Mixed-integer Linear Programming Optimization Model Research Articles

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.

Potentials of Mixed-Integer Linear Programming (MILP)-Based Optimization for Low-Carbon Hydrogen Production and Development Pathways in China

Hydrogen (H2) is considered one of the main pillars for transforming the conventional “dark” energy system to a net-zero carbon or “green” energy system. This work reviewed the potential resources for producing low-carbon hydrogen in China, as well as the possible hydrogen production methods based on the available resources. The analysis and comparison of the levelized cost of hydrogen (LCOH) for different hydrogen production pathways, and the optimal technology mixes to produce H2 in China from 2020 to 2050 were obtained using the mixed-integer linear programming (MILP) optimization model. The results were concluded as three major ones: (a) By 2050, the LCOH of solar- and onshore-wind-powered hydrogen will reach around 70–80 $/MWh, which is lower than the current H2 price and the future low-carbon H2 price. (b) Fuel costs (>40%) and capital investments (~20%) of different hydrogen technologies are the major cost components, and also are the major direction to further reduce the hydrogen price. (c) For the optimal hydrogen technology mix under the higher renewable ratio (70%) in 2050, the installed capacities of the renewable-powered electrolysers are all more than 200 GW, and the overall LCOH is 68.46 $/MWh. This value is higher than the LCOH (62.95 $/MWh) of the scenario with higher coal gasification with carbon capture and the storage (CG-CCS) ratio (>50%). Overall, this work is the first time that hydrogen production methods in China has been discussed comprehensively, as well as the acquisition of the optimal H2 production technology mix by the MILP optimization model, which can provide guidance on future hydrogen development pathways and technology development potential in China.

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.

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

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

A 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.

Inter-firm exchanges, distributed renewable energy generation, and battery energy storage system integration via microgrids for energy symbiosis

Policymakers and entrepreneurs are aware that reducing energy waste and underutilization are mandatory to actually foster the green transition. Nevertheless, small–medium enterprises usually meet technical and overwhelming financial constraints. They are unable to make profits, become less energy-sensitive, and cut down on their emissions simultaneously. Industrial districts are a source of both wealth and GHG (greenhouse gas) emissions. Eco-industrial parks (EIPs) supply a suitable strategy to ease symbiotic exchanges among various organizations. Surplus electricity from larger, energy-autonomous companies will be a new input for more vulnerable ones. This type of district is challenging, and it can provide an unexplored opportunity to cooperate, invest in renewable energy sources, and form alliances. To better exploit underutilized energy in industrial districts, it is essential to explore energy symbiosis (ES), i.e., an energy-based perspective of industrial symbiosis. This study presents an original mixed-integer linear programming (MILP) optimization model that aims to identify possible inter-firm exchanges and introduce microgrid-based support for distributed renewable-energy generators (DREGs) and battery energy storage systems (BESS) over a one-year simulation period. The model simultaneously targets economic and ecological objectives. The paper compares two case studies, one with battery support and one without. The optimization model was tested using a case study and found to improve energy efficiency (with a 43.46% saving in energy costs) and reduce greenhouse gas emissions (with an 84.59% reduction in GHG) by facilitating symbiotic exchanges among SMEs in industrial districts. The inclusion of BESS support further enhanced the model's ability to utilize green and recovered energy. These findings have implications for policymakers, entrepreneurs, and SMEs seeking to transition to more sustainable energy practices. Future work could explore the applicability of the MILP optimization model in other contexts and the potential for scaling up the model to larger industrial districts.

A hierarchical two-level MILP optimization model for the management of grid-connected BESS considering accurate physical model

This work proposes a new Energy Management System (EMS) for Battery Energy Storage Systems (BESS). The goal is to make a BESS profitable in the new environment considering massive use of batteries that can be foreseen in the next future, due to the predictive increase of clean energy resources. The developed EMS considers two levels of optimization. The first level models the participation of the BESS in an Ancillary Service Market and schedules the BESS. The second level, the most innovative, is responsible for optimally distributing the power set-points obtained previously among the various battery banks considering, in addition to the battery aging, also the different efficiencies of battery banks, converters, and transformers. Moreover, this second-level manages both active and reactive power flows, and losses. Both optimization algorithms have been modeled as Mixed Integer Linear Programming (MILP) and implemented in GAMS using CPLEX as a solver. The results are encouraging: compared with the common industrial practice in which the load profile is equally shared among the individual batteries within a BESS, the two new proposed EMS strategies guarantee for a long period of operation (10-years) a consistent reduction in the number of batteries replacement (around 47%), thus ensuring significant cost savings. Moreover, the proposed BESS model accurately approximates the real physical behavior of the system, leading to an average error in State-of Energy (SoE) evaluation below 0.6%, which is almost one order of magnitude lower than the ones obtained by simpler models from literature with degradation only SoE-dependent.

