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Measuring efficiency of a recycling production system with imprecise data

  • * Corresponding author: Cheng-Feng Hu

    * Corresponding author: Cheng-Feng Hu 

The first author is supported by MOST grant 109-2221-E-415-010

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  • Resources scarcity and environmental degradation have made sustainable resource utilization and environmental protection worldwide. A circular economy system considers economic production activities as closed-loop feedback cycles in which resources are used sustainably and cyclically. Improving the eco-efficiency of the circular economy system has both theoretical value and practical meaning. In this work, the efficiency measurement model of the circular economy system with imprecise data based on network data envelopment analysis is proposed. The two-level mathematical programming approach is employed for measuring the system and process efficiencies. The lower and upper bounds of the efficiencies scores are calculated by transformed conventional one-level linear programs so that the existing solution methods can be applied. The proposed method is applied to assess the circular economy system of EU countries. Our results show that most countries have large difference among fuzzy efficiencies between the production efficiency and recycling efficiency stages, which reveals the source that causes the low efficiency of the circular economy system.

    Mathematics Subject Classification: Primary: 90B30, 90C70; Secondary: 90B50.

    Citation:

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  • Figure 1.  A recycling production system

    Figure 2.  Notations of a recycling production system

    Table 1.  Data set for assessing the recycling production system of EU countries

    DMU $ X^1_1 $ $ X^1_2 $ $ X^1_3 $ $ Y^{1g} $ $ Y^{1b} $ $ X^2 $ $ Y^{2b}_1 $ $ Y^{2b}_2 $ $ Y^{2g}_1 $ $ Y^{2g}_2 $ $ Y^{2g}_3 $
    BE $ 5004 $ $ 109635 $ $ 36332 $ $ 46000 $ $ 63150004 $ $ 2246 $ $ 401821505 $ $ 260944420 $ $ 4855292916 $ $ 0 $ $ 796941524 $
    BG $ 4025 $ $ 9889 $ $ 9662 $ $ 20900 $ $ 120510053 $ $ 262 $ $ 11377402360 $ $ 1228940 $ $ 624743431 $ $ 0 $ $ 47630543 $
    CZ $ 5387 $ $ 48753 $ $ 24880 $ $ 34200 $ $ 25380325 $ $ 489 $ $ 421402923 $ $ 8969823 $ $ 1256506220 $ $ 736788139 $ $ 114365359 $
    DK $ 3024 $ $ 62642 $ $ 14449 $ $ 49300 $ $ 20981701 $ $ 73 $ $ 611036025 $ $ 453589 $ $ 1077685765 $ $ 0 $ $ 408994682 $
    DE $ 43294 $ $ 696913 $ $ 216447 $ $ 49800 $ $ 400049839 $ $ 5139 $ $ 7258425559 $ $ 474079860 $ $ 17091404085 $ $ 10641085528 $ $ 4539988852 $
    EE $ 694 $ $ 5212 $ $ 2818 $ $ 30200 $ $ 24277641 $ $ 39 $ $ 1571046418 $ $ 7207 $ $ 523501743 $ $ 271321686 $ $ 61887076 $
    IE $ 2248 $ $ 97003 $ $ 11609 $ $ 69100 $ $ 15483387 $ $ 11 $ $ 595176663 $ $ 3974931 $ $ 163521509 $ $ 712096348 $ $ 73569252 $
    EL $ 4906 $ $ 22630 $ $ 16702 $ $ 27400 $ $ 69009312 $ $ 1045 $ $ 6101405554 $ $ 2254867 $ $ 223834033 $ $ 559291350 $ $ 14145383 $
    ES $ 23016 $ $ 247385 $ $ 82497 $ $ 37200 $ $ 128946782 $ $ 5561 $ $ 6917730969 $ $ 1630152 $ $ 4782727890 $ $ 729903060 $ $ 462686172 $
