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

  • * Corresponding authorr: Yi Jing

    * Corresponding authorr: Yi Jing 
Abstract Full Text(HTML) Figure(3) / Table(18) Related Papers Cited by
  • 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.

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

    Citation:

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  • Figure 1.  Diagrammatic sketch for the two - point crossover

    Figure 2.  Diagrammatic sketch for the inverted sequence mutation

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

    Table 1.  The generation intervals of decision variables in encoding

    VariablesGeneration intervalVariablesGeneration 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}]$
     | Show Table
    DownLoad: CSV

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

    AB-1B-2C-1C-2D
    110401
    101041
    101041
     | Show Table
    DownLoad: CSV

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

    $j=$12345
    $p=$123123123123123
    $t=1$378384400394395396365367389370391405398408423
    $t=2$387407402380387394376395399368378393409416416
    $t=3$380397393376391409384389384374397393365367389
    $t=4$393395390381388391370395383393395390376395399
    $t=5$398408423370391405381387394394395396374389384
    $t=6$409416416368378393385386397380387394370395383
     | Show Table
    DownLoad: CSV

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

    $j=$12345
    $p=$123123123123123
    $t=1$157163165158166170168172172158160162158167171
    $t=2$160162169160162173162163165163169171167170172
    $t=3$155156160162168175158167171162168175152159166
    $t=4$162163165156159168167170172156159168158163170
    $t=5$158160162152159166167174174157163165155156160
    $t=6$163169171158163170151163166160162169162163165
     | Show Table
    DownLoad: CSV

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

    $j=$12345
    $p=$123123123123123
    $t=1$186188189186191197191192187184184190187198202
    $t=2$190198199184195198198193195192195198199207205
    $t=3$184184190181195195187198202181195195196198205
    $t=4$192195198197190199199204204197190199182190191
    $t=5$174198204187179195189184198186191197198193195
    $t=6$182190191188189191180193194184195198187179195
     | Show Table
    DownLoad: CSV

    Table 6.  The parameters data about joint recycling center

    $c$ $p$
    123456123
    $UDC_{ct} $353030252530 $SDT_{pt} $100012001200
    $ICQC_{ct}^{a} $101010555 $UDTC_{pt} $100100100
    $\theta_{ct} $0.950.920.920.900.900.85 $ICRP_{pt}^{a} $101010
     | Show Table
    DownLoad: CSV

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

    $i=$123
    $p=$123123123
    $SA_{pit} $250003000035000250003000035000250003000035000
    $SRA_{pit} $250003000035000250003000035000250003000035000
    $UAC_{pit} $590074007900600075008000605075508050
    $URAC_{pit} $590074007900600075008000605075508050
    $ICNP_{pit}^{f} $202020202020202020
    $ICRMP_{pit}^{f} $202020202020202020
     | Show Table
    DownLoad: CSV

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

    i=123
    c=123456123456123456
    SPcit250002000024000150001800018000250002000024000150001800018000250002000024000150001800018000
    SRPcit100006000700050006000500010000600070005000600050001000060007000500060005000
    UPCcit3900240027007095950400025002800751001000410026002900801051050
    URPCcit95055065022283251000600700253035010506507502832375
    ICQCcitf101010555101010555101010555
    ICNCcitf151515101010151515101010151515101010
    ICRCcitf151515101010151515101010151515101010
    UTCacitf403030151525453535151530403030151525
    PPCcit820520540135135355820520540135135355800500520120120345
    MPci240080016003200640024002400800160032006400240024008001600320064002400
    MRPci105035070014002800105010503507001400280010501050350700140028001050
     | Show Table
    DownLoad: CSV

    Table 9.  The parameters data about distributors

    j=12345
    p=123123123123123
    URCCpjt100011501150100011501150105012001200105012001200110012501250
    URCDpjt90010501050900105010509501100110095011001100100011501150
    SPNpjt181602067021340181602066521340181502068021345181502068021345181702069021365
    SPRpjt125701474015400125701474015400125801474015410125801474015410125901476015430
    USNPpjt412046904840412046904840411046904840411046904840412046904850
    USRPpjt285033403490285033403490285033403500285033403500286033503500
    UTCpjtda303030353535303030353535303030
    ICNPpjtd202020202020202020202020202020
    ICRMPpjtd202020202020202020202020202020
    ICRPpjtd101010101010101010101010101010
     | Show Table
    DownLoad: CSV

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

    i123
    j123451234512345
    MPN1ijt154401544015460154601550015840158701578015780158401610016070161001610016070
    MPN2ijt176401764017670176701772017990180001798017980179901829018270182901829018270
    MPN3ijt182201822018260182601830018580186001856018560185801886018850188601886018850
    MPR1ijt107301073010770107701081010970109901095010950108701109011070110901109011070
    MPR2ijt126301263012650126501269012860128801284012840128601297012950129701297012950
    MPR3ijt132001320013240132401329013430134501341013410134301355013530135501355013530
    UTCpijtfd404050506060504050606050504040
     | Show Table
    DownLoad: CSV

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

    AlgorithmRunning resultConvergence generation
    BestMeanWorstProportion of Best ResultStandard DeviationBestMeanWorst
    SGA(Pcr = 0:6, Pmu = 0:005)10301400210248836510201769436%453083712736754
    SGA(Pcr = 0:6, Pmu = 0:02)10489119010390498010330972820%672762616658682
    SGA(Pcr = 0:8, Pmu = 0:005)10349936010314128010244155246%432193658688712
    SGA(Pcr = 0:8, Pmu = 0:02)10451489410386140910330972842%566313724742766
    AGA10657088410636021210591170654%262057458489511
    SAGA10730207810721756210698445262%124847489527557
     | Show Table
    DownLoad: CSV

    Table 12.  Definition of the subscripts

    NotationDescription
    $t$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
     | Show Table
    DownLoad: CSV

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

    NotationDescription
    $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
     | Show Table
    DownLoad: CSV

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

    NotationDescription
    $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
     | Show Table
    DownLoad: CSV

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

    NotationDescription
    $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
     | Show Table
    DownLoad: CSV

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

    NotationDescription
    $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
     | Show Table
    DownLoad: CSV

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

    NotationDescription
    $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
     | Show Table
    DownLoad: CSV

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

    NotationDescription
    $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
     | Show Table
    DownLoad: CSV
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