3350	3500
UTC_pjt^da	30	30	30	35	35	35	30	30	30	35	35	35	30	30	30
ICNP_pjt^d	20	20	20	20	20	20	20	20	20	20	20	20	20	20	20
ICRMP_pjt^d	20	20	20	20	20	20	20	20	20	20	20	20	20	20	20
ICRP_pjt^d	10	10	10	10	10	10	10	10	10	10	10	10	10	10	10

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Table 10. The unit transportation cost of products from factories to distributors

i	1					2					3
j	1	2	3	4	5	1	2	3	4	5	1	2	3	4	5
MPN_1ijt	15440	15440	15460	15460	15500	15840	15870	15780	15780	15840	16100	16070	16100	16100	16070
MPN_2ijt	17640	17640	17670	17670	17720	17990	18000	17980	17980	17990	18290	18270	18290	18290	18270
MPN_3ijt	18220	18220	18260	18260	18300	18580	18600	18560	18560	18580	18860	18850	18860	18860	18850
MPR_1ijt	10730	10730	10770	10770	10810	10970	10990	10950	10950	10870	11090	11070	11090	11090	11070
MPR_2ijt	12630	12630	12650	12650	12690	12860	12880	12840	12840	12860	12970	12950	12970	12970	12950
MPR_3ijt	13200	13200	13240	13240	13290	13430	13450	13410	13410	13430	13550	13530	13550	13550	13530
UTC_pijt^fd	40	40	50	50	60	60	50	40	50	60	60	50	50	40	40

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Table 11. The comparison results among SGA, AGA and SAGA

Algorithm	Running result					Convergence generation
	Best	Mean	Worst	Proportion of Best Result	Standard Deviation	Best	Mean	Worst
SGA(P_cr = 0:6, P_mu = 0:005)	103014002	102488365	102017694	36%	453083	712	736	754
SGA(P_cr = 0:6, P_mu = 0:02)	104891190	103904980	103309728	20%	672762	616	658	682
SGA(P_cr = 0:8, P_mu = 0:005)	103499360	103141280	102441552	46%	432193	658	688	712
SGA(P_cr = 0:8, P_mu = 0:02)	104514894	103861409	103309728	42%	566313	724	742	766
AGA	106570884	106360212	105911706	54%	262057	458	489	511
SAGA	107302078	107217562	106984452	62%	124847	489	527	557

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Table 12. Definition of the subscripts

Notation	Description
$t$	the index set of periods, $\{1, 2, \cdots, T\}$
$p$	the index set of product type, $\{1, 2, \cdots, P\}$
$c$	the index set of component kind, $\{1, 2, \cdots, C\}$
$i$	the index set of manufacturing/remanufacturing factory, $\{1,$ $ 2,$ $ \cdots,$ $ I\}$
$j$	the index set of distributor, $\{1, 2, \cdots, J\}$
$lt_{1},lt_{2},lt_{3} $	the accumulative leading time of the joint recycling center, manufacturing/remanufacturing factories and distribution centers, respectively

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Table 13. Definition of the variables occurred in the first level model

Notation	Description
$af_{cit} $	the quantity of batches of qualified component $c$ to be transported from the recycling center to factory $i$ in period $t$
$da_{pjt} $	the quantity of batches of return product $p$ to be transported from distributor $j$ to the recycling center in period $t$
$\sigma_{pt} $	the binary variable indicating whether return product $p$ is disassembled & tested in batches in period $t$
$dt_{pt} $	the quantity of batches of return product $p$ to be disassembled & tested in period $t$
$d_{ct} $	the quantity of component $c$ to be disposed in period $t$
$\alpha_{pt}^{a},\beta_{ct}^{a} $	the inventory of return product $p$ and qualified component $c$ at the recycling center at the end of period $t$, respectively

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Table 14. Definition of the variables occurred in the second level model

