Augmented E-constraint Method Research Articles

A new approach for reliability modeling in green closed-loop supply chain design under post-pandemic conditions: A case study

Climate change, pandemics, and economic crises have created complex challenges for supply chains. Managing such situations requires the development of reliable decision-making frameworks. In this paper, a multi-level, multi-product, and multi-period closed-loop supply chain is studied with environmental considerations. A bi-objective mixed-integer linear programming model is presented for facility location, flow allocation, and transportation mode determination. The objectives of the model are to minimize the total cost and maximize the reliability of suppliers to meet the needs of factories. In the area of reliability engineering, a new approach is defined for modeling the probability of supplier availability considering catastrophic failures caused by pandemics, economic sanctions, and other failure modes. Furthermore, the decision-maker can handle the emission of greenhouse gases by an upper-bound constraint. In order to face the simultaneous uncertainty of demand and the maximum CO2 emission allowed, a scenario-based two-stage stochastic programming approach is proposed. The improved version of the augmented ε-constraint method, known as AUGMECON2, is used to solve the proposed model. The efficiency of the model and the proposed solution approach are investigated through a real-world case study of a battery manufacturing company in Iran.

Physical internet enabled sustainable and resilient production-routing problem with modular capacity

PurposeModular capacity units enable rapid reconfiguration, providing tactical flexibility to efficiently meet customer demand during disruptions and ensuring sustainability. Moreover, the Physical Internet (PI) enhances the potential of modular capacity in addressing efficiency, sustainability, and resilience challenges. To evaluate the sustainability and resilience advantages of the PI-enabled reconfigurable modular system (PI-M system), this paper studies a PI-enabled sustainable and resilient production-routing problem with modular capacity.Design/methodology/approachWe develop a multi-objective optimization model to assess the sustainability and resilience benefits of combining PI and modular capacity in a chemical industry case study. A hybrid solution approach, combining the augmented e-constraint method, construction heuristic, and hybrid adaptive large neighborhood search, is developed.FindingsThe experimental results reveal that the proposed solution approach is capable of obtaining better solutions than the Gurobi and the existing heuristic in a shorter running time. Moreover, compared with the traditional system, the PI only and traditional with modular capacity systems, PI-M system has significant advantages in both sustainability and resilience.Originality/valueTo the best of our knowledge, this study is the first to integrate the PI and modular capacity and investigate sustainability and resilience in the production-routing problem.

Multi-objective shipment consolidation and dispatching problem

In recent years, with the increase in global production and demand, transportation problems have become a widely studied area, and studies focus on providing high-quality service at the lowest cost. This study considers a bi-objective shipment consolidation and dispatching problem with the objectives of minimizing the total cost and the total distance. To the best of our knowledge, this is the first study to include both objectives in this problem. Additionally, different from the literature, where usually predefined routes are assumed, we incorporate the routing decisions in our model. In order to create a non-dominated solution set, a multi-objective mixed integer linear programming model is developed and augmented ϵ-constraint method is used to generate the non-dominated frontier. However, this approach is not capable of finding the non-dominated solution set in a reasonable time, even for small-sized instances, and therefore, we propose a multi-objective variable neighborhood search heuristic. To measure the performance of the proposed approach, a computational experiment is conducted on randomly generated instances available in the literature. The experimental results indicate that the multi-objective variable neighborhood search heuristic performs efficiently in reasonable time.

Multi-objective location-routing model and algorithm study of material reserve bases for large-scale railway engineering construction projects

Material supply is an important support for engineering construction and an important factor affecting the progress and quality of engineering construction. A multi-objective mixed-integer nonlinear programming model is proposed for the location routing problem of the material reserve base of large-scale railway engineering construction projects, considering realistic factors like the construction period, the cycle of the material reserve, the variety of materials, the heterogeneous fleet, and demand splitting. An improved Non-dominated Sorting Genetic Algorithm-II (NSGA- II) is developed for solving this model. This paper optimises obtaining the initial population based on the linear feature of railway engineering, improves the fitness function, and designs a two-stage crossover operator. In addition, the algorithm is compared with the augmented ϵ-constraint method with the help of a practical example. Three metrics are used to assess the performance of the algorithm's outputs, and two metrics are used to assess the similarity of the Pareto fronts obtained by the two algorithms. The results show that the proposed algorithm performs better in terms of ‘quantity’ and ‘spacing’, that the Pareto solutions obtained are accurate, and that the speed of solution is almost 10 times that of the augmented ϵ-constraint (AUGMECON) method.

