Multi-objective Linear Programming Model Research Articles

Supporting tactical harvest planning decisions of major fruits through a multi-objective modeling approach by using exact methods

An important stage of the agri-food supply chain is production (agricultural practices and harvesting), where relevant decisions are made in a short period of intensive activity. Regarding the major fruit supply chain, the complexity of these decisions increases because most fruit export companies manage several orchards with different fruit species and varieties. Moreover, the amount of labor and resources must be estimated at least two months in advance of the harvest so that they can be relied upon during the harvest season. In this study, a multi-objective modeling approach for supporting tactical harvest planning decisions of major fruits is developed, aiming to evidence its adequacy and to identify different harvest plans according to the prioritized objectives. Therefore, a multi-objective linear programming (MOLP) model, which considers three conflicting objectives, is proposed. The three objectives correspond to minimizing harvest costs, fruit loss and harvest days. For solving the MOLP model, five a posteriori multi-objective exact methods are compared using a synthetic instance based on a real case. The Pareto frontiers obtained by these methods are analyzed using three metrics related to accuracy, cardinality, and diversity criteria, so that the most suitable method can be selected. Thus, the selected method is applied to an actual case study of a Chilean fruit export company. In addition, the ε-constraint method is used in this case study to compare the obtention of non-dominated solutions in the convex and non-convex regions of the Pareto frontier. The results show that harvest plans vary significantly according to the prioritization of the objective functions. Thus, the percentage difference between each objective function’s worst and best values is around 497% when the harvest costs are minimized, around 1,448% when the fruit loss is minimized, and around 18% when the number of harvest days is minimized. In addition, the adequacy of the multi-objective approach rather than the mono-objective approach to support tactical harvest planning decisions is demonstrated. Furthermore, a scenario analysis for considering changes in the harvest periods is carried out by considering three possible scenarios. This analysis is required because these periods can change every year due to different factors, such as weather conditions and agricultural practices, among others. The results show that the harvest costs and fruit loss increase, on average, 87% and 100%, respectively, when the harvest period is short, that is, one day. Finally, managerial insights about the information obtained by the MOLP model are discussed.

A novel approach for multi-objective linear programming model under spherical fuzzy environment and its application

Every decision-making process particularly those involving real-life issues is disproportionately plagued by uncertainty. It is also unavoidable and obvious. Since its conception are several ways for representing uncertainty have been proposed by numerous academics to cope with uncertainty. Fuzzy sets and hierarchical such as picture fuzzy sets stand out among them as excellent representation techniques for modeling uncertainty. However, there are several significant drawbacks to the current uncertainty modeling techniques. Due to its vast versatility and benefits we here embrace the idea of the spherical fuzzy set, an extension of the picture fuzzy set. On the other hand amid uncertainty in real life the multi-objective plays a critical role. In this research paper determining a Multi-Objective Linear Programming Problem of Spherical fuzzy sets serves to stimulate nous. The score function corresponding to the degree positive, negative and neutral is the foundation upon which the suggested approach is developed. Additionally we apply the suggested strategy to the solution of the multi-objective linear programming problem to demonstrate its superiority through certain numerical examples. Maximization or Minimizing of the cost is the primary goal of the multi-objective linear programming problem. Using an explicitly defined score function the suggested solution transformed the Spherical Fuzzy Multi-Objective Linear Programming Problem into a Crisp Multi-Objective Linear Programming Problem (CMOLPP). We establish some theorems to show that the efficient solution of CMOLPP is likewise an efficient solution of SFMOLPP. The CMOLPP is then further simplified into a single-objective Linear Programming Problem (LPP) thus we revamp the modified Zimmermann’s approach in the environment of a nonlinear membership function with the aid of the suggested technique. It is possible to simply solve this single-objective LPP using any software or standard LPP algorithm. The suggested approach achieves the fuzzy optimum result without altering the nature of the issue. An application of the suggested approach has been used to illustrate it and its results have been distinguished from those of other preexisting methods found in the literature. To determine the importance of the suggested technique which adjudicate thorough theorem and result analysis is conducted.

