Integer Linear Optimization Model Research Articles

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.

When should shelf stocking be done at night? A workforce management optimization approach for retailers

This research examines the economic viability of night shelf stocking in the retail industry. By analyzing real data on the costs and benefits of both night and day stocking, we propose a novel integer linear optimization model to determine the optimal structure of shelf stocker shifts for individual stores. The model is tested on a standard Chilean supermarket, with a sensitivity analysis performed on key parameters including product demands, shelf capacity, and cost factors. The results reveal that a daytime shelf stocking system is impractical and costly for high-demand outlets. We recommend combining day and night stockings, as night stocking proves to be more efficient, reducing stockouts and salary costs. Additionally, an analysis incorporating semi-night shifts as an alternative to traditional shift patterns demonstrates that combining day, night, and semi-night shift structures is the most cost-effective solution, minimizing labor and stocking expenses without compromising service quality. This study highlights the economic advantages of night shelf stocking and provides valuable insights for retailers seeking to optimize their operations.

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.

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.

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.

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.

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.

Distribution network optimization: predicting computation times to design scenario analysis for network operators

AbstractThe increased use of renewable energies promotes decarbonization and raises the load on power distribution networks, forcing responsible distribution network operators to re-evaluate and re-design their networks. Infrastructure planners employ a rolling-horizon planning procedure with frequent recalculations to face informational uncertainty, which require solving multiple scenarios. Keeping complexity manageable is particularly challenging as distribution network areas may span multiple cities and counties. In this study, we focus on infrastructural decomposition, where the distribution network is decomposed into multiple parts and planning problems, which are then optimized separately. However, infrastructure planners lack the knowledge of how they should design a scenario analysis for a subnetwork to account for informational uncertainties subject to limited planning time and computing resources. Based on empirical requirements from literature and discussions with experts, we present a novel mixed integer linear optimization model that allows to use exact solution approaches for realistic large-scale distribution networks. Our approach considers the primary and secondary distribution network in an integrated way and designs a flexible topology for high reliability power distribution. We perform extensive computational experiments and a sensitivity analysis to determine correlations between the values of model parameters and computation times required to solve the resulting model instances to optimality. The results of the sensitivity analysis indicate that the combination of the number of buses, lines and the considered action scope have a considerable influence on the solving time. In contrast, a higher number of available transformers led to a better solvability of the model. From these computational insights, we derive implications for infrastructure planners who wish to perform scenario analysis for planning their power distribution networks.

Exploring the value of electric vehicles to domestic end-users

Owing to the recent ban on the sales of new petrol and diesel cars in the United Kingdom (UK) by 2030, combined with the UK’s commitment to net-zero emission of greenhouse gases by 2050, a projected increase in the growth rate of electric vehicles (EVs) is inevitable. In recent years, there has been an increase in the adoption of EVs, but not at a rate sufficient to meet net-zero targets. Although benefits do exist for current EV owners, barriers such as the availability of charging infrastructure, total cost of ownership, battery costs, amongst others still present a challenge for the required adoption rate. In this work, we therefore aim to address some of these barriers, specifically the total cost of ownership and battery costs, by exploring the value a range of EVs on the market give to domestic end-users with different usage classes. Using a techno-economic-environmental mixed integer linear optimisation model which considers local energy demands, retail electricity tariffs, local renewable energy generation and battery degradation, potential benefits for EVs adopters are analysed from a cost or Carbon dioxide (CO2) minimisation objective. This model adopted considered a range of vehicle types – EVs and non-EVs – and properties, installed PV sizes, and user travel behaviour classes, and results showed that although EVs have a relatively higher purchase costs, total cost values are comparable, in some cases cheaper, when compared with conventional non-EVs. EV users further gain from environmental benefits through a reduction in the CO2 emitted irrespective of the user’s desired goal. A dominance analysis was also carried out to determine the order of importance of key input variables to the optimisation model in predicting costs and CO2 emission quantities. The results obtained are helpful to end-users in prioritising EV features during purchase based on personal goals of cost or carbon emissions reduction.