Designing a sustainable supply chain for battery PVC cases: A multi-objective optimization approach

Nowadays, Polyvinyl Chloride (PVC) and its derivatives are being used in a wide range of products, including car battery cases, due to their corrosion resistance and exceptional durability. As PVC production has grown, the amount of non-hazardous waste generated from PVC products has dramatically increased. In this context, incorporating PVC waste management into the PVC supply chain can effectively address the PVC waste generation issue. This study investigates the design of the Polyvinyl Chloride Closed-Loop Supply Chain (PVCCLSC) based on a triple-objective model for Abadan Petrochemical Company. The first objective aims to minimize the total cost of PVCCLSC, the second objective focuses on minimizing environmental impact, and the third objective maximizes the improvement of Occupational Health and Safety (OHS). In this study, an integrated solution approach is developed encompassing four main phases: (i) Developing an accelerated K-means clustering algorithm, along with the Elbow Method (EM) and Average Silhouette Method (ASM), to estimate the quality of returned PVC products, (ii) Employing a robust optimization method to capture the uncertainty, (iii) Implementing an augmented ε-constraint method to solve the proposed multi-objective model, and (iv) Applying a Bender’s Decomposition Algorithm (BDA) to solve the model and determine optimal solutions. As a result of the proposed BDA, relative optimality gaps have been reduced from 4.56 % in the conventional solution to zeros, and runtime has been reduced from 55 min to 20 min. Furthermore, as a result of this study, more than 44 % of returned PVC products should be recycled using the tertiary method to fulfill environmental requirements.

AUGMECON2-based multi-objective optimization of virtual power plant considering economical and security operation of the distribution networks

With the rapid development of massive multivariate distributed energy resources on the demand side, the distribution network is transforming from traditional passive to active management. By constructing the virtual power plant, distribution network operators will handle the management and transactions of those distributed resources as their participation in the electricity market becomes normal. Moreover, distributed resources will affect the operating economy and security of the distribution network, such as network losses and peak loads. Thus, distribution network operators must consider both the security of distribution networks as well as the economics of distributed resources. To address this issue, a virtual power plant with the distribution network operator as the stakeholder has been built. A multi-objective optimization model based on the improved augmented ε-constraint method (AUGMECON2) method is then proposed. The key objective is to maximize operating benefits while also accounting for network losses and peak-to-valley load disparity of the slack bus. To address the uncertainty of renewable energy, a dynamic reserve capacity calculation approach is developed, taking into account the economics as well as transaction reliability. The Pareto frontier of the multi-objective optimal problem is obtained by AUGMECON2, and a compromised solution considering fairness is proposed. Finally, the proposed method is verified with case studies based on the modified IEEE33-node distribution network system.

Designing a green-resilient closed-loop supply chain to preserve business continuity under interrelated disruptions (a case study of the automotive battery industry)

Improving profitability, implementing the recycling cycle to reduce resource consumption, and managing interrelated disturbances to maintain business continuity are important issues for supply chain management. Accordingly, this study proposes a multi-objective optimization model to design a green-resilient closed-loop supply chain considering pricing decisions under multiple interrelated disturbances. Herein, the fuzzy c-means clustering method is employed to lessen probable scenarios and cluster main suppliers and target markets to reduce mathematical complexity. The multi-objective model is solved by adopting the improved augmented ε-constraint method to achieve the minimum total cost, total environmental impact, and network non-resiliency. The mixed uncertainty is coped with by developing a novel robust optimization method. Finally, an automotive battery manufacturing industry case study is applied to the model. The results reveal that the mutual effects of disturbances intensify the deterioration of objective functions. Also, the dynamic pricing of products reduces the financial vulnerability of the supply chain.