    FR $ 30319 $ $ 539810 $ $ 147158 $ $ 43200 $ $ 323467567 $ $ 10927(p) $ $ 8912319950 $ $ 529931991 $ $ 17805492324 $ $ 3347460780 $ $ 1751551681 $
    HR $ 1833 $ $ 10352 $ $ 6639 $ $ 23800 $ $ 5280553 $ $ 3 $ $ 252644927 $ $ 8025 $ $ 248979558 $ $ 21330946 $ $ 5091818 $
    IT $ 25584 $ $ 318657 $ $ 115930 $ $ 37600 $ $ 163997388 $ $ 10323 $ $ 2330759325 $ $ 448068861 $ $ 12940757588 $ $ 16749969 $ $ 663403006 $
    CY $ 611 $ $ 3610 $ $ 1758 $ $ 36100 $ $ 3384016 $ $ 37 $ $ 195647721 $ $ 0 $ $ 35308927 $ $ 94608345 $ $ 12836602 $
    LV $ 1008 $ $ 5019 $ $ 3820 $ $ 26200 $ $ 2531726 $ $ 86 $ $ 51514453 $ $ 27299 $ $ 181524359 $ $ 2877570 $ $ 17228886 $
    LT $ 1481 $ $ 8090 $ $ 5108 $ $ 30700 $ $ 6645689 $ $ 146 $ $ 376219111 $ $ 265115 $ $ 222175413 $ $ 27546012 $ $ 38363239 $
    LU $ 281 $ $ 10079 $ $ 4038 $ $ 105400 $ $ 10129884 $ $ 136 $ $ 394682009 $ $ 447 $ $ 352026252 $ $ 244913566 $ $ 21366130 $
    HU $ 4686 $ $ 24195 $ $ 17865 $ $ 28300 $ $ 15908526 $ $ 159 $ $ 544534135 $ $ 9173793 $ $ 861341728 $ $ 58137346 $ $ 117665638 $
    MT $ 212 $ $ 2613 $ $ 583 $ $ 40100 $ $ 1971253 $ $ 58 $ $ 33840198 $ $ 729659 $ $ 37642029 $ $ 124913458 $ $ 0 $
    NL $ 9050 $ $ 154915 $ $ 49517 $ $ 52800 $ $ 141027997 $ $ 3827 $ $ 6484656382 $ $ 123312495 $ $ 6429380745 $ $ 0 $ $ 1065450090 $
    AT $ 4535 $ $ 90187 $ $ 28127 $ $ 49000 $ $ 61226583 $ $ 174 $ $ 2809451363 $ $ \tilde{Y}^{2b}_2 $ $ 2264108063 $ $ 675844441 $ $ \tilde{Y}^{2g}_3 $
    PL $ 18393 $ $ 84961 $ $ 66652 $ $ 28300 $ $ 181990641 $ $ 372 $ $ 5095006125 $ $ 63893549 $ $ 8399307294 $ $ 4036605469 $ $ 604251699 $
    PT $ 5207 $ $ 31296 $ $ 16114 $ $ 29600 $ $ 14734417 $ $ 425.5(e) $ $ 510697523 $ $ 3546142 $ $ 640596720 $ $ 140172510 $ $ 178428819 $
    RO $ 8939 $ $ 43109 $ $ 22280 $ $ 22900 $ $ 177557398 $ $ 508 $ $ 16702885666 $ $ 10101348 $ $ 714524681 $ $ 77559190 $ $ 250668909 $
    SI $ 996 $ $ 7859 $ $ 4875 $ $ 32900 $ $ 5517787 $ $ 42 $ $ 38252271 $ $ 4285174 $ $ 332376636 $ $ 150325015 $ $ 26539590 $
    SK $ 2762 $ $ 19021 $ $ 10418 $ $ 32000 $ $ 10606352 $ $ 319.7(p) $ $ 506588801 $ $ 4865030 $ $ 424682144 $ $ 49836276 $ $ 74662989 $
    FI $ 2687 $ $ 51490 $ $ 25248 $ $ 43400 $ $ 122869413 $ $ 75 $ $ 10816368847 $ $ 5368598 $ $ 908084245 $ $ 0 $ $ 557119580 $
    SE $ 5245 $ $ 123749 $ $ 32590 $ $ 50800 $ $ 141622198 $ $ 760 $ $ 10806010637 $ $ 22813777 $ $ 1702475279 $ $ 694274083 $ $ 936645999 $
    UK $ 33693 $ $ 437140 $ $ 133688 $ $ 43800 $ $ 277272474 $ $ 13601 $ $ 10410809602 $ $ 735540574 $ $ 13457214835 $ $ 2175093717 $ $ 948588194 $
    1. BE: Belgium; BG: Bulgaria; CZ: Czechia; DK: Denmark; DE: Germany; EE: Estonia; IE: Ireland; EL: Greece; ES: Spain; FR: France; HR: Croatia; IT: Italy; CY: Cyprus; LV: Latvia; LT: Lithuania; LU: Luxembourg; HU: Hungary; MT: Malta; NL: Netherlands; AT: Austria; PL: Poland; PT: Portugal; RO: Romania; SI: Slovenia; SK: Slovakia; FI: Finland; SE: Sweden; UK: United Kingdom
    2. Available flags: p: provisional; e: estimated
     | Show Table
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    Table 2.  $ \alpha $-cuts of the fuzzy system efficiencies

