Epsilon Constraint Research Articles

Multiobjective model to optimize charging station location for the decarbonization process in Mexico

AbstractElectric vehicles (EVs) offer significant potential for advancing sustainable environmental goals. However, their widespread adoption has been concentrated in urban areas, raising challenges for interurban travel. In many countries, charging station networks are primarily located within cities, highlighting a key opportunity for expansion to support longer distance journeys. This article addresses the facility location problem for EV charging stations to enable interurban travel. We propose a multiobjective optimization model based on the flow refueling location model with three objectives: maximizing CO2 emissions reduction, minimizing total costs, and reducing user charging time. The model is solved using an epsilon constraint approach, and Mexico's charging station network is used as a case study. Through computational experiments, various scenarios are evaluated, and a comparative analysis is performed between electric and internal combustion vehicles. Results show that deploying 20 strategically located charging stations could mitigate 3.1 million tons of CO2, requiring an investment of nearly USD 3.9 million.

Accelerating Benders Decomposition for sustainable food closed-loop supply chain network under uncertainty: a case study

PurposeThe purpose of this study was to address waste management in the food supply chain (FSC) through the integration of inspection processes in production and distribution centers under uncertain conditions, aiming to enhance sustainability across environmental, economic and social dimensions. The study introduces a sustainable forward and reverse FSC network using a closed-loop supply chain network approach to prevent the transfer of spoiled products, ultimately providing competitive advantages to stakeholders.Design/methodology/approachA robust multi-objective mathematical programming model is proposed, incorporating inspection processes to manage perishable products effectively. The model is solved using the Augmented Epsilon Constraint technique implemented in GAMS software, providing Pareto-optimal solutions tailored to decision-makers’ preferences. Furthermore, the methodology is applied in a real-world case study and solved with the Benders Decomposition algorithm to validate its practicality and effectiveness.FindingsThe proposed methodology effectively minimizes waste and enhances sustainability in the FSC by optimizing decision-making processes under uncertainty. The illustrative examples and real case study demonstrate the efficiency of the model and solution approach, highlighting the significant role of inspection in improving all three dimensions of sustainability.Practical implicationsThe study offers valuable insights into and tools for food industry managers to make informed strategic and tactical decisions. By addressing waste management through advanced supply chain modeling, the research helps organizations reduce costs, improve sustainability and gain a competitive edge in the market.Originality/valueThis research is novel in its focus on integrating inspection into the FSC network and addressing uncertainty through robust mathematical modeling. It contributes to the existing literature by demonstrating the impact of inspection on sustainability in FSCs and providing practical solutions for real-world implementation.

Research on multi-objective hierarchical site selection coverage of fire station

The fire station location has essential theoretical and practical values, not only in terms of maintaining the safety of life and property, but also enriching the optimization theory of site selection problems. To study the multi-objective siting problem of fire stations, we firstly divided demand areas and fire stations into three levels to form a comprehensive hierarchical emergency coverage network covering fire risk areas. Secondly, the nodes of the original location of the fire station were added to the set of nodes of the planned construction of the fire station. By introducing the coverage attenuation function, the multi-objective level fire station location model covering the maximum fire risk value and the minimum construction cost of the fire station was established. Then, the epsilon constraint method was used to address the multi-objective model, followed by designing the genetic algorithm based on the problem characteristics for solutions. To validate the effectiveness of the proposed model and algorithm, numerical experiments were performed, which took an urban area in China as an example. The solutions indicated that although retaining more of the original fire stations reduced the siting costs, most strategies tended to fail to cover higher values of fire risk, and the service coverage increases with the number of new fire stations. Additionally, sensitivity analysis was conducted to explore the effect of different parameters on the maximum fire risk value that can be covered by a fire station. A compromise coordinated siting scheme with a hierarchy of fire stations can be obtained by solving the proposed model. It can provide decision support for related departments to develop optimal siting configurations.

Transit passenger-oriented optimisation of arrival aircraft sequencing

Abstract This study presents a model that aims to optimise the sequencing arrival aircraft around the terminal manoeuvring area (TMA). The model considers the transit passenger counts of these aircraft and employs the point merge at Sabiha Gokcen Airport. In this study, aircraft were categorised into two groups, namely ‘High or Low Transit Passenger (HTP/LTP)’. Subsequently, multi-objective models were employed to solve the test problems. Weighted sum scalarisation (WSS), conic scalarization (CS), and epsilon constraint (EC) models were utilised to increase robustness and their results were compared with a single-objective optimisation model. This approach aims to provide decision-makers with a variety of outcomes, thus expanding their options. Simultaneously, efforts are made within the model to allow aircraft with HTP counts to have minimal delays. Additionally, emission calculations were conducted to offer a critical perspective on the environmental implications, and the delay results of the multi-objective optimisation (MOO) models underwent statistical analysis.