Routing Heterogeneous Traffic in Delay-Tolerant Satellite Networks

Delay-tolerant networking (DTN) offers a novel architecture that can be used to enhance store-carry-forward routing in satellite networks. Since these networks can take advantage of scheduled contact plans, distributed algorithms like the Contact Graph Routing (CGR) can be utilized to optimize data delivery performance. However, despite the numerous improvements made to CGR, there is a lack of proposals to prioritize traffic with distinct quality of service (QoS) requirements. This study presents adaptations to CGR to improve QoS-compliant delivery ratio when transmitting traffic with different latency constraints, along with an integer linear programming optimization model that serves as a performance upper bound. The extensive results obtained by simulating different scenarios show that the proposed algorithms can effectively improve the delivery ratio and energy efficiency while meeting latency constraints.

Multi-Energy Microgrids Incorporating EV Integration: Optimal Design and Resilient Operation

There are numerous opportunities and challenges in integrating multiple energy sources, for example, electrical, heat, and electrified transportation. The operation of multi-energy sources needs to be coordinated and optimized to achieve maximum benefits and reliability. To address the electrical, thermal, and transportation electrification energy demands in a sustainable and environmentally friendly multi-energy microgrid, this paper presents a mixed integer linear optimization model that determines an optimized blend of energy sources (battery, combined heat and power units, thermal energy storage, gas boiler, and photovoltaic generators), size, and associated dispatch. The proposed energy management system seeks to minimize total annual expenses while simultaneously boosting system resilience during extended grid outages, based on an hourly electrical and thermal load profile. This approach has been tested in a hospital equipped with an EV charging station in Okinawa, Japan through several case studies. Following a M1/M2/c queuing model, the proposed grid-tied microgrid successfully integrates EVs into the system and assures continued and economic power supply even during grid failures in different weather conditions.

Cost minimisation of renewable hydrogen in a Dutch neighbourhood while meeting European Union sustainability targets

Decentralised renewable energy production in the form of fuels or electricity can have large scale deployment in future energy systems, but the feasibility needs to be assessed. The novelty of this paper is in the design and implementation of a mixed integer linear programming optimisation model to minimise the net present cost of decentralised hydrogen production for different energy demands on neighbourhood urban scale, while simultaneously adhering to European Union targets on greenhouse gas emission reductions. The energy system configurations optimised were assumed to possibly consist of a variable number or size of wind turbines, solar photovoltaics, grey grid electricity usage, battery storage, electrolyser, and hydrogen storage. The demands served are hydrogen for heating and mobility, and electricity for the households. A hydrogen residential heating project currently being developed in Hoogeveen, The Netherlands, served as a case study. Six scenarios were compared, each taking one or multiple energy demand services into question. For each scenario the levelised cost of hydrogen was calculated. The lowest levelised cost of hydrogen was found for the combined heating and mobility scenario: 8.36 € kg−1 for heating and 9.83 € kg−1 for mobility. The results support potential cost reductions of combined demand patterns of different energy services. A sensitivity analysis showed a strong influence of electrolyser efficiency, wind turbine parameters, and emission reduction factor on levelised cost. Wind energy was strongly preferred because of the lower cost and the low greenhouse gas emissions, compared to solar photovoltaics and grid electricity. Increasing electrolyser efficiency and greenhouse gas emission reduction of the used technologies deserve further research.

Replacing coal in Georgia's power plants with woody biomass to increase carbon benefit: A mixed integer linear programming model

To combat climate change, reducing carbon emissions from coal consumption in the power sector can be an effective strategy. We developed a price-exogenous mixed integer linear optimization model satisfying both traditional timber demand in Georgia and its neighboring states (Alabama, Florida, North Carolina, South Carolina, and Tennessee) and additional bioenergy demand to replace coal in the power plants of Georgia for 50 years, maximizing social welfare. We used Forest Inventory & Analysis unit level yield of five forest types (planted softwood, natural softwood, upland hardwood, bottomland hardwood, and mixed forest), timber demand, and price information, and developed three scenarios. In the Baseline scenario, traditional annual timber demand (152 million tons of wood) was satisfied with no coal replacement. In Scenario 1, 100% coal (7.34 million tons annually) was replaced using pulpwood only, along with traditional demand. In Scenario 2, also with traditional demand, 100% coal was replaced using pulpwood and logging residues. It would require approximately 336 and 98 thousand acres of additional annual timberland harvested in Scenario 1 and Scenario 2, respectively, compared to Baseline (1280 thousand acres). During 50 years, a total of 9.3, 10.2, and 9.6 billion tons of timber was produced in Baseline, Scenario 1, and Scenario 2, respectively. About one-third of all torrefaction plants would be located in the central region of Georgia. The net change in stand carbon was positive in all three scenarios—the highest in Baseline (1330 million tons C), followed by Scenario 2 (1261 million tons C), and the lowest in Scenario 1 (872 million tons C). About 240 million tons of carbon was avoided by using biomass instead of coal in Scenario 1 and Scenario 2. In Baseline, with continued emission from coal usage in the power plant for 50 years (285 million tons C), net carbon benefit was 1046 million tons C. Replacing 100% of coal with both pulpwood and logging residues provided a net benefit of 1501 million tons C, about 43% higher compared to baseline.

