Linear Programming Approach Research Articles

Integrating Energy Generation and Demand in the Design and Operation Optimization of Energy Communities

The optimization of the energy system serving users’ aggregations at urban level, such as Energy Communities, is commonly addressed by optimizing separately the set of energy conversion and storage systems from the scheduling of energy demand. Conversely, this paper proposes an integrated approach to include the demand side in the design and operation optimization of the energy system of an Energy Community. The goal is to evaluate the economic, energetic, and environmental benefits when users with different demands are aggregated, and different degrees of flexibility of their electricity demand are considered. The optimization is based on a Mixed-Integer Linear Programming approach and is solved multiple times by varying (i) the share of each type of user (residential, commercial, and office), (ii) the allowed variation of the hourly electricity demand, and (iii) the maximum permitted CO2 emissions. Results show that an hourly flexibility of up to 50% in electricity demand reduces the overall system cost and the amount of energy withdrawn from the grid by up to 25% and 31%, respectively, compared to a non-flexible system. Moreover, the aggregation of users whose demands match well with electricity generation from renewable sources can reduce CO2 emissions by up to 30%.

Optimizing Multi-Echelon Delivery Routes for Perishable Goods with Time Constraints

As the logistics industry modernizes, living standards improve, and consumption patterns shift, the demand for fresh food continues to grow, making cold chain logistics for perishable goods a critical component in ensuring food quality and safety. However, the presence of both soft and hard time windows among demand nodes can complicate the single-network distribution of perishable goods. In response to these challenges, this paper proposes an optimization model for multi-distribution center perishable goods delivery, considering both one-echelon and two-echelon network joint distributions. The model aims to minimize total costs, including transportation, fixed, refrigeration, goods damage, and penalty costs, while measuring customer satisfaction by the start time of service at each demand node. A two-stage heuristic algorithm is designed to solve the model. In the first stage, an initial solution is constructed using a greedy approach based on the principles of the k-medoids clustering algorithm, which considers both spatial and temporal distances. In the second stage, the initial routing solution is optimized using a linear programming approach from the Ortools solver combined with an Improved Adaptive Large Neighborhood Search (IALNS) algorithm. The effectiveness of the proposed model and algorithm is validated through a case study analysis. The results demonstrate that the initial solutions obtained through the k-medoids clustering algorithm based on spatio-temporal distance improved the overall cost optimization by 1.85% and 4.74% compared to the other two algorithms. Among the three two-stage heuristic algorithms, the Ortools-IALNS proposed here showed enhancements in the overall cost optimization over the IALNS, with improvements of 3.24%, 1.12%, and 0.41%, respectively. The two-stage heuristic algorithm designed in this study also converged faster than the other two heuristic algorithms, with overall optimization improvements of 1.55% and 1.28%, further validating the superior performance of the proposed heuristic algorithm.

A regression based approach to phylogenetic reconstruction from multi-sample bulk DNA sequencing of tumors.

DNA sequencing of multiple bulk samples from a tumor provides the opportunity to investigate tumor heterogeneity and reconstruct a phylogeny of a patient's cancer. However, since bulk DNA sequencing of tumor tissue measures thousands of cells from a heterogeneous mixture of distinct sub-populations, accurate reconstruction of the tumor phylogeny requires simultaneous deconvolution of cancer clones and inference of ancestral relationships, leading to a challenging computational problem. Many existing methods for phylogenetic reconstruction from bulk sequencing data do not scale to large datasets, such as recent datasets containing upwards of ninety samples with dozens of distinct sub-populations. We develop an approach to reconstruct phylogenetic trees from multi-sample bulk DNA sequencing data by separating the reconstruction problem into two parts: a structured regression problem for a fixed tree [Formula: see text], and an optimization over tree space. We derive an algorithm for the regression sub-problem by exploiting the unique, combinatorial structure of the matrices appearing within the problem. This algorithm has both asymptotic and empirical improvements over linear programming (LP) approaches to the problem. Using our algorithm for this regression sub-problem, we develop fastBE, a simple method for phylogenetic inference from multi-sample bulk DNA sequencing data. We demonstrate on simulated data with hundreds of samples and upwards of a thousand distinct sub-populations that fastBE outperforms existing approaches in terms of reconstruction accuracy, sample efficiency, and runtime. Owing to its scalability, fastBE enables both phylogenetic reconstruction directly from indvidual mutations without requiring the clustering of mutations into clones, as well as a new phylogeny constrained mutation clustering algorithm. On real data from fourteen B-progenitor acute lymphoblastic leukemia patients, fastBE infers mutation phylogenies with fewer violations of a widely used evolutionary constraint and better agreement to the observed mutational frequencies. Using our phylogeny constrained mutation clustering algorithm, we also find mutation clusters with lower distortion compared to state-of-the-art approaches. Finally, we show that on two patient-derived colorectal cancer models, fastBE infers mutation phylogenies with less violation of a widely used evolutionary constraint compared to existing methods.

