Goal Programming Method Research Articles

Accurate preference-based method to obtain the deterministically optimal and satisfactory fairness-efficiency trade-off

The resource allocation problem is a classic multi-objective challenge, particularly when balancing the fairness-efficiency trade-off. To achieve a deterministically optimal and satisfactory solution, researchers frequently employ preference-based methods, including selecting among Pareto solutions based on the decision-maker's a posteriori preference and using deterministic models incorporating a priori preferences. In this study, we address two main challenges—specifically, (1) the limitations in measuring the abstract concepts of fairness and efficiency and (2) finding a deterministically optimal and satisfactory balance between fairness and efficiency. We apply a Gini impurity index derived from the classification and regression tree to calculate fairness, ensuring the Gini index function's differentiability. Additionally, we unify the scales of fairness and efficiency to facilitate calculation. Using accurate preference information, we employ the extended interval goal programming method to solve the model and achieve a deterministically optimal and satisfactory solution. The comparative analysis results demonstrate that our model (1) efficiently addresses the real-world water resource allocation problem concerning the fairness-efficiency trade-off; and (2) generates fewer penalties, with an average improvement ratio of 8% in the case study, using more refined penalty functions that align closer to the decision-maker's real and nonlinear preferences.

Optimizing banana production in aroma Lumajang business using goal programming method and sensitivity analysis

Optimizing banana production in aroma Lumajang business using goal programming method and sensitivity analysis

A multi-objective method for large multi-lane roundabout design through microscopic traffic simulation and SSAM analysis

Urban traffic congestion poses a significant challenge, impacting both economic efficiency and environmental sustainability. Roundabouts, recognized for their ability to improve traffic flow and reduce collisions, have become a focal point in traffic management strategies in urban areas. Different types and sizes of single and multi-lane roundabouts can be used, including conventional and innovative roundabouts with small, medium or large size diameters. Many optimization models are available for designing conventional roundabouts but not large roundabouts. To partially cover this gap, the present paper introduces a novel approach integrating simulation-based analysis with a goal programming method to optimize large roundabout design. By leveraging advanced traffic simulation tools like AIMSUN Next and Surrogate Safety Assessment Models (SSAMs), this methodology evaluates multiple design scenarios to enhance traffic flow, safety, and environmental performance. A case study of a complex large roundabout in the Italian greenest and sustainable city demonstrates the efficacy of this methodological approach. The findings provide valuable insights for traffic and highway engineers, emphasizing a data-driven, holistic approach to sustainable traffic management and roundabout optimization.

Data-driven planning in socially responsible textile units amidst uncertainty

Social responsibility is a key factor for organizations to achieve sustainable success in the modern competitive market. This study proposes a hybrid VIKOR method to evaluate textile suppliers based on their social performance under uncertain and multi-objective conditions. The method can handle fuzzy, stochastic, and interval data simultaneously. The social criteria for the evaluation are derived from the literature review, the SA8000 standards, and the United Nations’ recommendations. Some of the criteria are also aligned with the World Bank’s Social Responsibility Diamond Model and the United Nations’ Sustainable Development Goals. Moreover, this study presents a fuzzy mathematical model for fabric purchasing that incorporates social criteria and the quality level into the optimization process. A goal programming method is developed based on the mathematical properties of the multi-objective model. A numerical study is conducted in the textile industry to demonstrate the efficiency and effectiveness of the proposed approaches. A comprehensive sensitivity analysis has been performed to investigate the behavior of the presented mathematical model under different conditions, and the results have been discussed concerning the insights for managers and stakeholders in the textile industry. The proposed model demonstrates that: 1) Customer demand and fabric orders have a direct relationship with increasing sales. 2) The fabric unit price has a direct impact on the quality value and requires cost control policies or pricing negotiations with suppliers. 3) Improving supplier and customer relations and formulating pricing consistent with social value are among the most important issues for the success of the textile and clothing industry. The best-fitting line successfully explains the variability of social performance and customer demand with an accuracy of 99.35 %.

