A new method namely, denominator objective restriction method based on simplex method is proposed for solving linear fractional programming problems. Further, another method namely, decomposition-restriction method based on decomposition principle and the denominator objective restriction method is proposed for obtaining an optimal fuzzy solution to the fully fuzzy linear fractional programming...

Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of pro...

In the present paper, we are concerned with a minimax fractional programming problem containing arbitrary norms and establish duality theorems for a dual model related to minimax fractional programming problem under the assumptions of second order (Φ, ρ)-invexity.

In this note we study multiple-ratio fractional 0–1 programs, a broad class of $$\mathcal {NP}$$ -hard combinatorial optimization problems. particular, under some relatively mild assumptions provide complete characterization the conditions, which ensure that single-ratio function is submodular. Then illustrate our theoretical results with assortment and facility location problems, discuss pract...