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Sustainable closed-loop supply chain network optimization for construction machinery recovering

  • * Corresponding author: Abdolhossein sadrnia

    * Corresponding author: Abdolhossein sadrnia 
Abstract Full Text(HTML) Figure(4) / Table(10) Related Papers Cited by
  • With regard to environmental pressures and economic benefits, some original construction equipment manufacturers, have focused on collecting and recovering construction machinery at the end of their life. The present study aimed to focus on Sustainable closed-loop supply chain network optimization for construction machinery recovering. To this purpose, different recovery options such as remanufacturing, recycling and reusing were implemented. A mixed integer linear programming model (MILP) including three objective functions was proposed in this regard. Based on the model, all three dimensions of sustainability including economic, environmental, and social dimensions were considered and could successfully determine the optimal values of the flow of used products, remanufactured products, recycled parts, re-usable parts. In order to demonstrate the applicability of the proposed model, a numerical example was used with the help of GAMS software to obtain the supply chain structure with the lowest cost and reduce the pollution caused by CO2. Finally, the model could maximize fixed and variable job opportunities.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:

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  • Figure 1.  Supply chain of closed loop for recovering machinery at the end of their life cycle based on sustainability dimensions

    Figure 2.  The change of the value of the objective function by changes in $ q_c $.

    Figure 3.  The change in the value of the objective function by changes in$ {\ DR}_c $.

    Figure 4.  The change in the value of the objective function by the changes in $ {\ V}_p $.