Strategical and tactical supply chain optimisation for smart production planning and control 4.0

Industry 4.0 (I4.0) technologies generate new opportunities for developing smart models, algorithms and tools to support supply chain (SC) production planning and control (PPC), or smart PPC (SPPC 4.0). Paired with opportunities, challenges arise in integrating sustainability and resilience in SC network design (SCND) according under I4.0. The main novelty of this paper is to propose two multi-objective models that integrate strategical and tactical PPC decisions into a sustainable-resilient SC under I4.0 towards SPPC 4.0. Sustainability is incorporated in terms of reducing costs and CO2 emissions, and a job creation factor. Resilience is incorporated in terms of contracting support suppliers. To solve the multi-objective models, the augmented epsilon constraint method (AUGMECON) was used. This algorithm minimises a target objective function while it treats the others as constraints. Our experiments indicate that AUGMECON is sensitive to the choice of epsilon values. Furthermore, a synthetic data generation tool called SR1-SR2_SynthDataGenerator was developed. This tool generates input datasets to validate and evaluate our models against benchmarks. A stochastic model (SR2) is also proposed that, with small datasets, takes 8.39 seconds to solve. The proposed models can be useful for industries that seek sustainable and resilient SCs to adapt to changing environments.

A closed-loop dual-channel supply chain network for leather products: An integrated simulation optimization clustering approach

The leather industry is pivotal to the economic development of certain countries; however, it also poses significant environmental challenges. Thus, this study aims to design a closed-loop leather supply chain network that incorporates waste recycling and product regeneration processes. In light of the growing prevalence of both in-store and online shopping, the concept of a dual-channel supply chain is examined. Furthermore, as advertising through traditional and social media continues to expand, this research uniquely investigates the impact of two advertising modalities—SMS and social networks—alongside the design and layout of retail environments, considering their effects on product sales within the supply chain context. Additionally, outlet stores are integrated into the model to facilitate the sale of products that may become outdated over time, thereby enhancing the model's real-world applicability. To achieve this, a multi-product, multi-period mathematical model is developed to minimize costs and maximize customer responsiveness in both forward and reverse supply chain flows. The K-means clustering method is employed to categorize customers based on recency, frequency, and monetary (RFM) features. Through simulation, demand parameters are derived for each customer cluster across various scenarios. Moreover, the Aghezzaf approach is utilized to address scenario-based uncertainties within the model, and the proposed multi-objective model is solved using the Augmented Epsilon constraint method. A real-world case study is conducted to apply the proposed model, and critical parameters are examined through sensitivity analysis to validate its effectiveness. The findings suggest that incorporating return flows into the supply chain can significantly enhance both producer profitability and customer responsiveness regarding leather products.

Providing a framework to optimize the sustainable construction material supply chain with the possibility of horizontal transfers

The application of Supply Chain Management (SCM) principles has gained considerable attention across various industries to enhance operational efficiency and business performance. In the construction sector, SCM can guide managers in strategic planning and foster collaboration with suppliers, leading to more effective project execution. Despite its importance, limited research has focused on designing sustainable supply chains for construction materials under uncertain conditions. This study aims to bridge this gap by introducing a robust optimization framework that incorporates sustainable development criteria, specifically the minimization of harmful environmental effects and the reduction of worker unemployment. Additionally, the research introduces an innovative concept of horizontal transfers between downstream members, which not only reduces supply deficiencies but also indirectly increases profitability for these members. This article is a part of a Doctoral dissertation. It follows a two-step approach. First, suppliers of construction materials are ranked based on sustainable development criteria using a multi-criteria decision-making method. The best-ranked supplier is then integrated into a mathematical model for optimizing the supply chain design. Given the NP-hard nature of the problem, the CPLEX 12.1 solver with the epsilon constraint method is used to solve small-scale models. For larger-scale problems, three meta-heuristic algorithms are developed: multi-objective ant-lion, multi-objective gray wolf, and multi-objective dragonfly. The results show that while both the ant-lion and gray wolf algorithms deliver comparable average performance, the gray wolf algorithm excels in terms of solution time, making it more effective for real-time problem-solving. This makes the gray wolf algorithm the most efficient choice for addressing large-scale, multi-objective supply chain challenges. This research introduces a novel framework for designing sustainable construction supply chains under uncertain conditions. By focusing on criteria such as minimizing harmful environmental effects and reducing worker unemployment, this study addresses key aspects of sustainable development. Additionally, the innovative horizontal transfer mechanism and the insights into algorithmic performance provide valuable contributions to the field, especially for real-world applications in the construction industry.

