Multi-period Mixed Integer Linear Programming Research Articles

Multi-objective optimization of gas-steam-power system for an integrated iron and steel mill considering carbon emission reduction and cost

The gas-steam-power system (GSPS) optimization is a complicated optimization problem considering economic and environmental benefits. This paper presents a multiperiod mixed integer linear programming (MILP) model for the GSPS in iron and steel enterprises simultaneously optimizing total cost and carbon emission reduction. It was used to determine the optimal operating strategy for the GSPS under multiobjective conditions. The model considers the influence of a blast furnace with top-gas recycling (TGR-BF) technology on the by-product gas supply and steam and power cogeneration system (SPCS) operation. The results showed that after the optimization aiming at the minimum total cost (Scenario A) and the maximum carbon emission reduction (Scenario B), the system total cost was the lowest (7.78 billion CNY) when the top gas recovery rate was 4%, and the carbon emission reduction peaked at 465,296.76 tCO2 when the top gas recovery rate was 12%. After multiobjective optimization (Scenario C), it was found that the system achieved carbon reduction only when the total cost attained a certain value. A sensitivity analysis revealed that a reduction in the grid emission factor and an increase in the green power increased the carbon emission reduction. When the coal price increased to 1800 CNY/t or the power price decreased to 0.2 CNY/kWh, the optimal system operation strategy was consistent under different optimization objectives. These research results provide guidance for steel enterprises to reduce carbon emissions and total cost.

Platelet inventory management with demand and supply uncertainty and variable pricing considerations

Managing the inventory of blood is a crucial operation in hospitals owing to its significance in medical treatment. At the same time, blood is characterized by unique attributes, such as perishability and the unpredictable nature of its supply and demand. While models have been developed to optimize the said process, gaps in literature exist in terms of considering the possibility of variable pricing and extensively accounting for uncertainties in the supply chain. In this light, the present study proposes a stochastic multi-period mixed integer linear programming cost minimization model that determines the optimal inventory plan for a hospital purchasing platelets, assuming that prices fluctuate along with the blood center’s supply. To implement uncertain supply and demand, the model considers a discrete set of scenarios for each parameter. A study was performed, and the results indicate a promising direction as inventory costs decreased relative to models without the new considerations.

Closed-loop supply network of electrical and electronic equipment under carbon tax policy.

Waste electrical and electronic equipment is one of the essential pollutants with significant negative impacts on the environment and human health. In this study, a multi-period mixed-integer linear programming model is developed to design a closed loop supply network for the management of electrical and electronic equipment by explicitly considering the economic and environmental sustainability with a budget constraint. Different recycling options like refurbishing, disassembling, remanufacturing, and disposal centers are considered in the design of the network. The model minimizes the total costs of the network and the total carbon emission tax. The literature review shows that the introduced model is more comprehensive than the other existing models because it simultaneously determines the location of facilities, the capacity of facilities, type of manufacturing technologies, variety of vehicles, and the allocation and transportation of materials and products. The model was applied to a real-life case study in Iran and could provide a profit of IRR 245,509,165M during the planning periods. The carbon tax policy with different echelons is applied to control the environmental impacts in which the carbon tax increases as carbon emissions increase. The results show a nearly linear relationship between the total costs of the network and the carbon tax. The carbon tax of equal to or more than 10,800 IRR/t CO2 can be a deterrent factor for the electrical and electronic equipment manufacturer in Iran to diminish emissions through investment in green technologies.

