Augmented Epsilon Constraint Research Articles

Optimizing the portfolio of road project stakeholders with cost and risk approach

The need for diverse expertise, abundant resources and coherent management are the most important results of project complexity. Therefore, construction project management is essential to achieve project goals. There are a variety of stakeholders who are interconnected and whose performance affects the success or failure of the project. In the present study, the selection of the optimal stakeholder composition is based on portfolio theory. So that more risky and costly stakeholders are selected for stakeholder management. Also, the correlation between stakeholders in construction projects is analyzed by social network analysis (SNA) method. The purpose of this research is to identify and analyze portfolio of stakeholders of construction projects for using the SNA and optimization method. First, stakeholders and their risk, cost and correlation coefficient were identified and evaluated through interviews and questionnaires. Then, using the NetMiner-4 software and augmented epsilon constraint method their risk and cost were optimized and Stakeholder portfolios are selected. In fact, the main focus would shift on such stakeholders in the selected portfolio, while others would receive their own due attention. Therefore, the research findings include identifying significant stakeholders based on the constraints and the impact they will have on the project to manage stakeholders.

Risk-Averse Multiobjective Optimization for Integrated Electricity and Heating System: An Augment Epsilon-Constraint Approach

Uncertainties including demand and environmental factors would increase the operational risk of the energy supply networks. It significantly affects the technical and financial aspects of the integrated electricity and heating system (IEHS). This article presents a risk-averse multiobjective optimization strategy for short-term decision-making. The objective is to optimize the total cost and the technical dissatisfaction in a way that the economy of system operation and energy supply quality for the risk-averse scheme is guaranteed simultaneously. Based on the trapezoidal fuzzy membership function, the fuzzy constraint is constructed to quantify the technical dissatisfaction of the nodal voltage and supply temperature. Then, a multiobjective min–max–min problem is formulated to hedge the IEHS against risk imposed by the uncertain variables. Since the formulated two objectives compete with each other, a risk-averse multiobjective solution procedure based on the augmented epsilon-constraint algorithm is developed to recast the multiobjective problem into its equivalent single objective problem. And the accurate Pareto fronts under different risk levels are obtained with several iterations. Numerical case studies are conducted to evaluate the effectiveness and applicability of the proposed method. It provides benefits in the aspect of balancing the economy and energy supply quality under network constraints and uncertainties.

Real-time collaborative feeder vehicle routing problem with flexible time windows

Today, transportation has become a vital service due to increased competition among businesses. In this regard, customer service is one of the major challenges of logistics units. Companies can improve logistics costs, capacity utilization, service levels, and customer satisfaction by sharing new demands. The need for fast, flexible, reliable, and low-cost delivery is another challenge in urban areas for the distribution of goods. As demand increases, more vehicles are needed to deliver goods and congestion increases in urban transportation networks. A feeder vehicle routing problem (FVRP) consists of a heterogeneous fleet of vehicles, including trucks and motorcycles. In this problem, motorcycles pass easily in crowded areas, and the traffic of urban logistics is distributed easily. More importantly, it reduces the number of returns to the physical depot, lowers the costs, and leads to time savings. This study introduces the real-time collaborative feeder vehicle routing problem (RTCFVRP) with flexible time windows in which vehicles are permitted to serve customers before and after the time window. We propose the mixed-integer linear programming model with the CPLEX mathematical programming solver applying the augmented epsilon constraint. Also, multi-objective particle swarm optimization (MOPSO) and MOPSO-variable neighborhood search (MOPSO-VNS) were developed regarding the complexity of the problem. The performance of these algorithms was compared with Pareto solutions generated by the non-dominated sorting genetic algorithm-II (NSGA-II) and multi-objective evolutionary algorithm based on decomposition (MOEA/D) in both static and dynamic modes. Finally, in addition to statistical analysis, the AHP-TOPSIS method is employed to analyze and prioritize algorithms. The obtained results show the better performance of the proposed algorithm in both static and dynamic modes in small and large-size instances.

