Mixed-integer Linear Optimization Model Research Articles

A machine learning approach to analysis of Canadian provincial power system decarbonization

Canada committed to reducing national greenhouse gas emissions by 40–45 % by 2030 and achieving net-zero by 2050, relying on low-carbon electrification across economic sectors. This study investigates the machine learning’s potential to analyze least-cost optimization of Canadian provincial power systems to 2050, to identify robust pathways for net-zero electricity system greenhouse gas emissions, and to provide policy insights respecting wind and solar generation, reducing emissions from natural gas generation, and expanding interprovincial transmission. Surrogate modeling is applied as sensitivities to generation technology capital costs, electricity demand, and carbon pricing to results from an existing capacity expansion mixed-integer linear optimization model. Under almost all future scenarios, six provinces develop new wind generation, with substantial deployment in Alberta (mean 27.3 GW, max. 62.7 GW), Ontario (mean 6.8 GW, max. 19.3 GW), Saskatchewan (mean 3.6 GW, max 8.9 GW) and Manitoba (mean 1.5 GW, max 3.5 GW). With the potential exception of BC, where higher-cost wind generation results in solar generation becoming the primary low-carbon electrical energy source (mean 25.2 GW), future solar generation across Canada is more limited (mean 37.1 GW) and less certain than wind generation in all other Canadian provinces. Existing natural gas generation is maintained in almost all scenarios in all provinces, providing support for maintaining these resources for reliability and reserve requirements. Very limited natural gas is developed under any scenarios, with the exception of British Columbia (mean 4.3 GW) where more than 80 % of scenarios include new natural gas capacity. Additional transmission transfer capacity is developed in most scenarios between BC-Alberta (∼60 % of scenarios), Saskatchewan-Manitoba (∼85 %), and Ontario-Quebec (∼75 %). Carbon prices, along with wind and solar capital costs, act as primary determinants of least-cost decarbonization pathways. These findings offer insights for Canadian policymakers into net-zero pathways for provincial electricity systems that remain robust despite variability in inputs.

Impact of tariff structures on energy community and grid operational parameters

This paper presents a mixed-integer linear programming optimization model of a renewable energy community comprised of members with local generators, battery energy storage systems, electric vehicles, and heat pumps and thermal energy storage, thus representing a local multi-energy system. The goal of the paper is to analyze the impact of different tariff structures for incentivizing energy sharing within energy communities on the distribution grid operational parameters. To achieve this, a comprehensive analysis of a hypothetical renewable energy community is conducted using the presented optimization model. Various tariff structures are evaluated, including flat and dynamic tariffs, reflecting the day-ahead market prices for energy and supply, as well as various network tariff designs, such as regulated charge reduction, time-of-use network tariffs and capacity payments. The results indicate that sharing energy within communities reduces energy losses in the grid, peak loads and reverse power flows and results in a smoother voltage profile. It is also found that tariffs that include dynamic electricity and supply costs can further increase these benefits, while including capacity payments as an incentive mechanism yields most favourable results for all analyzed criteria.

Closed loop model predictive control of a hybrid battery-hydrogen energy storage system using mixed-integer linear programming

The derivation of an efficient operational strategy for storing intermittent renewable energies using a hybrid battery-hydrogen energy storage system is a difficult task. One approach for deriving an efficient operational strategy is using mathematical optimization in the context of model predictive control. However, mathematical optimization derives an operational strategy based on a non-exact mathematical system representation for a specified prediction horizon to optimize a specified target. Thus, the resulting operational strategies can vary depending on the optimization settings.This work focuses on evaluating potential improvements in the operational strategy for a hybrid battery-hydrogen energy storage system using mathematical optimization. To investigate the operation, a simulation model of a hybrid energy storage system and a tailor-made mixed integer linear programming optimization model of this specific system are utilized in the context of a model predictive control framework. The resulting operational strategies for different settings of the model predictive control framework are compared to a rule-based controller to show the potential benefits of model predictive control compared to a conventional approach. Furthermore, an in-depth analysis of different factors that impact the effectiveness of the model predictive controller is done. Therefore, a sensitivity analysis of the effect of different electricity demands and resource sizes on the performance relative to a rule-based controller is conducted. The model predictive controller reduced the energy consumption by at least 3.9 % and up to 17.9% compared to a rule-based controller. Finally, Pareto fronts for multi-objective optimizations with different prediction and control horizons are derived and compared to the results of a rule-based controller. A cost reduction of up to 47 % is achieved by a model predictive controller with a prediction horizon of 7 days and perfect foresight.

