Multi-objective Linear Model Research Articles

A risk-averse sustainable perishable food supply chain considering production and delivery times with real-world application.

In recent years, a relatively novel paradigm known as sustainable development has been introduced in response to concerns regarding the adverse impact of industrial activities on the environment and society. Managers in the food sector have been attempting to incorporate the principle of sustainable development in their supply chains owing to the paramount importance of social and environmental considerations in creating a competitive advantage for food products. To this end, we propose a multi-objective linear mathematical model considering the three dimensions of sustainability, i.e. economic, environmental, and social, to design a sustainable food supply chain. Given today's volatile business environment, we employ a robust optimization model by incorporating Conditional Value-at-Risk into the configuration of two-stage stochastic programming to tackle uncertainty and take up a risk-averse strategy in supply chain design. The model aims to identify the optimal production and delivery times of the products, investigate the effects of their perishability characteristic on inventory decisions, and assess the financial and environmental advantages of transportation decisions to improve the sustainability of logistics operations. A novel version of fuzzy goal programming approach is applied to solve the proposed model. Next, the applicability of the proposed model and its solution method is verified based on computational experiments on a real-world case study of a processed food company. Lastly, conflicts between the sustainability aspects are examined, and several sensitivity analyses on risk-aversion parameters are performed to provide managerial insights for industry executives seeking to optimize their network concerning sustainability issues and well-performance under worst-case scenarios.

Comparison of Multi-Object Control Methods Using Multi-Objective Optimization

The aim of this work is to obtain multi-objective linear programming algorithms that can be used to solve the global problem of multi-object safety control processes in order to minimize the risk of collisions. In multi-objective linear optimization models, satisfactory trade-off assesses and resolves the conflict between different control objectives. A comparison of single-, bi-, and tri-objective linear programming algorithms allows us to adapt the appropriate optimization method to the conditions of the control process. An important outcome of the present research is the demonstration of the greater effectiveness of bi- and tri-objective optimization compared to single-objective optimization, reflecting the compromises taken into account when choosing between objects and achieving a minimum risk of collision when passing them.

A preventive–reactive approach for nurse scheduling considering absenteeism and nurses’ preferences

The nurse scheduling problem (NSP) has become significant in recent years due to its direct impact on patient healthcare. This problem involves assigning nurses’ shifts while fulfilling a set of hard constraints associated with labor regulations and soft constraints related to personal preferences, workload balance, among others. Most studies have focused on providing solutions for deterministic scenarios without considering unexpected disruptions, such as an unscheduled nurse absence. This study integrates two of the most common approaches to address absenteeism: preventive and reactive. First, we propose a multiobjective linear model for staff scheduling that preventively assigns backup nurses for each day. The NSP is known to be an NP-hard problem. Therefore, we used a genetic algorithm to obtain solutions in a reasonable amount of time. To mitigate the effect of unscheduled nurse absences, we propose two reactive rescheduling policies, one that seeks to maintain the baseline schedule and another that prioritizes the exclusive use of backup nurses. We used Montecarlo simulation under different problem settings to compare the proposed policies with a policy that does not use the preventive approach. The probability that a nurse will accept an additional shift to cover an absence was also considered. Simulation results suggest that both of our preventive–reactive policies outperform the non-preventive policy, especially in the presence of a small probability that a nurse will accept an additional shift. Finally, we used the proposed policies to create the monthly nursing schedule in a reference hospital in Bogotá-Colombia.

Optimizing the planning of crop transformation to adapt to climate change in Ninh Phuoc district, Ninh Thuan province

Optimizing agricultural land use plans to suit natural conditions, economic development, and environmental protection, especially adaptation to climate change has scientific and practical significance. In this paper, we proposed an optimal crop structure transformation plan according to economic, social and environmental objectives based on using a multi-objective linear planning model and GIS technology. The multi-objective linear planning model supported the determination of the optimal land used structure and GIS technology, assisting the planner in the spatial arrangement of land use. This study was carried out in Ninh Phuoc district, Ninh Thuan province. The results obtained imply high practical significance and could expand the research scale for the whole Ninh Thuan province and other localities with similar conditions.