Multi-objective transportation route optimization for hazardous materials based on GIS

Safety and security are of paramount importance, it is important to optimize and improve the routes of trucks that carry hazardous materials. In this study, we not only ensure the risk in the network, but also consider the transportation cost and the factors such as buildings and emergency facilities around the routes. The Geographic Information System (GIS) is used to quantify the factors on each section in the network. We present an epsilon constrained multi-objective mixed-integer linear programming optimization model to find the robust and stable transportation optimization solutions. At the end, we complete a case analysis of the proposed methodology to determine the motorway segments in Jiangsu province, China and test the above algorithm on the network, which has 144 nodes and 388 sections. The results we get show that the factors of buildings play a very important role in the model, and the multi-objective mixed-integer linear optimization model is reasonable and performs good quality.

Optimal joint maintenance and orienteering strategy for complex mission-oriented systems: A case study in offshore wind energy

This paper introduces and solves the joint maintenance and orienteering problem with an application to offshore wind farms. The quest for sustainable energy production is fueling the growth of offshore wind electricity generation. Energy producing offshore wind turbines are typically dispersed across several remote wind farms and must be maintained and operated with high reliability levels for long time-periods separated by scheduled maintenance rotations. Due to resource constraints such as travel time, cost, and availability of repair crews, only a subset of turbines and their components can be selected for maintenance operations during maintenance trips. This paper proposes a novel joint maintenance and orienteering framework to address the selection of turbines to visit, the components to maintain, the maintenance levels to be performed, the assignment of repair crews, and their routing with the goal of minimizing total cost while satisfying a minimum required reliability threshold during the next operating mission until the next maintenance rotation. A mixed-integer linear programming optimization model is developed and fully discussed. To solve the problem for large-scale instances, a column generation method based on Dantzig–Wolfe decomposition and labeling algorithm is proposed. Several numerical experiments demonstrate the validity of the proposed model and the benefit of jointly optimizing maintenance and orienteering decisions. The results show that inclusion of detailed reliability and multiple maintenance levels allows better maintenance and routing decisions. Numerical results also show trade-offs between reliability requirement, shift duration and total cost.

Optimization of Passenger-like Container Train Running Plan Considering Empty Container Dispatch

Railway container transportation plays an important role in the sustainable development of transportation. In order to improve the efficiency of container transportation and maximize the transportation revenue of railway enterprises, taking the passenger-like container train running plan as the research object, we established an optimization model. The model considers the transportation requirements of empty and heavy containers, aiming at the maximum revenue of railway transportation enterprises, the conservation of container flow, train stops, container reloading, and other constraints. It is a mixed-integer linear programming optimization model. First, the shortest path between nodes was solved by the Floyd algorithm as the candidate set of the train to be run, and then the particle swarm algorithm was designed to solve the model. Numerical experiments were carried out by taking a container network with 34 nodes as an example to verify the validity of the model and algorithm. The experimental results showed that when the minimum average loading rate of trains is 70%, 47 lines need to be run, which is 163 less than the candidate lines. The running cost of all trains is 31,901,200 yuan, and total revenue of the transportation enterprise is 10,930,568 yuan. Compared with the existing container transportation mode, the passenger-like container transportation mode has a higher average number of trains and faster velocity. However, it has a lower average loading rate and proportion of direct container flow. The results were compared in three different minimum average loading rate values: 50%, 60%, and 70%. It was found that with the increase of the minimum average loading rate of trains, the number of lines to be opened decreases, the cost of running decreases, and the revenue of transportation enterprises increases.