Comparative modeling of cost-optimal energy system flexibility for Swedish and Austrian regions

This study develops a reproducible method for estimating the cost-efficient flexibility potential of a local or regional energy system. Future scenarios that achieve ambitious climate targets and estimate the cost-efficient flexibility potential of demonstration sites were defined. Flexible potentials for energy system assessment are upscaled from the demonstration sites in Eskilstuna (Sweden) and Lower Austria (Austria). As heat pumps (HPs) and district heating (DH) are critical for future heat demand, these sites are representative types of DH networks in terms of size and integration with the electricity grid. In both regions a TIMES model is used for energy system optimization, while for upscaling, Eskilstuna uses the building-stock model ECCABS, whereas Lower Austria uses a mixed integer linear programming optimization model, and the BALMOREL power system model. According to the modeling, HPs will dominate Eskilstuna’s heating sector by 2040. In Lower Austria, DH becomes more prevalent, in combination with wood biomass and HPs. These findings are explained by the postulated technological-economic parameters, energy prices, and CO2 prices. We conclude that future electricity prices will determine future heating systems: either a high share of centralized HPs (if electricity prices are low) or a high share of combined heat-and-power (if electricity prices are high). Large-scale energy storage and biomass can be essential solutions as may deliver increased cost-effectiveness, if available and under certain conditions.

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.

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.

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.

Valuing the social cost of carbon: Do economists really care about climate change?

The aim of the article is to analyse the scientific literature of the last decade on the social cost of carbon to identify and discuss the best values representing the external cost of CO2 emis-sions calculated with a damage valuation approach, to use in cost-benefit analysis and in other external costs applications, such as Life Cycle Assessment. The social cost of carbon repre-sents the present value of the global damages of climate change attributable to the emission of an additional ton of carbon dioxide into the atmosphere. The measurement of the social cost of carbon is fundamental in the transition to a net zero emissions economy because it allows bal-ancing the costs of investments needed for decarbonization with their benefits in terms of avoided climate damages. The paper develops and applies a method for identifying the best social cost of carbon estimates, that starts from study reviews conducted within institutional processes (IPCC, OECD, US Government bodies), to then analyse the study reviews made in academic or research contexts and only in the end it delves into selected academic studies that provide original estimates of the social cost of carbon. The method allowed to identify and dis-cuss a robust even if conservative estimate of the social cost of carbon for emissions in the period 2020-2080, recently elaborated by the US Environmental Protection Agency, that can be used worldwide, for example to update the reference external cost values for CO2 emis-sions recommended by the European Commission Handbook on external cost of transport.

Bidding strategy of storage hydropower plants in reserve markets

The increasing share of intermittent sources of energy will increase the need for frequency-control reserves. However, the supply from gas and coal-fired power plants might decrease in the following years. Being the procurement of reserves mostly market-based in Europe, the market design should send price signals to encourage participation in these markets. This pa-per analyses the incentives provided by the French market design for seasonal storage and pumped storage hydropower plants to participate in reserve markets. To that end, a determinis-tic mixed-integer linear optimization model is presented. The objective is to maximize profits in the energy and reserve markets according to 2019 market prices. By optimising the trade-offs between the day-ahead and the reserve markets, the storage hydropower plant increase its profits. The pumped storage hydropower plant sometimes chooses the Frequency Contain-ment Reserve market or the day-ahead market only. The apparition of some hours of FCR par-ticipation with the pumped storage plant is explained by its higher number of generating hours and by the higher volatility of reserve energy prices. These two factors also explain the greater response of the pumped storage plant to the incentive measures on the FCR market.