    C = $ \left\{1,2,\dots ,c\right\} $Set of consumer zone
    D = $ \left\{1,2,\dots ,d\right\} $Set of collection /distribution centers
    A = $ \left\{1,2,\dots ,a\right\} $Set of potential Assembly / Disassembly centers locations
    RM = $ \left\{1,2,\dots ,rm\right\} $Set of potential remanufacture centers locations
    RC = $ \left\{1,2,\dots ,rc\right\} $Set of potential recycling centers locations
    RU = $ \left\{1,2,\dots ,ru\right\} $Set of potential reusing centers locations
    L = $ \left\{1,2,\dots ,l\right\} $Set of disposal centers
    S = $ \left\{1,2,\dots ,s\right\} $Set of suppliers
    TC = $ \left\{1,2,\dots ,tc\right\} $Transportation options from consumers
    TD = $ \left\{1,2,\dots ,td\right\} $Transportation options from collection /distribution centers
    TA = $ \left\{1,2,\dots ,ta\right\} $Transportation options from Assembly / Disassembly centers
    TS = $ \left\{1,2,\dots ,ts\right\} $Transportation options from suppliers
    M = $ \left\{1,2,\dots ,m\right\} $Set of products
    P = $ \left\{1,2,\dots ,p\right\} $Set of components
     | Show Table
    DownLoad: CSV
    $ {CTR}^m_{tc\ c\ d} $The transportation cost of used products per km between consumer zone and collection /distribution centers with transportation option tc.
    $ {CTR}^m_{td\ d\ a} $The transportation cost of used products per km between collection /distribution centers and Assembly / Disassembly centers with transportation option td.
    $ {CTR}^p_{ta\ a\ rm} $The transportation cost of used parts per km between Assembly/ Disassembly centers and remanufacturing centers with transportation option ta.
    $ {CTR}^p_{ta\ a\ rc} $The transportation cost of used parts per km between Assembly/ Disassembly centers and recycling centers with transportation option ta.
    $ {CTR}^p_{ta\ a\ ru} $The transportation cost of reusable parts per km between Assembly/ Disassembly centers and reusing centers with transportation option ta.
    $ {CTR}^p_{ta\ a\ l} $The transportation cost of disposal parts per km between Assembly/ Disassembly centers and disposal centers with transportation option ta.
    $ {CTR}^p_{ts\ \ s\ a} $The transportation cost of new parts per km between suppliers and Assembly / Disassembly centers with transportation option ts.
    $ {CTR}^p_{tc\ ru\ c} $The transportation cost of reusable parts per km between reusing centers and consumer zone with transportation option tc.
    $ {CTR}^p_{ts\ rc\ s} $The transportation cost of recycled parts per km between recycle centers and suppliers with transportation option ts.
    $ {CTR}^p_{ta\ rm\ a} $The transportation cost of remanufactured parts per km between remanufacturing centers and Assembly/ Disassembly centers with transportation option ta.
    $ {CTR}^m_{ta\ a\ d} $The transportation cost of remanufactured products per km between Assembly / Disassembly centers and collection /distribution centers with transportation option ta.
    $ {CTR}^m_{td\ d\ c} $The transportation cost of remanufactured products per km between collection /distribution centers and consumer zone with transportation option td.
    $ {dis}_{c\ d} $Distance from c to d
    $ {dis}_{d\ a} $Distance from d to a
    $ {dis}_{a\ l} $Distance from a to l
    $ {dis}_{a\ rm} $Distance from a to rm
    $ {dis}_{a\ rc} $Distance from a to rc
    $ {dis}_{a\ ru} $Distance from a to ru
    $ {dis}_{rc\ s} $Distance from rc to s
    $ {dis}_{s\ a} $Distance from s to a
    $ {CAP}_a $Capacity of Assembly / Disassembly centers
    $ {CAP}_{rm} $Capacity of remanufacturing centers for parts
    $ {CAP}_{rc} $Capacity of recycling centers for parts
    $ {CAP}_{ru} $Capacity of reusing centers for parts
    $ {cd}_m $Unit dismantling cost for product m in Assembly / Disassembly centers
    $ {ca}_m $Unit assembling cost for product m in Assembly / Disassembly centers
    $ c_i $Unit inspection cost for parts
    $ {crm}_p $Unit remanufacturing costs for part p in remanufacturing centers
    $ {crc}_p $Unit recycling costs for part p in recycling centers
    $ {cru}_p $Unit preparing cost for reusing the parts in reusing center
    $ {cs}_p $Unit supplying cost for the parts
    $ F_a $Fixed cost for opening Assembly / Disassembly centers
    $ F_{rm} $Fixed cost for opening remanufacturing centers
    $ F_{rc} $Fixed cost for opening recycling centers
    $ F_{ru} $Fixed cost for opening reusing centers
    $ F_d $Cost for expanding a distribution center to a combined collection / distribution facility
    $ {\lambda }_c $Collection ratio in the consumer's zone
    $\hat I$Badly-damaged ratio of the used part
    $\hat I$Remanufacturing ratio of the used part
    $\hat I$Recycling ratio of the used part
    ${\hat I}_{¸} $Reusing ratio of the used part
    $ q_c $Supply for the used product in the consumer's zone
    $ {DR}_c $Demand for the remanufactured product in the consumer's zone
    $ V_p $Unit volume of the part in product
    $ e_{rm} $Rate of released $ {CO}_2 $ to remanufacture one unit of the product in remanufacturing centers