Optimization and analysis of a hydrogen supply chain in terms of cost, CO2 emissions, and risk: the case of Turkey

The transportation sector, which is largely dependent on oil, is faced with many problems such as the danger of depletion of fossil fuels that are harmful to the environment. Moreover, the situations such as epidemics and war cause excessive fluctuations in oil prices. Therefore, there is a need for new solutions based on alternative energy sources for a sustainable transportation sector. Hydrogen fuel cell electric vehicles (HFCEV) are one of the significant alternatives for an efficient, zero emissions and sustainable transportation system. Considering the potential investment in HFCEV technology, the need for a cost effective, green, and low risk Hydrogen Supply Chain (HSC) network infrastructure is inevitable. In this study, the HSC design of the Turkish transportation sector over a 25-year period (2026–2050) is investigated. The problem is modeled using a multi-period mixed integer linear programming (MIP) model. Three objectives are addresses: cost, carbon dioxide (CO2) emissions and safety risk. In order to consider the uncertainty in the hydrogen demand, five different scenarios are analyzed using fuzzy concept. There are four main results. First, unit hydrogen cost is found to be very high due to low demand and high capital cost in the initial period (2026–2031). Second, HSC network is established in a decentralized setting in all scenario solutions. The level of decentralization gets stronger over time and with increasing demand. Third, short-distance road transport is generally preferred for hydrogen transport. Fourth, since the aim is to minimize cost, CO2 emissions, and risk level, a mixed production strategy based on cost-oriented SMR and zero-emissions-oriented Electrolysis (ELE) is observed in all scenarios.

Marine vessel powertrain design optimization: Multiperiod modeling considering retrofits and alternative fuels

Over the coming decades, maritime transportation will transition from fossil hydrocarbon fuels to hydrogen, ammonia, and synthetic hydrocarbon fuels produced using renewable electricity as the primary energy source. In this context, a shipowner needs to identify a cost-efficient plan for the adoption of alternative fuels and onboard energy conversion system retrofits. This paper presents a multiperiod decision model for the selection of energy system components under increasingly stringent CO2 emissions regulations and cost forecasts over a multidecade planning horizon. The model considers the choice of newbuild architecture, timing of retrofits, component sizes, and allocation of fuels to converters with the objective of minimizing total cost of ownership (TCO). The decision problem is formulated as a discrete time multiperiod mixed-integer linear program. The application of the model is numerically illustrated for a Baltic Sea roll-on/roll-off ferry. The main findings are: (i) modifying the energy system with retrofits obtains 43% lower TCO compared to fuel switching alone; (ii) batteries contribute to 23% lower TCO; (iii) optimal component installation period can be shorter than their maximum lifetime; (iv) running an engine with hydrogen is favored over fuel cells and (v) hybrid propulsion is the key future-proofing design choice for short sea vessels.

Improving distribution system resilience by undergrounding lines and deploying mobile generators

To improve the resilience of electric distribution systems, this paper proposes a stochastic multi-period mixed-integer linear programming model that determines where to underground new distribution lines and how to coordinate mobile generators in order to serve critical loads during extreme events. The proposed model represents the service restoration process using the linearized DistFlow approximation of the AC power flow equations as well as binary variables for the undergrounding decisions of the lines, the configurations of switches, and the locations of mobile generators during each time period. The model also enforces a radial configuration of the distribution network and considers the transportation times needed to deploy the mobile generators. It is shown that long-term line undergrounding decisions which are cognizant of short-term mobile generator deployments yield superior results relative to undergrounding decisions made without considering mobile generators. Using an extended version of the IEEE 123-bus test system, numerical simulations show that combining the ability to underground distribution lines with the deployment of mobile generators can significantly improve the resilience of the power supply to critical loads. • Resilience can be improved via mobile generators and underground lines. • Stochastic optimization for siting underground lines and operating mobile generators. • Show benefits from jointly considering undergrounding and mobile generator decisions.

