Multi-objective Linear Programming Research Articles

Fuzzy Multi-Objective Linear Programming Problem Using DM's Perspective

In this paper, a two-stage method has been proposed for solving Fuzzy Multi-objective Linear Programming Problem (FMOLPP) with Interval Type-2 Triangular Fuzzy Numbers (IT2TFNs) as its coefficients. In the first stage of problem solving, the imprecise nature of the problem has been handled. All technological coefficients given by IT2TFNs are first converted to a closed interval and then the objectives are made crisp by reducing a closed interval into a crisp number and constraints are made crisp by using the concept of acceptability index. The amount by which a specific constraint can be relaxed is decided by the decision maker and thus the problem reduces to a crisp multi-objective linear programming problem (MOLPP). In the second stage of problem solving, the multi-objective nature of the problem is handled by using fuzzy mathematical programming approach. In order to explain the methodology, two numerical examples of the proposed methodology in Production planning and Diet planning problems have also been worked out in this paper.

Centralized resource allocation based on energy saving and environmental pollution reduction using data envelopment analysis models

Environmental pollution has caused governments to be concerned about energy saving and the reduction of environmental pollution. Some researchers have presented resource allocation models as multi-objective linear programming (MOLP) in order to pay more attention to energy saving and environmental pollution reduction. Energy saving affects both desirable and undesirable outputs. In this paper, we argue for the inapplicability of the existing models for reducing the undesirable outputs through energy saving. The purpose of this paper is to design a model based on data envelopment analysis (DEA) that would result in reduced pollution through energy saving. Moreover, since an undesirable output is considered as a function of the total desirable outputs, if necessary, the changes should be applied to the total desirable outputs and there is no need to reduce each desirable output individually. Finally, the model proposed based on goal programming (GP) is used in 20 different regions in China. The results produced by this model indicate that the reduction proportion of total environmental pollution emissions per energy saving was larger than the reduction proportion of total desirable outputs.

Optimal Matching Metaheuristic Algorithm for Potential Areas of Agricultural Economic Resources Development Based on Spatial Relationship

The agriculture sector is the backbone of the economies of many Asian countries such as India, China, and Bangladesh. The agriculture sector can contribute a major share to the GDP of such countries where the main occupation of the citizens is agriculture or the dependency of the citizens is mainly on the agricultural productivity. It is important to study the potential areas of agricultural economic resource development. The existing methods are not efficient enough to map the potential areas of agricultural productivity with economic resource development, and hence, it has motivated us to study the aspects which impact the economic resource development based on agricultural productivity. There are numerous factors such as low productivity, high irrigation amount, high labor charges, low proportion of planning optimization, and low crop yield that should be considered to study the correlation between economic development and agricultural productivity. Firstly, the spatial relationship of potential areas of agricultural economic resources development is analyzed in this paper. Secondly, the multiobjective linear programming model is proposed. Based on this multiobjective model, the optimal matching model for potential areas of agricultural economic resource development is constructed, and the improved genetic algorithm is used to solve the model to realize the optimal matching of potential areas of agricultural productivity and economic resource development. The experimental results show that the proposed method has high economic benefit, low irrigation amount, and high proportion of planning optimization with high crop yield.

Intuitionistic fuzzy optimization approach in optimal irrigation planning of Ukai-Kakrapar irrigation project, India

ABSTRACT This article addresses the formulation of the Intuitionistic Multiobjective fuzzy linear programming (IFO MOFLP) model for optimal allocation of crops in the command area of the Ukai-Kakrapar Irrigation Project, India. Initially, the crisp linear programming (LP) model is applied to acquire the optimal results of three conflicting objectives, namely, maximization of net irrigation benefits (NIBs), minimization of cost of cultivation (CC) and maximization of revenue generation from industrial and municipal supplies (MI). Subsequently, the LP solutions were used to develop the IFO MOFLP, IFO MOFLP with a hesitation index and two-phase IFO MOFLP (TPIFO MOFLP) models for the complete command area. The performance of the aforesaid models is assessed in terms of irrigation intensity, degree of acceptance (α), rejection (β) and hesitation index (π) for inflows at 75% probability of exceedance. The irrigation intensity from the proposed TPIFO MOFLP model has been found to be 101.28%, while NIB, CC and MI from the proposed model are 10,575.38, 5438.42 and 2638.20 million Rs, respectively, with α = 0.64, β = 0.18 and π = 0.18, respectively. The proposed TPIFO MOFLP model has been compared better with MOFLP as the former gives additional uncertainty controlling parameters like α, β and π, which would help the planner to take better decisions for real-world problems.