Park-and-ride facility location optimization: A case study for Nashville, Tennessee

Strategic placement of park-and-ride (P&R) facilities is important to ensure the facilities are effectively utilized by commuters, avoiding oversubscription or underutilization after placement. This study develops a framework that integrates a demand model and an optimization model to study the optimal placement of P&R facilities to maximize the total number of commuters who switch from single occupancy vehicles to public transit. The framework first develops a P&R demand model through a discrete choice model, specifically the multinomial logit model, to characterize the mode choice behavior of individuals in a multimodal network. Next, it leverages the estimated proportion of commuters that are expected to switch to P&Rs from alternatives in a mixed integer linear programming optimization model to prescribe the optimal locations of P&R facilities. This study also accounts for practical considerations and introduces an approach to estimate the potentially unknown demand for P&R facilities. The framework is applied through a case study for the City of Nashville, a major metropolitan area in the State of Tennessee, US. Model calibration is performed using the literature and available data at Nashville. The results of the case study are then presented and sensitivity analysis is performed to provide further insights. The results of the case study suggest that the optimal placement of P&R facilities has the potential to improve the network performance, and reduce emission and vehicle kilometer traveled.

A hyper-matheuristic approach for solving mixed integer linear optimization models in the context of data envelopment analysis.

Mixed Integer Linear Programs (MILPs) are usually NP-hard mathematical programming problems, which present difficulties to obtain optimal solutions in a reasonable time for large scale models. Nowadays, metaheuristics are one of the potential tools for solving this type of problems in any context. In this paper, we focus our attention on MILPs in the specific framework of Data Envelopment Analysis (DEA), where the determination of a score of technical efficiency of a set of Decision Making Units (DMUs) is one of the main objectives. In particular, we propose a new hyper-matheuristic grounded on a MILP-based decomposition in which the optimization problem is divided into two hierarchical subproblems. The new approach decomposes the model into discrete and continuous variables, treating each subproblem through different optimization methods. In particular, metaheuristics are used for dealing with the discrete variables, whereas exact methods are used for the set of continuous variables. The metaheuristics use an indirect representation that encodes an incomplete solution for the problem, whereas the exact method is applied to decode the solution and generate a complete solution. The experimental results, based on simulated data in the context of Data Envelopment Analysis, show that the solutions obtained through the new approach outperform those found by solving the problem globally using a metaheuristic method. Finally, regarding the new hyper-matheuristic scheme, the best algorithm selection is found for a set of cooperative metaheuristics ans exact optimization algorithms.

H-Rank Consensus Models for Fuzzy Preference Relations Considering Eliminating Rank Violations

Fuzzy preference relations (FPRs) have been widely used when ranking alternatives using pairwise comparison. However, when the FPRs have rank violations, the ranking results tend to contradict the decision makers’ (DMs) preferences. To date, no studies have examined the elimination of these FPR rank violations. Further, traditional consensus models utilizing distance measures between individual preferences are not suitable to manage classification-based consensus problems. To overcome these problems, this article develops several optimization models to address rank violations and h-rank consensus issues. First, the conditions that satisfy the FPRs’ preservation of order preferences (POPs) are analyzed and a system of constraints derived to ensure that the POPs are explicitly controlled by the optimization model, after which a mixed integer linear optimization model is developed to assist DMs to satisfy both the POP conditions and acceptable consistency. Finally, a linear model for the h-rank ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$h \geq 2$</tex-math></inline-formula> ) consensus reaching process is designed to ensure that each individual FPR also satisfies the POP conditions and acceptable consistency. The feasibility of the proposed models is illustrated using numerical examples, with extensive comparisons further validating the usefulness of the proposed models for group decision-making problems.

