Linear Optimization Model Research Articles

Embodied residential building carbon emissions reduction in Nepal using linear optimization modeling

The study of embodied residential carbon emissions has attracted significant attention in sustainability research amidst growing awareness of climate change. As Nepal experiences economic growth and urbanization, urban areas are witnessing a significant surge in carbon emissions, in contrast to past decades. Despite national level initiatives aimed at achieving net zero emissions by 2045, there is a noticeable gap in actionable approaches at provincial, ecological, and city levels regarding the tracking and mitigation of carbon emissions. This research combines building component data from the National Statistics Office (NSO) of Nepal and emissions data from literature in order to model three distinct emissions forecasting scenarios: (1) the current optimized, (2) a 50 % reduction emissions, and (3) a 75 % reduction in emissions. Based on these estimations, Bagmati province is found to exhibit the highest levels of embodied emissions, while Karnali province is found to have the lowest emissions. This can aid in the formulation of region-specific policy frameworks aimed at reducing emissions in high-emission areas. Additionally, the study highlights that urban emissions outweigh rural emissions by a factor of more than two, suggesting a need for policymakers to concentrate their efforts on urban areas.

Fertilizer Logistics in Brazil: Application of a Mixed-Integer Programming Mathematical Model for Optimal Mixer Locations

Background: Brazil is one of the largest consumers of fertilizers and is highly dependent on the international market to meet its demand for agricultural production inputs. The complexity of the fertilizer supply chain motivated us to carry out this study on redesigning the fertilizer logistics chain and evaluate strategies for reducing logistics costs by redesigning the fertilizer mixing network in Brazil, a country that is heavily dependent on imported fertilizers for agriculture. Methods: We introduce a multi-product mixed-integer linear programming optimization model encompassing the logistics network, from import ports to mixing factories and agricultural fertilizer supply centers. This model includes logistics infrastructure and taxes, accounting for greenhouse gas emissions (specifically carbon dioxide) in fertilizer logistics. Results: The results indicate that expanding the port capacity for fertilizer importation can significantly reduce logistics costs and greenhouse gas emissions by up to 22.5%, decreasing by 23.9% compared to the baseline. We also observed that removing taxes on fertilizer importation can reduce logistics costs by approximately 11%, but it increases greenhouse gas emissions by 2.25% due to increased reliance on road transport. We identified 15 highly resilient regions for establishing mixing factories, evaluated various scenarios and determined the importance of these locations in optimizing the fertilizer supply network in the country. Moreover, the results suggest a significant potential to enhance the role of Brazil’s Northern Arc region in fertilizer import flows. Conclusions: Public policies and private initiatives could be directed toward encouraging the establishment of mixing factories in the identified regions and increasing transport capacity in the Northern Arc region. Improving the logistical conditions of the fertilizer network would contribute to food security by reducing the costs of essential inputs in food production and promoting sustainability by reducing greenhouse gas emissions.

Voltage Stability Constrained Operation Optimization: An Ensemble Sparse Oblique Regression Tree Method

Voltage stability remains a main challenge for high renewable penetrated power systems. In future power systems, the dispatch needs to consider the voltage stability margin. However, considering static and transient voltage stability is challenging because a complex relationship exists between voltage stability and operation state variables. This paper proposes an ensemble sparse oblique regression tree method for voltage stability constrained operation optimization. First, we train multiple oblique regression trees on voltage stability simulation datasets. The trained trees are then grouped into ensemble using a boosting method to extract accurate and understandable voltage stability rules. Finally, the rules are embedded as mixed-integer linear programming constraints in a linear optimal power flow model. Validation on the IEEE-14 case shows the interpretability and efficiency of the proposed algorithm. Case studies on the Qinghai power grid and IEEE-118 further show that the proposed strategy can effectively improve the voltage stability margin of optimized operation states.

Energy Management System for a Smart Green Nanogrid feeding a Research Laboratory with Autonomous Mobile Robots

This paper proposes a mixed-integer linear programming optimization model used to define an energy management system tailored for nanogrids in buildings, integrating renewable energy sources, battery energy storage systems and task-executing autonomous mobile robots. Focused on a nanogrid to be realised at the Savona Campus of the University of Genoa, the energy management system optimizes power flows and robot task scheduling in order to minimize the operating costs, the curtailment of the photovoltaic source and the number of unperformed tasks. Its novelty lies in combining energy and task planning constraints, offering significant potential for sustainable building energy management.