Dual resource constrained flexible job shop scheduling with sequence‐dependent setup time

AbstractThis study addresses the imperative need for efficient solutions in the context of the dual resource constrained flexible job shop scheduling problem with sequence‐dependent setup times (DRCFJS‐SDSTs). We introduce a pioneering tri‐objective mixed‐integer linear mathematical model tailored to this complex challenge. Our model is designed to optimize the assignment of operations to candidate multi‐skilled machines and operators, with the primary goals of minimizing operators' idleness cost and sequence‐dependent setup time‐related expenses. Additionally, it aims to mitigate total tardiness and earliness penalties while regulating maximum machine workload. Given the NP‐hard nature of the proposed DRCFJS‐SDST, we employ the epsilon constraint method to derive exact optimal solutions for small‐scale problems. For larger instances, we develop a modified variant of the multi‐objective invasive weed optimization (MOIWO) algorithm, enhanced by a fuzzy sorting algorithm for competitive exclusion. In the absence of established benchmarks in the literature, we validate our solutions against those generated by multi‐objective particle swarm optimization (MOPSO) and non‐dominated sorted genetic algorithm (NSGA‐II). Through comparative analysis, we demonstrate the superior performance of MOIWO. Specifically, when compared with NSGA‐II, MOIWO achieves success rates of 90.83% and shows similar performance in 4.17% of cases. Moreover, compared with MOPSO, MOIWO achieves success rates of 84.17% and exhibits similar performance in 9.17% of cases. These findings contribute significantly to the advancement of scheduling optimization methodologies.

Balancing Possibilist-probabilistic risk assessment for smart energy hubs: Enabling secure peer-to-peer energy sharing with CCUS technology and cyber-security

This paper introduces the Possibilistic-Probabilistic Risk-based Smart Energy Hub (PPR-SEH) scheduling model, addressing cybersecurity challenges in the transition to advanced energy systems characterized by decarbonization, decentralization, and digitalization. The model integrates cutting-edge technologies like Carbon Capture Utilization and Storage (CCUS) and demand response programs. It addresses uncertainties from renewable energy sources, demand variability, fuel supply, and energy price fluctuations using a Z-number-based approach. Covering various energy types—electricity, heat, cooling, gas, and water—the PPR-SEH model offers a comprehensive energy management solution. Employing a mixed-integer linear programming (MILP) framework optimized with the CPLEX solver in GAMS software, it uses an epsilon constraint method and a fuzzy satisfying approach for solution selection. The model also evaluates the economic and environmental impacts of peer-to-peer energy-sharing markets linked with carbon emission trading, enhancing the efficiency and sustainability of energy distribution. The findings reveal that incorporating robust cybersecurity measures and integrating demand response and CCUS significantly influence operational efficiency and sustainability, evidenced by an increase in costs and pollution by approximately 11.43 % and 1.8 %, respectively, compared to deterministic approaches. This study underscores the importance of robust planning and the beneficial impact of a carbon system on load curve management and economic returns in smart energy systems.

Enhancing pharmaceutical supply chain resilience: A multi-objective study with disruption management

In this study, we tackle the problem of pharmaceutical supply chain optimization using a multi-objective model that simultaneously considers cost minimization, environmental impact minimization, and maximizing of service level equity (minimum ratio). This represents the three alms of sustainability which are key in manufacturing. Furthermore, we developed a disruption model capable of effectively managing disruptions within the supply chain and compared the capabilities with the baseline model.The result shows how the supply chain network behaves under different objectives. Minimizing costs led to maximizing capacity utilization, while environmental objectives result in reduced production levels to meet coverage requirements, and maximizing the minimum ratio expands more facilities. Using an epsilon constraint, the trade-off shows that the environmental budget limits the flexibility between the other total cost achievable and the minimum ratio. Comparing the baseline model and the disruption model underscores the importance of proactive disruption management in maintaining service levels and managing costs effectively. Ultimately, our study offers practical insights for optimizing pharmaceutical supply chains, balancing economic efficiency with social responsibility to navigate disruptions and challenges successfully.

