Grey-fuzzy solution for multi-objective linear programming with interval coefficients

2018 ◽  
Vol 8 (3) ◽  
pp. 312-327 ◽  
Author(s):  
Amin Mahmoudi ◽  
Mohammad Reza Feylizadeh ◽  
Davood Darvishi ◽  
Sifeng Liu
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Fuzzy Programming ◽  
Feasible Region ◽  
Grey Theory ◽  
Acceptable Solution ◽  
Content Type ◽  
Multi Objective ◽  
Interval Coefficients ◽  
Interactive Fuzzy Programming

Purpose The purpose of this paper is to propose a method for solving multi-objective linear programming (MOLP) with interval coefficients using positioned programming and interactive fuzzy programming approaches. Design/methodology/approach In the proposed algorithm, first, lower and upper bounds of each objective function in its feasible region will be determined. Afterwards using fuzzy approach, considering a membership function for each objective function and finally using grey linear programming, the solution for this problem will be obtained. Findings According to the presented example, in this paper, the proposed method is both simple in use and suitable for solving different problems. In the numerical example mentioned in this paper, the proposed method provides an acceptable solution for such problems. Practical implications As in most real-world situations, the coefficients of decision models are not known and exact. In this paper, the authors consider the model of MOLP with interval data, since one of the solutions to cover uncertainty is using interval theory. Originality/value Based on using grey theory and interactive fuzzy programming approaches, an appropriate method has been presented for solving MOLP problems with interval coefficients. The proposed method, against the complex methods, has less effort and offers acceptable solutions.

A multi-objective optimization model for logistic planning in the crisis response phase

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohammad Mahdi Ershadi ◽  
Hossein Shams Shemirani
Keyword(s):  
Objective Function ◽  
Optimization Model ◽  
Crisis Response ◽  
Multi Objective Optimization ◽  
Content Type ◽  
Multi Objective ◽  
Proposed Model ◽  
Different Types ◽  
Response Phase ◽  
Logistic Planning

PurposeProper planning for the response phase of humanitarian relief can significantly prevent many financial and human losses. To this aim, a multi-objective optimization model is proposed in this paper that considers different types of injured people, different vehicles with determining capacities and multi-period logistic planning. This model can be updated based on new information about resources and newly identified injured people.Design/methodology/approachThe main objective function of the proposed model in this paper is minimizing the unsatisfied prioritized injured people in the network. Besides, the total transportation activities of different types of vehicles are considered as another objective function. Therefore, these objectives are optimized hierarchically in the proposed model using the Lexicographic method. This method finds the best value for the first objective function. Then, it tries to optimize transportation activities as the second objective function while maintaining the optimality of the first objective function.FindingsThe performances of the proposed model were analyzed in different cases and its robust approach for different problems was shown within the framework of a case study. Besides, the sensitivity analysis of results shows the logical behavior of the proposed model against various factors.Practical implicationsThe proposed methodology can be applied to find the best response plan for all crises.Originality/valueIn this paper, we have tried to use a multi-objective optimization model to guide and correct response programs to deal with the occurred crisis. This is important because it can help emergency managers to improve their plans.

Plant propagation algorithm for integration of distributed generation in power systems

2018 ◽  
Vol 37 (1) ◽  
pp. 401-417
Author(s):  
Shreya Mahajan ◽  
Shelly Vadhera
Keyword(s):  
Power System ◽  
Objective Function ◽  
Distributed Generation ◽  
Weighting Factor ◽  
Voltage Profile ◽  
Plant Propagation ◽  
Content Type ◽  
Multi Objective ◽  
Propagation Algorithm ◽  
Optimisation Techniques

Purpose The purpose of this study/paper is to integrate distributed generation optimally in power system using plant propagation algorithm. Distributed generation is a growing concept in the field of electricity generation. It mainly comprises small generation units installed at calculated points of a power system network. The challenge of optimal allocation and sizing of DG is of utmost importance. Design/methodology/approach Plant propagation algorithm and particle swarm optimisation techniques have been implemented where a weighting factor-based multi-objective function is minimised. The objective is to cut down real losses and to improve the voltage profile of the system. Findings The results obtained using plant propagation algorithm technique for IEEE 33-bus systems are compared to those attained using particle swarm optimisation technique. The paper deals with the optimisation of weighting factor-based objective function, which counterpoises the losses and improves the voltage profile of the system and, therefore, helps to deliver the best outcomes. Originality/value This paper fulfils an identified need to study the multi-objective optimisation techniques for integration of distributed generation in the concerned power system network. The paper proposes a novel plant-propagation-algorithm-based technique in appropriate allocation and sizing of distributed generation unit.

scholarly journals GENERATING PARETO OPTIMAL SOLUTIONS OF MULTI-OBJECTIVE LFPP WITH INTERVAL COEFFICIENTS USING E-CONSTRAINT METHOD

2015 ◽  
Vol 20 (3) ◽  
pp. 329-345 ◽  
Author(s):  
Suvasis Nayak ◽  
Akshay Ojha
Keyword(s):  
Closed Interval ◽  
Fuzzy Programming ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective ◽  
Decision Variables ◽  
Interval Coefficients ◽  
Constraint Method ◽  
Linear Fractional Programming Problem

This paper illustrates a procedure to generate pareto optimal solutions of multi-objective linear fractional programming problem (MOLFPP) with closed interval coefficients of decision variables both in objective and constraint functions. E-constraint method is applied to produce pareto optimal solutions comprising most preferred solution to satisfy all objectives. A numerical example is solved using our proposed method and the result so obtained is compared with that of fuzzy programming which justifies the efficiency and authenticity of the proposed method.

A note on “a multi-objective programming approach to solve grey linear programming”

2018 ◽  
Vol 8 (1) ◽  
pp. 35-45 ◽  
Author(s):  
Amin Mahmoudi ◽  
Mohammad Reza Feylizadeh ◽  
Davood Darvishi
Keyword(s):  
Linear Programming ◽  
Linear Problem ◽  
Grey System Theory ◽  
Correct Solution ◽  
Programming Approach ◽  
Grey System ◽  
Content Type ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Linear Programming Problems

Purpose The purpose of this paper is to examine the shortcomings and problems associated with the method proposed by Razavi Hajiagha et al. (2012). Design/methodology/approach A multi-objective approach is proposed to solve the grey linear programming problems. In this method, the grey linear problem is converted into a multi-objective problem and then solved. Findings According to the numerical example presented in the study by Razavi Hajiagha et al. (2012), this method does not have a correct solution because the solution does not satisfy the constraints and the upper bounds of the variables are equal or less than their lower bound. Originality/value In recent years, various methods have been proposed for solving grey linear programming problems. Razavi Hajiagha et al. (2012) proposed a multi-objective approach to solve grey linear programming problems, but this method does not have a correct solution and using this method in other researches studies can reduce the value of the grey system theory.

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