An efficient algorithm for solving multilevel multi-objective linear fractional optimization problem with neutrosophic parameters

This work demonstrates the modeling of the multilevel-multiobjective linear fractional optimization (ML-MOLFO) problem in a neutrosophic decision environment. The primary driving force behind this work is to determine how to handle a ML-MOLFO problem while taking into account a real-life decision-making scenario. There is a hierarchy of decision-makers and many decision-making processes, such as agree, not-sure, and disagree, in a real-life decision-making setting. By taking into account such genuine situations, all resource, coefficient of objective, and constraint functions are represented as single-valued trapezoidal neutrosophic numbers. As far as we can tell, there is no established technique for resolving the ML-MOLFO problem with neutrosophic parameters in the literature review. Therefore, by outlining goal programming methods in the intuitionistic fuzzy environment, we create our new intuitionistic fuzzy Chebyshev goal programming (IFCGP) method to address the introduced problem. In the proposed method, first we used a modified ranking function to transform the problem into an analogous crisp ML-MOLFO problem, and then it was converted into a multilevel multiobjective linear optimization problem through linearized techniques. The linearization procedure in the proposed method, unlike the existing one, does not require derivatives, additional variables, or inequality constraints, which makes it simpler. To illustrate the adequacy and performance of the proposed new method, we considered numerical tests and application problems. We also compared the performance of the resulting optimal solution with existing approaches using the distance metric, which indicates our method is non-dominated.

Neutrosophic linear fractional optimization problem using fuzzy goal programming approach

This research paper develops an algorithm to solve a neutrosophic linear fractional optimization problem, where the cost of the objective functions, the technology coefficients, and the resources are neutrosophic numbers (triangular and trapezoidal numbers). Two defuzzification methods are used here to convert the neutrosophic linear fractional optimization problem into a multi-objective linear fractional optimization problem (MOLFOP). The fractional objective function is defuzzified using the component-wise optimization method, and the linear constraints are defuzzified using the aggregation ranking function strategy. Hence, the MOLFOP is then solved using the fuzzy goal programming method. In order to further explain our suggested algorithm, two numerical examples are solved at the end, and the outcomes obtained by our method are compared with the outcomes obtained using the other algorithm.

Optimal Decision on Pricing and Replenishment of Vegetable Products Based on Goal Planning

Developing replenishment and pricing plans has always been the key for fresh food supermarkets to gain more profits. This paper analyzes various situations and provides the optimal solution through Spearman correlation analysis, Lasso regression, goal programming and other methods and models. We use normality testing and box plots to present the distribution patterns of major categories and individual products from both vertical and horizontal perspectives. Establish a single objective programming model and solve it with Lingo to obtain a maximum profit of 98513 yuan for 7 days. The largest total replenishment amount is for the flower and leaf category, the smallest is for edible mushrooms, the highest average cost markup rate is for aquatic roots and stems, and the lowest is for cauliflower. This has certain reference value and theoretical significance for fresh food supermarkets to formulate replenishment and pricing plans.

A multi-objective model for selecting response strategies of primary and secondary project risks under interval-valued fuzzy uncertainty

Risks are uncertain events that can affect criteria such as project cost, quality, and completion time and ultimately lead to project failure. That is why the project risk management process, which is one of the most fundamental parts of project management, must be done properly. In this paper, a new multi-objective fuzzy model is proposed to respond appropriately to the primary and secondary project risks. The contributions, such as risk interdependency, considering the project with multi-mode activities, resource considerations, as well as attention to interval-valued fuzzy uncertainties are regarded simultaneously for the first time. The purpose of the proposed multi-objective mathematical model is to minimize cost, quality reduction, and project completion time. Then, a new two-stage uncertain solution approach is introduced in this paper. In this solution approach, using an equivalent method in the first step and then using an extended multi-choice goal programming method in the second step, for both lower and upper limits of the membership functions for interval-valued fuzzy numbers, the computational processes are performed. To show the application and effectiveness of the proposed model, a case study adapted from the literature is given. Finally, sensitivity analysis is conducted to analyze the behavior of the developed mixed-integer programming model. The analysis of obtained results indicates that the utilization of the proposed model leads to better and more appropriate solutions.

Hybrid quantitative–qualitative method for technology portfolio selection: a case study of Iran’s space industry

The space industry is known as an economic driver for many world economies. In Iran, the acquisition of satellite technology knowledge is one of the achievements of the country’s scientific and technological indicators in recent years, but the position and importance of optimal investment in this industry in Iran have been ignored. The optimal technology portfolio is one of the tools that can cover this gap and lead to better decision-making by policymakers. In this paper, the optimum technology portfolio determination regarding its goals, attributes and challenges is addressed for Iran’s space industry with a hybrid quantitative–qualitative method in two short and medium-term periods. We formulate a technology portfolio selection model with these multi-objective functions: maximization of benefits in using different technologies comprising of both short and medium-term portfolios, maximizing the total summation of all Technology Readiness Levels (TRLs) of technologies, maximizing the acquisition speed for the technologies, and minimizing the acquisition risk of technologies in each portfolio. In the proposed model, the usability, acquisition cost, and complexity of each technology are considered meticulously. Also, the goal programming method is used to integrate the objective functions. Another novelty of this paper is the formulation of two portfolios with two different periods in which their corresponding inputs and outputs affect the other. This research can significantly help in directing the country’s investment in the space industry, spatial ecosystem orientation, facilitating the creation of space-based businesses, improving economic growth, and also providing guidelines to improve the related policies in this area. In addition, this research can be an inspiration for other developing countries in the space industry.