Design of a multi-user CO2 intermediate storage facility in the Grenland region of Norway

This paper describes a design and pre-feasibility study of a multi-user intermediate CO2 storage facility in the Grenland region of Norway, considering upstream and downstream issues. The study focuses on the principles for designing and installing a generic hub facility so that the results can be considered at other sites. The pre-feasibility study found that design pressures of 7 and 15 bar are feasible transport conditions; moreover, it showed that economies of scale might reduce the total cost for a CO2 network. It is recognised that cooperation across the chain is crucial in managing impurities due to the likely diverse sources of CO2. An intermediate storage facility can support the continuous supply of CO2 via a pipeline system for reservoir injection, improving the integrity of the injection well and equipment and the reservoir performance. A mixed-integer linear programming optimisation model has been developed for sizing and costing intermediate storage hubs of CO2 in Grenland and shipping connections between them and stationary emitters. The model considers an aggregated flow of 2 million tonnes per annum of CO2 for 30 years. The 7 bar design pressure has shown lower total costs when compared with the 15 bar scenario. This is due to the higher costs for shipping and intermediate storage when operating at higher pressure, which is larger than the cost reduction from liquefying CO2 to a higher pressure and higher temperature than those required for a 7 bar scenario. The estimated levelised costs were 21,6 € tonne−1 at 7 bar pressure and 27,8 € tonne−1 at 15 bar pressure.

Optimal design and sensitivity analysis of the stand-alone hybrid energy system with PV and biomass-CHP for remote villages

Reliable access to electricity is still a serious problem for remote villages, however, abundant solar radiation and biomass have the potentials to provide energy supply in a sustainable way. This paper focuses on the optimal design and techno-economic analysis of the stand-alone hybrid energy system for a typical rural village in the northwest of China. Based on the estimation of local renewable energy potential and the investigation of heat and power consumption patterns, a mixed-integer linear programming optimization model is presented with the aim of minimum total annualized cost. The techno-economic analysis of different system configurations is conducted and compared. Particularly, the levelized cost of energy production and levelized cost of energy consumption is proposed to evaluate the economic-cost of energy from both supply and demand-side respectively. Furthermore, sensitivity analysis and scenario analysis is conducted to demonstrate the influences of the variations and uncertain environmental policy on total system cost and performance. The results demonstrate that the PV/biomass-CHP/diesel generator/gas boiler/battery/thermal energy storage hybrid energy system is the most economical option with a total annualized cost of 652 × 103 $. The levelized cost of energy consumption (0.355 $/kWh) is greater than that of energy production (0.275 $/kWh), implying a great potential for local electrification and more flexible heat/power output equipment.

Optimization of a distributed energy system with multiple waste heat sources and heat storage of different temperatures based on the energy quality

Distributed energy systems (DESs) have garnered significant attention because of their flexibility and high efficiency. Owing to the diversity of user demand and the complex composition of the DES, the optimization of operation and planning for the entire system is complex. A mixed integer linear programming (MILP) model can be used to solve the optimization problem effectively. Different nonlinear factors should be considered and linearized in the model such that it is more accurate and practicalfor application. It is important to match waste heat recovery technologies (WHRTs) with various heat sources of different temperatures based on energy quality, which can improve efficiency of the entire system. Consequently, a new method is proposed herein to match multiple heat sources with various WHRTs and heat storage of different temperatures in the MILP optimization model. The optimization model can select the most suitable WHRTs, including their capacity for the DES, according to energy quality and user demand. Additionally, a one-year operating schedule of all the technologies can be optimized. The practicability of the method in real applications is validated by the dynamic simulation of waste heat distribution to different WHRTs. Hence, two cases are studied. One case indicates that the model can match the WHRTs with multiple heat sources of different temperatures with a short time needed to solve the optimization (22 s with a gap of 0.001%). The other case proves that the model can distinguish the energy qualities of low- and high-temperature heat storage, and that a 1189 kWh output cooling during a typical day is increased by high-temperature heat storage.