Optimization model growth and equalization of farmer’s income in the rotiklot dam service area on the border area of Indonesia-Timor Leste

The study aims to analyze optimization models of growth and income distribution. The study used a survey method in Fatuketi Village, Kakuluk Mesak District as the Rotiklot Dam service area, with a sample of 300 respondents. Data analysis uses a multi-objective linear programming model for growth and equal distribution of agricultural income. The results of the analysis show that an income of IDR 11,576,192.00 per year is an income that optimizes growth and income distribution. Optimizing growth and equal distribution shows that the average income of farmers in the first planting season was IDR. 4,132,108 and IDR. 7,444,084 in planting season II. The marginal land used is 300 ha with the volume of water needed to meet all plant needs as much as 1,986,565.16 m3. Agricultural income can still be increased for the third planting season because there is still excess water of 948,434.84 m3.

Power Generation Mix Optimization under Auction Mechanism for Carbon Emission Rights

As the international community attaches importance to environmental and climate issues, carbon dioxide emissions in various countries have been subject to constraints and limits. The carbon trading market, as a market tool to reduce greenhouse gas emissions, has gone through a development process from a pilot carbon market to a national carbon market in China. At present, the industries included in the national carbon market are mainly the electric power industry, and the carbon emissions of the electric power industry account for about 40% of the national carbon emissions. According to the construction history of foreign carbon markets, China’s future carbon quota allocation will gradually transition from free allocation to auction allocation, and the auction mechanism will bring a heavy economic burden to the electric power industry, especially the thermal power generation industry. Therefore, this study takes Guangdong Province as an example to optimize the power generation mix with the objective of minimizing the total economic cost after the innovative introduction of the carbon quota auction mechanism, constructs an optimization model of the power generation mix based on the auction ratio by comprehensively applying the system dynamics model and the multi-objective linear programming model, systematically researches the power generation structure under different auction ratios with the time scale of months, and quantitatively evaluates the economic inputs needed to reduce the greenhouse gas emissions. The results of the study show that after comprehensively comparing the total economic cost, renewable energy development, and carbon emissions, it is the most scientific and reasonable to set the auction ratio of carbon allowances at 20%, which achieves the best level of economic and environmental benefits.

Solution of Z-number-based multi-objective linear programming models with different membership functions

In a universe full of fuzziness and uncertainty, it is an absolute blessing if some information is reliable to some degree. Considering the amount of uncertainty, Zadeh proposed the idea of Z-number, which carries both uncertainty and the reliability of the information. Uncertain information can be reliably conveyed using Z-numbers. On the other hand, one of the important and widely used decision-making techniques is linear programming. Currently, linear programming has been extensively explored using fuzzy information. Decisions made using linear programming with uncertain data are highly uncertain due to the lack of reliability of the information. An effective decision-making method is multi-objective linear programming (MOLP), in which the decision-maker attempts to draw conclusions from information containing conflicting attributes. In the MOLP problem, there may be different solution vectors corresponding to each objective function. One needs to find a compromise solution vector that satisfies each objective function to a certain extent based on the decision maker's suggested preferences. In this study, we use Z-number and MOLP to model the Z-number MOLP problem (ZMOLPP). Furthermore, we propose a strategy for solving ZMOLPP by transforming it into a crisp MOLP problem, and finally converting this crisp MOLP problem into a single-objective linear programming problem (LPP) using different shape functions. Additionally, we compare the results with existing MOLP problems in fuzzy settings to validate the proposed strategy.

A multi-objective optimization approach for disruption management in an intermodal freight transport network

The growing demand for freight transportation is leading to pay more attention to the management of intermodal freight transport network (IFTN). The optimization of IFTN management will have many benefits in terms of sustainability, reducing costs and pollution. Although many studies on the optimization of IFTN operations exist, the management of disruptions deserves a particular attention since disruptions may lead to a significant drop of performance in the entire network. In particular, seaport terminals are prone to disruptions because of their key role in connecting the land side and the sea-side operations. The availability and reliability of the entire network is directly affected by their disruptions. In this paper, a multi-objective linear programming model is developed to minimize congestion in an IFTN, which is originated from the occurrence of a disruption in a seaport terminal. The model aims to minimize cost and emissions, simultaneously. Computational results of a realistic case study, inspired by an Italian IFTN, shows the effectiveness of the developed model to improve the performance of the entire network.