Application of Sequential Linear Goal Programming Method and Modified Simplex Method for Production Planning Optimization

Production planning is an important thing in company management. Every company aims to seek maximum profit in its business activities, so it must be able to utilize its resources as optimally as possible. This study was conducted to determine whether or not any production planning that has been implemented at Istana Roti Hilyah Bakery is optimal. This research aimed to maximize revenue and profit, minimize production costs and raw material usage and optimize production quantities using the sequential linear goal programming method and the simplex modification method with the assistance of LINGO software. Based on the study's results, the revenue increased by IDR 60,000, and the profit increased by IDR 66,679. The minimization value of production costs decreased by IDR 6,679, with the production amount of White Bread as many as 60 pcs, Almond Crumble Bread as many as 45 pcs, Chocolate Crumble Bread as many as 50 pcs, Wheat Bran Bread as many as 55 pcs, Sweet Comb Bread as many as 82 pcs and Jam Comb Bread as many as 84 pcs.

A Sustainable Multi-Objective Model for Capacitated-Electric-Vehicle-Routing-Problem Considering Hard and Soft Time Windows as Well as Partial Recharging.

Due to the high pollution of the transportation sector, nowadays the role of electric vehicles has been noticed more and more by governments, organizations, and environmentally friendly people. On the other hand, the problem of electric vehicle routing (EVRP) has been widely studied in recent years. This paper deals with an extended version of EVRP, in which electric vehicles (EVs) deliver goods to customers. The limited battery capacity of EVs causes their operational domains to be less than those of gasoline vehicles. For this purpose, several charging stations are considered in this study for EVs. In addition, depending on the operational domain, a full charge may not be needed, which reduces the operation time. Therefore, partial recharging is also taken into account in the present research. This problem is formulated as a multi-objective integer linear programming model, whose objective functions include economic, environmental, and social aspects. Then, the preemptive fuzzy goal programming method (PFGP) is exploited as an exact method to solve small-sized problems. Also, two hybrid meta-heuristic algorithms inspired by nature, including MOSA, MOGWO, MOPSO, and NSGAII_TLBO, are utilized to solve large-sized problems. The results obtained from solving the numerous test problems demonstrate that the hybrid meta-heuristic algorithm can provide efficient solutions in terms of quality and non-dominated solutions in all test problems. In addition, the performance of the algorithms was compared in terms of four indexes: time, MID, MOCV, and HV. Moreover, statistical analysis is performed to investigate whether there is a significant difference between the performance of the algorithms. The results indicate that the MOSA algorithm performs better in terms of the time index. On the other hand, the NSGA-II-TLBO algorithm outperforms in terms of the MID, MOCV, and HV indexes.

Green-resilient model for smartphone closed-loop supply chain network design: A novel four-valued refined neutrosophic optimization

This study endeavors to integrate green supply chain and resilience proactive strategies within a closed-loop supply chain network. The research employs a three-step methodology. In the first phase, a multi-objective, multi-period, multi-node, mixed integer linear programming model (MILP) is developed. The objective of this study is to maximize resilience while minimizing both greenhouse gas (GHG) emissions and costs. The environmental footprint is assessed using the life cycle assessment (LCA) tool as part of the green supply chain strategy. To optimize resilience strategies, proximate nodes in the closed-loop supply chain network implement measures involving node criticality and inventory availability. In the second step, a novel four-valued refined multi-objective neutrosophic optimization algorithm is introduced to resolve the model. In contrast to traditional optimization approaches, neutrosophic optimization integrates elements of truth, falsity, contradictions, and uncertainty into the decision-making process. In the third phase, a case study of the smartphone supply chain is presented, advocating for the adoption of circular economy practices to prevent future waste. To assess the resilience of the model, a sensitivity analysis has been conducted, examining various key parameters associated with the market, and studying their impact on the objective function. The model's performance is validated by comparing the solution methodology with other goal programming and interactive fuzzy multi-objective methods. The results highlight the better performance of four-valued refined neutrosophic optimization, achieving 3.59 and 3.38 times greater cumulative gap reduction than other methods. The optimal solution recommends green strategies for an optimal trade-off among cost, GHG emissions, and resilience.