Optimization of multi-period investment planning in street lighting systems by mixed-integer linear programming

This article proposed the use of multi-period mixed-integer linear programming method for investment planning to support decision-making processes in upgrading and managing street lighting systems. The technique incorporates a multi-variate model that maximizes energy-saving by considering budget constraints, the state of the lighting system, and the available technology in the market to replace the existing streetlights. This topic is novel because the complexity of the problem relies on the existence of several potentially large investments. As explained in this paper, the proposed method optimally considers the investments and returns as a combination that maximizes energy savings. The method was tested using actual data from an undisclosed public lighting system in Colombia. The results obtained revealed that multi-period investment optimization based on mixed-integer linear programming is an ideal investment plan, particularly in streetlight systems. Therefore, it forms an invaluable tool for street lighting systems' administrators and decision-makers in optimizing and facilitating the critical decision-making process in their work environment.

A mixed-integer optimization model for water sector planning and policy making in arid regions

Water sector planning and policy making in arid and semi-arid regions are challenging because many drivers and decision criteria require consideration. In this study, a multi-period mixed-integer linear programming model was developed to integrate and economically evaluate water management options for water supply in arid regions. The applicability of the proposed approach was demonstrated through a case study in the Emirate of Abu Dhabi (EAD), United Arab Emirates. The model was programmed in general algebraic modeling system (GAMS) and solved using the Cplex solver. The model determined the optimal economic and environmental costs, capacity expansion of treatment plants and water transmission systems, and other environmental aspects including the carbon footprint and brine discharge. Results show that the capacity contribution of reverse osmosis for desalination is expected to increase from 5.1% in 2021 to 18.1% in 2050. Based on the model's results for the case study, it was concluded that even with moderate consideration of environmental aspects, desalination plants in the EAD need a major technology transformation from thermal desalination to reverse osmosis The proposed model is proved to be effective for integrated water resources management and infrastructure planning in the EAD, and has the potential for effective application in other arid or semi-arid countries.

Optimal producer well placement and multiperiod production scheduling using surrogate modeling

The main objective of this paper is to determine the optimal placement of oilfield producer wells while accounting for surface infrastructure constraints. To accomplish this objective, we replace a first-principles optimization model with a hybrid approach, which draws the correlations for oil production from data obtained by rigorous simulations of grid discretized reservoir models. We use these correlations to build a Multiperiod Mixed-Integer Linear Programming (MILP) problem with the production constraints and maximization of the Net Present Value (NPV) as the objective function. A computationally efficient multiperiod MILP model is proposed to evaluate the performance of this methodology with a surrogate correlation for the oil production rate built in ALAMO. This set of equations takes into account the distance of the producer well from the injection well, the depth of the producer well, and the time of operation. This model allows higher levels of grid discretization and longer time horizons of interest. In order to address systems where high spatial resolution is necessary and computational expense is high, we introduce a methodology of Spatial Aggregation and Disaggregation. In such method, we first simplify the problem through aggregation to then decompose the obtained solution, producing highly resolved well placement strategies. With this approach, it is shown that the optimal well placement locations can be obtained with order of magnitude reductions in computational expense.

Time-dependent on-street parking planning in a connected and automated environment

Parking remains a serious difficulty in metropolitan transport mainly because of the supply shortage in downtown areas. The parking experience will be improved with the support of connected and automated vehicle (CAV) technologies, enabled by remote parking functionality. Nevertheless, remote parking of CAVs not only results in additional surface traffic but also increases the total vehicle miles traveled (VMT). On the other hand, it is possible to manage the overall traffic by a centralized system with the assistance of CAV technology, which brings the potential for using road resources more flexibly. Inspired by the above ideas, this paper investigates a novel scheme to transfer some lanes to provide on-street parking spaces for CAVs within a necessary period to reduce “cruise-for-parking” travel; as such transfer compromises road capacity, a methodological framework is required to optimally plan the scheme for maximizing certain social goals. We formulate the on-street planning problem as a multi-period mixed-integer linear program with inter-period constraints, which determines the locations and opening durations of on-street parking lots, as well as the assignment of all parking demands across the network. Approximate approaches are adopted to solve the problem for large-scale instances. Numerical experiments are conducted on a real-world network in Wangjing District, Beijing. The results indicate that appropriate time-dependent planning of on-street parking can reduce the total VMT by 10%–27% under various demand levels.