    $ {eCD}^{tc} $The amount of CO$ {}_{2} $ released by transportation option tc to send a unit of the used product from the consumer's zone to collection /distribution centers for a unit distance.
    $ {eDA}^{td} $The amount of CO$ {}_{2} $ released by transportation option td to send a unit of the used product from collection /distribution centers to Assembly / Disassembly centers for a unit distance.
    $ {eARM}^{ta} $The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the used part from Assembly / Disassembly centers to remanufacturing centers for a unit distance.
    $ {eARC}^{ta} $The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the used part from Assembly / Disassembly centers to recycling centers for a unit distance.
    $ {eARU}^{ta} $The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the used part from Assembly / Disassembly centers to reusing centers for a unit distance.
    $ {eAL}^{ta} $The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the disposal part from Assembly / Disassembly centers to disposal centers for a unit distance.
    $ {eSA}^{ts} $The amount of CO$ {}_{2} $ released by transportation option ts to send a unit of the new part from suppliers to Assembly / Disassembly centers for a unit distance.
    $ {eRUC}^{tc} $The amount of CO$ {}_{2} $ released by transportation option tc to send a unit of the reusable part from reusing centers to the consumer's zone for a unit distance.
    $ {eRCS}^{ts} $The amount of CO$ {}_{2} $ released by transportation option ts to send a unit of the recycled part from recycling centers to suppliers for a unit distance.
    $ {eRMA}^{ta} $The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the remanufactured part from remanufacturing centers to Assembly / Disassembly centers for a unit distance.
    $ {eAD}^{ta} $The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the remanufactured product from Assembly / Disassembly centers to collection /distribution centers for a unit distance.
    $ {eDC}^{td} $The amount of CO$ {}_{2} $ released by transportation option td to send a unit of the remanufactured product from collection /distribution centers to the consumer's zone for a unit distance.
    $ H_{tc} $Capacity of transportation option tc
    $ H_{td} $Capacity of transportation option td
    $ H_{ta} $Capacity of transportation option ta
    $ H_{ts} $Capacity of transportation option ts
    $ {\varphi }_a $The number of the fixed job opportunities created by launching the Assembly / Disassembly centers
    $ {\varphi }_{rm} $The number of the fixed job opportunities created by launching the remanufacturing centers
    $ {\varphi }_{rc} $The number of the fixed job opportunities created by launching the recycling centers
    $ {\varphi }_{ru} $The number of the fixed job opportunities created by launching the reusing centers
    $ {\mu }_a $The number of the created variable job opportunities by working in Assembly / Disassembly centers
    $ {\mu }_{rm} $The number of the created variable job opportunities by working in remanufacturing centers
    $ {\mu }_{rc} $The number of the created variable job opportunities by working in recycling centers
    $ {\mu }_{ru} $The number of the created variable job opportunities by working in reusing centers
     | Show Table
    DownLoad: CSV
    $ Q^m_{tc\ c\ d} $Quantity of the used products m from C to D with transportation option tc
    $ Q^m_{td\ d\ a} $Quantity of the used products m from D to A with transportation option td
    $ Q^p_{ta\ a\ rm} $Quantity of the used parts p from A to RM with transportation option ta
    $ Q^p_{ta\ a\ rc} $Quantity of the used parts p from A to RC with transportation option ta
    $ Q^p_{ta\ a\ ru} $Quantity of the reusable parts p from A to RU with transportation option ta
    $ Q^p_{ta\ a\ l} $Quantity of the disposal parts p from A to L with transportation option ta
    $ Q^p_{ts\ s\ a} $Quantity of the new parts p from S to A with transportation option ts
    $ Q^p_{tc\ ru\ c} $Quantity of the reusable parts p from RU to C with transportation option tc
    $ Q^p_{ts\ rc\ s} $Quantity of the recycled parts p from RC to S with transportation option ts
    $ Q^p_{ta\ rm\ a} $Quantity of the remanufactured parts p from RM to A with transportation option ta
    $ Q^m_{ta\ a\ d} $Quantity of the remanufactured products m from A to D with transportation option ta
    $ Q^m_{td\ d\ c} $Quantity of the remanufactured products m from D to C with transportation option td
     | Show Table
    DownLoad: CSV
    $ X_a $$ {{\rm X}}_{{\rm a}}{\rm = 1\ } $if Assembly / Disassembly center is open. Otherwise, $ {\rm \ }{{\rm X}}_{{\rm a}}{\rm = 0} $
    $ Y_{rm} $$ {{\rm Y}}_{{\rm rm}}{\rm = 1} $ if remanufacturing center is open. Otherwise, $ {{\rm Y}}_{{\rm rm}}{\rm = 0} $
    $ Z_{rc} $$ {{\rm Z}}_{{\rm rc}}{\rm = 1} $ if recycling center is open$ .\ {\rm Otherwise,\ }{\rm \ }{{\rm Z}}_{{\rm rc}}{\rm = 0} $
    $ W_{ru} $$ {{\rm W}}_{{\rm ru}}{\rm = 1} $ if reusing center is open$ .{\rm Otherwise,}{\rm \ }{{\rm W}}_{{\rm ru}}{\rm = 0} $
     | Show Table
    DownLoad: CSV