A novel fuzzy mathematical model for an integrated supply chain planning using multi-objective evolutionary algorithm

Due to the high competition in today’s global market, design of an efficient supply chain is necessary to achieve competitive advantages. Having concerned this issue, scheduling is one of critical concepts in supply chain management that leads to increase efficiency and customer satisfaction as well as decrease costs. Recently, build-to-order supply chain (BTO-SC) system has attracted considerable attention because of its successful implementation in high-tech companies such as Dell, BMW, Compaq, and Gateway. Despite several studies in the context of BTO-SC, there has been revealed several gaps that this study attempts to eliminate them. In this paper, a fuzzy mixed-integer linear programming optimization model is proposed for an integrated supply, production, and distribution supply chain of multi-product, multi-level, multi-plant. Because of uncertainty, imprecision and variability associated with real data, fuzzy approach is utilized for processing such information in modeling the problem. Usually, supply chain problems have conflicting objectives that should be optimized simultaneously. Thus, the proposed model aims to optimize customer satisfaction as well as chain supply costs, simultaneously. Due to high complexity and lack of proper benchmark for this problem, the model is solved by some popular multi-objective meta-heuristic algorithms. Also, Taguchi method is deployed to calibrate as well as control the parameters in four mentioned algorithms. Finally, a new framework is proposed for ranking of these algorithms use of fuzzy VIKOR method. The presented framework is an excellent comparison dashboard, and it is applicable not only for comparing multi-objective genetic algorithms but also for comparing all of multi-objective meta-heuristic algorithms.

Tackling the unique challenges of capacity planning for autologous cell therapies

<h3>Background & Aim</h3> Capacity planning has been a long-standing issue in the pharmaceutical industry; setting up Good Manufacturing Practices (GMP) compliant facilities is time-consuming and capital-intensive, but for products to be able to generate maximal economic returns during the market exclusivity period, timely availability of manufacturing capacity is vital. Capacity crunches faced by the monoclonal antibody (mAb) industry in the 1990s were estimated to have caused around $3-$4 billion losses in total revenue due to insufficient product supply. In addition, the uncertainties in clinical trial outcomes, market pressures, and regulations make the multi-objective optimisation of capacity planning and product development decisions critical for the industry. In this work, we present a detailed analysis of the above challenges, and propose to develop a mixed-integer linear programming optimisation model to address the unique challenges of autologous cell therapies. <h3>Methods, Results & Conclusion</h3> Previous studies have considered the optimisation of investment strategies for product development, manufacturing facility investment decisions and global multi-site supply chain optimisation for drugs and multi-site continuous bioprocess optimisation for biologics. As more advanced therapeutic medicinal products (ATMPs) move from bench to clinic, the unique challenges for autologous cell therapies present a new problem in the capacity planning domain. Firstly, the unique requirement for autologous cell therapies to be produced on-demand with cell material originating from patients has proven to be commercially challenging. Secondly, with geographical and supply chain constraints, companies are considering building multiple facilities in different regions or finding alternative arrangements such as licensing and outsourcing. Thirdly, fast-track regulatory frameworks introduced by various regulatory authorities are improving the speed-to-market and have allowed faster commercialisation of ATMPs for life-threatening diseases. The clinical development duration can be reduced from 6-7 years (phase 1, phase 2, phase 3 clinical trial) to 2-3 years (small scale clinical trials with surrogate end-points). Therefore, the commercialisation timeline for process, CMC development, and capacity planning decisions should also be considered earlier. The approach can potentially allow the industry to make better-informed investment decisions and accelerate the commercialisation of these life-saving therapies.

Three-stage design of high-resolution microalgae-based biofuel supply chain using geographic information system

This research suggests a three-stage model framework for the design of a microalgae-based biofuel supply chain to meet the goal of economic commercialization. First, the design stage decides the spatial layouts and dimensions of each scale of biorefineries and economic analyses are done to estimate the capital costs and operating costs for different design options. Using the spatial dimensions determined in the first stage, the second stage selects the candidate locations for the biorefineries using an geographic information system (GIS) based site evaluation. This stage screens the available land area for the biorefineries, and also reduces the computational burden of the latter stage. In the mathematical optimization stage, a mixed-integer linear programming optimization model is formulated to make multi-period strategic and tactical decisions of the supply chain under the total cost minimization objective. Since the formulated problem is computationally intensive, a two-stage decomposition solution strategy is proposed to solve the problem in a reasonable time. The model framework is demonstrated through a case study cast in Texas, U.S., with a time horizon of ten years, using the suggested decomposition method. As a result, the minimum fuel selling price (MFSP) of microalgae-based biodiesel is calculated as $10.92/galbiodiesel, which is about three times higher than the current biodiesel price $3.51/galbiodiesel. To reduce the cost, the strategies of biomass storage and maximum delivery are investigated to deal with the productivity fluctuation. In the scenario analysis, the underutilization of production capacities is alleviated resulting in reduced MFSP of $7.90/galbiodiesel, $7.92/galbiodiesel, and $7.43/galbiodiesel respectively. Clearly, for economic feasibility, the production cost should be further reduced by developing more cost-efficient technologies and integrating high-value coproducts into the biorefinery portfolio.