Mixed Marginal Rates of Substitution for Analyzing Banking Efficiency Using a Linear Programming Approach

This paper introduces a Mixed Marginal Rates of Substitution (MMRS) approach for analyzing banking efficiency within a linear programming framework. For this purpose, a linear programming model is proposed that efficiently calculates Marginal Rates, revealing how partial input changes affect multiple outputs simultaneously. Applying this methodology to data from the Taiwanese banking system spanning 2010 to 2020 reveals diverse efficiency patterns across financial institutions. The analysis demonstrates that while increased financial inputs generally improve outputs, individual banks exhibit varying sensitivity to these changes. Some institutions were resilient to input fluctuations, while others showed marked sensitivity, particularly in loans and investments. As a result, the proposed MMRS framework provides a robust tool for analyzing indicator relationships within efficient units, offering valuable insights for tailored management strategies and policy formulation in the banking sector. The findings emphasize the importance of institution-specific approaches to enhancing banking efficiency and managing risk effectively, contributing to a more nuanced understanding of economic outcomes in the financial industry. Additionally, symmetry concepts in input–output relationships are suggested as a potential area for future research, offering a possible framework for identifying balanced efficiency patterns among banks.

A novel linear programming-based predictive control method for building battery operations with reduced cost and enhanced computational efficiency

Battery energy storage systems can be readily integrated with buildings to enhance renewable energy self-consumptions while leveraging time-variant electricity tariffs for possible operation cost reductions. The extensive variability in building operating conditions presents significant challenges in developing universally applicable methods for optimal controls. To ensure reliable and robust controls, this study integrates predictive control with efficient linear programming to effectively fine-tune battery controls for real-time operations. An adaptive time aggregation scheme has been proposed to streamline the optimization process by accounting for unique changes in energy balances and tariffs. Comprehensive data experiments, based on measurements from 95 unique building operation scenarios, have been conducted to quantify the control performance given different optimization formulations, varying types and levels of prediction uncertainties in building energy demands and PV generations. The results validate the value of the method proposed, leading to 11.75% to 34.63% operation cost reductions on average, while reducing computation steps by 87.75% to 92.60% compared with conventional linear programming approaches. The insights obtained are useful for developing flexible building control strategies with improved computation efficiency and robustness, while providing extensible optimization frameworks for buildings with various energy patterns and storage systems.

Graph topology-constrained BILP for optimal PMU placements

In the monitoring and control of power systems, the deployment of Phasor Measurement Units (PMUs) is of paramount importance, yet their high installation costs have limited their widespread application. To address this issue, this paper proposes an innovative method based on graph topology constraints, known as the Graph Topology-constrained Binary Integer Linear Programming (GT-BILP) approach, aimed at achieving the optimal configuration of PMUs. This method not only takes into account cost-effectiveness but also ensures the complete observability of the system. By quantifying the contribution of each node and bus to the system's observability within the network, a novel contribution matrix is constructed. This matrix integrates the dynamic characteristics of network topology and information flow, providing precise decision support for the deployment of PMUs. By combining the matrix with the network's planning model, the GT-BILP model is obtained, which can effectively solve the PMU layout requirements for large power grids. For the special case of zero-injection buses (ZIBs), the Topology Transformation algorithm has been improved, significantly enhancing the solution efficiency and quality. Through simulation experiments on multiple IEEE standard test systems, the effectiveness and superiority of the proposed GT-BILP model have been verified. This research is of significant importance for improving the monitoring and control capabilities of power systems and provides a new perspective for technological advancement in this field.