A robust multi-objective joint scheduling of integrated electricity and gas grids considering high penetration of wind and solar units and flexible loads towards achieving a sustainable operation

The cooperative planning of interconnected networks to achieve a sustainable operation and satisfy the welfare of all agents has become a critical issue. This paper optimizes the joint scheduling of integrated electricity and gas grids composed of wind turbines, photovoltaics, storage systems, power to gas and gas to power units. In this regard, a risk-constrained multi-objective programming is suggested to simultaneously model the operation costs of both networks and a robust augmented epsilon constraint method is applied to solve the problem and obtain the Pareto set. In order to simulate realistic conditions, uncertainties of wind and solar energies, electrical and gas loads and energy and gas prices are also considered. As well, the impact of flexible electrical and gas loads is analyzed using a time-of-use demand response program. According to the simulations, the presented approach is capable to create a good equilibrium between both networks. The results validate that the risk-averse strategy significantly increases the costs of electrical and gas grids by 21.41% and 10.36% compared to the risk-neutral strategy, respectively. In return, the robustness is improved against fluctuations caused by uncertain parameters. Moreover, responsive loads enhance decision flexibility and decrease the mentioned costs by 2.26% and 7.83%, respectively.

Coordination of humanitarian logistic based on the quantity flexibility contract and buying in the spot market under demand uncertainty using NSGA-II and NRGA algorithms

The extant study aimed to create a kind of coordination in the humanitarian chain by using a quantity flexibility (QF) contract. The QF contract considers a kind of coordination between a relief organization and a producer for inventory management determining order volumes. Due to insufficiency of amenities or time limits during the crisis, an internal producer can outsource a part of its duties to an external producer to produce items and accelerate the relief process. Hence, this study proposed a completely novel bi-objective mathematical model to coordinate relief items’ supply and distribution by using QF contracts and buying in the spot market under demand uncertainty conditions to reduce costs and accelerate relief services. The augmented epsilon constraint method was used to solve the small scales of this model and NSGA-II and NRGA algorithms were employed to solve large scales. The results indicated the powerful performance of NRGA in terms of most evaluation indicators.

Investigating a citrus fruit supply chain network considering CO2 emissions using meta-heuristic algorithms

AbstractAccording to the increasing carbon dioxide released through vehicles and the shortage of water resources, decision-makers decided to combine the environmental and economic effects in the Agri-Food Supply Chain Network (AFSCN) in developing countries. This paper focuses on the citrus fruit supply chain network. The novelty of this study is the proposal of a mathematical model for a three-echelon AFSCN considering simultaneously CO2 emissions, coefficient water, and time window. Additionally, a bi-objective mixed-integer non-linear programming is formulated for production–distribution-inventory-allocation problem. The model seeks to minimise the total cost and CO+ emission simultaneously. To solve the multi-objective model in this paper, the Augmented Epsilon-constraint method is utilised for small- and medium-sized problems. The Augmented Epsilon-constraint method is not able to solve large-scale problems due to its high computational time. This method is a well-known approach to dealing with multi-objective problems. It allows for producing a set of Pareto solutions for multi-objective problems. Multi-Objective Ant Colony Optimisation, fast Pareto genetic algorithm, non-dominated sorting genetic algorithm II, and multi-objective simulated annealing are used to solve the model. Then, a hybrid meta-heuristic algorithm called Hybrid multi-objective Ant Colony Optimisation with multi-objective Simulated Annealing (HACO-SA) is developed to solve the model. In the HACO-SA algorithm, an initial temperature and temperature reduction rate is utilised to ensure a faster convergence rate and to optimise the ability of exploitation and exploration as input data of the SA algorithm. The computational results show the superiority of the Augmented Epsilon-constraint method in small-sized problems, while HACO-SA indicates that is better than the suggested original algorithms in the medium- and large-sized problems.

Green reverse logistics network design for medical waste management: A circular economy transition through case approach

The lack of proper management of medical waste leads to environmental pollution and threatens the lives of communities. Good medical waste management means appropriate planning and monitoring at all stages, including collection, separation, treatment, recycling, and disposal which promotes a circular approach. This paper presents a multi-item, multi-period, and bi-objective mixed-integer linear programming circular economy transition model for medical waste management considering the uncertainty in the amount of waste generated to design a green reverse network. In this paper, for the first time, the concept of queuing theory is applied to manage the waiting time of trucks carrying infectious waste in treatment centers. In addition, the proposed model simultaneously addresses the centers' location and heterogeneous vehicles routing, and uses a stochastic scenario-based approach to deal with uncertainty of the waste generated. The purpose of the proposed model is to minimize total cost and population risk, and for this end, to employ an improved augmented epsilon-constraint method (AUGMECON2). Finally, the efficiency of the proposed model and solution approach is examined using the data of a case study in Alborz province that includes six hospitals, three potential collection centers, three potential treatment centers, four potential recycling centers, and three potential disposal centers.

