Minmax Goal Programming Research Articles

Mathematical modeling and dragonfly algorithm for optimizing sustainable agritourism supply chains

The management of agritourism supply chains plays a pivotal role in promoting sustainable rural development and cultivating economic growth within agricultural communities. The study devises a comprehensive methodology aimed at designing and optimizing agritourism supply chain networks. To achieve this purpose, a two-objective mixed-integer linear programming mathematical model is introduced, tailored to accommodate diverse water consumption priorities across different gardens within the chain. Recognizing the NP-hardness of this intricate problem, a metaheuristic-driven solution approach based on MIN-MAX goal programming and dragonfly algorithm is presented to solve the designed model, aiming to simultaneously maximize the total profit and minimize overall water consumption within the supply chain. To assess the effectiveness of the proposed methodology, we adopted a real-world case study of an agritourism supply chain in China. The obtained results indicate the adoption of the proposed method can efficiently lead to the development and mechanization of agriculture in villages. The numerical analysis highlights that recruitment and production costs significantly influence the total profit of the agritourism supply chain. Additionally, the research underscores the pivotal role of sustainable rural development in creating job opportunities within the agritourism supply chain, thereby stimulating economic growth and fostering more profitable enterprises.

A sustainable network design of a hybrid biomass supply chain by considering the water–energy–carbon nexus

AbstractNowadays, with population growth, rising global energy demand, increasing water consumption, carbon emissions, and excessive use of fossil fuels, the world faces a major challenge. Biomass is one of the most attractive sources of energy production, with positive effects on the economy, environment, and society, which can decrease the world's reliance on fossil fuels and deal with this universal challenge. Consequently, the biomass supply chain network design has received more attention in recent decades. Since energy and water are two significant sources for society's sustainable development and carbon emissions are essential for environmental health, the study of the water–energy–carbon (WEC) nexus is essential. In this study, a multiobjective multiperiod model for designing a sustainable supply chain network based on hybrid second‐generation (i.e., Jatropha, agricultural waste, and animal waste) and third‐generation (i.e., microalgae) biomasses is presented. The proposed multiobjective model consists of five objective functions that maximize the total energy produced and the number of jobs created and minimize the total water consumed, carbon emitted, and total costs. Case study results demonstrate the performance of the model utilizing the MINMAX goal programming approach. Based on the results, energy production from Jatropha is more appropriate in comparison with energy production from microalgae, agriculture waste, and animal waste. The findings also show that the proposed model in this research considering the WEC nexus performs significantly better than the classical model without considering the WEC nexus.

A goal programming approach for agile-based software development resource allocation

In the current proposal, three objectives have defined which need to be considered while solving the resource allocation problem in ASD. This multi objective has then been solved using Goal Programming approach. The three approaches to solving a Goal Programming Problem i.e. the Weighted Approach (or the Archimedean Goal Programming), the Preemptive Approach (or the Lexicographic Approach) and the Chebyshev Approach (or the Min–Max Goal Programming) have been discussed to cater to the problem thoroughly. Furthermore, the three objectives have been handled singularly as well, i.e. as a single objective problem. The proposed optimization models have been validated on an agile-based software development dataset. Sensitivity analysis has been performed to gauge the impact of the variables involved.

Flexible Goal Programming for Supporting Lake Karla’s (Greece) Sustainable Operation

Sustainable management is a prerequisite for a lake to provide a range of ecosystem services. The prioritization of needs is a difficult task, especially when the needs are in conflict and threaten water security. Lake Karla, situated in the Thessaly plain, Greece, was decimated in 1957–1962; due to environmental impacts, it was later refilled as a multipurpose reservoir with high ecological significance. The research objective is to achieve a compromise with respect to both the economic benefits derived from agricultural water use and environmental protection based on the minimum intersection. For this purpose, first, new managerial practices are introduced. Second, the ideas are quantified based on the hydrological budget, and these are used as input for flexible (fuzzy) programming. Under hypotheses about the acceptable range, the (flexible) fuzzy programming is identical with the MINMAX goal programming model, although the weights are not used directly in the first case. An understandable compromise (the maximum economic benefit from irrigation areas and the minimization of water retention time) is achieved, and the values of the membership functions can be used to verify the solution. The proposed solution leads to a quantitative proposition, incorporating new findings from modeling the recent real operation of the reservoir.