    Table 1.  The initial values of parameters

    parameter value parameter value
    $ {CTR}^m_{tc\ c\ d} $ floor(uniform(1, 1500)) $ F_d $ floor(uniform(1, 8000000))
    $ {CTR}^m_{td\ d\ a} $ floor(uniform(1, 1650)) $ q_c $ floor(uniform(1, 25))
    $ {CTR}^p_{ta\ a\ rm} $ floor(uniform(1, 1867)) $ {DR}_c $ floor(uniform(1,100))
    $ {CTR}^p_{ta\ a\ rc} $ floor(uniform(1, 1900)) $ V_p $ floor(uniform(1, 10))
    $ {CTR}^p_{ta\ a\ ru} $ floor(uniform(1, 1972)) $ e_{rm} $ floor(uniform(1, 10))
    $ {CTR}^p_{ta\ a\ l} $ floor(uniform(1, 2000)) $ {eCD}^{tc} $ floor(uniform(1, 30))
    $ {CTR}^p_{ts\ \ s\ a} $ floor(uniform(1, 3613)) $ {eDA}^{td} $ floor(uniform(1, 40))
    $ {CTR}^p_{tc\ ru\ c} $ floor(uniform(1, 2890)) $ {eARM}^{ta} $ floor(uniform(1, 50))
    $ {CTR}^p_{ts\ rc\ s} $ floor(uniform(1, 4561)) $ {eARC}^{ta} $ floor(uniform(1, 90))
    $ {CTR}^p_{ta\ rm\ a} $ floor(uniform(1, 3000)) $ {eARU}^{ta} $ floor(uniform(1, 80))
    $ {CTR}^m_{ta\ a\ d} $ floor(uniform(1, 3700)) $ {eAL}^{ta} $ floor(uniform(1,100))
    $ {CTR}^m_{td\ d\ c} $ floor(uniform(1, 9000)) $ {eSA}^{ts} $ floor(uniform(1, 70))
    $ {dis}_{c\ d} $ floor(uniform(1,100)) $ {eRUC}^{tc} $ floor(uniform(1,120))
    $ {dis}_{d\ a} $ floor(uniform(1,150)) $ {eRCS}^{ts} $ floor(uniform(1,150))
    $ {dis}_{a\ l} $ floor(uniform(1,200)) $ {eRMA}^{ta} $ floor(uniform(1,190))
    $ {dis}_{a\ rm} $ floor(uniform(1,300)) $ {eAD}^{ta} $ floor(uniform(1, 60))
    $ {dis}_{a\ rc} $ floor(uniform(1,450)) $ {eDC}^{td} $ floor(uniform(1,170))
    $ {dis}_{a\ ru} $ floor(uniform(1,700)) $ H_{tc} $ floor (uniform(1, 5))
    $ {dis}_{rc\ s} $ floor(uniform(1,950)) $ H_{td} $ floor (uniform(1, 5))
    $ {dis}_{s\ a} $ floor(uniform(1,800)) $ H_{ta} $ floor (uniform(1, 5))
    $ {CAP}_a $ floor(uniform(120,150)) $ H_{ts} $ floor (uniform(1, 5))
    $ {CAP}_{rm} $ floor(uniform(10, 50)) $ {\varphi }_a $ floor(uniform(1, 6000)
    $ {CAP}_{rc} $ floor(uniform(10, 50)) $ {\varphi }_{rm} $ floor(uniform(1, 8500))
    $ {CAP}_{ru} $ floor(uniform(10, 50)) $ {\varphi }_{rc} $ floor(uniform(1, 7000))
    $ {cd}_m $ floor(uniform(1,100)) $ {\varphi }_{ru} $ floor(uniform(1, 9500))
    $ {ca}_m $ floor(uniform(1,130)) $ {\mu }_a $ floor(uniform(1, 5000))
    $ c_i $ floor(uniform(1, 90)) $ {\mu }_{rm} $ floor(uniform(1, 7000))
    $ {crm}_p $ floor(uniform(1,170)) $ {\mu }_{rc} $ floor(uniform(1, 9000))
    $ {crc}_p $floor(uniform(1,200)) $ {\mu }_{ru} $floor(uniform(1, 1000))
    $ {cru}_p $floor(uniform(1,350)) $ {\lambda }_c $uniform(0, 1)
    $ {cs}_p $floor(uniform(1,100)) $\hat I$uniform(0, 1)
    $ F_a $floor(uniform(1, 1000000)) $\hat I$uniform(0, 0.001)
    $ F_{rm} $floor(uniform(1, 3000000)) $\hat I$uniform(0, 1)
    $ F_{rc} $floor(uniform(1, 5000000)) ${\hat I}_¸ $uniform(0, 0.001)
    $ F_{ru} $floor(uniform(1, 4000000))
     | Show Table
    DownLoad: CSV