Multi-Objective Stochastic Synchronous Timetable Optimization Model Based on a Chance-Constrained Programming Method Combined with Augmented Epsilon Constraint Algorithm

The design of the timetable is essential to improve the service quality of the public transport system. A lot of random factors in the actual operation environment will affect the implementation of the synchronous timetable, and adjusting timetables to improve synchronization will break the order of normal service and increase the cost of operation. A multi-objective bus timetable optimization problem is characterized by considering the randomness of vehicle travel time and passenger transfer demand. A multi-objective optimization model is proposed, aiming at minimizing the total waiting time of passengers in the whole bus network and the inconsistency between the timetable after synchronous optimization and the original timetable. Through large sample analysis, it is found that the random variables in the model obey normal distribution, so the stochastic programming problem is transformed into the traditional deterministic programming problem by the chance-constrained programming method. A model solving method based on the augmented epsilon-constraint algorithm is designed. Examples show that when the random variables are considered, the proposed algorithm can obtain multiple high-quality Pareto optimal solutions in a short time, which can provide more practical benefits for decisionmakers. Ignoring the random influence will reduce the effectiveness of the schedule optimization scheme. Finally, sensitivity analysis of random variables and constraint confidence in the model is made.

Multi-Objective Sustainable Closed-Loop Supply Chain Network Design Considering Multiple Products with Different Quality Levels

International laws and increasing consumer awareness have led to drastic changes in traditional supply chain network designs. Moreover, because of environmental and social requirements, traditional supply chain networks have changed to sustainable supply chain networks. On the other hand, reverse logistics can be effective in terms of environmental and economic aspects, so the design of the supply chain network as a closed loop is necessary. In addition, customers have a demand for different products with different quality levels. Considering different types of customers with a variety of consumption trends can be a challenging issue, and is addressed in this study. The main contributions of this research are considering different quality levels for products as well as different tendencies of customers towards environmental issues. In this study, a sustainable closed-loop supply chain model is designed that seeks to balance economic, environmental, and social responsibilities. In this paper, costs and customer demands for different types of products at different quality levels are considered under uncertain conditions using a robust possibilistic programming method. The proposed multi-objective model is solved using the Augmented Epsilon Constraint (AEC) method that provides an efficient set of solutions for all decision-making levels. The results show that the robust possibilistic programming method is more effective in dealing with uncertainties than the possibilistic programming method.

Life cycle evaluation of microalgae based biorefinery supply network: A sustainable multi-criteria approach

Due to enjoying such features as ability to produce high volumes of oil and reducing and eliminating environment carbon dioxide, microalgae is a promising solution for producing biofuels. In order to help the commercialization of this emerging industry, the present study offers a sustainable mixed integer linear programming model (MILP) for designing and planning microalgae biofuel production and distribution network. As objective functions, this model considers minimizing the total cost of the network and maximizing greenhouse gas emission saving simultaneously. In order to design microalgae biofuel sustainable production and distribution network, a two-stage approach is developed. In order to reduce computational complexity, at first place, data envelopment analysis approach (DEA) and Combinative Distance-Based Assessment (CODAS) approach as well as best worst method (BWM) are developed respectively for determining the location of suitable candidates for establishing microalgae production facilities and constructing biorefinery based on economic, social and environmental criteria. In the second stage, the environmental effects of microalgae biofuel supply chain network are measured using one of the newest and most effective methods that is based upon environmental life cycle assessment as well as OpenLCA software and then followed by formulizing a bi-objective linear programming model. For solving the offered model, augmented epsilon constraint method is used. Finally, a realistic case study conducted at national level concerning microalgae biofuel supply chain. The results indicate that based on the offered model by replacing fossil fuels with biofuel we can achieve greenhouse gases emission saving by 99 %.