A robust optimization approach to a repair shop network planning

Robust optimization model is a paradigm for decision-making under uncertainty, where parameters are given in the form of uncertainty sets. In this paper, we develop a robust optimization model for a repair shop network planning problem. The linear optimization model involves product of uncertain parameters in the constraints. We formulate its robust counterpart with the help of min-max regret and Lagrangian dual approach, considering the partial information of uncertain parameters is given in the form of ellipsoidal and polyhedral uncertainty sets. We also consider ellipsoidal+polyhedral uncertainty set, which is the intersection of ellipsoidal and polyhedral uncertainty sets. We apply the robust optimization model to a bi-objective multi-plant repair shop network planning problem where multiple pieces of equipment are repaired and overhauled using several resources over a multi-period planning horizon. We consider uncertainty in resource and demand parameters. Numerical examples are presented for illustrating the theoretical results.

Linear Optimization Modeling for Smart Specialization in Primary Sectors of a Developing Country

Linear Optimization Modeling for Smart Specialization in Primary Sectors of a Developing Country

МОДЕЛЮВАННЯ ЗАДАЧ ОПТИМІЗАЦІЇ УПРАВЛІННЯ ІТ-ПРОЕКТАМИ

Abstract. The article focuses on exploring mathematical models for optimizing business processes in project management within IT companies in the context of contemporary trends and challenges. Project management involves the process of guiding and coordinating people's activities, as well as managing material and financial resources throughout the project's lifecycle. This process encompasses applying modern management methods and techniques to achieve project goals. The dynamic allocation modeling of IT projects among teams to ensure high-quality development at maximum efficiency with minimal costs is a pertinent task in IT project management. The article's objective is to select a mathematical framework for decision-making regarding the optimal IT project management program to enhance the efficiency of each IT team and the entire IT company. The research involved an analysis of scientific literature on modeling project management in IT companies. The article proposes focusing on developing dynamic multi-criteria optimization models for human resource management, emphasizing the distribution of IT projects among executing teams. The research aims to elevate the strategic and operational levels of IT personnel management to achieve optimal outcomes in information technology. The analysis concludes that despite the advantages of various mathematical modeling methods, none of them in isolation allows for constructing a sufficiently detailed mathematical model. Methods and models addressing IT enterprise modeling problems may oversimplify the issue or, conversely, overly complicate it, complicating the selection of input data. The functioning of the IT enterprise was analyzed through the lens of external and internal indicators concerning the solved task. A verbal model of IT project distribution among teams, considering the time factor, was developed. This model formulated a system of basic concepts and ideas, allowing the dynamic formulation of the problem using widely accepted linear optimization models. This will facilitate finding optimal solutions for IT project distribution tasks over a specific period. Future research should focus on selecting a solution method for the model and implementing the constructed mathematical model using appropriate tools. The research findings presented can serve as a basis for further academic exploration and practical application in the field of IT project management. Keywords: modeling, optimization, business processes, project management, labor resources, IT projects.

Optimizing islanded green ammonia and hydrogen production and export from Saudi Arabia

Hydrogen and its derivatives hold significant promise for decarbonizing power and transport. This study proposes a mixed-integer linear optimization model for the flexible production and transportation of islanded green hydrogen and ammonia. Wind and solar databases of three coastal locations across the Kingdom of Saudi Arabia were utilized to provide a holistic geographic perspective. The results show that plant optimization can lead to production levelized costs of ammonia of 383 USD/tonne NH3, and production levelized costs of hydrogen down to 1.57 USD/kg H2 by 2030. The single largest cost driver is the energy cost, representing 60–70 % of the total project cost. In low-wind resource areas, battery storage technology plays a critical role in supplying consistent energy for continuous ammonia synthesis. Transportation to final demand centers in Europe or Asia can lead to additional costs of less than 40 USD/tonne NH3 and less than 0.8 USD/kg H2 via liquid hydrogen route.

Estimating the impacts of a new power system on electricity prices under dual carbon targets

The construction of a new power system dominated by renewables is crucial for achieving China's goals of carbon emission peaking and carbon neutrality. While numerous studies have investigated grid parity for large-scale renewables, some have overlooked the fact that the integration of variable renewable energy requires coordination with regulating resources. This coordination introduces additional costs, leading to subsequent increases in electricity prices. Our study comprehensively considers the total system costs and proposes a dynamic recursive linear optimization model. This model aims to simulate both short-term and long-term impacts of constructing a new power system on electricity prices in China. It evaluates the short-term effects of the Russia-Ukraine conflict and the COVID-19 pandemic on energy prices and demand, as well as the long-term effects of renewable energy penetration on ancillary service costs and technological progress on system costs. The results show that China's electricity price is projected to rise by 10.2% in 2030 for carbon peaking. By 2060, with an 83.3% renewable energy penetration for carbon neutrality, the electricity price will reach 0.859 CNY/kWh, representing a 27.2% increase. Ancillary service costs will experience the highest growth rate, accounting for 15.5% of system costs by 2060. Our study also proposes optimal technological pathways for the new power system and provides valuable data to support the development of effective electricity price mechanisms.