Hybrid optimization and discrete-event simulation model to reduce waiting times in a primary health center

In the early stages of health attention, such as in the examination rooms, patients are generally treated using a First In First Treat (FIFT) logic. This treatment style is inefficient from an operational view as it leads to long waiting times for critical patients. Based on optimization and discrete-event simulation, this paper introduces a hybrid model to assign patients priorities and exam rooms. Patients arrive to the system following a probability function, and for every discrete interval, a mixed-integer linear optimization model is used to allocate patients, considering health priority, preparation times, and availability of time and resources. Instances of the problem are defined using information from a health system in Mexico. Additional to the linear model, a heuristic algorithm is proposed, composed of two phases and aims to provide good, feasible, and fast solutions without ensuring optimality. Computational experiments showed that the linear model is more appropriate for small instances since the heuristic is faster and the relative deviations with respect to the linear model are below five percent. Finally, the discrete-event simulation is run for two cases: (1) with a FIFT logic and (2) using the optimization model. The hybrid model reduces the global waiting times up to 90% and the number of high health priority patients who are not treated up to 100%.

Multi-objective fuzzy surgical scheduling during post-disaster with Nash equilibrium

The post-disaster surgical scheduling is a type of scheduling problem in healthcare system that occurs after a sudden disaster event. The rescue capacity of hospitals has faced an unprecedented challenge by increasing surgical loads due to the disaster occurrence. Hospital became excessively burdened by the influx of patients, who occupy inpatient beds and operation rooms (ORs), making the availability of medical resources uncertain and scarce. This paper focuses on the post-disaster surgical scheduling problem, considering uncertain demands such as the unknown surgical operation durations or random arrivals of emergency/urgent patients, as well as the interests of multiple stakeholders (patients and hospital managers). The objective of fuzzy post-disaster surgical scheduling (FPDSS) is to simultaneously minimize the expected recovery completion time for all patients (makespan), expected average makespan while prioritizing emergency/ urgent patients, as well as the expected total idle time of ORs. This problem can be formulated as a mixed integer linear multi-objective optimization model, and an improved hunger games search based on Nash equilibrium (IHGS-NE) is developed for FPDSS. Finally, experimental studies have been used to test the performance of the proposed approach, and the presented surgical scheduling scheme is validated. Results show that the IHGS-NE approach is an effective method on the research of the multi-objective FPDSS problem.

Decarbonizing integrated chlor-alkali and vinyl chloride monomer production: Reducing the cost with industrial flexibility

Industrial demand response will become increasingly important in power grids with high shares of variable renewables, yet the existing knowledge on how the industrial electricity demand and flexibility will change with the decarbonization of chemical processes is limited. Here we develop a mixed-integer linear optimization model, which we use to compare the cost and flexibility of the most relevant decarbonization options for the combined chlor-alkali electrolysis (CAE) and vinyl chloride monomer (VCM) production process. We combine product and energy storage to enable the full flexibility potential of the decarbonized process. Our results show that flexible operation of the CAE process is deemed technically possible but limited by internal process dependencies due to decarbonization of the VCM production. Combining energy and product storage for demand response enables up to 4% operational cost reduction by shifting loads during peak price hours. High overcapacity of PEM electrolyzers is required to release the full flexibility potential in the hydrogen based decarbonization option, while the less flexible direct electrification option shows a potential for OPEX reduction. Full decarbonization of the combined CAE and VCM process without increasing operational cost significantly appears difficult. Our study emphasizes demand response through product and energy storages as a viable pathway for minimizing the added cost, and also enables a significant reduction of electric demand in high-price hours.