Equitable post-disaster relief distribution: a robust multi-objective multi-stage optimization approach

PurposeThis paper aims to address a location-distribution-routing problem for distributing relief commodities during a disaster under uncertainty by creating a multi-stage model that can consider information updates during the disaster. This model aims to create a relief network that chooses distribution centers with the highest value while maximizing equity and minimizing response time.Design/methodology/approachA hybrid algorithm of adaptive large neighborhood search (ALNS) and multi-dimensional local search (MDLS) is introduced to solve the problem. Its results are compared to ALNS and an augmented epsilon constraint (AUGMECON) method.FindingsThe results show that the hybrid algorithm can obtain high-quality solutions within reasonable computation time compared to the exact solution. However, while it yields better solutions compared to ALNS, the solution is obtained in a little longer amount of time.Research limitations/implicationsIn this paper, the uncertain nature of some key features of the relief operations problem is not discussed. Moreover, some assumptions assumed to simplify the proposed model should be verified in future studies.Practical implicationsIn order to verify the effectiveness of the designed model, a case study of the Sarpol Zahab earthquake in 2017 is illustrated and based on the results and the sensitivity analyses, some managerial insights are listed to help disaster managers make better decisions during disasters.Originality/valueA novel robust multi-stage linear programming model is designed to address the location-distribution-routing problem during a disaster and to solve this model an efficient hybrid meta-heuristic model is developed.

Green two-echelon closed and open location-routing problem: application of NSGA-II and MOGWO metaheuristic approaches.

Nowadays organizations outsource transportation of goods or services to reduce cost which leads to a particular type of problem called open location-routing. Also, each logistic organization possesses a limited number of specific vehicles that may not be enough in certain circumstances. This issue indicates the importance of simultaneously considering both open and closed routs. On the other hand, the growing concerns about the detrimental environmental impacts of human activities reveal the necessity of paying attention to environmental issues in logistics. In this study, a bi-objective mathematical programming model is proposed for two-echelon close and open location-routing problem (2E-COLRP) including two echelons of factories, depots and customers to minimize costs and CO2 emissions. The proposed model finds the optimal routs, optimal number of vehicles and facilities as well as the locations of facilities. The augmented epsilon constraint method is used as an exact method to solve the small-sized problems. Due to complexity of model, two metaheuristic algorithms named MOGWO and NSGA-II are utilized to tackle the problems. The efficiency of two aforementioned algorithms is evaluated in terms of several indices considering 22 problem instances with various sizes. The results show that MOGWO performs better than NSGA-II.

A sustainability approach to vehicle modular platform design: A mathematical model

Today, sustainability and its economic, social, and environmental pillars are the main elements of new product market development. Therefore, manufacturers, considering all stages of a product life-cycle, consider it necessary to have a framework for producing sustainable products. Moreover, new product design and development processes especially sub-process of product definition and detailed design processes can play a very critical role in developing product sustainability. This paper considers the role that the car platform can play in creating a family of products and with regard to various data related to the environmental, economic, and social pillars of each of the 15 modules of a car platform and also, using the best–worst method technique and multi-objective mathematical programming with the augmented epsilon constraint method, we were able to achieve a set of platforms with maximum sustainability. The present study explores the possibility of determining the most efficient combinations of modules for every one of the 23 cars’ platforms to produce a collection of products. Through these methods, the 54 efficient solutions in the Pareto front were achieved, and out of this number, after considering all the factors and weights of the objective functions, solution no. 51 was selected as the most efficient. Subsequently, all the 15 module variants of the 23 platforms were determined for solution no. 51. Finally, these variants were ranked on the basis of the SAW technique, and finally, sensitivity analysis is done.

A bi-stage multi-objectives optimization of smart multi energy system with active consumers

The optimal energy consumption and production is one of main aims in the many countries to improve technical, economic and environmental issues by smart energy systems. This paper proposes a bi-stage multi-objectives optimization of the smart multi energy system with optimal coordination of active consumers than electrical and thermal prices in the day-ahead market. The optimization is implemented under uncertainty of demand and price for electrical and thermal energies. In the first stage, original electrical and thermal demand curves are optimized using demand shifting strategy based on energy prices. Then, optimized electrical and thermal demand curves are applied in the second stage for solve a multi-objective functions such as minimization of the emission polluting, operation costs and maximizing the smart multi energy systems flexibility. Moreover, reliability indices and participation of the battery energy storage system as local generation are analyzed to improve the resiliency of the smart multi energy systems by some active consumers. Using the augmented epsilon-constraint method Pareto frontier solutions of multi-objective in the second stage are extracted and the best solution is determined in the decision-making approach by TOPSIS procedure. To demonstrate superiority and validation of the proposed optimization, three cases studies are examined to improve economic, environmental and resilience indices.