An evolutionary genetic algorithm for a multi-objective two-sided assembly line balancing problem: a case study of automotive manufacturing operations

ABSTRACT Assembly lines are often indispensable in factories, and a good assembly-line balancing model is very important for manufacturers to maximize their profit using limited resources in a competitive environment. To maintain a productive assembly line, multiple objectives with different importance must be considered at the same time. In this paper, a two-sided assembly-line balancing problem (TALBP) with multiple objectives is examined. A fuzzy multi-objective linear programming-weighted model (FMOLP-W) for solving the TALBP is constructed first with the consideration of the importance weights of the line balancing performance factors, including minimizing the number of workstations, minimizing cycle time, maximizing line efficiency, minimizing smoothness index and minimizing workstation idle time. An evolutionary genetic algorithm (GA) is proposed next to tackle large-scale problems when the problems are too complex to be solved by the FMOLP-W.

Optimal Operation of Multiple Energy System Based on Multi-Objective Theory and Grey Theory

The manufacturing industry consumes electricity and natural gas to provide the power and heat required for manufacturing. Additionally, large amounts of electric energy and heat energy are used, and the electricity cost, amount of environmental pollution, and equipment maintenance cost are high. Thus, optimizing the management of equipment with new energy is important to satisfy the load demand from the system. This paper formulates the scheduling problem of these multiple energy systems as a multi-objective linear regression model (MLRM), and an energy management system is designed focusing on the economy and on greenhouse gas emissions. Furthermore, a variety of optimization objectives and constraints are proposed to make the energy management scheme more practical. Then, grey theory is combined with the common MLRM to accurately represent the uncertainty in the system and to make the model better reflect the actual situation. This paper takes load fluctuation, total grid operation cost, and environmental pollution value as reference standards to measure the effect of the gray optimization algorithm. Lastly, the model is applied to optimize the energy supply plan and its performance is demonstrated using numerical examples. The verification results meet the optimized operating conditions of the multi-energy microgrid system.

A Novel Scenario-Based Bi-objective Optimization Model for Sustainable Food Supply Chain During the COVID-19: a Case Study

Since food is one of the essential human needs, studies on this topic have always been a global concern. With the advent of COVID-19 and the emergence of many problems in all aspects of the food supply chain (such as production, transportation, distribution), this issue has become doubly important. This paper discusses an MINLP optimization model for handling the impact of the COVID-19 pandemic based on the food supply network through Food Hubs (FHs). In this research, the concept of FH has been used for a more effective and faster connection of consumers to production sites. Due to prevention of the spread of coronavirus and the quarantine conditions, the areas have been divided into two parts (high-risk and low-risk) and two scenarios have been defined for this supply chain. The purpose of this paper is to reduce costs and environmental impacts as much as possible. The proposed model is solved by GAMS software for small- and middle-size test problems, and it is solved with genetic optimization algorithm as a meta-heuristic approach for large-size problems. Also, to solve the developed linear multi-objective model, augmented ɛ-constraint approach is applied, and a real case study from Iran is examined to illustrate the validation of the proposed model. Numerical and computational results are provided to prove the efficiency and feasibility of the presented model. Finally, sensitivity analysis is presented to evaluate the effect of changing some parameters on variables and objective functions.

Presentation and implementation multi-objective mathematical models to balance the assembly line

The use of assembly lines is one of the important approaches in mass production of industrial products. Imbalance of assembly lines increases cycle time and idle times, resulting in reduced production rates, line efficiency, and increased system costs, which ultimately lead to low productivity. A hybrid model assembly line is a type of production line on which various models of products are assembled. These assembly lines are increasingly accepted in the industry in order to overcome the diversity of customer demand. The hybrid model assembly line is able to respond quickly to sudden changes in demand for different models of a product without maintaining a large inventory.The purpose of this paper is to present a multi-objective integer linear mathematical programming model for balancing assembly lines, which is solved using the general criteria method. The three objective functions considered in this model are: (1) Minimizing cycle time (2) Minimize the idle time of each station and (3) increase the efficiency of the assembly line. In order to investigate the model, Iran-Shargh Neishabour Company has been considered as a case study. After implementing the proposed model of the paper, the results show the optimal performance of the proposed model and the studied parameters in line balancing have been significantly improved.

