Fuzzy Multi-objective Linear Programming Research Articles

Applying fuzzy multi-objective linear programming to a project management decision with nonlinear fuzzy membership functions

This paper investigates a multi-objective project management problem where the goals of the decision maker are fuzzy. Prior research on this topic has considered linear membership functions to model uncertain project goals. Linear membership functions, however, are not much flexible to model uncertain information of projects in many situations, and therefore, fuzzy models with linear membership functions are not suitable to be applied in many practical situations. Hence, the purpose of this paper is to apply nonlinear membership functions in order to develop a better representation of fuzzy project planning in practice. This approach supports managers in examining different solution strategies and in planning projects more realistically. In doing so, a fuzzy mathematical project planning model with exponential fuzzy goals is developed first which takes account of (a) the time between events, (b) the crashing time for activities, and (c) the available budget. Following, a weighted max---min model is applied for solving the multi-objective project management problem. The performance of the developed solution procedure is compared with the literature that applied linear membership functions to this problem, and it is shown that the model developed in this paper outperforms the existing solution.

Iterative Goal Programming Approach for Solving Multi-objective Intuitionistic Fuzzy Linear Programming Problem

This paper presents an Iterative goal programming approach for solving Multi-objective Intuitionistic Fuzzy Linear Programming Problem (MOIFLPP). The MOIFLP problem involving aspiration level and the right hand side constraints are trapezoidal intuitionistic fuzzy number (TIFN). The concept of ∝-cut of IFN is used to convert the TIFN into crisp one. A solution algorithm is proposed to solve the MOIFLPP and a numerical example is given in detail to explain the solution procedure. Furthermore, the proposed method is easy to apply in real-life situations which give more accurate solution in the sense that the objective values are sufficiently closer to the aspiration levels. Finally, a real life example is used and a compromise solution is found out to satisfy the decision maker.

Fuzzy multi-objective linear programming for a stochastic hub maximal covering problem with uncertain shipments

When there are many origins and destinations in a network, the use of hubs helps to benefit from the economies of scale in transportation and considerable reduction in the number of required links. We propose a bi-objective mathematical model for a stochastic hub maximal covering problem formulated under two real-world assumptions. In many networks, there are some risks for the shipments among the nodes. In order to consider such risks, a second objective, in addition to maximising the utility of covered nodes, is aimed at maximising the safety of weakest path in the network. Also, similar to the real world situation, it is assumed that the transport times are normal random variables. An efficient nonlinear mixed-integer model is developed and after linearising, a fuzzy multi-objective linear programming method is applied to solve it. Notably, the single objective version of our model has smaller number of variables and equations than the previous ones. The computational results by establishing 24 test problems extracted from the Turkish dataset confirm: 1) the validity of proposed formulations for single objective hub maximal covering problem; 2) the satisfying performance of proposed bi-objective model in improving the safety of designed network.

A Fuzzy Scheduling Approach for Medicine Supply in Hospital Management Information System with Uncertain Demand

Generally, it is very difficult to determine the medicine supply in hospital under uncertain environment. Here, the medical supply decision problem in uncertain environment is modeled as a fuzzy multi-objective linear programming model. First, the medicine supply in hospital management system is analyzed and the uncertainties in medicine supply are modeled as fuzzy numbers. Second, a fuzzy medicine scheduling is built to fit the uncertain demand and the solving steps are illustrated too. Third, a numerical example is presented to demonstrate the proposed model, and the compared results verify its effectiveness. Last, some important conclusions and future work are sum up at the end of the paper.