Field‐tested signal controller to mitigate spillover using trajectory data

AbstractTrajectory data from connected vehicles (CVs) provide a continuous and reliable means of obtaining information that can be leveraged to optimize traffic signals. This paper proposes a real‐time traffic signal control method using CV trajectory data as the sole input. The primary goal of the proposed signal control method is to prevent queue spillover, which may significantly decrease the traffic efficiency on urban networks and induce high delays to the travelers. The proposed method formulates the signal control problem via a linear quadratic optimization model, considering the constraints related to the duration and variability of green lights in practical traffic signal control systems. Compared to conventional max‐pressure‐based methods, the optimization model offers enhanced efficiency in handling these constraints, making it highly suitable for real‐life implementation. The proposed method has undergone testing in both simulated environments and real‐world applications. In the simulation experiments, the proposed method has been demonstrated to effectively reduce spillover risks and outperform a conventional max‐pressure‐based approach even when the CV penetration rate is as low as 5%. In the real‐world experiment, the proposed method had been tested in a traffic network around the Beijing Capital International Airport for several months. The severity of spillovers, which was represented by two performance indicators, had been significantly reduced after implementing the proposed method.

Scheduling the repair and replacement of individual components in operating systems: a bi-objective mathematical optimization model

Preventive maintenance (PM) is performed so that failure is avoided while corrective maintenance is performed after a failure has occurred in order to restore the system back to an operational state. This research aims at scheduling PM activities for a multi-component system within a finite time horizon. We consider a setting with two stakeholders, being the system operator and the maintenance workshop, and two different contract types governing their joint activities, namely an availability contract and a turn-around time contract. Components in the systems that are to be maintained are sent to the maintenance workshop, which needs to schedule and perform all maintenance activities while at the same time satisfying the contract and not exceeding the workshop capacity. Our modelling is based on a mixed-binary linear optimization model of a PM scheduling problem with so-called interval costs over a finite and discretized time horizon. We enhance this scheduling model with the flow of individual components through the maintenance workshop, including stocks of spare components, both those components that need repair and the repaired ones. The resulting scheduling model is then utilized in the optimization of two main contracts, namely maximizing the availability of repaired (or new) components and minimizing the deviation from the contracted turn-around times for the components in the maintenance loop. Each of these objectives is combined with the objective to minimize the costs for maintenance of the operating system, leading to two bi-objective optimization problems. We analyse the two contracting forms between the stakeholders by studying and comparing the Pareto fronts resulting from different parameter settings, regarding minimum allowed stock levels and investments in repair capacity of the workshop. Our bi-objective mixed-binary linear optimization model is able to capture important properties of the results from the contracting forms as well as to show that, in our setting, an availability contract performs better than a turn-around time contract in terms of tractability.

A novel state estimation method for distribution networks with low observability based on linear AC optimal power flow model

The state estimation (SE) problem is one of the key functions in real-time control and management of modern electrical distribution networks. However, due to the complex network configuration and the limited number of measuring devices in these networks, the SE problem faces many challenges. In this manuscript, a new state estimation methodology is proposed based on the AC optimal power flow (ACOPF) model for distribution networks with a small number of real-time measurements. The proposed method is formulated in the form of a mixed integer linear programming problem (MILP), where the estimated states are regarded as the decision variables in the optimization problem. The load consumption values are also assumed as the decision variables where the estimation limits of these variables are determined by pseudo-measurements taken from the historical data. The main objective function is to maximize the state estimation accuracy, while the power flow equations are defined as the problem constraints. The efficiency of the proposed methodology is evaluated by implementing on the test networks and comparing the estimation results accuracy with the conventional weighted least squares (WLS) method. The obtained numerical results show the superior performance of OPF-based SE model to WLS method. Moreover, linearizing the formulation demonstrates an acceptable precision while ensuring convergence and optimum solution in low observability conditions.