Scalarizing fuzzy multi-objective linear fractional programming with application

Scalarizing fuzzy multi-objective linear fractional programming with application

Application of fuzzy random-based multi-objective linear fractional programming to inventory management problem

This research article aims to study a multi-objective linear fractional programming (FMOLFP) problem having fuzzy random coefficients as well as fuzzy pseudorandom decision variables. Initially, the FMOLFP model is converted to a single objective fuzzy linear programming (FLP) model. Secondly, we show that a fuzzy random optimal solution of an FLP problem is resolved into a class of random optimal solution of relative pseudorandom linear programming (LP) model. As a result, some of theorems show that a fuzzy random optimal solution of a fuzzy pseudorandom LP problem is combined with a series of random optimal solutions of relative pseudorandom LP problems. As an application, the developed approach is implemented to an inventory management problem by taking the parameters as trapezoidal fuzzy numbers, ultimately resulting in a new initiative for modelling real-world problems for optimization. In the last, some numerical examples are introduced to clarify the obtained results and their applicability.

Electromagnetic Signal Classification Based on Class Exemplar Selection and Multi-Objective Linear Programming

In the increasingly complex electromagnetic environment, a variety of new signal types are appearing; however, existing electromagnetic signal classification (ESC) models cannot handle new signal types. In this context, the emergence of class-incremental learning aims to incrementally update the classification model as new categories emerge. In this paper, an electromagnetic signal classification framework based on class exemplar selection and a multi-objective linear programming classifier (CES-MOLPC) is proposed in order to continuously learn new classes in an incremental manner. Specifically, our approach involves the adaptive selection of class exemplars considering normalized mutual information and a multi-objective linear programming classifier. The former is used to maintain the classification capability of the model for previous categories by selecting key samples, while the latter is used to allow the model to adapt quickly to new categories. Meanwhile, a weighted loss function based on cross-entropy and distillation loss is presented in order to fine-tune the model. We demonstrate the effectiveness of the proposed CES-MOLPC method through extensive experiments on the public RML2016.04c data set and the large-scale real-world ACARS signal data set. The results of the comparative experiments demonstrate that our method can achieve significant improvements over state-of-the-art methods.

Extension principle-based solution approach to full fuzzy multi-objective linear fractional programming

Extension principle-based solution approach to full fuzzy multi-objective linear fractional programming

Using a Product Life Cycle Cost Model to Solve Supplier Selection Problems in a Sustainable, Resilient Supply Chain

Supplier selection constitutes a crucial component of manufacturing procurement. We developed a product life cycle cost (PLCC) model to support Taiwanese light-emitting diode (LED) manufacturers in capacity planning for sustainable and resilient supply chain (SC) management. For firms, supply chain PLCC (SCPLCC) is a key consideration, but relevant evidence is scarce. We applied two types of goal programming, namely multiobjective linear programming and revised multichoice goal programming (RMCGP), to develop a PLCC-based model that minimizes net costs, rejections, and late deliveries. Moreover, we constructed a decision-making tool for application to a case of SC sustainable procurement management in a high-tech Taiwanese LED company. Managers can resolve relevant problems by employing the two approaches of the SCPLCC model with various parameters. The implementation of RMCGP with weighted linear goal programming sensitivity analysis produced sufficient findings, according to a study of five models for practical implications. The primary findings of the current model assist business decision-makers in minimizing PLCC, reducing PLCC cost, minimizing net cost, number of rejections, number of late deliveries, achieving PLCC goals, and selecting the best supplier in the context of sustainable SC development.

Fuzzy harmonic mean technique for solving fully fuzzy multilevel multiobjective linear programming problems

This paper illustrates how the fuzzy harmonic mean technique can efficiently solve fully fuzzy multilevel multiobjective linear programming (FFMMLP) problems. First, at each level, the FFMMLP problem can be converted into three crisp multiobjective linear programming (CMLP) problems using the crisp linear technique. Then, the fuzzy harmonic mean technique is utilized to aggregate each crisp problem's multiobjective into a single objective. Second, the ensuing final, single-objective problem is constructed using the harmonic mean for each level. Finally, it is solved to obtain a fuzzy compromise solution for the FFMMLP problem in general. Two examples are given to obtain the application of the proposed method. One example is applying the proposed approach to a multilevel multiobjective production planning model for a supply chain under a fully fuzzy environment.

