We present an algorithm to solve a bi-level multi-objective fractional integer programming problem involving fuzzy numbers in the right-hand side of the constraints. The suggested algorithm combine the method of Taylor series together with the Kuhn Tucker conditions to solve fuzzy bi-level multi-objective fractional integer programming problem (FBLMOFIPP) then Gomory cuts are added till the int...

This paper presents a bi level large scale multi objective quadratic programming problem (BLLSMOQPP) with fuzzy parameters in the objective functions problem. In the first phase convert the fuzzy parameters of the problem to equivalent crisp problem to make it easy in solving. In the second phase use Taylor series to convert the quadratic problem to linear problem to be easy for solving with th...

To obtain a better understanding of the trade-offs between various objectives, Bi-Objective Integer Programming (BOIP) algorithms calculate the set of all non-dominated vectors and present these as the solution to a BOIP problem. Historically, these algorithms have been compared in terms of the number of single-objective IPs solved and total CPU time taken to produce the solution to a problem. ...

An interactive pareto optimal with advantage (IPOA) approach for bi-objective programming is proposed and applied on capacitor placement and sizing problem. Two main contradictory concerned which including cost and quality properties are considered as bi-objective programming formulation. The IPOA approach can provide a valuable trade-off pareto-optimal solution by following the intention of de...

Bi-level programming techniques are developed to handle decentralized problems with two-level decision makers, leaders and followers, who may have more than one objective to achieve. This paper proposes a λ-cut and goal programming based algorithm to solve fuzzy linear multiple objective bi-level (FLMOB) decision problems. First, based on the definition of a distance measure between two fuzzy v...

a theorem was recently introduced to establish a relationship betweengoal programming and fuzzy programming for vectormaximum problems.in this short note it is shown that the relationship does not exist underall circumstances. the necessary correction is proposed.

High amounts of waste paper are disposed of every year in Iran posing the health hazard and environmental damages instead of being recovered. Collection, recovery and proper disposal of waste paper without damaging the environment need to design an efficient closed-loop supply chain network. The main objective of this paper is introducing a bi-objective, multi-echelon, multi-product and single-...