Multicriteria optimization techniques for understanding the case mix landscape of a hospital

Various medical and surgical units operate in a typical hospital and to treat their patients these units compete for infrastructure like operating rooms (OR) and ward beds. How that competition is regulated affects the capacity and output of a hospital. This article considers the impact of treating different patient case mix (PCM). As each case mix has an economic consequence and a unique profile of hospital resource usage, this consideration is important. To better understand the case mix landscape and to identify those which are optimal from a capacity utilisation perspective, an improved multicriteria optimization (MCO) approach is proposed. As there are many patient types in a typical hospital, the task of generating an archive of non-dominated (i.e., Pareto optimal) case mix is computationally challenging. To generate a better archive, an improved parallelised epsilon constraint method (ECM) is introduced. Our parallel random corrective approach is significantly faster than prior methods and is not restricted to evaluating points on a structured uniform mesh. As such we can generate more solutions. The application of KD-Trees is another new contribution. We use them to perform proximity testing and to store the high dimensional Pareto frontier (PF). For generating, viewing, navigating, and querying an archive, the development of a suitable decision support tool (DST) is proposed and demonstrated.

A robust mixed-integer binary programming model for operating theater scheduling to the patient and the surgeon under uncertainty in an open-heart Surgery Department

In hospitals, the surgical ward is both a cost and revenue center. In this ward, hospitals face challenges such as increasing demand, limited resources, and rising costs. Consequently, the decisions made have an implications effect on the hospital's performance. Therefore, in this paper a robust mixed-integer binary programming model is proposed with three objectives of maximizing the efficiency of available resources, minimizing the patients waiting time, and minimizing surgery costs that are formulated utilizing the augmented epsilon constraint approach. This model allocates the operating room to the patient and the surgeon and then obtains the required bed capacity inside the downstream units for stand-alone cardiac hospitals. This model includes different preferences for hospital, surgeon, and patient: waiting time, patient cancellations, tardiness, uncertainties in surgery durations, the patient operation start times, the overtime per working day, time windows, SICU beds, planning horizon, and the idle times of the surgeons, operating theater, and working day. The proposed model is solved using robust optimization to deal with stochastic. The proposed model is formulated on the stochastic programming method proposed by Bertsimas and Sim. In the proposed model, a rolling horizon method is used to reschedule the program after cancellation. The computational results illustrate that the rolling horizon method reduces waiting time and increases throughput. The results illustrate that the benefit obtained from the introduced model has improvements in reducing the surgery costs, and patient waiting time, and increasing the efficiency of available resources. This study has been performed at Shahid Rajaei Heart Hospital in Iran.

An optimization-based design methodology to manage the sustainable biomass-to-biodiesel supply chain under disruptions: A case study

The detrimental effects of excessive fossil fuel consumption have recently become a major global concern. Moreover, fuel supply chains are vulnerable to disruptive and operational risks. This study proposes a robust-stochastic approach to design a resilient sustainable biodiesel supply chain from Jatropha and waste cooking oil, while facilities and transportation links are vulnerable to multiple site-dependent disruptions. The main contributions are implementing preventive resiliency strategies to manage risks, integrating sustainability and resiliency, and selecting biodiesel conversion technology based on byproducts’ demands. Herein, candidate locations are identified to cultivate Jatropha using the best-worst method and geographical information system. Moreover, the supply chain network is designed to optimize economic performance, network non-resiliency, and social impacts. The Monte Carlo simulation approach, k-means clustering, augmented epsilon constraint, and Mulvey robust optimization are adopted to generate and reduce probable scenarios, manage multiple objectives, and handle uncertainty, respectively. The results showed that the non-resilient supply chain experiences a 20.11 % additional cost in disruption scenarios; however, even with a higher initial cost, adopting resiliency strategies reduces disruption cost effects by 9.46 %. Managerial insights have demonstrated that resilience and sustainability are positively correlated in biofuel supply chain management, and rising biodiesel demand enhances social welfare and economic performance.