Stochastic facility and transfer point covering problem with a soft capacity constraint

Existing models for transfer point location problems (TPLPs) do not guarantee the desired service time to customers. In this paper, a facility and TPLP is formulated based on a given service time that is targeted by a decision maker. Similar to real-world situations, transportation times and costs are assumed to be random. In general, facilities are capacitated. However, in emergency services, they are not allowed to reject the customers for out of capacity reasons. Therefore, a soft capacity constraint for the facilities and a second objective to minimize the overtime in the facility with highest assigned demand are proposed. To solve the biobjective model with random variables, a variance minimization technique and chance-constraint programming are applied. Thereafter, using fuzzy multiple objective linear programming, the proposed biobjective model is converted to a single objective. Computational results on 30 randomly designed experimental problems confirm satisfactory performance of the proposed model in reducing the variance of solutions as well as the overtime in the busiest facility.

Stratified simplex method for solving fuzzy multi-objective linear programming problem

This paper is to deal with a kind of fuzzy multi-objective linear programming (FMOLP) problem with symmetric trapezoidal fuzzy numbers. Several methods has been proposed in order to obtain fuzzy efficient solution to FMOLP problem. In this paper, we change FMOLP problem into the complete stratified fuzzy linear programming problem, then use the stratified simplex method to obtain the fuzzy optimal solution directly without converting them to crisp linear programming problem. We then prove that this fuzzy optimal solution is the fuzzy efficient solution of the original FMOLP problem. A numerical example is given to illustrate the proposed method.

Pareto-optimal solutions for multi-objective flexible linear programming

The aim of this paper is twofold. Firstly, to define a solution concept of Pareto-optimality for a multi-objective flexible linear programming (MOFLP) problem (or multi-objective fuzzy linear programming problem) and design a method to extract a Pareto-optimal solution of MOFLP problem from the set of optimal solutions of equivalent optimization problem formulated by Dubey and Mehra (2013). Secondly, to extend this study to multi-objective linear programming problem involving hard and flexible constraints with interval uncertainty. A flexible constraint with interval uncertainty generalizes a flexible constraint by allowing preferences to be expressed in the form of intervals. An optimistic-pessimistic approach is proposed to solve multi- objective flexible linear programming with interval uncertainty (MOFLPIU) using an interval-valued fuzzy set representation and the Hurwicz optimism-pessimism criterion.

Electricity monitoring system with fuzzy multi-objective linear programming integrated in carbon footprint labeling system for manufacturing decision making

In the novel electricity monitoring system designed in this study, manufacturing data with energy consumption are transformed in real time in the communication module and analysis module and then sent to such information devices as notebooks, i-Pads, or i-Phones. A fuzzy multiple objective linear programming (FMOLP) model is formulated to integrate the designed system for making decision associated with about environmental regulations and cost-effectiveness of carbon emissions in manufacturing firms given a carbon footprint label (CFL). Implementation results demonstrate that the proposed system is very effective in terms of CFL, cost-effectiveness, and manufacturing capacity. Importantly, the electric monitoring system can be practically installed in specific equipment to acquire electric consumption in real time and then helped decision makers to achieve a satisfactory solution in which manufacturing costs and CFL are simultaneously considered under restrain of electricity uncertainty.

A multi-objective fuzzy linear programming model for optimization of natural gas supply chain through a greenhouse gas reduction approach

Natural gas is one of the most important sources of energy for many of the industrial and residential users in the world. It has a complex and huge supply chain which is in need of heavy investments in all the stages of exploration, extraction, production, transportation, storage and distribution. The aim of this study is evaluation and optimization of natural gas supply chain using a multi-objective multi-period fuzzy linear programming model considering economic and environmental objectives. In the proposed model, to deal with uncertainty, the parameters of problem including demand, capacity and cost are considered as fuzzy parameters. To solve the problem, a combination of possibilistic programming approach based on previous approach is used to verify and validate the model. A small-sized problem was solved using GAMS 23.2 software and sensitivity analysis is conducted on its parameters. To the best of our knowledge, this is the first study that presents a multi-objective fuzzy linear programming model for optimization of natural gas supply chain through a greenhouse gas reduction approach.

Fuzzy Multi Objective Linear Programming Problem with Imprecise Aspiration Level and Parameters

This paper considers the multi-objective linear programming problems with fuzzygoal for each of the objective functions and constraints. Most existing works deal withlinear membership functions for fuzzy goals. In this paper, exponential membershipfunction is used.

