Combinatorial Efficiency Evaluation: The Knapsack Problem in Data Envelopment Analysis

Table 6

The data of Example 2.

Project	Input	O1	O2	O3	O4	O5	Efficiency
1	84.20	67.53	70.82	62.64	44.91	46.28	0.6543
2	90.00	58.94	62.86	57.47	42.84	45.64	0.5512
3	50.20	22.27	19.68	6.73	10.99	5.92	0.3360
4	67.50	47.32	47.05	21.75	20.82	19.64	0.5283
5	75.40	48.96	48.48	34.90	32.73	26.21	0.5064
6	90.00	58.88	77.16	35.42	29.11	26.08	0.6148
7	87.40	50.10	58.20	36.12	32.46	18.90	0.5060
8	88.80	47.46	49.54	46.89	24.54	36.35	0.4204
9	95.90	55.26	61.09	38.93	47.71	29.47	0.5177
10	77.50	52.40	55.09	53.45	19.52	46.57	0.5431
11	76.50	55.13	55.54	55.13	23.36	46.31	0.5618
12	47.50	32.09	34.04	33.57	10.60	29.36	0.5525
13	58.50	27.49	39.00	34.51	21.25	25.74	0.5045
14	95.00	77.17	83.35	60.01	41.37	51.91	0.6539
15	83.80	72.00	68.32	25.84	36.64	25.84	0.6518
16	35.40	39.74	34.54	38.01	15.79	33.06	0.8542
17	32.10	38.50	28.65	51.18	59.59	48.82	1.0000
18	46.70	41.23	47.18	40.01	10.18	38.86	0.7618
19	78.60	53.02	51.34	42.48	17.42	46.30	0.5179
20	54.10	19.91	18.98	25.49	8.66	27.04	0.3523
21	74.40	50.96	53.56	55.47	30.23	54.72	0.6022
22	82.10	53.36	46.47	49.72	36.53	50.44	0.5068
23	75.60	61.60	66.59	64.54	39.10	51.12	0.6754
24	92.30	52.56	55.11	57.58	39.69	56.49	0.5003
25	68.50	31.22	29.84	33.08	13.27	36.75	0.4024
26	69.30	54.64	58.05	60.03	31.16	46.71	0.6633
27	57.10	50.40	53.58	53.06	26.68	48.85	0.7420
28	80.00	30.76	32.45	36.63	25.45	34.79	0.3478
29	72.00	48.97	54.97	51.52	23.02	45.75	0.5784
30	82.90	59.68	63.78	54.80	15.94	44.04	0.5505
31	44.60	48.28	55.58	53.30	7.61	36.74	0.9459
32	54.50	39.78	51.69	35.10	5.30	29.57	0.6393
33	52.70	24.93	29.72	28.72	8.38	23.45	0.4299
34	28.00	22.32	33.12	18.94	4.03	9.58	0.7973
35	36.00	48.83	53.41	40.82	10.45	33.72	1.0000
36	64.10	61.45	70.22	58.26	19.53	49.33	0.7708
37	66.40	57.78	72.10	43.83	16.14	31.32	0.7391