Integrated planning for planting and harvesting sugarcane and energy-cane for the production of sucrose and energy

The main products obtained from sugarcane for the global market are sugar, ethanol and energy. Although the demand for these products is high, in Brazil there is no longer space to expand sugarcane cultivation due to other important food crops and environmental protection areas. Therefore, current research seeks ways to increase sugarcane productivity without expanding the planted area. Consequently, a type of cane with higher concentration of fiber has been developed and cultivated called energy-cane. This cane type has more fiber than sucrose in its composition, which makes it better for producing energy and ethanol and inappropriate for sugar production. To meet the demands for these three products, both energy-cane and sugarcane are needed, making the planning and decision-making more difficult in the energy-sugar sector. In this context, a mixed integer linear optimization model for the integrated planning of the planting and harvesting of sugarcane and energy-cane for a sugar-energy plant is proposed to determine an optimized planting and harvesting schedule, that aims to maximize the sucrose and fiber production in the cane fields. The model takes into account a flexible harvest period to meet the demands of the consumer market and respect the operational constraints of the company, which can cause variations in productivity. To solve real-life instances where exact methods fail, a heuristic based on the relax-and-fix and fix-and-optimize concepts is proposed. Numerical experiences with random instances were generated to test both the model and the heuristic. Feasible solutions with an error close to 1% were obtained, consuming one tenth of the CPU time, on average. Thus, the mathematical model and the heuristic method developed have great potential to support decision-making in sugarcane and energy-cane production planning.

Coupling biogeochemical simulation and mathematical optimisation towards eco-industrial energy systems design

Process industry remains one of the difficult-to-decarbonise sectors globally. To mitigate industrial greenhouse gas (GHGs) emissions, an eco-industrial energy systems (e-IES) optimisation framework is proposed by coupling mathematical optimisation with clustering algorithms and first principle modelling. Within the framework, a rooftop farming database was developed using biogeochemical simulations, which models seven crop growth in response to 10 cultivation conditions. Clustering algorithm was applied to analyse energy system data, along with the rooftop farming database, to inform the optimisation model. A Mixed Integer Linear Programming optimisation model was developed to optimize system design considering the trade-off between economic and environmental objectives. The implications of rooftop design on e-IES and their interactive effects on industrial decarbonisation were addressed. A case study at an industrial park in Suzhou China reveals that rooftop farming could generate mutual benefits from both cost and GHG reduction perspectives. Planting lettuce indicates a cost-efficient solution, and planting tomato could contribute the most to GHG emission reduction. Compared to the rooftop PV and the spare rooftop, 2.4% and 5.6% cost savings, as well as 10.2% and 16.3% emission savings, could be achieved respectively by implementing rooftop farming. Overall, this study demonstrates an emerging perspective on decarbonising the industrial sector by coupling biogeochemical simulation and energy system optimisation and adopting cross-disciplinary approaches.

An exact model for a slitting problem in the steel industry

From an economic point of view, the steel industry plays an important role and, when it comes to responding to new challenges, innovation is a crucial factor. This paper proposes a mathematical methodology to solve the slitting problem in a steel company located in Europe. The slitting problem occurs when large width steel coils are slit into narrower coils, known as strips, to meet the requirements of the customers. A major challenge here is defining a slitting plan to fulfil all these requirements, as well as ongoing operational constraints and customer demands. The company looks for a reduction of the leftovers generated in the entire process, while maximising the overall accuracy of the orders. These leftovers may be used in the future as part of new orders provided they are able to respond to specific requirements, or otherwise they are discarded and considered as scrap. This paper introduces a novel mixed integer linear optimisation model to respond to a specific slitting problem. The model is validated with real data and it outperforms the results obtained by the company in different ways: by adjusting the orders that are to be served, by reducing the amount of scrap and by using the retails for future orders. Furthermore, the model is solved in only a few minutes, while the company needs several hours to prepare the scheduling in the current operating process.