Notation	Description
$fdn_{pijt},fdr_{pijt} $	the quantity of batches of new and remanufacturing product $p$ to be transported from factory $i$ to distributor $j$ in period $t$, respectively
$\eta_{pit},\delta_{pit} $	the binary variable indicating whether new and remanufacturing product $p$ is assembled by factory $i$ in batches in period $t$, respectively
$x_{pit},y_{pit} $	the quantity of batches of new and remanufactured product $p$ to be assembled at factory $i$ in period $t$, respectively
$\pi_{cit},\tau_{cit} $	the binary variable indicating whether component $c$ is newly processed and reprocessed by factory $i$ in batches in period $t$, respectively
$v_{cit},z_{cit} $	the quantity of batches of component $c$ to be processed and reprocessed at factory $i$ in period $t$, respectively
$\lambda_{pit}^{f},\chi_{pit}^{f} $	the inventory of new and remanufactured product $p$ at factory $i$ at the end of period $t$, respectively
$\beta_{cit}^{f},\zeta_{cit}^{f},\xi_{cit}^{f} $	the inventory of qualified, new and remanufactured component $c$ at factory $i$ at the end of period $t$, respectively
$subc_{cit} $	the quantity of one-way substitution for component $c$ at factory $i$ in period $t$
$af_{cit} $	this notation has occurred in the first level model

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Table 15. Definition of the variables occurred in the third level model

Notation	Description
$nss_{pjt},rss_{pjt} $	the quantity of new and remanufactured product $p$ in short supply at distributor $j$ in period $t$, respectively
$\gamma_{pjt} $	the quantity of EOL product $p$ to be recycled by distributor $j$ from downstream markets in period $t$
$\lambda_{pjt}^{d},\chi_{pjt}^{d},\alpha_{pjt}^{d} $	the inventory of new, remanufactured and return product $p$ at distributor $j$ at the end of period $t$, respectively
$da_{pjt} $	this natation has occurred in the first level model
$fdn_{pijt},fdr_{pijt} $	these notations have occurred in second level model

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Table 16. Definition of the parameters occurred in the first level model

Notation	Description
$tcb_{c} $	the quantity of qualified component $c$ transported per batch from the recycling center to factories
$trb_{p} $	the quantity of return product $p$ transported per batch from distributors to the recycling center
$dtb_{p} $	the quantity of return product $p$ disassembled & tested per batch
$PPC_{cit} $	the unit purchase cost of qualified component $c$ paid to the recycling center by factory $i$ in period $t$
$URCC_{pjt} $	the unit recycling cost of return product $p$ paid to distributor $j$ by the recycling center in period $t$
$SDT_{pt} $	the set-up cost incurred if return product $p$ is disassembled & tested in batches in period $t$
$UDTC_{pt} $	the unit disassembly & tested cost of return product $p$ in period $t$
$UDC_{ct} $	the unit disposing cost of component $c$ in period $t$
$ICQC_{ct}^{a},ICRP_{pt}^{a} $	the unit inventory cost of qualified component $c$ and return product $p$ at the recycling center in period $t$, respectively
$UTC_{cit}^{af} $	the unit transportation cost of qualified component $c$ from the recycling center to factory $i$ in period $t$
$BOC_{pc} $	the bill of component $c$ to product $p$
$\theta_{ct} $	the remanufacturable rate of component $c$ in period $t$
$\overline \alpha_{p}^{a},\overline \beta_{c}^{a} $	the maximum inventory level of return products and qualified components at the recycling center, respectively
$MDT_{p} $	the maximum quantity of return product $p$ can be disassembled & tested in every periods
$MT^{a}$	the maximum quantity of qualified components can be transported from the recycling center to factories in every periods

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Table 17. Definition of the parameters occurred in the second level model