Optimal design and operation of integrated microgrids under intermittent renewable energy sources coupled with green hydrogen and demand scenarios

Renewable energy integration into existing or new energy hubs together with Green technologies such as Power to Gas and Green Hydrogen has become essential because of the aim of keeping the average global temperature rise within 2 °C with regard to the Paris Agreement. Hence, all energy markets are expected to face substantial transitions worldwide. On the other hand, investigation of renewable energy systems integrated with green chemical conversion, and in particular combination of green hydrogen and synthetic methanation, is still a scarce subject in the literature in terms of optimal and simultaneous design and operation for integrated energy grids under weather intermittency and demand uncertainty. In fact, the integration of such promising new technologies has been studied mainly in the operational phase, without considering design and management simultaneously. Thus, in this work, a multi-period mixed-integer linear programming (MILP) model is formulated to deal with the aforementioned challenges. Under current carbon dioxide limitations dictated by the Paris Agreement, this model computes the best configuration of the renewable and non-renewable-based generators, their optimal rated powers, capacities and scheduling sequences from a large candidate pool containing thirty-nine different equipment simultaneously. Moreover, the effect of the intermittent nature of renewable resources is analyzed comprehensively under three different scenarios for a specific location. Accordingly, a practical scenario generation method is proposed in this work. It is observed that photovoltaic, oil co-generator, reciprocating ICE, micro turbine, and bio-gasifier are the equipment that is commonly chosen under the three different scenarios. Results also show that concepts such as green hydrogen and power-to-gas are currently not preferable for the investigated location. On the other hand, analysis shows that if the emission limits are getting tightened, it is expected that constructing renewable resource-based grids will be economically more feasible.

Integrated ethanol and gasoline supply chain planning under environmental constraints: A case study of Brazil

The petroleum infrastructure, hydrocarbon costs, and process and distribution networks influence integrated supply chains of mixed biofuels and petroleum derivatives (gasoline and diesel). Furthermore, the seasonality of biomass feedstock poses more complexities when optimizing such a combined bio-fossil-fuel industry. As such, a multi-period mixed-integer linear programming (MILP) planning model proposal addresses this supply chain mixed fuels, whereby strategic and tactical decisions under environmental constraints account for different process design in response to demand fluctuations along the long-term horizon. This work is applied in the bio-fossil-fuel market in Brazil by considering diverse plant configurations and different feedstock with their seasonality. Results yield an optimal facility location and plant configurations optimizing over time the evolution of installed capacities, capacity utilization, carbon credit and emissions profiles. The study involves ethanol streams to be added in the gasoline mix considering exclusive and flex sugarcane and corn-based processing plants.

A multi-period fuzzy optimization strategy for managing a centralized blood supply chain

Blood supply chains (BSCs) are highly complex systems that present many challenges in their optimal management, such as different collection methods, demand and supply uncertainty, blood perishability, blood group distinction, and compatible substitutions. This article presents the study of the critical problem of sizing and managing a centralized version of such BSCs in a developing country. The problem is initially formulated as a multi-period mixed-integer linear programming (MILP) model simultaneously addressing strategic, tactical, and operational decisions over a given time horizon. The formers are related to selecting the technology for blood collection and processing, the tactical ones determine not only where and when donation campaigns are made but also the periodic delivery of surplus plasma for further fractionation, while the operational ones specify the amounts of blood collected, donor allocation to each collection method, and quantities of blood components produced, distributed, and kept in stock daily. The problem aims to minimize three conflictive objective functions: the shortage, the total costs, and the number of substitutions. To appropriately address the multiple goals, their imprecise target values, and the fuzziness in some parameters, the model is reformulated as a fuzzy mixed-integer goal programming (FMIGP) one, which is then solved using a crisp strategy to find a compromise solution. A real-life case study from the public sector of Bahía Blanca city in Argentina shows the advantages of the presented approach. Numerical results demonstrate the integrated model can significatively increase demand satisfaction while reducing costs, less favorable substitutions, and wastes.