The bi-objective multi-depot split delivery location routing problems under uncertain conditions

This research focuses on addressing the multi-depot location-routing problem with split delivery and multiple objectives under uncertain conditions. A mathematical model is proposed to effectively tackle this problem by considering various constraints and considerations. The paper emphasises the use of split delivery as an effective approach for reducing transportation costs. Furthermore, the study explores bi-objective optimisation, specifically cost minimisation and distance balancing. To assess the robustness of the proposed model under different scenarios, sensitivity analysis tools are employed. Numerical examples are presented to demonstrate the effectiveness of the model. Bi-objective optimisation is conducted using the augmented ε-constraint method, enabling decision-makers to analyse trade-offs between cost minimisation and distance balancing objectives. The findings of the study reveal that an increase in demand leads to higher cost minimisation and lower distance balancing. Conversely, an increase in transportation costs results in higher distance balancing. The research also highlights the robustness of the model and its potential for cost reduction through split delivery compared to scenarios without uncertainty.

Designing a sustainable vaccine supply chain by considering demand substitution and value-added function during a pandemic outbreak

The severe social, economic, and health detriments caused by pandemics (such as COVID-19) lead governments toward exploring survivability challenges. In this regard, some countries produce national vaccines along with receiving global medical supplies, which necessitates the design of a sustainable vaccine supply chain and the evaluation of value-added gained by each vaccine application. Given each vaccine possesses specific efficacy and expiration time, this study addresses products’ brand-based efficacy and perishability derived from existing literature. Additionally, shortages are inevitable in a chaotic pandemic situation as a consequence of limitations in the procurement, distribution, and storage networks of vaccines. Therefore, we investigate the effect of demand substitution based on vaccine efficacy to reduce the unsatisfied demand and combat the prevalence of infection. Moreover, this study implements mobile vaccination centers as well as permanent centers (for instance hospitals and clinics) to relax the personal and geographical constraints of different segments of society and expedite the vaccination. To optimize the multi-objective mathematical model, the augmented ε-constraint method has been utilized, and a real case study is provided to assess the application of the proposed model. The numerical results and sensitivity analysis show the proper utilization of vaccination centers’ combination in our proposed model, also 60% of shortages are compensated by substitutable products, which leads to expeditious immunization.

Is localization better than globalization for sustainability? Evidence from the nutraceuticals industry for managing malnutrition in India

The socioeconomic consequences of the worldwide burden of malnutrition are substantial, with long-term consequences for individuals, their families, and their countries. Despite being one of the world's greatest producers of various agricultural products, India has regularly performed poorly in the Global Hunger Index. The World Food Programme provides funds to deliver a nutraceutical product (Plumpy Nut) to malnourished children in Low- and Medium-Income Countries (LMIC). The cost of obtaining these items from the international market is high, and worldwide logistics contribute to pollution. Despite these efforts, there has been insufficient food to feed nearly 40% of malnourished children in India, owing to budget constraints. This research provides a linear programming model and the Augmented ε-Constraint Method for developing a sustainable nutraceutical network. The model examines whether localizing the availability of nutraceutical items, in comparison to global sourcing, might be a viable option for improved managing malnutrition in LMIC's. The findings illustrate that localization can lead to a significant reduction in both cost (50%) and greenhouse gas emissions (90%). In addition, localization leads to feeding increased number of malnourished children in the budget constraint environment. Localization can also lead to a reduction in lead time related to due import-related logistical delays. The study offers insights into various policy interventions for stakeholders such as the government, producers, malnourished children (consumers), and others, to reduce malnutrition, while contributing towards United Nations Sustainable Development Goals of Zero Hunger and Responsible Consumption-Production by 2030. We use a case study from India to validate the model.