Sustainable Integrated Fuzzy Optimization for Multimodal Petroleum Supply Chain Design with Pipeline System: The Case Study of Vietnam

Over the years, oil-related energy sources have played an irreplaceable role in both developed and developing countries. Therefore, the efficiency of petroleum supply chains is a key factor that significantly affects the economy. This research aimed to optimize the configuration of the uncertainty multimodal petroleum supply chain in terms of economy, energy and environment (3E assessment). This study proposes a novel integration methodology between a heuristic algorithm and exact solution optimization. In the first stage, this study determines the facilities’ potential geographical coordinates using heuristic algorithm. Then, the fuzzy min-max goal programming model (FMMGPM) was developed to find the multi-objective solutions. In particular, this model allows analysis of supply chain uncertainty through simultaneous factors such as demand, resource, cost and price. These uncertainty factors are expressed as triangular fuzzy parameters that can be analyzed in terms of both probability and magnitude. Moreover, the model is applied to the entire petroleum supply chain in Vietnam, including downstream and upstream activities. In addition, another novelty is that for the first time, pipeline systems in logistics activities are considered in Vietnam’s petroleum supply chain optimization study. The results also show the short-term and long-term benefits of developing a pipeline system for oil transportation in Vietnam’s petroleum supply chain. To evaluate the effects of uncertainty on design decisions, this study also performed a sensitivity analysis with scenarios constructed based on different magnitudes and probabilities of uncertainty.

Intuitionistic fuzzy multi-stage multi-objective fixed-charge solid transportation problem in a green supply chain

This research mainly focuses on presenting an innovative study of a multi-stage multi-objective fixed-charge solid transportation problem (MMFSTP) with a green supply chain network system under an intuitionistic fuzzy environment. The most controversial issue in recent years is that greenhouse gas emissions such as carbon dioxide, methane, etc. induce air pollution and global warming, thus motivating us to formulate the proposed research. In real-world situations the parameters of MMFSTP via a green supply chain network system usually have unknown quantities, and thus we assume trapezoidal intuitionistic fuzzy numbers to accommodate them and then employ the expected value operator to convert intuitionistic fuzzy MMFSTP into deterministic MMFSTP. Next, the methodologies are constructed to solve the deterministic MMFSTP by weighted Tchebycheff metrics programming and min-max goal programming, which provide Pareto-optimal solutions. A comparison is then drawn between the Pareto-optimal solutions that are extracted from the programming, and thereafter a procedure is performed to analyze the sensitivity analysis of the target values in the min–max goal programming. Finally, we incorporate an application example connected with a real-life industrial problem to display the feasibility and potentiality of the proposed model. Conclusions about the findings and future study directions are also offered.

The water‐energy nexus at the hybrid bioenergy supply chain: A sustainable network design model

Nowadays, the fossil fuel price fluctuations are high, their doubtless exhaustion is distressing, air pollution is a severe problem, and these issues seriously threaten the global economy. Bioenergy is a significant alternative source, with positive environmental, social, and economic impacts, that can reduce the world’s heavy dependence on fossil fuels. As a result, the importance of the design, implementation, and management of bioenergy supply chains have increased in recent years. This research, hence, is aimed to develop a bioenergy supply chain network design (BSCND) model to study the hybrid second (i.e., Jatropha; agricultural residues; and livestock manure) and third (i.e., microalgae) generations of biomass. Since water and energy are two momentous sources for sustainable development of societies where the increasing demand has become a worldwide concern, the water-energy nexus concept is another subject discussed in this study. And since sustainability is another issue to be dealt with in modern energy supply chains, a multi-objective sustainable mathematical model is developed in this study to present. A three-echelon sustainable hybrid bioenergy supply chain model has been proposed with four objective functions that minimize the total cost, reduce the environmental impacts, maximize the energy production, and minimize the water consumption to produce bioenergy. The GIS-based model, also, has been used to form a suitability map of Jatropha/microalgae cultivation. Results of a case study conducted to show the model performance using the MINMAX goal programming method. It has revealed that producing energy from microalgae/Jatropha is more viable compared to agricultural residues and livestock manure.