Flexibility-based generation maintenance scheduling in presence of uncertain wind power plants forecasted by deep learning considering demand response programs portfolio

The special characteristics of renewable energy resources, such as non-emission and low operating costs, have increased the penetration rate of renewable energy resources in the power system. However, the variability nature of renewable energy resources has led to some challenges in power system studies. Therefore, system flexibility has been taken into account, which plays a key role in dealing with renewable energy resources uncertainty. On the other hand, generation maintenance scheduling is one of the most important and effective programs for short-term studies of the power system. It seems necessary to implement a flexibility-based generation maintenance scheduling in order to achieve more flexible operation as a consequence of providing flexible resources. Here, a novel framework for flexibility-based multi-objective generation maintenance scheduling associated with a portfolio of demand response programs is introduced. Hence, a system flexibility index has been applied in this paper. Moreover, a portfolio of multifarious demand response programs as a negawatt resource has been applied as a provider of flexibility from demand-side point of view. In this paper, direct load control, real-time pricing, and emergency demand response programs are implemented as flexibility providers through comprehensive modelling of DRPs. Herein, proper modeling and forecasting of renewable energy resources production will increase the scheduling accuracy. Hence, the uncertainty of wind power plants is considered by deep learning methodology in Python. Reducing costs such as operation and maintenance costs, leveling the reserve margin and increasing flexibility index are regarded as multifarious objectives of flexibility-based generation maintenance scheduling. Due to the good handling of large-scale, non-convex and non-proportional objective functions, the augmented epsilon constraint method is utilized to evaluate flexibility-based multi-objective generation maintenance scheduling. According to the results, the system flexibility has been improved without increasing costs. Several analyses are carried out on a modified IEEE-RTS 24 bus to trace the capability of the proposed structure.

Toward a safe supply chain: Incorporating accident, physical, psychosocial and mental overload risks into supply chain network

Considering health and safety factors in supply chain network design brings safer place for employee and helps firm to have better image in the society. There are many health and safety factors overlooked by literature studies of supply chain. This paper takes advantage of the results of occupational safety and health in the transport sector studies and connects this field of science with the supply chain network design. This study incorporates health and safety factors such as accident, physical, psychosocial and mental overload risks as an objective function besides cost- and environmental-oriented objective functions. We formulated a multi-objective closed-loop supply chain network as a mixed integer linear programming model and customized augmented epsilon constraint algorithm to solve our multi-objective problem to offer multiple choices for decision makers. Eventually, we analyzed the effects of incorporating health and safety factors in supply chain and demonstrated how it will minimize the health and safety risks of supply chain employees, environmental pollution and the total cost of the network simultaneously.

Coordinated routing system for fire detection by patrolling trucks with drones

Vehicle routing problem with drones (VRPD) is an extension of classical vehicle routing, which involves the usage of trucks and drones. Nowadays, bushfires are taken into account as a major global challenging subject. Indeed, forests are very vulnerable to fires, and the classical patrol systems cannot patrol all areas of the forest and pastures due to the difficult crossing of some routes.The literature survey demonstrated that the mathematical models are an efficient approach for planning forest and rangeland patrols. Drones and trucks are used in cooperation for forest monitoring in this study, with drones acting as an efficient and accurate means of monitoring routes that are impassable to ground vehicles. However, this novel approach deals with several substantial challenges, including limitation in the drone's battery and the routing problem in an integrated truck-drone system based on considering hard-to-reach areas and creating a trade-off between time and cost of the patrol process. These issues make significant differences between the proposed novel approach and the classical vehicle routing problem. Thus, it is essential to develop a comprehensive approach to resolve these crucial issues. The present study develops a multi-objective mathematical programming model as mixed-integer programming for simultaneous patrolling of trucks and drones. The augmented epsilon constraint (AEC) method has been considered to solve the two-objective mathematical programming model. Besides, Benders' decomposition (BD) algorithm has been employed to evaluate the achieved results in large-size problems. The performance of the BD algorithm has been confirmed in this study. The findings indicated that the proposed model efficiently protected the forest via monitoring all areas, including impassable areas where ground patrolling is impossible (e.g., the lack of roads due to dense vegetation). Also, it was proved that this system was a novel, cost-effective patrol, which prevents uncontrollable fires in the shortest possible time.