Scenario-based design of a steel sustainable closed-loop supply chain network considering production technology

Nowadays, many organizations are trying to balance the social, environmental, and economic aspects of their supply chains to gain competitive advantages against their rivals and have a sustainable supply chain. Steel is one of the most critical raw materials practically used in every aspect of our life, directly or indirectly influencing the industry and economy of a country. The final products of the steel industry can be reused at the end of their lifecycle, making the principles of reverse logistics applicable in the supply chain and turning it to a closed-loop supply chain. In this research, a multi-objective linear mathematical model under uncertainty is developed to optimize a steel sustainable closed-loop supply chain. The existed uncertainty is modeled through a scenario-based method in the stochastic environment, and the proposed multi-objective model is developed following a fuzzy goal programming approach. A real case study is explored in one of the active steel supply chains in Iran to validate the model. The model optimizes total profit, energy, and water consumption, CO2 emission, job opportunity created, and lost working days through determining optimal production technology, whether retailers get changed to hybrid centers or not, and the flow of material and products. The final results show that a mere 1% decrease in the profit can alleviate the harmful environmental effects by 5%. Finally, several managerial implications derived from final results and sensitivity analysis are discussed to provide insights for industry leaders who desire to increase their profits with regard to environmental and social effects.

Optimal design of a forest supply chain in Argentina considering economic and social aspects

Even though the social aspect is a significant issue since it involves the welfare and development of the affected population, it is not usually borne in mind when designing a supply chain, which is imbued with an economic perspective. From a sustainability point of view, the social impact caused by the location of facilities in a region should be specially assessed. This work proposes a mixed integer linear multiobjective model which considers the social dimension in supply chain design, evaluating the location of different productive units in sites with particular social characteristics. A new Social Indicator involving specific attributes of the environment (population size and unemployment rate) is presented. The viability and capacity for appropriately evaluating the performance of a solution are analyzed from the social point of view for the forest industry in the northeastern region of Argentina. In addition, a comparison with other indicators proposed in the literature is provided.

Fuzzy multi-objective medical service organization selection model considering limited resources and stochastic demand in emergency management.

In recent years, most countries around the world have faced increasing pressures in the realm of emergency management than ever before. Medical service organization selection is one of the most vital facets of emergency management. Meanwhile, during the selection process, many criteria may conflict with one another and information is uncertain, rendering decision-making processes complex. Hence, multi-objective optimization, fuzzy way and stochastic theories serve as suitable means of addressing such problems. In this paper, a fuzzy multi-objective linear model is developed to overcome medical service organization selection issues and uncertain information. Meanwhile, a fuzzy objective and weight are applied to enable the decision-maker to select suitable schemes while considering stochastic medical service demand. Moreover, real data cannot been obtained. Hence, according to actual conditions, we assume relative information. For illustrative purposes, a numerical example is presented to verify the effectiveness of the proposed model from experimental data.

Optimization of Hazardous Chemical Waste Location-Routing Logistics Based on Uncertain Conditions

In order to effectively solve the hazardous chemical waste location-routing problem, based on the existing literatures, this paper considers chemical waste production and uncertainties in the processing technology, and establishes a multi-objective optimization calculation model involving transportation and location risks, costs and risk equity. It uses an example to verify the proposed model, and then establishes a measurement method with location-routing risk equity based on the fuzzy description of the chemical waste production by the triangular fuzzy membership function. The calculation model takes into account the variable cost and location risk of the waste disposal centre, reducing the error from single-objective calculation. Through the inverse fuzzy algorithm, the multi-objective fuzzy model is converted into a multi-objective linear model. The verification results of the example show that: if the variable cost is not considered, the total risk is increased by 110.68%; if the location risk is not considered, the cost is increased by 21.35%; if the risk equity is not considered, the total cost is decreased by 8.71%, while the risk is increased by 48.32%, which proves that the combinatorial optimization of multi-objective function model established will lead to a slight increase in cost, but a significant reduction of related risks, thus making the location-routing scheme more in line with the actual situation and needs.