Integrated design of a sustainable waste management system with co-modal transportation network: A robust bi-level decision support system

Efficient waste management practices play a critical role in addressing the acute challenges of environmental protection, public health and resource conservation. A well-designed system guarantees that waste is efficiently collected, treated and disposed while minimizing negative impacts on ecosystems and human well-being. This work presents a robust bi-level decision support system to establish a sustainable waste management system using a co-modal transportation network to treat municipal solid waste timely and efficiently. Consequently, two integrated multi-objective mathematical models are developed to formulate the problem. Configuring the municipal solid waste network in the first level of the suggested decision support system, the transportation network is designed in the second level taking into account non-identical modes. The objectives are to minimize total cost and total emission in both levels, while maximization of total job creation is also addressed in the first level. Robust optimization method and weighted goal programming method are then utilized to accommodate the developed decision support system against uncertainty and multi-objectiveness, respectively. To validate the efficiency of these methods, they are assessed against possibilistic linear programming technique and Lp-metric approach with the help of simple additive weighting (SAW) method, respectively. Eventually, several numerical examples are generated based on the benchmarks given in the literature, which are then tackled using CPLEX solve to appraise the applicability and complexity of the developed methodology. The findings reveal the efficacy of the decision support system in terms of finding solutions in less than 448 s on average. Finally, sensitivity analyses are performed to draw out useful practical implications and decision aids.

Optimizing the Quantity of Pile Production Using Goal Programming Method

Goal Programming (GP) is a mathematical model that is used as a basis for making a decision to analyze and make solutions to problems that involve many objectives so that optimal alternative problem solving is obtained. PT Bungah Andya Teknik is a telecommunication network contractor company established on December 24, 2018. PT Bungah Andya Teknik focuses on the production of poles for fiber optic networks. this company only produces 250 pcs of poles every month with a production target that should be 300 pcs of poles every month, with a production cost of IDR 1,500,000 per pcs of poles and with a sales profit of IDR 300,000 per pcs of poles. The revenue obtained by the company in real terms for the period August 2023 to October 2023 is IDR 261,800,000, - and the revenue obtained from the calculation results using the Goal Programming method is IDR 403,900,000, -, so it can be concluded that the Goal Programming method can provide the best solution and the revenue obtained is greater than the company's real income.

Optimization investment portfolio of ESG capital market in Indonesia: An investigation of Polynomial Goal Programming based on higher moments

The development of capital market investors in Indonesia has experienced rapid growth, leading to increasingly volatile movements in the domestic market. Companies or investment managers must form asset portfolios with optimal expected returns and measurable risks to address this issue. This study aims to analyze the potential combinations that can be formed using ESG Capital Market Indonesia 2022 and safe-haven instruments, utilizing the Markowitz theory and Polynomial Goal Programming (PGP) method. This research uses secondary data, and the research variables used are ESG Capital Market Indonesia 2022 and Gold from January 2007 to December 2022. Based on the previous research, the formation of portfolio combinations using safe-haven instruments, employing the Markowitz theory and Polynomial Goal Programming (PGP) method can provide better investment portfolio combinations during crises. Furthermore, the performance of each formed combination is measured using the Sharpe Ratio. The findings indicate that Markowitz's theory can generate better performance than the PGP method. However, it exhibits suboptimal skewness and kurtosis values compared to the PGP method.

On Pareto optimality using novel goal programming approach for fully intuitionistic fuzzy multiobjective quadratic problems

Nowadays, intuitionistic fuzzy theory is gaining rapid acceptability as it emphasizes non-membership degree also, in addition to membership degree. In this paper, a simplified novel goal programming method under intuitionistic fuzzy environment (analogous to Angelov’s approach) using both membership/non-membership functions is developed. It is then applied to obtain a Pareto optimal solution to a multiobjective quadratic programming problem (QPP) with all the parameters and variables as intuitionistic fuzzy numbers. The relations between the multiobjective intuitionistic fuzzy QPP and its equivalent crisp problems under various membership/ non-membership functions using goal programming are also established by proving theorems at appropriate places. Moreover, a numerical example and a practical problem in production planning have been projected to illustrate the steps involved in the proposed approach.