    Table 2.  Optimal values of the objective functions

    The optimal value of the first objective The optimal value of the second objective function The optimal value of the third objective function
    2.764708E+8 6.2554E+9 47600.110
     | Show Table
    DownLoad: CSV

    Table 3.  The values obtained from the GAMS software for variables

    Consumer Zones Collection & Distribution Product Type 1
    Centers Transportation option 1 Transportation option 2
    1 $ \longrightarrow $ 1 3.245 0
    $ Q^m_{tc\ c\ d} $ 1 $ \longrightarrow $ 2 0 1.023
    2 $ \longrightarrow $ 2 13.311 0
    Consumer Zones Collection & Distribution Product Type 2
    Centers Transportation option 2
    1 $ \longrightarrow $ 1 3.245
    2 $ \longrightarrow $ 2 14.334
    Consumer Zones Collection & Distribution Product Type 3
    Centers Transportation option 1 Transportation option 2
    1 $ \longrightarrow $ 2 1.023 0
    2 $ \longrightarrow $ 103.245
    2 $ \longrightarrow $ 2013.311
    Collection & DistributionDisassemble & AssembleProduct Type 1
    CentersTransportation option 1Transportation option 2
    $ Q^m_{td\ d\ a} $2 $ \longrightarrow $ 1016.556
    2 $ \longrightarrow $ 21.0230
    Collection & Distribution Disassemble & AssembleProduct Type 2
    CentersTransportation option 1Transportation option 2
    2 $ \longrightarrow $ 21.02316.556
    Collection & DistributionDisassemble & AssembleProduct Type 3
    CentersTransportation option 1Transportation option 2
    2 $ \longrightarrow $ 112.020
    2 $ \longrightarrow $ 207.98
    Disassemble & AssembleRemanufacturecomponent Type 1
    $ Q^p_{ta\ a\ rm} $CentersTransportation option 1
    2 $ \longrightarrow $ 18.897504E-4
    2 $ \longrightarrow $ 20.014
    Disassemble & AssembleRemanufacturecomponent Type 2
    CentersTransportation option 1
    2 $ \longrightarrow $ 10.006
    2 $ \longrightarrow $ 20.101
    Disassemble & AssembleRecyclecomponent Type 1
    CentersTransportation option 1Transportation option 2
    1 $ \longrightarrow $ 2012.429
    2 $ \longrightarrow $ 10.7680
    $ Q^p_{ta\ a\ rc} $Disassemble & AssembleRecyclecomponent Type 2
    1 $ \longrightarrow $ 15.3780
    1 $ \longrightarrow $ 2046.000
    2 $ \longrightarrow $ 241.0000
    Disassemble & AssembleRe-usecomponent Type 1
    $ Q^p_{ta\ a\ ru} $CentersTransportation option 1Transportation option 2
    1 $ \longrightarrow $ 100.233
    2 $ \longrightarrow $ 23.7630
    Disassemble & AssembleRe-usecomponent Type 2
    CentersTransportation option 2
    2 $ \longrightarrow $ 11.628
    2 $ \longrightarrow $ 226.341
    Disassemble & AssembleDisposalcomponent Type 1
    CentersTransportation option 2
    $ Q^p_{ta\ a\ l} $2 $ \longrightarrow $ 10.022
    2 $ \longrightarrow $ 20.350
    Disassemble & AssembleDisposalcomponent Type 2
    CentersTransportation option 2
    2 $ \longrightarrow $ 10.151
    2 $ \longrightarrow $ 22.450
    SupplierDisassemble & Assemblecomponent Type 1
    $ Q^p_{ts\ s\ a} $CentersTransportation option 1Transportation option 2
    2 $ \longrightarrow $ 24.27754.708
    SupplierDisassemble & Assemblecomponent Type 2
    CentersTransportation option 1Transportation option 2
    2 $ \longrightarrow $ 24.27254.621
    Re-useConsumer Zonescomponent Type 1
    CentersTransportation option 1
    $ Q^p_{tc\ ru\ c} $1 $ \longrightarrow $ 13.763
    2 $ \longrightarrow $ 20.233
    Re-useConsumer Zonescomponent Type 2
    CentersTransportation option 1
    1 $ \longrightarrow $ 227.969
    RecycleSuppliercomponent Type 1
    CentersTransportation option 1
    $ Q^p_{ts\ rc\ s} $1 $ \longrightarrow $ 10.768
    1 $ \longrightarrow $ 212.429
    RecycleSuppliercomponent Type 2
    CentersTransportation option 1
    1 $ \longrightarrow $ 146.378
    2 $ \longrightarrow $ 246.000
    RemanufactureDisassemble & Assemblecomponent Type 1
    CentersTransportation option 1Transportation option 2
    $ Q^p_{ta\ rm\ a} $2 $ \longrightarrow $ 18.897504E-40.014
    RemanufactureDisassemble & Assemblecomponent Type 2
    CentersTransportation option 1Transportation option 2
    2 $ \longrightarrow $ 10.0060.101
    Disassemble & AssembleCollectionDistributionProduct Type 1
    CentersTransportation option 1Transportation option 2
    $ Q^m_{ta\ a\ d} $1 $ \longrightarrow $ 2054.722
    2 $ \longrightarrow $ 14.2780
    Disassemble & AssembleCollectionDistributionProduct Type 2
    CentersTransportation option 1Transportation option 2
    1 $ \longrightarrow $ 2011.560
    2 $ \longrightarrow $ 15.8770
    Disassemble & AssembleCollectionDistributionProduct Type 3
    CentersTransportation option 1Transportation option 2
    1 $ \longrightarrow $ 14.2780
    2 $ \longrightarrow $ 2054.722
    CollectionDistributionConsumer ZonesProduct Type 1
    CentersTransportation option 1Transportation option 2
    1 $ \longrightarrow $ 104.278
    1 $ \longrightarrow $ 218.0000
    2 $ \longrightarrow $ 2036.722
    CollectionDistributionConsumer ZonesProduct Type 2
    $ Q^m_{td\ d\ c} $CentersTransportation option 1Transportation option 2
    1 $ \longrightarrow $ 1041.000
    1 $ \longrightarrow $ 24.2780
    2 $ \longrightarrow $ 113.7220
    CollectionDistributionConsumer ZonesProduct Type 3
    CentersTransportation option 1Transportation option 2
    1 $ \longrightarrow $ 213.72241.000
    2 $ \longrightarrow $ 14.2780
     | Show Table
    DownLoad: CSV