    DMU System Sub-system 1 Sub-system 2
    Belgium (0.4029, 0.4185) (0.0014, 0.0018) (0.9593, 1.0000)
    Bulgaria (0.1067, 0.1376) (0.1077, 0.1377) (0.0272, 0.0309)
    Czechia (0.3176, 0.3177) (0.0678, 0.0734) (0.9328, 0.9433)
    Denmark (0.4708, 0.5354) (0.0907, 0.1084) (1.0000, 1.0000)
    Germany (0.2082, 0.2963) (0.0024, 0.0032) (0.5834, 0.6320)
    Estonia (0.6148, 0.6150) (0.2746, 0.2897) (0.9908, 1.0000)
    Ireland (0.6397, 0.6433) (0.3472, 0.3494) (1.0000, 1.0000)
    Greece (0.0768, 0.0788) (0.0756, 0.0789) (0.0025, 0.0031)
    Spain (0.0159, 0.0252) (0.0285, 0.0433) (0.0155, 0.0243)
    France (0.0823, 0.0839) (0.0006, 0.0006) (0.1034, 0.1038)
    Croatia (1.0000, 1.0000) (1.0000, 1.0000) (1.0000, 1.0000)
    Italy (0.3056, 0.3398) (0.0079, 0.0085) (0.7341, 0.8466)
    Cyprus (0.9489, 1.0000) (1.0000, 1.0000) (0.9942, 1.0000)
    Latvia (1.0000, 1.0000) (1.0000, 1.0000) (1.0000, 1.0000)
    Lithuania (0.2470, 0.2473) (0.2472, 0.2473) (0.0243, 0.0720)
    Luxembourg (1.0000, 1.0000) (1.0000, 1.0000) (1.0000, 1.0000)
    Hungary (0.1631, 0.1789) (0.0167, 0.0277) (0.2482, 0.2539)
    Malta (0.9553, 1.0000) (0.9228, 1.0000) (0.9768, 1.0000)
    Netherlands (0.0257, 0.0544) (0.0184, 0.0407) (0.0488, 0.0603)
    Austria (0.1721, 0.1732) (0.0723, 0.0746) (0.1936, 0.1965)
    Poland (0.4481, 0.4577) (0.0058, 0.0063) (1.0000, 1.0000)
    Portugal (0.0616, 0.0839) (0.0038, 0.0047) (0.1947, 0.1913)
    Romania (0.0346, 0.0680) (0.0043, 0.0085) (0.0689, 0.0732)
    Slovenia (0.6530, 0.6577) (0.3634, 0.3735) (1.0000, 1.0000)
    Slovakia (0.1095, 0.1096) (0.1096, 0.1096) (0.0637, 0.0639)
    Finland (0.3443, 0.5039) (0.0065, 0.0079) (0.8635, 1.0000)
    Sweden (0.1767, 0.1825) (0.0527, 0.0636) (0.1865, 0.2012)
    United Kingdom (0.0291, 0.0298) (0.0022, 0.0029) (0.0320, 0.0321)
     | Show Table
    DownLoad: CSV
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