The role of energy supply in abatement cost curves for CO2 capture from process industry – A case study of a Swedish refinery

Carbon capture and storage (CCS) activities need to be ramped up to address the climate crisis. Abatement cost curves can help to identify low-cost starting points and formulate roadmaps for the implementation of CCS at industrial sites. In this work, we introduce the concept of energy supply cost curves to enhance the usefulness and accuracy of abatement cost curves. We use a multi-period mixed-integer linear programming (MILP) approach to find an optimal mix of heat sources considering the existing site energy system. For a Swedish refinery, we found that residual heat and existing boiler capacities can provide the heat necessary for CCS that avoids >75% of the site’s CO2 emissions. Disregarding the existing site energy system and relying on new heat supply capacities instead, would lead to capture costs that are 40–57% higher per tonne of CO2-avoided (excl. CO2 liquefaction, transport, and final storage). Furthermore, we estimated that temporal variations of heat sources (intermittent residual heat) increases the heat supply cost and emissions by 7–26% and 9–66%, respectively. The proposed method for optimization of the energy supply mix considering temporal variations of heat sources enables detailed estimates of energy supply costs for CO2 capture rates ranging from partial to full capture, and thus, improve abatement cost curves.

Multi-period optimization of hydrogen supply chain utilizing natural gas pipelines and byproduct hydrogen

Establishing hydrogen infrastructure is essential for achieving a hydrogen economy in the future. However, the levelized cost of hydrogen is expensive in the early market due to the absence of infrastructure. In the present study, our aim was to minimize the capital and operating costs of the hydrogen supply chain (HSC) using multi-period mixed-integer linear programming. The proposed HSC includes existing infrastructure for byproduct hydrogen and natural gas (NG) pipelines. We determined the economic benefits of utilizing NG pipelines and byproduct hydrogen and how existing infrastructure outperformed other technologies for the optimization of the HSC. Compared to the non-utilization scenario, the average levelized costs of hydrogen decreased by 0.93, 1.40, and 2.03 $/kg–H2 if byproduct hydrogen, NG pipelines, or both were available, respectively, in the HSC. The optimal HSC networks indicate that NG pipelines and byproduct hydrogen have synergetic effects on reducing the total costs owing to the decentralization of production facilities.

A multi‐period optimization model for power sector withCO2emission considerations

A multi-period mixed-integer linear programming model was developed to minimize the cumulative cost associated with electricity generation and reduce the carbon dioxide emissions. Fuel balancing and carbon capture and sequestration were investigated for carbon dioxide mitigation. The developed model was implemented on the power sector of Pakistan for a period of 11 years starting from 2020. All the existing and new planned power plants were included, and capacity expansion was only considered where required. Low, normal, and high gross domestic product growth rate-based electricity demands were considered, keeping summer and winter demands separately. Fuel balancing can mitigate 38.5% average carbon dioxide emissions for both summer and winter, whereas carbon capture and sequestration can mitigate 26.2% and 2.2% average carbon dioxide emissions for summer and winter, respectively. Carbon capture and sequestration can mitigate 23.4% average carbon dioxide emissions (for normal gross domestic product summer) compared to 16.5% mitigation in fuel balancing (for normal gross domestic product summer and winter). Carbon dioxide emissions mitigation was negligible in carbon dioxide case (ie, 1.1%) for normal gross domestic product winter. For high gross domestic product case, fuel balancing could not mitigate carbon dioxide emissions, and carbon capture and sequestration was the only option for carbon dioxide mitigation, which resulted in 23.4% and 6.3% mitigation for summer and winter, respectively.

