Combinatorial Efficiency Evaluation: The Knapsack Problem in Data Envelopment Analysis

Table 8

Combinatorial efficiency evaluation with different budget restrictions.

(a) Budget restriction: 200

Methodology	Solution	Combinatorial efficiency
Cook and Green’s	{16,17,31,34,35}	1.2544
Our proposed	{16,17,23,35}	1.3781

(b) Budget restriction: 500

Methodology	Solution	Combinatorial efficiency
Cook and Green’s	{16,17,18,23,26,27,31,34,35,36}	1.3132
Our proposed	{16,17,18,23,26,27,31,34,35,36}	1.3132

(c) Budget restriction: 800

Methodology	Solution	Combinatorial efficiency
Cook and Green’s	{1,14,16,17,18,23,26,27,31,32,34,35,36,37}	1.2837
Our proposed	{1,11,16,17,18,21,23,26,27,29,31,34,35,36}	1.3041

(d) Budget restriction: 1000

Methodology	Solution	Combinatorial efficiency
Cook and Green’s	{1,6,14,15,16,17,18,23,26,27,31,32,34,35,36,37}	1.2719
Our proposed	{1,10,11,12,16,17,18,21,23,26,27,29,30,31,35,36}	1.3186

(e) Budget restriction: 1200

Methodology	Solution	Combinatorial efficiency
Cook and Green’s	{1,6,12,14,15,16,17,18,21,23,26,27,29,31,32,34,35,36,37}	1.2504
Our proposed	{1,2,11,13,14,16,17,18,21,23,26,27,29,31,32,34,35,36,37}	1.2880

(f) Budget restriction: 1500

Methodology	Solution	Combinatorial efficiency
Cook and Green’s	{1,2,6,11,12,13,14,15,16,17,18,21,23,26,27,29,30,31,32,34,35,36,37}	1.2648
Our proposed	{1,2,5,6,7,9,13,14,15,16,17,21,22,23,24,26,27,28,29,34,35}	1.4587