Modeling third-party reverse logistics for healthcare waste recycling in the post-pandemic era

The COVID-19 pandemic has increased the demand for life-saving devices known as ‘ventilators,’ which help critically ill patients breathe. Owing to the high global demand for ventilators and other medical equipment, many Indian nonmedical equipment companies have risen to meet this demand. This unexpected demand for ventilators during the COVID-19 pandemic, similar to that for other EOL electronic medical devices, has become a severe problem for the nation. Consequently, the healthcare industry must efficiently handle EOL ventilators, which can be outsourced to 3PRLPs. 3PRLPs play a vital role in a company’s reverse logistics activities. This study emphasises the 3PRLP selection process as a complex decision-making problem and the optimisation of order allocation to qualified 3PRLPs. As a result, this study proposes a two-phase hybrid decision-making problem. First phase combines the two multi-attribute decision-making methods to select 3PRLPs based on their assessed SPS and Second phase, the evaluated SPS was utilised as one of the objectives of a multi-objective linear programming model to allocate orders to the selected 3PRLPs. To solve the proposed model, both classical and modern approaches were used. The results show that the proposed framework can be successfully implemented in the current scenario of the healthcare industry.

Optimal maintenance planning for offshore wind farms under an uncertain environment

The operation and maintenance costs of wind power generation systems can be reduced through the implementation of maintenance policies at suitable procurement indenture and maintenance levels. Purchasing components involves uncertainties associated with cost and component reliability due to objectives which frequently lack precision. In order to solve fuzzy multi-objective lot-sizing decisions of spare parts for a long term predictive maintenance planning problem in offshore wind farms, this study develops a novel fuzzy multi-objective linear programming model with piecewise linear membership function and S-curve membership function to simultaneously evaluate maintenance cost and system reliability. This model integrates multi-OWT (offshore wind turbines), multi-component, multi-supplier, and component reliability functions for offshore wind systems under an uncertain environment. The analytical results can help operation and maintenance managers to systematically analyze the cost-effectiveness and system reliability of predictive maintenance planning in practical applications.

Optimal selection and investment-allocation decisions for sustainable supplier development practices

Organization’s sustainability performance is influenced by its suppliers’ sustainability performance. This relationship makes sustainable supplier development a strategic competitive option for a buyer or focal organization. When considering sustainable supplier development practices (SSDPs) adoption, organizations have to balance and consider their limited financial resources and operational constraints. It becomes necessary to both select the best SSDPs set and investment allocation among the selected SSDP set such that the organization can maximize overall sustainability performance level. In this paper, an integrated formal modeling methodology using DEMATEL, the NK model, and multi-objective linear programming model is used support this objective. The proposed methodology is evaluated in a practical sustainable supply chain field study of an equipment manufacturing company in China. Through case study, we found that the interdependency among SSDPs must be considered in SSDPs selection and investment allocation problem. Theoretical, managerial and methodology implications, conclusions, and directions for future research are also presented.

Target-Oriented Compromised Sales and Profit Approach for Production and Distribution Planning in a Supply Chain

This paper aims to determine optimal aggregate production and distribution plans in a supply chain system that simultaneously achieve two business targets of total profit and total sales, with uncertain parameters, e.g., production rate during regular time and overtime, inventory holding costs for a manufacturer and distribution centers, and transportation cost. A fuzzy multi-objective linear programming (FMOLP) model is developed to represent the planning problem. The proposed method that minimizes maximum deviation from satisfaction targets of fuzzy profits and sales is more effective, compared with the method that maximizes minimum satisfaction of fuzzy profits and sale, to determine various compromised solutions, which are Pareto-optimal, and to allow a planner to select the most desirable solution based on his/her opinion. This paper has made a significant contribution since it is the first one that proposes the FMOLP approach to determine compromised solutions with two target-based objectives of simultaneously achieving total fuzzy profit targets and total sales target.