A sustainable supply chain for organic, conventional agro-food products: The role of demand substitution, climate change and public health

Abstract In today's marketplace, conventional agricultural products are produced all around the world due to economic reasons. However, recent environmental challenges such as global warming and climate change has strongly been affected by the high volumes of chemical pesticides and fertilizers used to produce these products. Several published reports have indicated the negative effects of the chemicals used in conventional agriculture as well as the effect of climate change on human health. The aim of this study is to develop and analyze a multi-objective linear mathematical model for a sustainable supply chain with an agro-food deteriorating product. The product is produced by two different methods, both by organic and conventional means. In this way, we attempt to create a balance between the production and consumption of conventional and organic products in order to achieve three objectives: reducing costs, reducing environmental degradation, and increasing levels of consumer health. Partial backorder for each product, as well as conventional demand substitution by organic products, are taken into account. In order to assess the impact of supply chain operations on public health, we define a new function based on each product's production and consumption amounts as well as the amount of wastes. The developed model is solved by augmented ɛ-constraint method. Numerical results indicate the important role of supply chain's managers in the formation of sustainable health production and consumption patterns.

Reliability‐based model for generation and transmission expansion planning

This study presents a mixed integer linear multi-objective model based on information gap decision theory, which is used to solve coordinated multiyear generation and transmission expansion planning problems. The model maximises the robustness of each uncertain parameter while a maximum allowable budget range is set. Fuel transportation price is considered. The results provide a numerical tool for system planner to help him adjust the appropriate level of robustness for each uncertain parameter of the problem. Extra limits on security, gaseous emission and fuel availability are considered. A multi-objective method called the ɛ-constraint method is used here to maximise the robust region of load and investment costs simultaneously. The model is implemented on a six-bus Garver test system and 24-bus IEEE test system. The numerical results show the good performance of the model.

A grey multi-objective linear model to find critical path of a project by using time, cost, quality and risk parameters

A project is a series of related activities which are organized to reach a defined goal or satisfy a certain need. Project management plays an important role in different fields of human life. The amount of resources spent on a project renders management of these resources a sensitive task. Determinant factors’ influencing the payoffs of a project mainly encompasses time, cost, quality and also the risk of each activity. Therefore, a critical path method is presented to find the longest path of a project completion time in order to draw managers’ attention to the critical activities. Critical path method is a well-known and widely accepted method to find the critical activities of a project and to concentrate on them for accomplishment of the project without any deviation. Classical critical path methods usually consider only a time factor, but growing complexity and importance of projects entail cost, quality and risk as the critical factors to be considered in project management. Due to the unavailability of certain information relating each factor of each activity, considering a novel approach to deal with such vague and unstable situations is really a controversial issue. Thus, another challenge of the project management contains uncertainty for approximating time, cost, quality, and risk factors of the project activities. Taking into account these two challenges, a grey multi-objective critical path model is proposed in this paper, where parameters of the activities are evaluated as grey numbers, dealing with their uncertainty. Meanwhile, a goal programming based method is illustrated to solve the problem of critical path identification, considering four considerable criteria including time, cost, quality, and risk. Eventually, a numerical example is represented to address applicability of the proposed method.

An Interactive Possibilistic Programming Approach for Blood Bank Locations with Emergency Referral

Regionalisation of Local Blood Banks (LBBs) is so vital for blood supply to facilitate the clinics in the obligated regions to go along with the requests in typical conditions and the moments of crisis. Determination of location of LBBs is a key factor in the selection of alternatives in the blood store networks. In this paper, we first develop a new multi-objective possibility mixed integer linear programming model (MOPMILP) for blood bank location problem considering distinctive contradictive goals at the same time and additionally the loose way of some basic parameters, for example, requirements of hospitals and number of emergency referrals for clinics or hospitals. At that point, in the wake of applying legitimate procedures for changing over this possibilistic model into a precise novel multi-objective linear model (MOLP), we propose a novel intelligent fuzzy method to understand this MOLP and find a proper trade off arrangement. Eventually, we propose a careful analysis and will see the performance of the proposed model.