A linear reduced-order model for the activated sludge process for the integration into a mixed-integer linear energy system optimisation model

Conventional wastewater treatment plants consume significant amounts of electricity. The constant aeration of the wastewater in order to foster the growth of microorganisms or the pumping of wastewater are two examples for energy-intensive processes within a plant. Case studies have shown that switching off blowers and inlet pumps for a certain period of time is possible without a loss in water quality. This yields a potential for wastewater treatment plants to provide demand response (DR) to the power system and thereby increase overall system flexibility. So far, the DR potential has only been quantified for individual plants, while the effects of large-scale DR provision by the wastewater treatment sector for the power system have not yet been studied. One reason for this is the lack of optimisation models which include both the wastewater treatment process and the power system operation in sufficient detail. Our model tackles this gap in the literature by providing a reduced-order linear biochemical model for the activated sludge process within a WWTP that can be incorporated into an operational energy system model. The results show that the effluent concentrations are predicted well by the linear reduced-order model in comparison to the results of the Standard Activated-Sludge model No. 1 (ASM1). Potential model applications are the variation of the airflow rate within a certain range and the variation of liquid influent flow rate to the system, which is a result of electricity load shedding of the inlet pumps and the blowers connected to the activated sludge tank.

The double stack railcar allocation problem at marine container terminals

This paper introduces and solves a real-world problem that arises at container ports, namely the double stack railcar allocation problem. The key challenge in the double stack railcar allocation problem is to balance the number of containers loaded and the railcar usage, while respecting the loading constraints for double stack trains. To capture the key characteristics of the double stack railcar allocation problem, an integer linear optimization model is presented. The model is found to be computationally prohibitive for a state-of-the-art off-the-shelf solver (CPLEX). Hence, a tailored solution method is proposed that manages to drastically reduce the computation times, sometimes by more than 99%. In a detailed case study, insights into the double stack railcar allocation problem are revealed and discussed.

Privacy-preserving adaptive traffic signal control in a connected vehicle environment

Although Connected Vehicles (CVs) have demonstrated tremendous potential to enhance traffic operations, they can impose privacy risks on individual travelers, e.g., leaking sensitive information about their frequently visited places, routing behavior, etc. Despite the large body of literature that devises various algorithms to exploit CV information, research on privacy-preserving traffic control is still in its infancy. In this paper, we aim to fill this research gap and propose a privacy-preserving adaptive traffic signal control method using partially connected vehicle data. Specifically, we proposed a privacy-preserving mechanism to protect CV data against three types of attacks: CV collusion attacks, database attacks, and inference attacks. The mechanism leverages secure Multi-Party Computation and differential privacy to aggregate individual-level CV data to calculate key traffic parameters without compromising the privacy of CV users. For seamless integration with the privacy-preserving mechanism, we develop a traffic signal optimization model and an arrival rate estimator relying only on aggregated CV data, being applied to both undersaturated and oversaturated traffic conditions. The optimization model is further extended to a stochastic programming problem to explicitly handle the noises added by the privacy-preserving mechanism. Evaluation results show that the linear optimization model preserves privacy with a marginal impact on control performance, and the stochastic programming model can significantly reduce residual queues compared to the linear programming model, with almost no increase in vehicle delay. Overall, our methods demonstrate the feasibility of incorporating privacy-preserving mechanisms in CV-based traffic modeling and control, which guarantees both utility and privacy.

Local energy management: A base model for the optimization of virtual economic units

As non-renewable resources are limited and the overall CO2 emissions need to be reduced drastically, there is an increasing need in making the energy supply more sustainable. This leads to a needed change in the traditional energy system, in which decentralized local energy resources must be better integrated. In order to face the challenges for a future energy management, the consideration of the domestic level is gaining more attention. In this paper, we aim to get insights into the potential value of local cooperations and focus on economic and control issues as to whether and how the domestic level can participate in upcoming solutions. We introduce a possible setup for a virtual economic unit representing a hybrid cooperation of domestic energy participants, whereby the objective of this cooperation is to realize the maximum possible savings for the community with specified individual contracts between the participants and assuming that participants continue to have additional contracts with their energy service provider. We propose a deterministic linear optimization model for determining optimal energy load profiles of the participants with the external suppliers and energy exchange between participants in a virtual economic unit. To efficiently solve this model and get an exact assignment of supply and demand, we present a maximum saving flow algorithm taking into account the underlying bipartite structure of this problem. The solution achieved is specified as a peer-to-peer allocation between the participants involved and provides insights into the aspects that determine the concrete assignment. It also has the advantage of leading to a robust solution within the collaboration case studies for a basic set-up demonstrate the impact of this approach on the economic potential of aggregating local generation and demand at the same time.