Notation	Description
$MPN_{pijt},MPR_{pijt} $	the middle price of new and remanufactured product $p$ paid to factory $i$ by distributor $j$ in period $t$, respectively
$tpb_{p} $	the quantity of new or remanufactured product $p$ transported per batch from factories todistributors
$ab_{pi},rab_{pi} $	the quantity of new and remanufactured product $p$ assembled per batch at factory $i$, respectively
$pb_{ci},rpb_{ci} $	the quantity of component $c$ processed and reprocessed per batch at factory $i$, respectively
$SA_{pit},SRA_{pit} $	the set-up cost incurred if new and remanufactured product $p$ is assembled in batches at factory $i$ in period $t$, respectively
$UAC_{pit},URAC_{pit} $	the unit assembly cost of new and remanufactured product $p$ at factory $i$ in period $t$, respectively
$SP_{cit},SRP_{cit} $	the set-up cost incurred if component $c$ is newly processed and reprocessed in batches at factory $i$ in period $t$, respectively
$UPC_{cit},URPC_{cit} $	the unit processing and reprocessing cost of component $c$ at factory $i$ in period $t$, respectively
$ICNP_{pit}^{f},ICRMP_{pit}^{f} $	the unit inventory cost of new and remanufactured product $p$ at factory $i$ in period $t$, respectively
$ICQC_{cit}^{f},ICNC_{cit}^{f},ICRC_{cit}^{f} $	the unit inventory cost of qualified, new and remanufactured component $c$ at factory $i$ in period $t$, respectively
$UTC_{pijt}^{fd} $	the unit transportation cost of product $p$ from factory $i$ to distributor $j$ in period $t$
$\overline \beta_{ci}^{f},\overline \zeta_{ci}^{f},\overline \xi_{ci}^{f},\overline \lambda_{pi}^{f},\overline \chi_{pi}^{f} $	the maximum inventory level of qualified components, new components, remanufactured components, new products andremanufactured products at factory $i$, respectively
$MA_{pi},MRA_{pi} $	the maximum quantity of new and remanufactured product $p$ can be assembled in factory $i$ in every periods, respectively
$MP_{ci},MRP_{ci} $	the maximum quantity of component $c$ can be processed and reprocessed in factory $i$ in every periods, respectively
$MT_{i}^{f} $	the maximum quantity of products can be transported from factory $i$ to distributors in every periods
$PPC_{cit},tcb_{c},BOC_{pc} $	these notations have occurred in the first level model

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Table 18. Definition of the parameters occurred in the third level model

Notation	Description
$SPN_{pjt},SPR_{pjt} $	the selling price of new and remanufactured product $p$ at distributor $j$ in period $t$, respectively
$DNM_{pjt},DRM_{pjt} $	the demands of new and remanufactured product $p$ in the market of distributor $j$ in period $t$, respectively
$URCD_{pjt} $	the unit recycling cost of EOL product $p$ paid to retailers or customers by distributor $j$ in period $t$
$USNP_{pjt},USRP_{pjt} $	the unit shortage cost of new and remanufactured product $p$ paid by distributor $j$ in period $t$, respectively
$ICNP_{pjt}^{d},ICRMP_{pjt}^{d},ICRP_{pjt}^{d} $	the unit inventory cost of new, remanufactured and return product $p$ at distributor $j$ in period $t$, respectively
$UTC_{pjt}^{da} $	the unit transportation cost of return product $p$ from distributor $j$ to the recycling center in period $t$
$EPA_{pjt} $	the quantity of EOL product $p$ available in the market of distributor $j$ in period $t$
$\overline \lambda_{pj}^{d},\overline \chi_{pj}^{d},\overline \alpha_{pj}^{d} $	the maximum inventory level of new, remanufactured and return products at distributor $j$, respectively
$MT_{j}^{d} $	the maximum quantity of return products can be transported from distributor $j$ to the recycling center in every periods
$URCC_{pjt},trb_{p} $	these notations have occurred in the first level model
$MPN_{pijt},tpb_{p},MPR_{pijt} $	these notations have occurred in the second level model

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