Integrating Energy-Efficient Train Control in railway Vertical Alignment Optimization: A novel Mixed-Integer Linear Programming approach

Incorporating train control into the railway design process enables a practical and comprehensive evaluation of the lifecycle utility of a track profile. This paper proposes a novel integrated approach, termed EETC-VAO, which combines railway track Vertical Alignment Optimization (VAO) and Energy-Efficient Train Control (EETC). Initially formulated as a Mixed-Integer Nonlinear Programming (MINLP) problem, EETC-VAO aims to meet various geometric constraints and simultaneously minimize construction costs, traction energy consumption, and section running times in both directions. The model is subsequently reformulated into an equivalent Mixed-Integer Linear Programming (MILP) model using linearization methods and is further enhanced with valid inequalities, logic cuts, and a warm start algorithm with random velocity generation. The model has been extensively tested across a variety of case studies and train types, from synthetic small-scale scenarios to challenging real-world cases spanning from 3 to 71.2 km. Our findings demonstrate that operational costs can be significantly reduced with only marginal increases in construction costs. The integrated approach achieves reductions in total lifecycle costs of up to 40%, revealing a critical trade-off between construction and operational expenses. Notably, our results also indicate that lower construction costs do not inherently conflict with reduced operational costs, emphasizing the critical importance of integrating the train control scheme into the VAO problem.

Phasor estimation using micro-phasor measurement unit (μPMU) in distribution network for situational awareness

Phasor estimation plays a critical role in island detection, fault detection, voltage stability monitoring, and state estimation within power systems. This paper proposes a phasor estimation method using micro-Phasor Measurement Units (µPMUs) in a Smart Distribution Network. A µPMU model is developed utilizing a recursive Discrete Fourier Transform (DFT) algorithm combined with high-precision filters to enhance accuracy. The optimal placement of µPMUs in the distribution network is determined using a Mixed-Integer Linear Programming (MILP) approach for the IEEE 33 bus test system. The model is tested on the IEEE 33 bus system with Electric Vehicle Charging Stations (EVCS) and Distributed Generators (DGs) under both nominal and off-nominal frequencies. The results comply with the IEEE C37.118.1 standard, achieving phasor magnitude errors as low as + 0.01% and frequency accuracy of 1 mHz with minimal ripple. This study demonstrates the robustness and precision of the µPMU model, highlighting its potential for enhancing real-time monitoring and control in smart grid applications.

Overview and advancement of power system topology addressing pre- and post-event strategies under abnormal operating conditions

The transition towards increased utilization of renewable energy and electric vehicles (EVs), along with the growing use of various other electrical devices, poses challenges to the stable and resilient operation of electric power systems (EPS), especially in the face of natural phenomena associated with climate change. This means that accurate topology and balanced EPS plays a key role to increase the capacity to respond quickly and in a coordinated manner to disaster situations such as cyber-attacks, earthquakes and floods. In this study, a new approach is presented to quickly and accurately detect topology attacks in EPS, thus contributing to making safer and more resilient. The proposed methods provide insights into maintaining uninterrupted electricity service by enabling EPS management through both post- and pre-event operational strategies. This approach is created by identifying faulty points with the obtained topology information and creating microgrid (MG) groups. Machine learning techniques have been integrated into the data intrusion attack detection (DIAD) system, enabling the detection of manipulated or faulty smart meters (SM). Concurrently, a topology identification (TI)-based graph learning algorithm is propounded to determine the exact fault locations before and after the event. For MV region restoration after determining the TI region, a mixed-integer linear programming (MILP) approach is employed to optimize the load restoration process in the MG regions. This approach aims to minimize losses and restore critical loads to their previous state as quickly as possible using flexible and emergency power balancing systems, including grid-support storage systems (GSSs), photovoltaic systems (PVs), electric vehicle charging stations (EVCS), and mobile generators. Moreover, a detailed compilation is presented under the topics of EPS topology, phase identification (PI) and its effect on power system resiliency (PSR), shedding light on the future development of EPS.

An Integrated Stochastic Optimization and Simulation Approach to SERU vs. Assembly Line Manufacturing Systems

This research compares SERU manufacturing systems to traditional assembly lines, focusing on the impact of uncertainty in task processing time on production output. The study considers worker skill levels and team identity, using a stochastic mixed integer linear programming approach to model uncertainty and optimize workforce allocation. Discrete event simulation is then integrated to evaluate performance using five key performance indicators (KPIs). Results show that SERU systems outperform traditional lines in terms of throughput when uncertainty is considered. The integrated approach provides more reliable performance data than deterministic optimization alone. The study also highlights the advantages of SERU systems when worker skill levels and team identity are factored in. This research fills a gap in the literature by proposing a stochastic optimization approach that considers uncertainty and worker skill levels, and by integrating stochastic optimization with simulation for comprehensive analysis. This approach provides valuable guidance for production managers in optimizing production systems.