A multi-objective planning and scheduling model for elective and emergency cases in the operating room under uncertainty

Hospitals are paramount hubs for delivering healthcare services, with their Operating Rooms (ORs) as a pivotal and financially substantial component. Efficient surgery ward planning is crucial in healthcare institutions, aiming to improve medical service quality while reducing costs. This research delves into the intricacies of integrated OR planning and scheduling, focusing on elective and emergency patients in an uncertain environment. To address these challenges, a mixed integer programming (MIP) framework is developed to minimize inactivity and patient wait times while optimizing high-priority resource allocation. Both upstream and downstream units of the ward, the Pre-operative Holding Unit (PHU), Post Anesthesia Care Unit (PACU), and Intensive Care Unit (ICU) are included. The inherently uncertain aspects of surgery, including surgical duration, Length of Stay (LOS), and the influx of emergency patients, demand an intelligent optimization approach. Consequently, a robust optimization strategy is harnessed to effectively grapple with this pervasive uncertainty. A deterministic model is introduced and improved using an enhanced epsilon constraint method. The culmination of this analytical journey yields a collection of Pareto-optimal solutions. Empirical results, supported by managerial insights, highlight the superiority of the proposed method over the traditional weighting approach.

Integrating IoT and blockchain for intelligent inventory management in supply chains: A multi-objective optimization approach for the insurance industry

This research aims to develop and optimize an intelligent supply chain framework tailored for the insurance industry by integrating an innovative inventory management policy supported by the Internet of Things (IoT) and blockchain technologies. Through an extensive literature review, key assumptions are established, needs are identified, and objectives are formulated. A multi-objective mathematical planning model is proposed to minimize cost and time within the supply chain, with optimization conducted under deterministic and fuzzy conditions. The model utilizes augmented epsilon constraint and weighted sum methods to address its multi-objectiveness. Noteworthy is the integration of advanced technologies such as Wireless Sensor Networks (WSN), Radio-Frequency Identification (RFID), blockchain, and online sales, distinguishing it from traditional approaches. Initial validation and testing in smaller dimensions demonstrate the model’s adaptability to precise methods, while larger dimensions necessitate the use of meta-heuristic algorithms for efficient problem resolution. Additionally, a comprehensive sensitivity analysis in the insurance industry on objective function coefficients reveals intricate relationships, offering valuable insights into optimization dynamics across diverse conditions.

Stochastic portfolio optimization: A regret-based approach on volatility risk measures: An empirical evidence from The New York stock market.

Portfolio optimization involves finding the ideal combination of securities and shares to reduce risk and increase profit in an investment. To assess the impact of risk in portfolio optimization, we utilize a significant volatility risk measure series. Behavioral finance biases play a critical role in portfolio optimization and the efficient allocation of stocks. Regret, within the realm of behavioral finance, is the feeling of remorse that causes hesitation in making significant decisions and avoiding actions that could lead to poor investment choices. This behavior often leads investors to hold onto losing investments for extended periods, refusing to acknowledge mistakes and accept losses. Ironically, by evading regret, investors may miss out on potential opportunities. in this paper, our purpose is to compare investment scenarios in the decision-making process and calculate the amount of regret obtained in each scenario. To accomplish this, we consider volatility risk metrics and utilize stochastic optimization to identify the most suitable scenario that not only maximizes yield in the investment portfolio and minimizes risk, but also minimizes resulting regret. To convert each multi-objective model into a single objective, we employ the augmented epsilon constraint (AEC) method to establish the Pareto efficiency frontier. As a means of validating the solution of this method, we analyze data spanning 20, 50, and 100 weeks from 150 selected stocks in the New York market based on fundamental analysis. The results show that the selection of the mad risk measure in the time horizon of 100 weeks with a regret rate of 0.104 is the most appropriate research scenario. this article recommended that investors diversify their portfolios by investing in a variety of assets. This can help reduce risk and increase overall returns and improve financial literacy among investors.