Economic, Environmental and Energy analysis of carbon capture systems coupled in coal power plants for the reduction of CO2 emissions in Brazil

This study assesses the contribution of the implementation of the Calcium Looping (CaL) process to capture carbon dioxide (CO2) from coal power plants in Brazil, as a strategy to meet the established environmental goals for 2030. A multi-objective linear programming model based on Input-Output analysis (IO-MOLP) is developed to evaluate the interrelations of economic, energy and environmental systems. Three objective functions are considered: maximization of Gross Domestic Product (GDP), minimization of Greenhouse Gas emissions (GHG), and minimization of energy consumption for exclusively energy purposes (CFE). Two scenarios are analyzed: (i) a baseline scenario (BL) which does not incorporate CaL in coal power plants, (ii) a scenario (S1) which incorporates CaL systems. In general, the implementation of CaL in coal power plants improves the overall environmental impact; however, in our results, this reduction was not found significant. On the other hand, a contraction in the economic system and an expansion in the consumption of energy resources may be triggered by this strategy. These results reaffirm the importance of assessing the effects of the environmental and energy decisions and policies on the country's economic system, by means of multi-objective models able to unveil the trade-offs at stake between multiple, conflicting and incommensurate evaluation axes of the merits of those policies.

A multi-product and multi-period aggregate production plan: a case of automobile component manufacturing firm

PurposeThe study attempts to develop a multi-product multi-period (MPMP) aggregate production plan (APP) to fulfill the customers' demand in terms of throughput and lead time for achieving market competence.Design/methodology/approachThis research proposes an integrated Fuzzy analytical hierarchy process (FAHP), multi-objective linear programming (MOLP), and simulation approach. Initially, FAHP is used to select the essential objectives a firm desires to achieve. Adopting the MOLP, an APP is formulated for the firm under study. Later, the simulation model of a firm is created in a discrete-event simulation (DES) software Arena© to evaluate the applicability of the proposed APP. A comparative analysis of the manufacturing performance levels (namely throughput, lead time, and resource utilization) achieved through the implication of an existing production plan and proposed APP is conducted further.FindingsThe findings from the study depict that the proposed MOLP-based APP can satisfy the customers' requirement (namely throughput and lead time) and improve the level of resource utilization compared with the firm's existing production plan.Research limitations/implicationsThe proposed research facilitates researchers and practitioners to understand the process of developing MOLP-based MPMP APP and analyzing its applicability through simulation technique to be utilized for developing APP at their firm.Originality/valueAn integrated FAHP-MOLP-simulation framework is the novel contribution to the literature on production planning. It can be extended to solve strategic, tactical, and operational problems in different domains like service, healthcare, supply chain, logistics, and project management.

Assessing the performance of exchange traded funds in the energy sector: a hybrid DEA multiobjective linear programming approach.

This paper proposes a two-step approach to build portfolio models. The first step employs the Data Envelopment Analysis (DEA) to select assets attaining efficient financial performance according to a set of indicators used as inputs and outputs. The second step builds interval multiobjective portfolio models to obtain the optimal composition of efficient portfolios previously identified with respect to investor preferences. The usefulness of this proposed methodology is illustrated through a selected sample of diversified Exchange Traded Funds (ETFs) operating in the US energy sector. Our results with respect to all models and time horizons mainly show that: (i) ETFs related to nuclear energy are more often viewed as efficient according to all DEA models considered; (ii) the efficient portfolios do not contain any ETFs related to the renewable energy sector; and (iii) natural gas and oil are the sectors that have the most ETFs represented in efficient portfolios.Supplementary InformationThe online version contains supplementary material available at 10.1007/s10479-021-04323-6.

Multi-Objective Approach for Managing Uncertain Delivery from Renewable Energy Sources within a Peer-to-Peer Energy Balancing Architecture

On the energy markets, conscious customers may exist who are not only interested in minimising the cost of energy purchase, but, simultaneously, in optimising some other quality criteria (arising from ecological concerns, or social responsibility of the energy producers). In this paper, we develop both a mathematical optimisation problem and a market framework for balancing a power system in a peer-to-peer market setup, where product differentiation can be considered directly on the market. Thus, origins of energy may be clearly identified, and product quality characteristics can be understood by various actors (including households). We derive a multi-objective (mixed-integer) linear programming optimisation problem for balancing the energy system in a peer-to-peer energy trading environment, where not only the cost but also other additional quality criteria are considered. We have identified many possible actors to be present within the proposed market setup. They include consumers, producers, brokers and flexible prosumers with storage. The approach was tested on the IEEE 30-bus standard test system, over three different scenarios, by analysing the impact of various actors/peers activities and different extensions. It has been shown that a multi-objective energy balancing scheme may be developed through crafted optimisation problem and that each type of studied peers may bring some added value to the power system balancing.