A new agile fuzzy multi-objective model for selecting/eliminating supplier

In today's highly competitive world, supplier selection is an important decision for efficient supply chain management. Appropriate suppliers reduce the purchasing price and lead-time and increase customer satisfaction. However, after supplier selection stage it is possible that some of the selected suppliers' performances are not acceptable and caused more cost for our supply chain. In an agile supply chain management, it is necessary to have a solution for these cases and eliminate these kinds of suppliers. In this paper, we introduce two crisp/fuzzy multi-objective linear models to eliminate the most costly supplier and determine the amount of purchase from the remaining suppliers. Here we have three objective functions: total purchasing cost that must be minimised, quality and service level that must be maximised. Finally, case studies are presented to illustrate how our proposed models work.

Assessment of habitat suitability in the Upper Reaches of the Min River in China

Habitat richness influences and even determines biological diversity. Plant habitat suitability assessment can provide technical guidance and information support for ecological restoration. Thirteen factors in three categories of terrain, meteorology and soil were chosen to build a habitat suitability assessment index framework in the Upper Reaches of the Min River, based on the local natural environment and the actual influencing factors of vegetative growth. Combined with the Analytic Hierarchy Process (AHP) and entropy method, which were used to calculate weights of indexes, habitat suitability was studied by using a multi-objective linear weighting model and geographic information systems (GIS) spatial analysis techniques. The assessment results are as follows: Altitude, soil stability, aspect and slope have more important effects on plant habitat suitability in the Upper Reaches of the Min River, and their weights are 0.311, 0.260, 0.198 and 0.125, respectively. Suitable and sub-suitable habitats cover 4431.80 km2 and 6171.12 km2, respectively; most of which are distributed along both sides of rivers and have higher suitability. Unsuitable habitats cover the largest area (6679.76 km2), accounting for 29.83% of the whole area; and the worst unsuitable habitats are 5107.23 km2 (22.81%); they account for more than half of the study area. These results indicate that the plant habitat in the Upper Reaches of the Min River is poor and ecological restoration is both urgent and difficult. Therefore, based on the principle of taking measures suitable to the habitat in ecological restoration projects, ecological and engineering measures should be combined to have better effects, while increasing the strength of ecological protection.

Number Theory for the Selection of an Investment Portfolio: An Application to the Mexican Stock Exchange

The calculation of variance is defined as a objective and increasing function, this definition allows establish the hypotheses to calculate diversified investment portfolios from the dominion of the function. In order to apply these hypotheses our mathematical multi-objective linear model is modified. Diversified portfolios are selected from the stocks of the Prices and Quotations Index of the Mexican Stock Exchange. It is shown with a statistical test using the coefficient of variation that the selected portfolio yields a higher profit at a lower risk.

Assessment on the Possibility of Low-Carbon Economic Development - Taking Zhejiang, China as a Case Study

Based on the principles of scientific, systematic, practicality, hierarchy, the paper constructs the evaluation index system of the Possibility of Low-carbon Economic Development, and determines the assessment of evaluation indexes applying the analytic hierarchy process (AHP), and builds the multi-objective linear weighted evaluation function model. Taking the Province of Zhejiang for example, the Possibility of Low-carbon Economic Development was evaluated. The results can be summarized as follows: The construction the evaluation index system of the Possibility of Low-carbon Economic Development is scientific and has a certain operability; The development of low-carbon economy in Zhejiang Province is potential, and the comprehensive evaluation has 4 levels; From certain aspects，such as the establishment and improvement of the low-carbon economy policy system，management system for carbon emissions and carbon exchanges，the introduction of foreign advanced low-carbon technologies，the promotion of low-carbon consumption and low-carbon lifestyle, measures can be taken to promote the development of a low- carbon economy in Zhejiang Province.