Designing a sustainable-resilient humanitarian supply chain for post-disaster relief process, an earthquake case study in Haiti

Purpose Throughout human history, the occurrence of disasters has been inevitable, leading to significant human, financial and emotional consequences. Therefore, it is crucial to establish a well-designed plan to efficiently manage such situations when disaster strikes. The purpose of this study is to develop a comprehensive program that encompasses multiple aspects of postdisaster relief. Design/methodology/approach A multiobjective model has been developed for postdisaster relief, with the aim of minimizing social dissatisfaction, economic costs and environmental damage. The model has been solved using exact methods for different scenarios. The objective is to achieve the most optimal outcomes in the context of postdisaster relief operations. Findings A real case study of an earthquake in Haiti has been conducted. The acquired results and subsequent management analysis have effectively assessed the logic of the model. As a result, the model’s performance has been validated and deemed reliable based on the findings and insights obtained. Originality/value Ultimately, the model provides the optimal quantities of each product to be shipped and determines the appropriate mode of transportation. Additionally, the application of the epsilon constraint method results in a set of Pareto optimal solutions. Through a comprehensive examination of the presented solutions, valuable insights and analyses can be obtained, contributing to a better understanding of the model’s effectiveness.

Bi-objective optimization modeling for biomass supply chain planning

Biomass energy plays an essential role in renewable energy for many reasons, such as reducing the dependence on fossil fuels and lowering greenhouse gas emissions, providing heat, electricity, and biofuels for various applications, and utilizing waste materials for helpful energy products. Besides, it can create employment opportunities and promote rural development, especially in developing countries where biomass resources are abundant and accessible. In the context of renewable energy research and application, this paper aims to develop a multi-objective mixed integer linear programming for designing multiple echelon biomass supply chain networks. The model is formulated to consider the economic costs and environmental impact of biomass distribution from the suppliers to the biomass plants. In this research, the Epsilon constraint method is adopted to generate Pareto fonts, which provides the trade-offs between two objectives. Moreover, sensitivity analysis is implemented to provide decision-makers with information about a network with changed parameters such as demand. Our model allows the decision maker to determine the capacity of warehouses and biomass power plants, inventory levels, type of trucks, etc. The proposed model is verified and evaluated using a practical dataset from Can Tho province, Central Mekong River Delta in Vietnam, generating several benefits for energy security and sustainability. Such a network includes 3 types of power plants, 3 scales of warehouses, 13 potential locations, and 41 suppliers. From the generated solutions, with the proportion of biomass electricity satisfaction varying from 5% to 30%, Hung Phu, O Mon, and Cai Rang industrial parks are the most suitable for power plants.

A bi-objective sustainable vehicle routing optimization model for solid waste networks with internet of things

Waste production is growing in most communities due to population expansion. Given the stated issue, managing the Solid Waste (SW) created worldwide would be vital. Effective Waste Management (WM) is essential to preserving the environment and lowering pollution. It aids in resource preservation, greenhouse gas emission reduction, and ecosystem protection. Additionally, the promotion of public health and sanitation is significantly aided by WM procedures. This study presents an integrated procedure to enhance the operations of a WM network for recycling SW. We propose a mathematical model to find the optimal sustainable vehicle routes, allocation, and Sequence Scheduling (SS) problem in the recycling industry to reduce costs and CO2 emissions and increase job opportunities. The fundamental innovation of this work is considering waste-vehicle and waste-technology compatibility and Internet of Things (IoT) systems in the model to decrease CO2 emissions and identify compatible waste for recycling centers to produce more final products. An LP-metric and an Epsilon Constraint (EC) approach are used to solve the suggested model. By comparing the two approaches, we have found EC performs better in results and CPU time. As a result, various test problems of different sizes are offered. Accordingly, sensitivity analyses are recommended to assess the suggested model’s effectiveness. Using vehicles compatible with waste reduces CO2 emissions. Utilizing IoT technology and optimization methods makes it feasible to save costs (20%), have a less destructive impact on the environment (36%), and ultimately increase the sustainability of the WM process.

Role of combinatorial optimization problems for the efficient decision making of a company- Case study-

All company seeks to improve their performance through achieving several objectives to stay in the labor market and increase competitiveness. The problem lies in the fact that it often relies on traditional methods for efficient decision-making, causing a waste of time and effort. The paper aims to find the best car service stations among several proposed stations by the Naftal Company, which seeks to achieve the two most important objectives; maximizing lubricants and tires revenues, and maximizing fuel and LPG revenues for the year 2019. The new applied case study was done with the help of the binary multi-objective knapsack problem, which is considered one of the most important problems in multi-objective combinatorial optimization problems. The problem was solved by the epsilon constraint method using MATLAB and CPLEX software. The study results confirmed that the proposed efficient solution set (Pareto optimal solutions) provides the decision maker with a comprehensive view of how to make their decision in a scientific, thoughtful, logical, and convincing manner that suits his situation and puts him at ease, away from trial and error or relying on self-experience.