A note on min-max goal programming approach for solving multi-objective de novo programming problems

Min-max goal programming approach for solving multi-objective de novo programming problems was studied by Nurullah Umarusman in 2013. The present study is a further attempt to examine the approach and present an improved version of the approach. In Umarusman's method, each of the goal constraints is having both positive and negative deviation variables, whereas in the proposed approach only one deviation variable has been used. The method of solution has been illustrated with the numerical examples. The solution obtained by proposed method yields objective values which are better than those obtained by Umarusman for the same set of weights.

A note on min-max goal programming approach for solving multi-objective de novo programming problems

Min-max goal programming approach for solving multi-objective de novo programming problems was studied by Nurullah Umarusman in 2013. The present study is a further attempt to examine the approach and present an improved version of the approach. In Umarusman's method, each of the goal constraints is having both positive and negative deviation variables, whereas in the proposed approach only one deviation variable has been used. The method of solution has been illustrated with the numerical examples. The solution obtained by proposed method yields objective values which are better than those obtained by Umarusman for the same set of weights.

One-Step Approach for Solving General Multi-Objective De Novo Programming Problem Involving Fuzzy Parameters

Multi-objective De Novo Programming is a user-friendly device for optimal system design. There exist no method for solving general multi-objective De Novo Programs. Only some special cases have been discussed. This paper proposes a one-step method for solving a general De Novo Programming Problem using a Min-max Goal Programming technique where the parameters involved are all fuzzy numbers. The solution obtained is an efficient solution of the problem considered. The present approach is much more realistic than the standard De Novo Programming with crisp parameters. Two numerical examples are given to illustrate the solution procedure.

Effect of Time-Varying Factors on Optimal Combination of Quality Inspectors for Offline Inspection Station

With advanced manufacturing technology, organizations like to cut their operational cost and improve product quality, yet the importance of human labor is still alive in some manufacturing industries. The performance of human-based systems depends much on the skill of labor that varies person to person within available manpower. Much work has been done on human resource and management, however, allocation of manpower based on their skill yet not investigated. For this purpose, this study considered offline inspection system where inspection is performed by the human labor of varying skill levels. A multi-objective optimization model is proposed based on Time-Varying factors; inspection skill, operation time and learning behavior. Min-max goal programming technique was used to determine the efficient combination of inspectors of each skill level at different time intervals of a running order. The optimized results ensured the achievement of all objectives of inspection station: the cost associated with inspectors, outgoing quality and inspected quantity. The obtained results proved that inspection performance of inspectors improves significantly with learning and revision of allocation of inspectors with the proposed model ensure better utilization of available manpower, maintain good quality and reduce cost as well.

Fuzzy Goal Programming Problem Based on Minmax Approach for Optimal System Design

Every system in nature evolved in order to carry on their existence and reach their targets with minimal losses. The fundamental condition of a system’s success lies on making the correct decision by evaluating multiple, complicated, and conflicting goals based on the present constraints. Many mathematical programming problems are make up of objective functions combined by the decision maker based on the constrains. This study investigates how an optimal design can be reached based on Minmax approach. Goal Programming and a Fuzzy Goal Programming known as MA approach are used in this study. The solution of a problem organized as a Multiple De novo programming in order to determine the resource amounts for a business in handcrafts is carried out based on these two approaches. Budget constrain is organized as a goal to solve the problem based on MA approach, and a solution is proposed accordingly. The acquired results suggest that the solution results of Minmax Goal Programming and MA approach are the same.