A goal programming approach for multi-objective linear fractional programming problem with LR possibilistic variables

A goal programming approach for multi-objective linear fractional programming problem with LR possibilistic variables

An Experimental Study with Objectives Functions for Portfolio Optimization Problem

This paper presents an experimental study with the objective’s functions of a portfolio optimization problem. This study is done by three optimization problems with a different number of objectives. A hybrid approach has been adopted for this which is a combination of a few methods, such as investor topology, cluster analysis, analytical hierarchy process (AHP), and optimization techniques. Teaching-learning-based optimization (TLBO), biogeography-based optimization (BBO), and fuzzy multi-objective linear programming (FMOLP) are compared in this paper for portfolio optimization. From this research, the conclusion comes that there should not be more options in the objective functions, otherwise the motive of the portfolio becomes misleading, but many more parameters can be used for stock valuation.

Alternate solution approach for ML-MOLFPP problems

This article presents an alternate solution approach for multi-level multi objective linear fractional programming problems (ML-MOLFPPs) with modifications in the modified fuzzy goal programming (FGP) approach suggested by Lachhwani [1]. In the proposed alternate technique, fractional objective functions at every level are individually considered and converted into individual membership function instead of treating numerator and denominator part of objective function separately for formulation of membership function. The proposed alternate approach for obtaining compromise optimal solution for ML-MOLFPPs is comparatively less computational and efficient. This is demonstrated with the use of proposed technique over numerical example and comparative analysis with earlier method.

A constructive method for solving a multi-objective linear program with bounded variables

The search for an optimal solution remains a central objective in optimisation, but in many situations the optimal solution cannot be obtained in polynomial time. For this, it would sometimes be necessary to find a good solution close to the optimum that can be obtained in a reasonable time. The aim of this paper is to find an ε-efficient or efficient solution for a multi-objective linear programming problem with polyhedral constraints and bounded decision variables. For this, we define an ε-efficient solution for which a characterisation theorem is proved, and where the ε-optimality criterion is formulated simultaneously for all the objectives of the problem. By using this concept of ε-efficiency, we develop an algorithm that combines the well known Benson's procedure in multi-objective linear programming and the adaptive method elaborated for finding ε-optimal solutions in mono-objective linear programming, based on the diminution of the suboptimality estimate. The proposed algorithm is illustrated by a numerical example and finally, it is implemented in MATLAB to solve a set of generated test problems. The efficient solutions found are located on the Pareto fronts of the same test problems treated by using the well-known Gamultiobj algorithm of MATLAB optimisation tool.

Profit and Satisfaction Aware Order Assignment for Online Food Delivery Systems Exploiting Water Wave Optimization

Online Food delivery, a specialized application of mobile crowdsourcing, has accelerated its popularity due to rushed urban lifestyle in recent times. The food delivery order assignment to workers that maximizes the service qualities, such as maximization of workers’ profit and minimization of order completion time to enhance the customer satisfaction at the same time, is a challenging problem. Existing works in the literature are limited either by focusing solely on minimizing order completion time or reduction of cost incurred in delivery of orders. In this paper, we develop a framework for optimal assignment of food delivery orders to workers as a multi-objective linear programming (MOLP) problem that makes a trade-off in between the worker profit and customer satisfaction. Due to NP-hardness of the above MOLP, a polynomial time solution of the food delivery problem has been developed, namely WWOFooD, exploiting Water Wave Optimization, a meta-heuristic algorithm. The WWOFooD not only explores ways of enhancing service quality of the customers, but also ensures giving additional incentives to the workers providing faster and reliable food delivery services. The results of simulation experiments depict that the WWOFooD offers competitive workers’ profit as well as significantly enhances customer satisfaction compared to the state-of-the-art works.

Research on Forest Management in the Context of Carbon Sequestration

As resources are exploited around the world, the environment is being affected as never before, and one of the more serious problems is global warming. This paper presents a more comprehensive study of forest management plans in areas such as the Cariboo Forest. First, the paper fit the relationship between tree age and volume using logistic regression, and then estimate the forest's maximum carbon storage 𝐶𝑠𝑢𝑚 using the biomass conversion factor method along with a modified Leslie model. In this paper, three aspects of economic benefit, social demand and carbon storage are balanced, and a forest decision-making model based on multi-objective linear programming is established. This paper applies the model to the Cariboo Forest area and optimizes the carbon sequestration assessment model using the first-order decay method (FOD), taking into account the carbon release from wood products.