A Self-Learning Based Dynamic Multi-Objective Evolutionary Algorithm for Resilient Scheduling Problems in Steelmaking Plants

Scheduling is one of the most important missions for plant-wide optimization in steelmaking manufacturing systems. In the context of dynamic scheduling, the decision-maker should simultaneously minimize economic objectives within the decision space and violation penalty out of the decision space. In this study, we introduce a resilient scheduling model in steelmaking plants, which provides flexible decisions, including buffering times in between stages and controllable processing speeds in the casting stage, to enable the solution to absorb random disturbances and recover quickly. We formulate the dynamic steelmaking scheduling problem with resilient responding strategies, which is a variant of dynamic multi-objective optimization problems (DMOP), and propose a resilient scheduling optimization framework to solve it over time. First, we employ a vector with problem-specific knowledge to map the whole decision space to sub-schedules in the casting stage, which contains casting priority, casting speed and scaling ratio. Next, we form a multi-objective linear programming model to evaluate these problem-specific vectors. Last but not least, we develop a self-learning based dynamic multi-objective differential evolutionary algorithm to solve the variant DMOP, in which a hypothesis-testing technique is used to detect and identify environmental changes. The sensitivity analysis and algorithm comparisons are performed on a wide range of problem instances under dynamic environments. Experimental evidence validates that the proposed resilient model and the optimization framework is effective to solve the dynamic scheduling problem in steelmaking plants. Note to Practitioners—This paper investigates a dynamic scheduling problem that comes from steelmaking manufacturing systems and is extensively studied in existing works. Because a decision-maker only has incomplete knowledge about the realistic environments, this paper simultaneously considers that both the decision and objective space of a scheduling problem dynamically changed over time. We develop a resilient scheduling model which can absorb the different types or scales of disturbances caused by unforeseen events, and recover rapidly to the original state. We formulate the resilience scheduling model and propose a dynamic multi-objective algorithm based on the self-learning differential evolutionary algorithm to solve it. The effectiveness of the proposed model and algorithm is validated via sensitivity analysis and comparison to other well-known algorithms. Furthermore, the resilient scheduling model and its optimization framework can also be applied to dynamic scheduling problems in other industries.

Solving Three Objectives Single-Machine Scheduling Problem Using Fuzzy Multi-Objective Linear Programming

In this paper, three criteria scheduling problem of n jobs on a single machine is considered. Each of these n jobs is to be processed without interruption and becomes available for processing at time zero. The problem is to minimize three objectives simultaneously, which are the completion time, maximum tardiness, and maximum earliness. Here, we develop a fuzzy multi-objective linear programming (FMOLP) model for solving multi-objective scheduling problem in a fuzzy environment by using piecewise linear membership function (PLMF). A numerical example demonstrates the feasibility of applying the proposed model to scheduling problem, and yields a compromised solution to help the decision maker’s overall levels of satisfaction. The algorithm is tested to show the ability of applying this model to three criteria.

Sustainability Fruit Supply Chain Design in the Context of Decentralized Smallholders: Modelling Framework and Sensitivity Analysis

Abstract This paper aims to examine the sustainability of smallholders’ citrus supply chain characterized by low coordination and the need to reinforce producers’ welfare, through optimization-based decision support method in the field where logistics specialization and global sustainability are required by agricultural producers. More specifically, a mixed-objective and multi-objective linear programming model is developed to achieve a sustainable balance: at the economic level, to reduce the logistics costs associated with the production chain as well as to reduce the environmental impacts in the form of carbon dioxide emissions generated during transport, while at the social level, integration through job creation into a three-echelons fruit supply chain including producers, intermediaries and retailers. The model is applied to four scenarios, whose analyses determine the importance of supply chain costs that cannot be neglected but which lead to an optimum that also reduces environmental burden and increases social welfare. In conclusion, the integration of opposing approaches represented by this model enables the improvement of the performance of the supply chain studied.