A sustainable multi-objective optimization model for the design of hybrid power supply networks under uncertainty

In today's industrialized world, the scarcity of fossil fuels and the adverse biological effects resulting from fossil fuel consumption, on one hand, and the increasing population and energy demands, on the other hand, have posed significant challenges to the sustainable development of societies. This research has developed an optimization model for designing a hybrid energy supply network that simultaneously addresses economic, environmental, and social objectives. The economic goal of the model is to maximize after-tax company profits, while the environmental objective is to minimize greenhouse gas emissions, and the social objective is to maximize social profit. The optimal solution for individual goals reveals that the gas field is active and beneficial for economic objectives, renewable plants are active for environmental goals, and for social objectives, the gas field, combined heat and power (CHP), and wind power are active. The model is solved using the augmented ε-constraint method, and the resulting Pareto optimal solutions are provided to decision-makers. To account for real-world complexities, uncertainties in key model parameters have been considered. Validation for this study has been conducted using data from Iran, an energy exporter to Pakistan.

Closed-Loop Supply Chain Network Design with Flexible Capacity under Uncertain Environment

This paper incorporates flexible facility capacity and government subsidy factors into the consideration of the design of a closed-loop supply chain(CLSC) network based on an uncertain environment. Considering the minimization of economic cost and carbon emission, a multi-objective multi-period multi-product mixed integer linear programming model with fixed and flexible facility capacity is constructed respectively. The robust optimization method is applied to deal with the uncertain environment of demand, recycled product quality, and recycling rate faced by the CLSC, and the robust models under six uncertain sets are constructed respectively. For model solving, the designed algorithm uses the augmented ϵ-constraint method to handle multi-objective problems and introduces a three-stage method on top of the Benders decomposition algorithm to accelerate the efficiency of solving the main problem. Finally, through numerical cases, a CSLC with a flexible supply strategy can manage economic and environmental costs to cope with the negative impacts of an uncertain environment, while this paper verifies the effectiveness of the government subsidy strategy under different conditions and analyzes the potential limitations.

An optimization model for energy project scheduling problem with cost-risk-quality-social consideration trade-off under uncertainty: A real-world application

To complete a successful energy project, all aspects and criteria which can influence the project should be considered. Classic time-cost trade-off (TCT) is used when the completion time of project is not acceptable for customers or top managers. This paper proposes a new cost-risk-quality-social consideration trade-off (CRQST) model for energy projects in a time-constrained problem for achieving specified due date under uncertainty. Moreover, a new comprehensive definition of risk criterion is proposed, and a novel approach for the quality criterion of project based on the dependence of the quality of activities with each other is presented. The internal and external environment of the energy project are considered simultaneously and a new criterion in TCT problem, called social consideration criterion, is introduced. A developed fuzzy augmented ε-constraint method is introduced for the presented multi-objective model to generate Pareto-optimal solutions. To depict the accuracy of results, the proposed model is solved by goal attainment method, and the results of two methods are compared. As a case study, a real oil and gas project is presented, and results show that the proposed method enables managers to effectively handle construction projects in real-world uncertain environments.

A hierarchical model for strategic and operational planning in blood transportation with drones.

Blood transportation is a critical aspect of the healthcare systems, ensuring whole blood and blood products are delivered to patients in a timely and efficient manner. However, transportation of blood and other medical supplies can be challenging, especially in urban areas with limited infrastructure and heavy traffic. Drones have become increasingly important in recent years as a means of delivering medical supplies, including blood, due to their ability to provide fast, reliable, and cost-effective transportation. This study proposes two mathematical programming models in the hierarchical structure to improve decision-making for strategic and operational planning in the blood supply chain network. The limited information available in strategic planning presents risks to the blood supply chain, making it imperative to address uncertainties. To tackle this challenge, a novel approach called Scenario-based Robust Bi-objective Optimization has been proposed. The first model employs this approach to efficiently handle demand uncertainty by simultaneously maximizing the covered demand and minimizing costs. The model is subsequently solved using the augmented ε-constraint method. The second model is a routing-scheduling operational model that aims to minimize the sum of operations time, taking into account time windows for blood collection centers and hospitals. The developed hierarchical model is implemented in a three-level supply chain of Tehran province under three crisis scenarios in different parts. The findings and analysis of this implementation suggest that it is beneficial to set up drone stations in cost-effective and central locations to avoid costly network design. Furthermore, utilizing the minimum number of feasible drones enhances operational time and results in cost savings and increased efficiency. Overall, this study highlights the potential of using drones for blood transportation in urban settings, which can have significant implications for improving the quality of healthcare delivery.