Integrated Electricity and Natural Gas Demand Response in Flexibility-Based Generation Maintenance Scheduling

Increasing emission concerns about greenhouse gases have led to an increasing tendency to use renewable energy sources (RERs) in the power system. Nevertheless, the probabilistic nature of RERs has led to an enhanced require to flexibility provision. Hence, it is necessary to implement a flexibility-based generation maintenance scheduling. For this purpose, it has used the flexibility index of the system in order to evaluate the flexibility of the power system. In flexibility studies, modeling and predicting the variability of renewable resources is important. In this paper, the uncertainties of wind are considered through forecasting by deep learning method in Python. Gas-fired power plants are one of the most important suppliers of flexibility in the supply-side. Therefore, the reliable operation of power system depends on the of natural gas availability. Furthermore, gas demand is subject to various uncertainties, especially in cold seasons, which will have significant effects on power system. in this paper, power-to-gas (P2G) technology as energy storages is modeled to mitigate the impact of wind output and gas demand uncertainty. Meanwhile, integrated natural gas and electricity demand response such as event-based and time-based model has been applied as a flexibility provision from demand-side point of view. In this paper, the objectives of reducing emission and costs, leveling the reserve margin and increasing flexibility are considered as the objectives of optimizing generation maintenance scheduling. In order to solve the multi-objective problem, the augmented Epsilon constraint method has been used. The proposed model has been implemented on a modified IEEE RTS 24 bus.

Course timetabling in medical universities given physicians' educational and clinical tasks

The physician assignment and course timetabling problem at medical universities is a generalized version of the academic timetabling problem. This problem entails assigning courses, educational and clinical tasks to physician faculty members over a semester or academic year. The problem of timetabling academic courses and scheduling physicians in a hospital has been investigated independently in previous studies in this field. These two fields of research are brought together in this article through the presentation of a multi-objective mixed-integer linear programming (MILP) model. The proposed model is based on two optimization criteria: minimizing workload imbalance and maximizing physician preferences. The model is applied to a case study involving the assignment of physicians to courses, educational and clinical tasks at Kurdistan University of Medical Sciences' Department of Infectious Diseases. Pareto solutions are obtained using an enhanced version of the augmented epsilon constraint implemented in the GAMS optimization software; one is selected as the most desirable solution using the TOPSIS method. The proposed model is generic and could be adapted for use in other departments or medical schools.

Multi-mode project portfolio selection and scheduling in a build-operate-transfer environment

Integrated decision-making about selecting and scheduling a project portfolio can lead to a more desirable performance. This paper considers the problem of selecting a portfolio among a set of possible projects which should be scheduled from vantage point of contractor simultaneously. Each project can be implemented in several modes, each of which has potential cash flows over the time horizon. Therefore, an NPV can be calculated for each project in a particular implementation mode. In this contribution, a structure composed of a fuzzy hybrid multi-criteria method and a fuzzy bi-objective mathematical programming model are presented to deal with quantitative and qualitative dimensions of the project portfolio selection and scheduling problem. To solve the problem, first the qualitative criteria are weighted by the fuzzy AHP, the obtained weights are applied to evaluate the projects in the fuzzy TOPSIS. Then, the fuzzy mathematical model is formulated with two objectives, including maximizing NPV of profit and portfolio score based on assumptions close to real conditions of build-operate-transfer (BOT) contract. According to the assumptions, projects have multi-period implementation and operation phases; there are a penalty and reward system to meet the deadlines. Also, the company is able to attract external capital. The fuzzy model is converted to its crisp counterpart, and then the model is solved using the augmented epsilon constraint method with the data of an Iranian company as a case-study. The results show that considering multiple modes for project implementation has better results in comparison with confining the implementation of each project to only one mode (the mode with the maximum NPV).