Unlocking the potential of the bioeconomy for climate change reduction: The optimal use of lignocellulosic biomass in Germany

AbstractThe concept of a circular bioeconomy has become a new economic leitmotif for reducing greenhouse gas (GHG) emissions. Its central narrative rests on the idea of replacing fossil resources with biobased ones for a broad spectrum of products including, for example, heat, electricity, fuels, plastics, or chemicals. Yet, the amount of available bio‐resources is limited, rendering some technologies successful while leaving behind others. Lignocellulosic biomass (LBM) is a key resource already used on a large scale for heating purposes or electricity production and increasingly for the production of chemicals and biofuels. Because market mechanisms do not necessarily drive a cost‐optimal use with respect to their GHG‐reduction potential, a new bi‐objective linear optimization model under long‐term scenarios was developed for Germany accounting for competition with non‐biobased technologies. In the biofuels and biochemicals sectors, multi‐output processes that address industrial symbiosis and fossil references are used to compute profits and GHG emission savings of biobased products. However, in the absence of a reference for heat, a detailed representation of the heat sector is used in which heat demand for 19 subsectors is met, thus deriving costs and emission savings endogenously. When explicitly accounting for GHG emission reduction targets, biomass is optimally used in high‐temperature industries whereas heat pumps dominate in building heat. Because of the optimal use of biomass in industrial usage, subsidies for biomass heating are found to be inefficient in the building sector. Catalytic hydropyrolysis to produce biogasoline and biodiesel using LBM dominates the production of biofuels while biochemicals—strongly depending on oil price developments—will become competitive on a large scale after 2030.

Interventions to increase circularity and reduce environmental impacts in food systems.

Applying specific circularity interventions to the food system may have environmental benefits. Using an iterative linear food system optimisation model (FOODSOM), we assess howchanges in human diets, imports and exports, and the utilisation of waste streams impact land use and greenhouse gas emissions (GHG). After including these circularity principles, land use and GHG emissions were on average 40% and 68% lower than in the current food system, primarily driven by a reduction in production volumes and a shift towards feeding the domestic population. Shifting from the current diet to a circular diet decreased land use with 43% and GHG emissions with 52%. Allowing up to half of each nutrient in the human diet to be imported, while balancing imports with equal exports in terms of nitrogen, phosphorus and potassium, also decreased land use (up to 34%) and GHG emissions (up to 26%) compared to no imported food. Our findings show that circularity interventions should not be implemented mutually exclusively; by combining a circular diet with imported food and fully utilising waste streams, the lowest land use and GHG emissions can be realised.

Batteries or silos: Optimizing storage capacity in direct air capture plants to maximize renewable energy use

Direct air capture (DAC) of carbon dioxide is among the technologies that is forecast to play a major role in achieving the global ambition to constrain atmospheric temperature rise to below two degrees Celsius by 2100. However, DAC is an energy intensive chemical process, whose designs are currently incompatible with intermittent renewable energy (RE) sources. This research develops a model to enable the flexible operation of DAC, to maximize RE usage. A new model of the chemical process flow of a liquid solvent DAC that includes silos to store CaCO3 and CaO is developed. A linear programming optimization model that minimizes energy costs while achieving the CO2 capture targets of the DAC plant is developed. Scenario analysis establishes the storage silo size and battery storage size needed to reduce renewable energy curtailment to zero for a given RE profile. Simulations with a representative 336-hour RE profile reveal that two silos of sizes 660 tons and 370 tons would be needed to support flexible DAC plant operations and reduce RE curtailment to zero. For the same profile, a 355 MWh/65 MW battery would be required to achieve zero renewable curtailment. The results demonstrate that flexible operation of DAC is achievable, and DAC plants can adapt to variable RE without the need for battery energy storage. Furthermore, considering the scale of storage needed to minimize RE curtailment in a commercial-scale DAC plant, the results suggest that using physical storage silos could be more cost-effective than using battery energy storage.

On basic arithmetic operations for interval-valued intuitionistic fuzzy sets using the Hamming distance with their application in decision making

Atanassov’s intuitionistic fuzzy sets play a vital role in handling vagueness and uncertainty successfully as they associate an additional non-membership degree to each element of the universal set. Interval-valued intuitionistic fuzzy (IVIF) sets are more generalized quantities in this direction as they use intervals (⊂[0,1]) to define the membership and non-membership grades of each element of the set. However, without defining basic arithmetic operations on the IVIF values/sets, the study is incomplete. This paper broadly examines the division and subtraction operations over any arbitrary IVIF values/sets using the concept of Hamming distance between them. A deterministic linear optimization model is proposed and solved in order to obtain the complete expressions for these operations. Next, various fundamental properties and relationships are examined and proved for the proposed arithmetic operations over IVIF values/sets. Furthermore, an example of a multi-criteria decision-making problem under uncertain conditions is studied and analyzed using the developed arithmetic operations on IVIF numbers.