Evolutionary technique based goal programming approach to chance constrained interval valued bilevel programming problems

The real world multiobjective decision environment involves great complexity and uncertainity. Many decision making problems often need to be modelled as a class of bilevel programming problems with inexact coefficients and chance constraints. To deal with these problems, a genetic algorithm (GA) based goal programming (GP) procedure for solving interval valued bilevel programming (BLP) problems in a large hierarchical decision making and planning organization is proposed. In the model formulation of the problem the chance constraints are converted to their deterministic equivalent using the notion of mean and variance. Further, the individual best and least solutions of the objectives of the decision makers (DMs) located at different hierarchical levels are determined by using GA method. The target intervals for achievement of each of the objectives as well as the target interval of the decision vector controlled by the upper-level DM are defined. Then, using interval arithmetic technique the interval valued objectives and control vectors are transformed into the conventional form of goal by introducing under- and over-deviational variables to each of them. In the solution process, both the aspects of minsum and minmax GP formulations are adopted to minimize the lower bounds of the regret intervals for goal achievement within the specified interval from the optimistic point of view. The potential use of the approach is illustrated by a numerical example

A distance-based framework to deal with ordinal and additive inconsistencies for fuzzy reciprocal preference relations

Consistency of preference relations is related to rationality, the lack of consistency in decision making often leads to misleading solutions. This paper studies the ordinal and cardinal consistency problems of fuzzy reciprocal preference relations. First, the concept of ordinal consistency of fuzzy reciprocal preference relations is introduced and analyzed. A lp distance-based method is proposed to formulate the underlying optimization problems as goal programming (GP) models for ordinal and additive consistency problems respectively. By setting different p, three GP models are obtained: (a) a linear GP model where p = 1; (b) a MINMAX GP model, where p = ∞; and (c) an extended GP model, which integrates the two previous models in particular cases. Utilizing these models, we can solve the ordinal and additive consistency problems for fuzzy reciprocal preference relations. The proposed model can preserve the initial preference information as much as possible. Finally, a numerical example and comparative analysis are provided to show effectiveness and validity of the proposed method.

A new normalized goal programming model for multi-objective problems: A case of supplier selection and order allocation

This paper models the problem of supplier selection as a multi-objective optimization problem (MOOP) where minimization of price, rejects and lead-time are considered as three objectives. The paper considers two different cases: (1) the crisp MOOP in which the goals of objectives are predetermined; and (2) the fuzzy MOOP in which the weights of objectives are predetermined. In both cases, the aim is to achieve some levels of consistency among different objectives. To do so, a normalized goal programming approach is developed and tested for both cases. In order to compare the effectiveness of the proposed method, a comparative analysis is presented which includes weighted goal programming, compromise programming, TOPSIS, weighted objectives, min–max goal programming and weighted max–min models. An illustrative example reveals that our proposed model is able to achieve the desirable consistency among all objectives.

A goal geometric programming problem (G2P2) with logarithmic deviational variables and its applications on two industrial problems

A very useful multi-objective technique is goal programming. There are many methodologies of goal programming such as weighted goal programming, min-max goal programming, and lexicographic goal programming. In this paper, weighted goal programming is reformulated as goal programming with logarithmic deviation variables. Here, a comparison of the proposed method and goal programming with weighted sum method is presented. A numerical example and applications on two industrial problems have also enriched this paper.

An Integrated Decentralized Energy Planning Model considering Demand-Side Management and Environmental Measures

Decentralized energy planning (DEP) is looked upon as an indisputable opportunity for energy planning of villages, isolated islands, and far spots. Nonetheless, at this decentralized planning level, the value of demand-side resources is not fairly examined, despite enjoying great advantages. Therefore, the core task of this study is to integrate demand-side resources, as a competing solution against supply-side alternatives, with decentralized energy planning decisions and demonstrate the rewarding role it plays. Moreover, sustainability indicators (SIs) are incorporated into DEP attempts in order to attain sustainable development. It is emphasized that unless these indicators are considered at lower energy planning levels, they will be ignored at higher planning levels as well. Hence, to the best knowledge of the authors, this study for the first time takes into account greenhouse gas (GHG) emissions produced by utilization of renewable energies in DEP optimization models. To address the issues mentioned previously, multiobjective linear programming model along with a min-max goal programming approach is employed. Finally, using data taken from the literature, the model is solved, and the obtained results are discussed. The results show that DSM policies have remarkably contributed to significant improvements especially in terms of environmental indicators.