Combined photovoltaic and wind power plant planning for the production and transportation of liquefied green hydrogen: A case study of Egypt

For the production of renewable hydrogen in Egypt and its transport to growing hydrogen demand centers such as Germany, relatively low costs are given in the literature. These low costs are attracting investors. However, due to the scope of the respective studies, not all techno-economic aspects of the supply-chain that influence levelized costs of hydrogen are considered. This work represents a systematical analysis of the levelized costs of hydrogen in Egypt by using wind and solar power for producing 40 kt per year of green hydrogen. A maximal investment volume of four billion euros, and an available area of 37 km2 in central Egypt is assumed. The techno-economic evaluation of the system, from the production site to the selling location, is conducted by a mixed-integer linear optimization model. Depending on the system configuration and production site, the study reveals energy losses of 52–61% of the harvested energy and a levelized costs of hydrogen of 7.17–12.31 €/kg.

Profitability of biomass-based district heating considering different technology combinations and building flexibility

District heating can help to integrate renewable generation within the electricity domain and thus reach climate and energy goals by providing flexibility services and stabilizing the electricity grid. To determine the economic viability of such flexibility services, this work presents a profitability analysis of a central heat pump and/or combined heat and power unit within a biomass-based district heating network, conducted with a mixed-integer linear optimization model. Subsequent business model development for district heating utilities is conducted using the Business Model Canvas and the Odyssey 3.14 approach. Business model development and innovation are crucial to make use of the existing flexibility potential. The results show that the district heating utility's profitability as annual net profit increases in comparison with the status quo of biomass heat-only boilers when an additional heat pump is installed that can operate both in spot and balancing markets. Furthermore, all use cases including governmental support (for the heat pump, the combined heat and power unit or for both) prove to be economically favorable. The innovated business models indicate additional value for increased customer segments, thus enabling additional revenue streams for the district heating utility which can therefore promote the provision of flexibility in district heating.

A multi-period multiple parts mixed integer linear programming model for AM adoption in the spare parts supply Chain

ABSTRACT This research proposes a multi-period multiple parts mixed-integer linear programming optimization model for the trade-off analysis of spare parts supply through computer numerical control (CNC) manufacturing and additive manufacturing (AM). The multiple spare parts have different characteristics such as volume, shape size, and geometry complexity. The model focuses on minimizing lead times and thus reducing downtime costs. Scenario analyses are developed for some parameters to assess the robustness of the model. The analysis shows that the mix between AM-based spare parts and CNC-based spare parts is sensitive to changes in demand. For the given data, the findings demonstrate that AM is cost-effective with spare parts having high geometry complexity while CNC-based manufacturing is economically feasible for spare parts with low geometry complexity and large sizes. The proposed model can support decision-makers in selecting the optimal manufacturing method for multiple spare parts having different characteristics and attributes. The paper concludes with limitations and future directions.

Multi-Period Optimisation of District-Scale Building Integrated Photovoltaic Deployment

The deployment of solar energy technologies such as building integrated photovoltaics (BIPVs) is one of many ways to mitigate present greenhouse gas emissions and abate GHG emissions in future urban development. The widespread deployment of BIPVs is therefore ideal, but deployment must be met with an understanding of the life cycle carbon associated with the technologies manufacturing and their availability as a finite resource. In this paper we describe deployment schedules over the next several decades for BIPVs in a redeveloping urban quarter in Zürich, Switzerland, known as Altstetten. Altstetten has near term goals for carbon neutral buildings that must be met through energy retrofits, higher building standards, and renewable energy. In solving how best to deploy BIPV systems to reduce the life cycle emissions of the buildings in Altstetten, we develop a multi period deployment scheme from a Mixed Integer Linear Programming optimization model that determines the optimal PV deployment within a larger urban multi-energy system. This approach intermingles spatially resolved optimisations with temporally resolved projections of how to deploy the BIPV systems. We analyse results of several optimal solutions sets to investigate the role urban morphology and BIPV embodied emissions play in BIPV utility. We find that different planning strategies (e.g. reduce cost before carbon emissions) play a role in the quantity and rate at which BIPV could be expected to be deployed and that a strategy of minimizing carbon before cost results in less required BIPV deployment than if cost is of the prime concern.

