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222 lines
4.8 KiB
222 lines
4.8 KiB
/* Data Envelopment Analysis (DEA)
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*
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* DEA quantifies the relative efficiency of decision making units (DMUs) by
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* finding the efficient frontier in multiple input multiple output data. The
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* inputs are resources (eg. number of employees, available machines, ...),
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* the outputs are productive outputs (eg. contracts made, total sales, ...).
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* The method is non-parametric. More details are available in the paper
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* below.
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*
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* Models according to: Seiford, Threall, "Recent developments in DEA", 1990.
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*
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* Implementation: Sebastian Nowozin <nowozin@gmail.com>
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*/
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### SETS ###
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set dmus; # Decision Making Units (DMU)
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set inputs; # Input parameters
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set outputs; # Output parameters
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### PARAMETERS ###
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param input_data{dmus,inputs} >= 0;
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param output_data{dmus,outputs} >= 0;
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### PROGRAM ###
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var theta{dmus} >= 0;
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var lambda{dmus,dmus} >= 0;
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minimize inefficiency: sum{td in dmus} theta[td];
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s.t. output_lower_limit{o in outputs, td in dmus}:
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sum{d in dmus} lambda[d,td]*output_data[d,o] >= output_data[td,o];
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s.t. input_upper_limit{i in inputs, td in dmus}:
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sum{d in dmus} lambda[d,td]*input_data[d,i] <= theta[td]*input_data[td,i];
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s.t. PI1{td in dmus}:
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sum{d in dmus} lambda[d,td] = 1;
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/*
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possibilities:
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i) (no constraint)
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ii) s.t. PI1{td in dmus}:
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sum{d in dmus} lambda[d,td] <= 1;
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iii) s.t. PI1{td in dmus}:
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sum{d in dmus} lambda[d,td] >= 1;
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*/
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### SOLVE AND PRINT SOLUTION ###
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solve;
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printf "DMU\tEfficiency\n";
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for {td in dmus} {
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printf "%s\t%1.4f\n", td, theta[td];
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}
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### DATA ###
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data;
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set dmus := 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
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41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
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61 62 63 64 65 66 67 68 69 ;
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set inputs := AvgInventory LaborCost OperatingCost Population ;
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set outputs := PrescrVol kDollarValue ;
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param input_data default 0.0 :
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AvgInventory LaborCost OperatingCost Population :=
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1 8000 17030 1280 1410
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2 9000 25890 2779 1523
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3 13694 29076 2372 1354
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4 4250 17506 1385 822
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5 6500 23208 639 746
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6 7000 12946 802 1281
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7 4500 18001 1130 1016
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8 5000 14473 1097 1070
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9 27000 31760 5559 1694
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10 21560 50972 15010 1910
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11 15000 39523 4799 1745
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12 8500 13076 3489 1353
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13 35000 35427 1704 500
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14 18000 27554 2882 1016
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15 59750 53848 14208 2500
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16 19200 38253 1480 2293
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17 40000 109404 83016 2718
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18 8466 18198 1278 2877
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19 16000 40891 7599 4150
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20 10000 45444 5556 4421
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21 25000 35623 2121 3883
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22 14000 20192 5515 3519
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23 12500 34973 10475 32366
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24 17260 32284 14498 3393
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25 7000 17920 7585 4489
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26 14000 42094 3742 2217
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27 16400 35422 14236 4641
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28 13000 19100 3529 5968
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29 30000 72167 8656 8715
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30 12530 19970 1714 5968
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31 31500 39183 4919 5607
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32 10000 32048 3483 7324
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33 22000 68877 12279 8685
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34 10000 29812 3332 8685
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35 16000 47686 2507 5420
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36 10000 33415 4738 7703
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37 9000 12359 4603 4665
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38 16439 23614 2989 6317
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39 14500 36069 1793 31839
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40 39000 76307 9539 15619
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41 24927 40706 12661 30213
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42 13858 39267 4609 34719
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43 33375 29509 11323 31839
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44 29044 44482 5542 34719
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45 32257 61365 20550 32366
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46 8800 49671 3306 43561
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47 47000 40425 10396 31263
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48 12000 33034 4915 31263
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49 28000 69163 4688 15173
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50 13300 28931 16735 73064
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51 13500 29758 4260 62309
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52 24000 40927 8285 23166
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53 16000 40403 2131 99836
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54 17000 38730 2539 60348
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55 25000 35978 2502 99836
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56 16000 37509 6278 99836
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57 20000 46950 10715 85925
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58 14000 35966 3144 85925
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59 22000 68318 8015 108987
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60 21879 69537 7778 108987
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61 15000 25425 2812 201404
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62 10000 19508 2454 201404
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63 20000 28191 3367 201404
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64 18000 37073 8624 108987
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65 19051 23763 3496 201404
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66 15000 28642 3366 201404
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67 10000 35919 3868 201404
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68 24000 54653 26494 108987
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69 1800 6276 3413 60348
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;
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param output_data default 0.0 :
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PrescrVol kDollarValue :=
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1 12293 61.00
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2 18400 92.00
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3 16789 92.65
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4 10700 45.00
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5 9800 50.00
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6 6500 29.00
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7 8200 56.00
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8 8680 45.00
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9 33800 183.00
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10 23710 156.00
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11 24000 120.00
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12 17500 75.00
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13 25000 130.00
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14 26000 122.00
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15 26830 178.513
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16 16600 106.00
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17 90000 450.00
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18 11140 73.624
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19 25868 136.00
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20 32700 191.295
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21 29117 152.864
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22 18000 100.00
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23 11100 60.00
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24 23030 137.778
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25 10656 58.00
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26 24682 152.095
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27 26908 120.00
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28 16464 80.00
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29 57000 321.00
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30 17532 94.747
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31 30035 168.00
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32 16000 100.00
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33 63700 277.00
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34 18000 90.00
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35 27339 139.134
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36 19500 116.00
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37 13000 80.00
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38 15370 102.00
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39 18446 90.00
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40 56000 260.00
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41 73845 364.951
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42 28600 145.00
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43 27000 243.00
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44 52423 279.816
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45 73759 363.388
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46 20500 80.00
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47 27100 115.00
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48 15000 110.00
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49 50895 277.852
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50 19707 128.00
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51 17994 78.80
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52 36135 167.222
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53 30000 153.00
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54 26195 125.00
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55 28000 216.00
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56 24658 152.551
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57 36850 190.00
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58 29250 183.69
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59 50000 250.00
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60 40078 265.443
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61 20200 110.00
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62 12500 75.00
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63 30890 195.00
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64 31000 175.00
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65 31277 192.992
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66 11500 75.00
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67 30000 175.668
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68 38383 190.00
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69 2075 8.650
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;
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end;
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