Integrated optimization of assortment, inventory and pricing considering omnichannel retailer’s risk aversion and customer’s time preference

This paper mainly discusses the joint optimization of product assortment, inventory and pricing for an omnichannel retailer under uncertain demand, seeking to maximize the retailer’s Worst-case Conditional Value-at-Risk (WCVaR) based profit and customer’s expected utility. The risk aversion of decision-maker and the time preference of customers are depicted by the WCVaR and quasi-hyperbolic discounting function, respectively. A bi-objective stochastic optimization model is developed. To alleviate the computational burden, a linearization method is applied to convert the problem into a mixed integer linear programming that proves to be solvable within reasonable CPU times using the augmented ε-constraint method. Numerical studies are conducted to investigate the applicability of the proposed model and the efficiency of the solution approach. Our experimental results show that offering customers with high expected utility typically requires low prices and small assortments. We also make other counterintuitive observation that the price of products sometimes increases when the expected utility increases. Furthermore, WCVaR has superiority compared with the risk-neutral model in terms of robustness and stability. The time preference of customers has non-negligible impacts on decision-making results. In addition, the further sensitivity analyses investigate the impacts of various key parameters on the performance of omnichannel retailing.

A novel two-stage multi-objective optimization model for sustainable soybean supply chain design under uncertainty

Soybean is one of the most important agricultural products in international markets due to its high global consumption. However, there are limited studies considering sustainability issues and global economic aspects of the soybean supply chain design and optimization. Moreover, it is challenging to integrate many sustainability criteria into a single-stage optimization model for a soybean supply chain configuration. This research proposes a novel two-stage approach, integrating a multi-criteria decision-making technique and a new multi-objective optimization model to design and optimize a soybean supply chain network in Canada, considering sustainability and global factors. In Stage 1, several qualitative and quantitative sustainability criteria are considered to calculate the sustainability scores for the potential suppliers, using the Interval Type 2 Trapezoidal Best Worst Method. Then, the scores are used as input in Stage 2, where a new optimization model with four objective functions is formulated to design and optimize a soybean supply chain. The objective functions include maximization of total profit, created job opportunities, and suppliers' sustainability, and minimization of CO2 emissions. Then, the Pareto frontier is generated, using the augmented ε-constraint method which helps policymakers to make appropriate decisions. Furthermore, four cases are proposed and analyzed to assess the impacts of the objective functions on strategic and tactical decisions. The results show the importance of the presented method as an integrated approach, considering sustainability pillars in agri-food supply chains. In addition, the results indicate that the proposed stochastic multi-objective model can handle fluctuations in uncertain parameters.

Optimizing sustainable biomass–coal co-firing power plant location problem under ambiguous supply

Promoting biomass–coal co-firing power generation technology in existing coal-fired power plants is a practical and relatively low-cost short-run choice for the coal-fired power industry to reduce carbon emissions and develop sustainably. However, the uncertainty of biomass supply complicates the location of co-firing power plants among existing coal-fired plants. To address the challenge that only limited historical data of uncertain supply are available, this paper proposes a new ambiguity distribution set to characterize the uncertain supply capacity, supply price, and supply quality (i.e., energy conversion coefficient). Accordingly, a novel bi-objective distributionally robust fuzzy optimization model is developed for the sustainable co-firing power plant location (SCPPL) problem to balance conflicting objectives of minimizing total cost and maximizing carbon emission reduction. Subsequently, the computationally tractable counterpart of the proposed model is derived against the worst-case distribution by reformulating the distributionally robust credibility objective and constraints as their solvable equivalent forms. Furthermore, the Pareto optimal solutions of the proposed bi-objective model are generated using the augmented ϵ-constraint method. Finally, a realistic case study of Heilongjiang Province in China is conducted to verify the feasibility and effectiveness of the proposed optimization method. The experimental results demonstrate that the proposed model can hedge against the distributional ambiguity of uncertain parameters and provides a robust co-firing power plant location strategy. By comparison with the nominal distribution model and analysis of the sensitivity of selected parameters, management insights are summarized for decision-makers.