    Table 4.  The amount of changes in the objective function for changes in $ q_c $

    Changes in$ {\mathbf \ \ }{{\mathbf q}}_{{\mathbf c}} $ Objective function
    Numerical example 1 Numerical example 2 Numerical example 3 Numerical example 4
    10 1868132000 2619831 393784200 17291600
    15 1917029000 3027281 406228600 17744600
    20 1973978000 3497575 424883000 18274400
    28 2323844000 6807494 439768100 21675600
    36 3050361000 13929150 458673000 28832300
    40 3491321000 18206340 469234000 33176500
    46 3976855000 22915890 469987000 37959900
     | Show Table
    DownLoad: CSV

    Table 5.  The amount of changes in the objective function for the changes in$ \ \ {DR}_c $

    Changes in $ {{\mathbf DR}}_{{\mathbf c}} $ Objective function
    Numerical example 1 Numerical example 2 Numerical example 3 Numerical example 4
    10 440529700 21170450 347895400 183145000
    50 1172853000 21968080 348972000 252260000
    100 2042508000 22915890 359998700 331765000
    150 2944460000 23905960 379543900 415302000
    212 4289378000 24850110 391134100 494550000
     | Show Table
    DownLoad: CSV

    Table 6.  The amount of changes in the objective function due to the changes in$ {\ V}_p $

    Changes in$ {{\mathbf \ \ }{\mathbf V}}_{{\mathbf p}} $ Objective function
    Numerical example 1 Numerical example 2 Numerical example 3
    5 4086738000 101785170 237854320
    10 4289378000 139202200 259873270
    15 5201699000 189831200 267134010
    19 6184267000 248501100 281294130
     | Show Table
    DownLoad: CSV
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