Reforming the Operation Mechanism of Chinese Electricity System: Benefits, Challenges and Possible Solutions

A new wave of electricity market reform was launched by the Chinese government in March 2015, and one of its major objectives was to optimize the power system operation by reforming the low-efficient equal share dispatch mechanism. To provide scientific decision-making support for the current reform, we establish a mixed-integer linear programming optimization model to simulate the post-reform results, and the reform benefits are subsequently estimated by comparing those results with the pre-reform results. Then, we develop a political economy framework to identify the challenges associated with implementation of economic dispatch. At last, we propose several regulatory and market measures to address these identified challenges.

A MILP optimization model for assessing the participation of distributed residential PV-battery systems in the ancillary services market

A novel non-linear stochastic method based on a Mixed-Integer Linear Programming (MILP) optimization model is proposed to optimally manage a high number of photovoltaic (PV)-battery systems for the provision of up and down regulation in the ancillary services market. This method, considers both the technical constraints of the power system, and those of the equipment used by all the prosumers. This allows an aggregator of many residential prosumers endowed with photovoltaic (PV)- battery systems to evaluate the baseline of the aggregate by minimizing the costs related to the electrical energy absorbed from the grid and then to assess the up and down flexibility curves with relative offer prices. As confirmed by simulation results carried out considering different realistic case studies, the method can effectively be used by an aggregator to evaluate the economic impact of its participation in the ancillary services market, both for the aggregator and for its prosumers.

A mixed-integer linear programming optimization model framework for capturing expert planning style in low dose rate prostate brachytherapy

Low dose rate (LDR) brachytherapy is a minimally invasive form of radiation therapy, used to treat prostate cancer, and it involves permanent implantation of radioactive sources (seeds) inside of the prostate gland. Treatment planning in brachytherapy involves a decision making process for the placement of the sources in order to deliver an effective dose of radiation to cancerous tissue in the prostate while sparing the surrounding healthy tissue. Such a decision making process can be modeled as a mixed-integer linear programming (MILP) problem. In this paper, we introduce a novel MILP optimization model framework for interstitial LDR prostate brachytherapy designed to explicitly mimic the qualities of treatment plans produced manually by expert planners. Our approach involves incorporating a unique set of clinically important constraints, called spatial constraints, into the optimization model. Computational results for an initial model reflecting clinical practice at our cancer center show that the treatment plans produced largely capture the spatial and dosimetric characteristics of manual plans created by expert planners.

Profitability of active retrofitting of multi-apartment buildings: Building-attached/integrated photovoltaics with special consideration of different heating systems

Multi-apartment buildings comprise almost half of the European housing stock and are for the most part old and energy inefficient, making active retrofitting an important topic. The objective of this paper is to determine the profitability and optimal size of different technology portfolios for renewable building energy. A mixed-integer linear programming optimisation model is developed in Matlab with the objective of maximising the Net Present Value over a time horizon of 20 years. To examine multiple use cases, a modular approach is used for realising different multi-apartment building set-ups. Building-attached and building-integrated photovoltaic systems on different parts of the building skin already achieve break-even. Heat pumps, pellet and district heating can hardly compete with gas heating yet. However, heat pumps have synergy effects with PV systems, thus reinforcing their implementation, as does a tenant portfolio with a good correlation with the sunshine hours. The profitability gap between investment costs for passive building renovation and resulting energy cost savings is significant. However, it is the smallest for buildings with quality standards. In conclusion, governmental subsidies and financial incentives such as the true cost pricing of CO2 emissions are necessary to trigger investments in reasonable combinations of passive and active retrofitting measures.