A Comparative Study of Redundant Constraints Identification Methods in Linear Programming Problems

Table 6

Comparison of five methods: small-scale problems.

	S. no.	1	2	3	4	5	6	7	8	9	10
	No. of constraints	3	3	3	4	4	3	4	5	5	7
	No. of variables	2	2	2	3	3	3	5	2	4	10
	Brearly’s method (constraint no.)	0	0	0	1 (4)	1 (4)	1 (3)	1 (4)	0	0	2 (3,7)
No. of multiplication/divisions	With redundant	93	93	93	311	311	336	336	505	535	1894
	Without redundant	93	93	93	167	167	186	186	505	535	883
	Linear programming method (constraint no.)	1 (3)	0	1 (3)	2 (3,4)	2 (1,4)	1 (3)	2 (3,4)	4 (2,3, 4,5)	2 (2,4)	5 (2,3, 4,6,7)
No. of multiplication/divisions	With redundant	93	93	93	311	311	336	336	505	535	1894
	Without redundant	42	93	42	76	75	97	88	70	50	161
	Deterministic method (constraint no.)	1 (3)	0	1 (3)	1(3)	2 (1,4)	2 (2,3)	2 (3,4)	2 (3,5)	1 (2)	0
No. of multiplication/divisions	With redundant	93	93	93	311	311	336	336	505	535	1894
	Without redundant	42	93	42	168	75	88	88	159	50	1894
	Stojković-Stanimirović method (constraint no.)	0	0	0	0	1 (1)	0	0	2 (2,3)	1 (2)	0
No. of multiplication/divisions	With redundant	93	93	93	311	311	336	336	505	535	1894
	Without redundant	93	93	93	311	167	178	336	159	167	1894
	Heuristic method (constraint no.)	1 (3)	1 (1)	1 (3)	2 (3,4)	2(1,4)	1 (3)	2 (3,4)	3 (3,4,5)	3 (2,3,4)	5 (2,3,4,6,7)
No. of multiplication/divisions	With redundant	93	93	93	311	311	336	336	505	535	1894
	Without redundant	42	42	42	76	75	97	88	70	50	161