Generation Expansion Planning with Energy Storage Systems Considering Renewable Energy Generation Profiles and Full-Year Hourly Power Balance Constraints

This paper proposes a methodology to develop generation expansion plans considering energy storage systems (ESSs), individual generation unit characteristics, and full-year hourly power balance constraints. Generation expansion planning (GEP) is a complex optimization problem. To get a realistic plan with the lowest cost, acceptable system reliability, and satisfactory CO2 emissions for the coming decades, a complex multi-period mixed integer linear programming (MILP) model needs to be formulated and solved with individual unit characteristics along with hourly power balance constraints. This problem requires huge computational effort since there are thousands of possible scenarios with millions of variables in a single calculation. However, in this paper, instead of finding the globally optimal solutions of such MILPs directly, a simplification process is proposed, breaking it down into multiple LP subproblems, which are easier to solve. In each subproblem, constraints relating to renewable energy generation profiles, charge-discharge patterns of ESSs, and system reliability can be included. The proposed process is tested against Thailand’s power development plan. The obtained solution is almost identical to that of the actual plan, but with less computational effort. The impacts of uncertainties as well as ESSs on GEP, e.g., system reliability, electricity cost, and CO2 emission, are also discussed.

Optimization Tool for the Strategic Outline and Sizing of District Heating Networks Using a Geographic Information System

The implementation of district heating networks into cities is a main topic in policy planning that looks for sustainable solutions to reduce CO2 emissions. However, their development into cities is generally limited by a high initial investment cost. The development of optimization methods intended to draft efficient systems using heating consumption profiles into a prescribed geographic area are useful in this purpose. Such tools are already referred to in the scientific literature, yet they are often restricted to limit the computational load. To bridge this gap, the present contribution proposes a multi-period mixed integer linear programming model for the optimal outline and sizing of a district heating network maximizing the net cash flow based on a geographic information system. This methodology targets a large range of problem sizes from small-scale to large-scale heating networks while guaranteeing numerical robustness. For sake of simplicity, the developed model is first applied to a scaled down case study with 3 available heating sources and a neighborhood of 16 streets. The full-scale model is presented afterwards to demonstrate the applicability of the tool for city-scale heating networks with around 2000 streets to potentially connect within a reasonable computational time of around only one hour.

Sustainable optimization of waste management network over extended planning time horizon

AbstractThis study proposes a multiperiod mixed integer linear programming model for the management of a single municipal solid waste (MSW) treatment plant with sustainability as the objective. Discrete and continuous variables define the capacity selections for diverse MSW technologies, and the operation of the MSW network, respectively. The economic target is considered to maximize the net present value. The environmental impact is the minimization of a normalized environmental objective function (NEOF). The social target is the maximization of jobs. An interesting feature about the research work is the requirement of biodrying technologies for MSW moisture content control. Due to the conflicted nature among the sustainability components, a multiobjective optimization (MO) is carried out to find the Pareto optimal solutions. The MO results show that the Pareto optimal solutions vary around profit range of $4.9–8.5 billion, NEOF impact range of 3.2–3.6 units, and social benefit range of 2700–4828 jobs.

Simultaneous integration of heat pumps and different thermal energy storages into a tightened multi-period MILP HENS superstructure formulation for industrial applications

Design optimization of industrial installations with help of mathematical programs offers high potential for energy savings and cost reduction, which steadily gains importance. Heat exchange network synthesis (HENS) is one of the commonly used and promising methods. This paper deals with simultaneous integration of heat pumps and two different storage types into mixed integer linear programming (MILP) HENS by extending a multi-period superstructure formulation proposed by Beck and Hofmann (2018c). Further measures for tightening the solution space for the coefficient of performance (COP) are introduced. This improves the accuracy of the heat pump (HP) approximation, reduces computational effort and prevents solutions with uneconomical low COP. The obtained approach allows to design cost efficient heat recovery systems with storages (ST) and HP for the improvement of the energy recovery capabilities. A constructed test case was used to analyze the performance of the method and to show its possible potential.