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