A multi-objective mixed integer linear programming model for thesis defence scheduling

In this paper, we address the thesis defence scheduling problem, a critical academic scheduling management process, which has been overshadowed in the literature by its counterparts, course timetabling and exam scheduling. Specifically, we address the single defence assignment type of thesis defence scheduling problems, where each committee is assigned to a single defence, scheduled for a specific day, hour and room. We formulate a multi-objective mixed-integer linear programming model, which aims to be applicable to a broader set of cases than other single defence assignment models present in the literature, which have a focus on the characteristics of their universities. For such a purpose, we introduce a different decision variable, propose constraint formulations that are not regulation and policy specific, and cover and offer new takes on the more common objectives seen in the literature. We also include new objective functions based on our experience with the problem at our university and by applying knowledge from other academic scheduling problems. We also propose a two-stage solution approach. The first stage is employed to find the number of schedulable defences, enabling the optimisation of instances with unschedulable defences. The second stage is an implementation of the augmented ϵ-constraint method, which allows for the search of a set of different and non-dominated solutions while skipping redundant iterations. The methodology is tested for case-studies from our university, significantly outperforming the solutions found by human schedulers. A novel instance generator for thesis scheduling problems is presented. Its main benefit is the generation of the availability of committee members and rooms in availability and unavailability blocks, resembling their real-world counterparts. A set of 96 randomly generated instances of varying sizes is solved and analysed regarding their relative computational performance, the number of schedulable defences and the distribution of the considered types of iterations. The proposed method can find the optimal number of schedulable defences and present non-dominated solutions within the set time limits for every tested instance.

Study on Location of Fire Stations in Chemical Industry Parks from a Public Safety Perspective: Considering the Domino Effect and the Identification of Major Hazard Installations for Hazardous Chemicals

In order to select the location of fire stations more scientifically and improve the efficiency of emergency management in chemical industry parks (CIPs), an improved risk calculation model for hazardous chemicals has been proposed by taking the domino effect and the identification of major hazardous installations for hazardous chemicals into account. In the analysis of the domino effect, the Monte Carlo simulation was used. Then, a location model of the fire stations was established with the optimization objectives of minimizing total cost and maximizing total risk coverage. The solving procedure of the location model is based on the augmented ε-constraint method combined with the TOPSIS method. Finally, a green chemical industry park was used as a case study for the validation and analysis of the location model. The results showed that the improved model could protect the high-risk areas, which is beneficial for the location decisions of fire stations.

Industrial symbiosis promoting material exchanges in Ulan Buh Demonstration Eco-industrial Park: A multi-objective MILP model

Industrial symbiosis (IS), which is a concept that allows enterprises to reduce material consumption and production cost, is widely used to optimize eco-industrial parks (EIPs). However, the IS formed in different regions and industrial fields may have different performances in terms of environmental, economic, and social aspects, and few studies are focusing on the IS optimization of material exchange relationships in EIPs in desert areas. Therefore, a multi-objective mixed-integer linear programming (MILP) model is proposed in the present study to optimize the environmental, economic, and social objectives of IS in Ulan Buh Demonstration Eco-industrial Park (UBD-EIP). Then the model is solved using the augmented ε-constraint method and 20 efficient solutions are obtained. The results show that the construction of IS can reduce the environmental impact by 50.24%–50.79%, decrease the operating costs by 42.95%–43.57%, and create a considerable number of job opportunities. The trade-off between environmental and economic objectives suggests that an increase in priority for economic objectives results in higher levels of raw material consumption and waste emissions. The proposed model can help decision-makers of EIPs to choose appropriate material exchange relationships according to objective priority choices. This article enriches the types of objective functions for multi-objective optimizations and provides a reference for IS optimization and sustainable development of industries in desert areas and mixed agricultural-industrial systems.