Modeling and Optimization of Combined Heating, Power, and Gas Production System Based on Renewable Energies

Electrical energy and gas fuel are two types of energy needed that increase environmental pollution by burning fossil fuels in power plants to produce electrical energy and direct combustion of gas fuel. In this research, an attempt has been made to model the electrical energy network in the presence of renewable energy sources and gas production systems. The advantage of this model compared to other models of similar studies can be found in providing a mixed integer linear optimization model of distributed generation sources with gas fuel, energy storage systems, and gas power systems, along with electric vehicles in an integrated electricity and gas system. In addition to the energy consumption of buildings, an electric vehicle is also considered a base load, which is one of the limitations in optimizing the maximum charging of an electric vehicle. Among the important results of this research, it can be mentioned that the investment cost of USD 879,340 in the first scenario, in which 37,374 kW of electric energy was purchased from the network to supply the electric load, and 556,233 m3 was purchased from the gas network to supply the required gas.

Collaborative optimization for train stop planning and train timetabling on high-speed railways based on passenger demand.

In recent years, with increasing passenger travel demand, high-speed railways have developed rapidly. The stop planning and timetabling problems are the core contents of high-speed railway transport planning and have important practical significance for improving efficiency of passenger travel and railway operation Dong et al. (2020). This study proposes a collaborative optimization approach that can be divided into two phases. In the first phase, a mixed-integer nonlinear programming model is constructed to obtain a stop plan by minimizing the total passenger travel time. The constraints of passenger origin-destination (OD) demand, train capacity, and stop frequency are considered in the first phase. In the second phase, the train timetable is optimized after the stop plan is obtained. A multiobjective mixed-integer linear optimization model is formulated by minimizing the total train travel time and the deviation between the expected and actual departure times from the origin station for all trains. Multiple types of trains and more refined headways are considered in the timetabling model. Finally, the approach is applied to China's high-speed railway, and the GUROBI optimizer is used to solve the models in the above two stages. By analyzing the results, the total passenger travel time and train travel time decreased by 2.81% and 3.34% respectively. The proposed method generates a more efficient solution for the railway system.

Minimizing the makespan and carbon emissions in the green flexible job shop scheduling problem with learning effects

One of the most difficult challenges for modern manufacturing is reducing carbon emissions. This paper focuses on the green scheduling problem in a flexible job shop system, taking into account energy consumption and worker learning effects. With the objective of simultaneously minimizing the makespan and total carbon emissions, the green flexible job shop scheduling problem (GFJSP) is formulated as a mixed integer linear multiobjective optimization model. Then, the improved multiobjective sparrow search algorithm (IMOSSA) is developed to find the optimal solution. Finally, we conduct computational experiments, including a comparison between IMOSSA and the nondominated sorting genetic algorithm II (NSGA-II), Jaya and the mixed integer linear programming (MILP) solver of CPLEX. The results demonstrate that IMOSSA has high precision, good convergence and excellent performance in solving the GFJSP in low-carbon manufacturing systems.

Equitable optimization of US airline route networks

Restructuring route networks (i.e., modifying the graph of origin-destination pairs) remains a promising alternative for reducing the airline industry's environmental impact. However, there exists a fundamental trade-off between emissions from flight and airport accessibility, since flights connecting underserved, low-accessibility communities tend to possess high CO2/seat-mile ratios. Thus, this work develops an open-source analytical framework and methodology that restructures U.S. airline route networks to simultaneously minimize emissions and maximize airport accessibility. To achieve this goal, this paper designs a metric to quantify airport accessibility and combines it with an open-source system-wide emissions estimation methodology. This facilitates the creation of a mixed-integer linear optimization model that returns revised flight frequencies and aircraft allotment. Using United Airlines 2019 Q3 data as a case study, this model is able to construct an alternative route network with a 25% reduction on the total number of flights, 4.4% decrease in the average emissions per seat-mile and a 17.6% improvement in the spread of the airports' accessibility scores, all while satisfying historic passenger demand.