Bi-criteria approach to containership slot allocation in liner shipping

Containership capacity allocation is an important issue since liner companies must avoid unused space on a voyage to maximize their revenue. Therefore, in the face of uncertain cargo demand and fiercely competitive markets, liner carriers build revenue management systems to maximize voyage profits through careful consideration of slot allocation and pricing. A containership slot allocation model is proposed in this article to deal with two conflicting objectives: carrier’s freight contribution and agents’ degree of satisfaction, as well as fuzzy constraints, that is, uncertainties of cargo transportation demand and weight. This model is formulated using fuzzy multi-objective programming for deep-sea liner service containership slot allocation. Interactive fuzzy multi-objective linear programming with fuzzy parameters is applied to solve this problem. The proposed model is applied to an Asia-Europe service route of a liner company to test its efficacy. Results show the model’s applicability and excellent performance in practice.

A random fuzzy multi-objective linear programming approach through possibility theory

This paper presents new methods for a multi-objective linear programming (MOLP) problem with random fuzzy variables (RFVs). First, a robust MOLP problem is introduced in which the coefficients of objective functions and constraints are RFVs. Then, the proposed problem is transformed into deterministic linear programming problems by new methods based on the idea of possibility theory and the random fuzzy chance-constrained programming. These methods can satisfy optimistic and pessimistic decision makers separately and simultaneously. Finally, an example is also solved to clarify the discussed methods. [Received 13 June 2013; Revised 24 November 2013; Revised 5 April 2014; Accepted 20 April 2014]

A mathematical programming model for a multi-objective supplier selection and order allocation problem with fuzzy objectives

This paper studies a multi-objective supplier selection and order allocation problem with fuzzy objectives. The problem is formulated as a linear programming model, and three interactive and non-interactive approaches are suggested for solving the problem, namely interactive fuzzy multi-objective linear programming (i-FMOLP), interactive fuzzy goal programming (IFGP) and a standard fuzzy programming approach. The objective of the paper is to efficiently obtain solutions that are close to the aspiration levels and the decision maker's satisfaction degree. The performance of the suggested approaches and the weighted max-min approach of an earlier study are evaluated by using a set of metric distance functions. The results obtained illustrate that the solutions of the approaches applied in this paper are closer to the ideal solution as compared to the compromise solution of the weighted max-min method used in an earlier study.

A goal programming procedure for solving fuzzy multiobjective fractional linear programming problems

This paper presents a modification of Pal, Moitra and Maulik's goal programming procedure for fuzzy multiobjective linear fractional programming problem solving. The proposed modification of the method allows simpler solving of economic multiple objective fractional linear programming (MOFLP) problems, enabling the obtained solutions to express the preferences of the decision maker defined by the objective function weights. The proposed method is tested on the production planning example.

Evaluating a green supplier selection problem using a hybrid MODM algorithm

The green supplier selection (GSS) problem is a well-known strategy to outsource with respect to environmental protection. Although different applications of GSS have been proposed in the literature, the fuzzy five-objective GSS model has not been studied yet. This paper develops a multi-objective fuzzy linear programming model for a GSS problem, including 17 criteria, formed into 5 clusters while a hybrid fuzzy multi objective decision making (MODM) is employed to solve it. The aim of this paper is to select the best set of suppliers regarding optimal allocation of order quantities while demand and supplier's capacity are restricted. In the proposed hybrid solution algorithm, fuzzy decision making trial and evaluation laboratory approach is used to understand the interrelation among criteria, and fuzzy analytical network process (ANP) provides the criteria weights with respect to their dependencies. Then, a hybrid of fuzzy ANP and fuzzy multi-objective linear programming presents optimal order allocation among the selected suppliers, verified and compared with two other methods. Finally, the conclusion and future research are presented.