Multi-period optimisation of flexible natural gas production network infrastructure with an operational perspective: A mixed integer linear programming approach

With the increased complexities in end markets, advanced quantitative tools became essential for efficient decision-making. Traditional methods that implement average forecasted demand and prices often fail to account for the dynamic nature of network behaviour. Hence, this study introduces a multi-period mixed integer linear programming (MILP) model for flexible natural gas allocation in complex networks. The model was formulated based on Qatar as a case study, utilising a Qatar-based natural gas monetisation network that includes four direct and two indirect monetisation processes. By integrating flexible operational boundaries with annual demand and price forecasts, the model optimises annual allocation strategies to maximise profitability. A scenario-based evaluation of three cases demonstrated the model’s robustness and potential for enhancing profitability. Scenarios limited to operational constraints achieved the highest profitability, especially in allocating high-value commodities such as ammonia and urea. However, the proposed production capacities surpass the current infrastructure capabilities, requiring further infrastructure investments. The validation of results showed a slight profitability decrease of 1.2% when these investment costs were included. Notably the case considering fixed and operating cost variables together as a single cost variable in the objective function, referred to as annualised cost (case C), offered optimal cost quantification with relaxed technical constraints. Overall, the multi-level multi-period MILP model aids decision-makers in understanding system capabilities and explores the benefits of flexible operation in proactively addressing endogenous and exogenous uncertainties.

Improving energy efficiency and fault tolerance of mission-critical cloud task scheduling: A mixed-integer linear programming approach

Cloud services have become indispensable in critical sectors such as healthcare, drones, digital twins, and autonomous vehicles, providing essential infrastructure for data processing and real-time analytics. These systems operate across multiple layers, including edge, fog, and cloud, requiring efficient resource management to ensure reliability and energy efficiency. However, increasing computational demands have led to rising energy consumption and frequent faults in cloud data centers. Inefficient task scheduling exacerbates these issues, causing resource overutilization, execution delays, and redundant processing. Current approaches struggle to optimize energy consumption, execution time, and fault tolerance simultaneously. While some methods offer partial solutions, they suffer from high computational complexity and fail to effectively balance the workloads or manage redundancy. Therefore, a comprehensive task scheduling solution is needed for mission-critical applications. In this article, we introduce a novel scheduling algorithm based on Mixed Integer Linear Programming (MILP) that optimizes task allocation across edge, fog, and cloud environments. Our solution reduces energy consumption, execution time, and failure rates while ensuring balanced distribution of computational loads across virtual machines. Additionally, it incorporates a fault tolerance mechanism that reduces the overlap between primary and backup tasks by distributing them across multiple availability zones. The scheduler’s efficiency is further enhanced by a custom-designed heuristic, ensuring scalability and practical applicability. The proposed MILP-based scheduler demonstrates significant average improvements over the best state-of-the-art algorithms evaluated. It achieves a 9.63% increase in task throughput, reduces energy consumption by 18.20%, shortens execution times by 9.35%, and lowers failure probabilities by 11.50% across all layers of the distributed cloud system. These results highlight the scheduler’s effectiveness in addressing key challenges in energy-efficient and reliable cloud computing for mission-critical applications.

Balancing Cost and Environmental Impact: A Linear Programming Approach to Sustainable Shopping

A linear programming model is devised for consumer purchasing decisions minimizing weighted cost and environmental impact using real-world data. Minor shifts towards environmental preferences can greatly reduce impact with minimal cost increase. Spending slightly more on the bundle than the cheapest option can cut environmental impact by a third. Conversely, less than 10% compromise in impact yields over 15% cost savings. Consumers can find efficient midpoints—cost-effective and environmentally sustainable options—through strategic decisions. Additionally, a synthetic dataset, modeling different societal dispositions through Beta distributions of cost-environment orientation parameters, simulates societal attitudes, showing that a 10% reduction in environmental impact is possible with a 23% higher economic burden, while 60% of this reduction can be achieved with only 3.1% increase in cost when maintaining a balanced societal disposition. This demonstrates the potential of optimization-based strategic purchasing decisions to achieve significant economic and environmental efficiencies when accompanied by increased environmental awareness.