Fuzzy goal programming approach to multi-objective mixed model assembly line balancing

This study addresses mixed model assembly line balancing problems arising in automotive plants. The main motivation for balancing a mixed model assembly line is to avoid inefficiencies among the stations. There exist many sources for these inefficiencies such as idle workers, extra stations, unbalanced workloads and unnecessary equipments along the line. All these factors can be involved in a multi-objective approach. However, the decision maker cannot determine precise target values for abovementioned objectives. Thus, fuzzy goal constraints are much more suitable for the problem solution. The problem stated above is formulated in this study as a mixed integer fuzzy-goal programming with the objectives of minimising number of workers and stations, minimising total unbalanced workloads and minimising total equipment costs. The problem is then linearised using Min-Max goal programming approach to solve mixed model assembly line balancing with above given objectives. This study includes a case study and determines the priority of each objective based on the judgments of the assembly line manager.

Conserving natural resources in olive orchards on sloping land: Alternative goal programming approaches towards effective design of cross-compliance and agri-environmental measures

Olive farming on sloping land in southern Europe is facing multiple challenges and it is reasonable to believe that farmers will opt for the abandonment of some systems and intensification or change to organic production of other systems. The issues at stake surpass financial farm viability and two EU policy instruments – cross-compliance and agri-environmental measures (AEM) – are available to address environmental objectives. This paper explores how cross-compliance and AEM policy options may lead to shifts in olive production systems and their social and environmental effects in Trás-os-Montes, NE Portugal over 25 years under two sets of conditions of uncertainty: decision-making by land users and market scenarios. Uncertainty in decision-making is addressed by employing five alternative goal programming models. The models include Linear Programming (LP), Weighted Goal Programming (WGP) and MINMAX Goal Programming (MINMAX GP), the GP variants of which are moreover formulated from a societal (S) and farmer (F) perspective. Uncertainty in market prospects is addressed by projecting olive oil and labour prices and trends in farm subsidies, distinguishing four price combinations in market scenarios. The models were validated by their capability to reproduce the initial configuration of olive production systems. Six policy options are evaluated under the complete ranges of uncertainty factors in a total of 6 × 5 × 4 = 120 model runs. Results show overall large effects of farmer decision-making and market scenarios. The cross-compliance and AEM policy instruments have an unequivocal effect on environmental performance and help to maintain work in rural areas. However, farmer income levels are insensitive to the policies, all work is absorbed by family labour and important environmental issues linked to more intensive systems such as pollution are not addressed. In a case study with the WGP (F) model which best reproduced the initial configuration of production systems, cross-compliance was moreover found to burden farmers under adverse market conditions, while AEM contributed to farmer’s objectives under favourable market conditions. A solution would be to focus cross-compliance regulations on intensive systems and offer appropriate AEM for traditional or abandoned orchards. Both policy instruments proved effective, but there is scope for removing substantial overlap between them.

Evaluation of Min–Max, Weighted and Preemptive Goal Programming Techniques with Reference to Mahanadi Reservoir Project Complex

An application of Goal Programming (GP) methodology with its three approaches namely Min–Max Goal Programming (MMGP), Weighted Goal Programming (WGP) and Preemptive Goal Programming (PGP) to a system of reservoir for optimal monthly operation has been presented in this paper. The objective of the present work is to find out an improved optimal operation model for Mahanadi Reservoir Project (MRP) system and to study the results in light of implicit fundamental philosophy associated with the models. The goal programming approach possesses significant advantage due to the fact that it may be based on physical operating criteria. The system goals and constraints are expressed deterministically. A constraint must be strictly satisfied, while for a goal it is desired to achieve the solution as close as possible to the specified target. The MMGP model is based on the philosophy of minimization of maximum range of deviation of all decision variables from their target value uniformly. WGP focus on the weights assigned to decision variables according to their relative importance. Whereas, PGP model deals sequentially with each goal according to their order of priorities. All the three GP models have been developed and applied to the MRP Complex which comprises of six multipurpose reservoirs with two inter basin linkage canals in the state of Chhattisgarh, India. The system goals and constraints are expressed deterministically for the application of model in perfect mode. The input data set was kept same to facilitate a justifiable comparison of performance of GP models. The strengths and limitations of all the three GP models have been analysed and the basic salient features of models in light of results obtained are discussed and presented. The best operating policy has been resulted from PGP model as compared to other two models.