Fuzzy linear programming problems : models and solutions

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, alpha-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately

A Direct Method to Compare Bipolar LR Fuzzy Numbers

We propose a new method for ordering bipolar fuzzy numbers. In this method, for comparison of bipolar LR fuzzy numbers, we use an extension of Kerre’s method being used in ordering of unipolar fuzzy numbers. We give a direct formula to compare two bipolar triangular fuzzy numbers in O(1) operations, making the process useful for many optimization algorithms. Also, we present an application of bipolar fuzzy number in a real life problem

New Method for Solving Fuzzy LR Interval Linear Systems Using Least Squares Models

Recently, Ghanbari and Mahdavi-Amiri [2015, Soft Computing] have proposed a model to characterize exact solutions and presented an algorithm to compute approximate solutions. Here, inspired by Ghanbari and Mahdavi-Amiri, we show that solving fuzzy LR interval linear systems is equivalent to solving fuzzy LR linear systems (FLRLSs). Then we develop some necessary and sufficient conditions for the solvability of FLRLSs. We then provide a new general concept for an approximate solution when an FLRLS lacks a solution. To compute an approximate solution, we propose an algorithm using a least squares method. Finally, we show the appropriateness of our proposed approximate solution recently introduced numerically

A genetic algorithm for solving bus terminal location problem using data envelopment analysis with multi-objective programming

Due to the urban expansion and population increasing, bus network design is an important problem in the public transportation. Functional aspect of bus networks such as the fuel consumption and depreciation of buses and also spatial aspects of bus networks such as station and terminal locations or access rate to the buses are not proper conditions in most cities. Therefore, having an efficient method to evaluate the performance of bus lines by considering both functional and spatial aspects is essential. In this paper, we propose a new model for the bus terminal location problem using data envelopment analysis with multi-objective programming approach. In this model, we want to find efficient allocation patterns for assigning stations terminals, and also we investigate the optimal locations for deploying terminals. Hence, we use a genetic algorithm for solving our model. By using the simultaneous combination of data envelopment analysis and bus terminal location problem, two types of efficiencies are optimized: Spatial efficiency as measured by finding allocation patterns with the most serving amount and the terminals’ efficiency in serving demands as measured by the data envelopment analysis efficiency score for selected allocation patterns. This approach is useful when terminals’ efficiency is one of the important criteria in choosing the optimal terminals location for decision-makers

A New Model for Reassignment of Tasks to Available Employees in Iraq’s Firms

Generalized assignment problem (GAP) is a well-known problem in the combinatorial optimization. This problem is a specific form of assignment problem (AP) when the employees can carry out more than one task simultaneously or each work can be assigned to more than one employee. In this paper, a new model is proposed for reassigning tasks on the available employees of Iraq companies when at least one of the jobholders is absent. Likewise, the returning workers from long holidays assumption are incorporated. Finally, a heuristic algorithm for solving reassignment tasks on laborers is introduced