A Parametric Approach to Solve Multi Objective Fuzzy Linear Programming Problem

A new method has been proposed by Senthilkumar and Rajendran (1) for solving fuzzy linear programming problem in parametric form. This paper extends this method for solving multi-objective fuzzy linear programming problem with fuzzy variables in parametric form. To obtain optimal solution, problem is converted into two auxiliary crisp linear programming problems corresponding to each objective functions. A numerical example is given to check the feasibility of the proposed method.

A Multi-Objective Fuzzy-Based Procedure for Reactive Power-Based Preventive Emergency Strategy

This paper proposes a multi-objective fuzzy linear programming (MFLP) procedure for maximizing the effects of preventive reactive power control actions to overcome any emergency condition when they occurred. The proposed procedure is very significant and seeks to eliminate violation constraints and give an optimal reactive power reserve for multi-operating conditions. The proposed multi-objective functions are: minimizing the real transmission losses, maximizing the reactive power reserve at certain generator and maximizing the reactive power reserve at all generation systems and/or switchable devices. The proposed MFLP is applied to 5-bus test system and the West Delta region system as a part of the Egyptian Unified network. The numerical results show that the proposed MFLP technique achieves a minimum real power loss with maximal reactive reserve for power systems for different operating conditions.

Computing a Pareto-optimal solution for multi-objective flexible linear programming in a bipolar framework

In this paper, we study the multi-objective flexible linear programming (MOFLP) problems (or fuzzy multi-objective linear programming problems) in the heterogeneous bipolar framework. Bipolarity allows us to distinguish between the negative and the positive preferences. Negative preferences denote what is unacceptable while positive preferences are less restrictive and express what is desirable. This viewpoint enables us to handle fuzzy sets representing constraints and objective functions separately and combine them in distinct ways. In this paper, a solution concept of Pareto-optimality for MOFLP problems is defined and an approach is proposed to single out such a solution for MOFLP with highest possible degree of feasibility.

Performance evaluation and a flow allocation decision model for a sustainable supply chain of an apparel industry

Abstract There is a growing concern that business enterprises and their supply chains focus primarily on economic activities and ignore their impact on the environment and society. This paper aims to help decision makers, managers, and practitioners to achieve economic growth, societal development, and environmental protection by developing sustainable supply chain performance measures and proposes a partner selection and flow allocation decision-making model. Survey data from 278 business organizations from the Indian apparel industry supply chain network were used, and an integrated method of structural equation modeling, fuzzy analytical hierarchy process, and fuzzy multi-objective linear programming was applied to the proposed model. The results of the structural equation modeling analysis indicate that the survey respondents considered sustainable production performance to be of prime importance, which thus indicates its significance in developing a sustainable supply chain for the apparel industry. To illustrate the use of the proposed model for partner selection and flow allocation decision making, real-time data from an apparel manufacturer are presented. Optimal results were obtained for two strategies—sustainability and cost saving—to show a cost–benefit trade-off when developing a sustainable supply chain. Using comparative performance, a decision maker can choose an appropriate strategy based on cost–benefit analysis of the presented trade-offs.

A Fuzzy Multi-Objective Linear Programming Model: A Case Study of an LPG Distribution Network

Supply chain management is a subject that has an increasing importance due to the developments in the global markets and technology. In this paper, a fuzzy multi-objective linear programming model is developed for the supply chain of a company dealing with procurement, storage, filling, and distribution of liquefied petroleum gas (LPG) in Turkey. The model intends to determine the quantities of LPG to be procured, stored, filled to cylinders, and transported between the plants and demand centers for six planning periods. In this model, which aims to minimize both total costs (sum of procurement, storage, filling, and transportation costs) and total transportation distances, demand quantities of the main demand centers and decision maker's aspiration levels about objective functions are fuzzy. After comparing the results obtained from the model with those obtained by using different methods, it is concluded that the proposed method can be applied to real world problems practically and it may be used in this type of problems in order to generate an efficient solution.