A hybrid meta-heuristic approach to design a Bi-objective cosmetic tourism supply chain: A case study

In recent decades, medical tourism especially cosmetic tourism has increased in many countries. In this study, a bi-objective mathematical model is designed for the cosmetic tourism supply chain for the first time. In the first objective function, the profit margin in the supply chain is maximized. In contrast, the distance between the medical and accommodation centers is minimized in the second objective function. The general revised multi-choice goal programming (GRMCGP) method is an exact method for optimizing the problem. To solve the problem, model is run by Lingo software. Then, a new hybrid genetic algorithm named genetic algorithm-general revised multi-choice goal programming (GA-GRMCGP), to solve large-scale instances, is utilized. Moreover, a case study is considered to validate the proposed mathematical model. Furthermore, sensitivity analyses are carried out to evaluate the effectiveness of the research. Finally, the results of the exact and meta-heuristic algorithms are compared and discussed.

An integrated Lexicographic goal programming and dynamic satisfaction function model for effective nurse scheduling

The nurse-scheduling is a common problem in hospitals. The problem requires a timetable considering hospital regulations and nurses’ demands and preferences. This study proposes an integrated Lexicographic goal programming and dynamic satisfaction function model for solving nurse-scheduling problems. The proposed model provides the head nurses with a balanced and fair automated schedule. The model considers two aspects related to hospital regulation constraints. First, the dynamic aspect allows the decision-makers to integrate their judgment to the changing circumstances caused by nurse absenteeism. Second, the satisfaction aspect considers the decision maker’s preferences in assigning nurses’ surplus or shortages to the shifts. The model’s primary goal is to give nurses a fair and balanced schedule with an evenly distributed workload. A fair and balanced schedule helps maintain nurses’ welfare and provide quality patient service. We present a case study in an intensive care unit to demonstrate the effectiveness of our approach compared to the conventional goal programming method.

Designing a sustainable-resilient-responsive supply chain network considering uncertainty in the COVID-19 era.

Effective supply chain management is crucial for economic growth, and sustainability is becoming a key consideration for large companies. COVID-19 has presented significant challenges to supply chains, making PCR testing a vital product during the pandemic. It detects the presence of the virus if you are infected at the time and detects fragments of the virus even after you are no longer infected. This paper proposes a multi-objective mathematical linear model to optimize a sustainable, resilient, and responsive supply chain for PCR diagnostic tests. The model aims to minimize costs, negative societal impact caused by shortages, and environmental impact, using a scenario-based approach with stochastic programming. The model is validated by investigating a real-life case study in one of Iran's high-risk supply chain areas. The proposed model is solved using the revised multi-choice goal programming method. Lastly, sensitivity analyses based on effective parameters are conducted to analyze the behavior of the developed Mixed-Integer Linear Programming. According to the results, not only is the model capable of balancing three objective functions, but it is also capable of providing resilient and responsive networks. To enhance the design of the supply chain network, this paper has considered various COVID-19 variants and their infectious rates, in contrast to prior studies that did not consider the variations in demand and societal impact exhibited by different virus variants.

Goal programming and multi-criteria methods in remanufacturing and reverse logistics: Systematic literature review and survey

Environmental concerns, largely caused by a linear take-make-dispose model of manufacturing, have raised the need to incorporate the flow of used products to capture their residual value, thus shifting the traditional linear model to a more circular one. Remanufacturing is considered a key element in achieving circularity goals, as it offers greater environmental and economic benefits than other existing used product recovery options. The incorporation of used products in the supply chain poses challenging problems in which it is often necessary to consider trade-offs between different conflicting objectives, where multi-criteria decision-making methods, such as goal programming (GP), are mostly used. Since the last known review of the literature about these topics considers publications up to the year 2017, and it is observed that the number of publications has been growing significantly in recent years, it seems appropriate to carry out a more up-to-date review. This paper presents a review of the recent literature on GP and other multi-criteria methods applied to closed-loop supply chain systems, with focus on reverse logistics and remanufacturing as one of the most frequently recovery option used in the industry. The review was carried out in a systematic manner, using four of the most recognized scientific document repositories and a period of time for publications ranging from 2011 to 2021. After a detailed filtering process of almost 150 documents initially found, a final database of 38 documents was obtained for an in-depth review. The 38 documents were classified in three categories: supply chain management and design, strategic decisions in circular economy, and production planning. Half of the documents reviewed fall into the category of production planning, with a particular interest in disassembly planning issues and the advantages offered by technological advances such as the Internet of Things (IoT). It was observed that most of the investigations consider the economic and environmental dimensions, leaving aside the social dimension. This confirms a trend previously observed in the literature. In addition, a global analysis of the collected documents was carried out to determine which are the most used decision-making criteria for closed-loop systems with product recovery. Legal, production planning and life cycle assessment aspects that deserve further study in the future are also suggested.