A Multiobjective Approach for Sector Duration Optimization in Stereotactic Radiosurgery Treatment Planning

Sector duration optimization (SDO) is a problem arising in treatment planning for stereotactic radiosurgery on Gamma Knife. Given a set of isocenter locations, SDO aims to select collimator size configurations and irradiation times thereof such that target tissues receive prescribed doses in a reasonable amount of treatment time and healthy tissues nearby are spared. We present a multiobjective linear programming model for SDO to generate a diverse collection of solutions so that clinicians can select the most appropriate treatment. We develop a generic two-phase solution strategy based on the ε-constraint method for solving multiobjective optimization models, 2phasε, which aims to systematically increase the number of high-quality solutions obtained, instead of conducting a traditional uniform search. To improve solution quality further and to accelerate the procedure, we incorporate some general and problem-specific enhancements. Moreover, we propose an alternative version of 2phasε, which makes use of machine learning tools to reduce the computational effort. In our computational study on eight previously treated real test cases, a significant portion of 2phasε solutions outperformed clinical results and those from a single-objective model from the literature. In addition to significant benefits of the algorithmic enhancements, our experiments illustrate the usefulness of machine learning strategies to reduce the overall run times nearly by half while maintaining or besting the clinical practice. History: Accepted by Paul Brooks, Area Editor for Applications in Biology, Medicine, and Healthcare. Funding: This work was supported in part by the Natural Sciences and Engineering Research Council of Canada [Discovery Grant RGPIN-2019-05588]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplementary Information [ https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1252 ] or is available from the IJOC GitHub software repository ( https://github.com/INFORMSJoC ) at [ http://dx.doi.org/10.5281/zenodo.7048848 ].

A multi-objective linear programming model for scheduling part families and designing a group layout in cellular manufacturing systems

Different industries compete to attract customers in different ways. In the field of production, group technology (GT) is defined by identifying and grouping similar parts based on their similarities in design and production. Cellular manufacturing (CM) is an application of GT to reconfigure the factory and job shop design. A manufacturing cell is a group of independent machines with different functions put together to produce a family of parts. Designing a cellular manufacturing system involves three major decisions: cell formation (CF), group layout (GL), and group scheduling (GS). Although these decisions are interrelated and can affect each other, they have been considered separately or sequentially in previous research. In this paper, CF, GL, and GS decisions are considered simultaneously. Accordingly, a multi-objective linear programming (MOLP) model is proposed to optimize weighted completion time, transportation cost, and machine idle time for a multi-product system. Finally, the model will be solved using the ϵ-constraint method, representing different scales solutions for decision-making. The proposed model is NP-hard. Therefore, a nondominated sorting genetic algorithm II (NSGA-II) is presented to solve it since GAMS software is unable to find optimal solutions for large-scale problems. Besides, to evaluate the performance of NSGA-II, the problem is solved by three metaheuristic algorithms.

Towards a green recovery in the EU: Aligning further emissions reductions with short- and long-term energy-sector employment gains

To tackle the negative socioeconomic implications of the COVID-19 pandemic, the European Union (EU) introduced the Recovery and Resilience Facility, a financial instrument to help Member States recover, on the basis that minimum 37% of the recovery funds flow towards the green transition. This study contributes to the emerging modelling literature on assessing COVID-19 vis-à-vis decarbonisation efforts, with a particular focus on employment, by optimally allocating the green part of the EU recovery stimulus in selected low-carbon technologies and quantifying the trade-offs between resulting emissions reductions and employment gains in the energy sector. We couple an integrated assessment model with a multi-objective linear-programming model and an uncertainty analysis framework aiming to identify robust portfolio mixes. We find that it is possible to allocate recovery packages to align mitigation goals with both short- and long-term energy-sector employment, although over-emphasising the longer-term sustainability of new energy-sector jobs may be costlier and more vulnerable to uncertainties compared to prioritising environmental and near-term employment gains. Robust portfolios with balanced performance across objectives consistently feature small shares of offshore wind and nuclear investments, while the largest chunks are dominated by onshore wind and biofuels, two technologies with opposite impacts on near- and long-term employment gains.

Does an Alternative Local Food Network Contribute to Improving Sustainable Food Security?

Food security is the state of having reliable access to a sufficient quantity of affordable, safe, and nutritious food for all people. It is a critical point to be achieved yet has many aspects to be considered, which include food availability, stability, access, and utilization. Each aspect has its own challenge, which makes food security a complex goal to achieve. Therefore, this paper aims to demonstrate how the Local Food Network (LFN) might be able to address the challenges of food security and eventually achieve it. Moreover, this paper also takes the standpoint of sustainability aspects to ensure food security can be achieved sustainably and responsibly. A case study in Indonesia is given in this paper to provide a concrete explanation of the topic. Rice commodity is used in this study as the staple food of Indonesia. To achieve the goal of this paper, a Multi-objective Linear Programming (MOLP) model, which reflects the LFN, is developed. Furthermore, sustainability’s social, economic, and environmental aspects are directly incorporated into the model. Through several measures obtained from the model results, this paper indicates that food security can be achieved sustainably through the concept of LFN.

New Advances on Fuzzy Linear Programming Problem by Semi-Infinite Programming Approach

As we are faced with more uncertainty problems in the real world, it is necessary to ‎provide ‎models that can provide appropriate solutions for dealing with these issues. In this ‎study, we ‎ proposed a new approach to solving linear programming problem in the fuzzy ‎environment ‎based on solving ‎a related multi-objective model. This kind of problem can be ‎reduced to a ‎fuzzy linear semi-infinite programming problem. In this way, we present a new ‎mixed ‎Multi-Objective Linear Semi-Infinite Programming (MOLSIP) model to solve the ‎main ‎problem, furthermore, as a practical case, we consider a fuzzy Data Envelopment ‎Analysis ‎‎(DEA) model which is a concern to‎ an evaluation of the performance of Decision-‎Making ‎Units (DMUs) in uncertainty environment, The new models show the advantage of ‎our ‎method over the previous ones in terms of certainty. Finally, numerical examples ‎are ‎included to illustrate the suggested solution procedure.‎

Optimizing the Service Network Design Problem for Railroad Intermodal Transportation of Hazardous Materials

The service network design problem is one of the key problems in the field of railroad intermodal transportation of hazardous materials (hazmat). It lies in determining the frequency of the trains and the allocation of both hazardous and ordinary shipments to these trains, as well as the railroad connecting plan of all shipments based on the established train formation plan. Based on a unified method, we build a multiobjective mixed-integer linear-programming model that comprehensively considers both hazardous and ordinary materials, the compatibility of goods and services, the capacity of the transfer station, and the delivery time limit of each shipment. An augmented ε-constraint algorithm is customized to solve the model. Computational results of a practical example in China show that an increase of 8.4 million yuan in the total cost could reduce nearly 24541 the total risk. Moreover, the algorithms comparison and sensitivity analysis indicate that the augmented ε-constraint algorithm is a more suitable approach to handle the model because of its advantage in the uniqueness of distinct nondominated solutions. Finally, the sensitivity analysis shows that the total cost and risk could simultaneously be reduced if the delivery time limit is relaxed or if the transfer time is shortened.

Pavement Maintenance Program at the Network Level: Mixed-Integer Programming with Multiple Objectives

Pavement network conditions deteriorate over the years of use. To keep pavement conditions at acceptable levels, highway agencies plan pavement maintenance and rehabilitation (M&R) programs and perform accordingly. Highway agencies usually face budget variability for pavement M&R activities because of limited resources, economic conditions, and changes in policies. The situation makes it difficult for highway agencies to keep an acceptable pavement condition at the network level. Therefore, it is important for highway agencies to adopt M&R policies that can maximize the network condition as well as handle the deviation of the network condition considering the available maintenance funds. In this paper, a multi-period multi-objective linear integer programming model is proposed. Two objectives, maximization of the average network condition and minimization of deviation of the network condition from an idealized network condition trend, are considered in the formulation. The model is formulated for fixed M&R budgets, as well as for variable M&R budgets. The proposed model provides an M&R program for the pavement network that helps decision makers to manage pavement maintenance programs considering budgetary constraints. A case study examining a network of 45 pavement sections is conducted. The solutions of the fixed-budget and variable-budget model are presented. In addition, the values of the system to the decision maker are discussed. Results show that the proposed model is an attractive way to manage pavement maintenance programs at the network level.