Optimizing Transportation Logistics for Cost Efficiency in a Garment Factory: A Linear Programming Approach Using LINDO

The garment industry in Bangladesh plays a pivotal role in the nation's economy, yet it faces significant challenges in optimizing transportation logistics to minimize costs and enhance efficiency. This paper uses linear programming techniques to negotiate the optimization of transportation logistics in a garment factory located in Gazipur, Bangladesh. The primary objective is to develop an optimized transportation plan that reduces costs while satisfying supply and demand constraints across multiple suppliers, production facilities, and distribution centers. The study formulates the transportation problem as a linear programming model and employs the simplex method to determine the optimal solution. LINDO software is utilized for model implementation and optimization. The model incorporates real data from the garment factory, including supply capacities, demand requirements, and transportation costs. Results from the LINDO optimization reveal a detailed transportation plan that minimizes total transportation costs, demonstrating significant cost savings compared to existing practices. The optimized plan improves operational efficiency and provides a robust decision-support tool for logistics managers. Sensitivity analysis is conducted to ensure the model's robustness under varying conditions. The methodologies and findings are scalable and adaptable to other industrial settings, offering valuable insights for enhancing logistical efficiency in the garment industry. The study also highlights potential areas for future research, including integrating environmental considerations and advanced optimization techniques. Through this research, the garment factory in Gazipur can achieve substantial cost reductions and operational improvements, enhancing its competitiveness in the global market.

Reallocation of chemotherapy appointments in a large health system using a mixed integer linear programming approach

ABSTRACT Outpatient chemotherapy scheduling has significant implications for both patients and health systems. Consideration of treatment location preference is important for patient satisfaction and outcomes, and it is a complex decision impacted by travel distance. In health systems with one treatment site that stands out from the rest as a destination medical center (the primary site), there are financial and resource utilization incentives to free up as much space as possible for appointments at that site. In this study, we demonstrate that leveraging the underutilized health system sites allows decompression of appointment volume at the primary site, and it takes full advantage of valuable resources such as oncology nurses and chair availability. A Mixed Integer Linear Programming approach was used to develop a model under four scenarios which reallocates appointments from the primary site to other health system sites based on patient travel distance to the sites. This approach was applied to data from the Mayo Clinic Health System Minnesota region, which demonstrated that the health system has the potential to move approximately 50% of eligible appointments out of the primary site, resulting in an overall volume change of approximately 30%. Implications for scheduling policies and infrastructure are discussed.

Optimization of the electric vehicle charging strategy problem for sustainable intercity travels with multiple refueling stops

Electric vehicle (EV) drivers considering long-distance trips still face range anxiety due to the limited range of EVs and the scarcity of charging stations. Thus, it becomes important to ensure the feasibility of the selected route and determine an optimal charging strategy. As a crucial aspect of decision support for EV drivers, this study proposes a mixed integer linear programming (MILP) approach for the EV charging strategy problem (EVCSP), incorporating a piecewise linear approximation technique to address the challenges posed by nonlinear charging times. The proposed optimization model, namely CSPM determines where, when, and how much to charge an EV for a specified route to minimize travel time and cost. The solution time of large-scale test problems and a case study on Türkiye reveal the robustness and reliability of the CSPM. Furthermore, two multi-objective optimization methods (the weighted sum and the lexicographic method) are applied to the case study, and the results are analyzed. The results indicate that the travel cost is more sensitive to the selected charging strategy, with a range of 46.09 % across the applied charging strategies, whereas travel time remains more resilient, with a maximum fluctuation of 19.77 %. A comparative analysis with a full charging strategy reveals that the CSPM reduces the travel time by 60.1 % and improves the cost efficiency by 105.72 %.

Optimisation of Ammonia Production and Supply Chain from Sugarcane Ethanol and Biomethane: A Robust Mixed-Integer Linear Programming Approach

Optimisation of Ammonia Production and Supply Chain from Sugarcane Ethanol and Biomethane: A Robust Mixed-Integer Linear Programming Approach

Stability of optimal spherical codes

For many extremal configurations of points on a sphere, the linear programming approach can be used to show their optimality. In this paper we establish the general framework for showing stability of such configurations and use this framework to prove the stability of the two spherical codes formed by minimal vectors of the lattice E8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_8$$\\end{document} and of the Leech lattice.

Multi-Horizon Model Predictive Control for Energy Management in Zero-Emission High-Speed Passenger Vessels

Abstract High-speed passenger vessels (HSPVs) play an important role in coastal regions due to their high energy consumption and emissions. This study develops an optimal energy management system (EMS) for a zero-emission hybrid power system, powered by a fuel cell (FC) and a battery energy storage system (BESS). The global optimal solution for loading the FC and operating the BESS is computed using a linear programming (LP) approach, assuming a priori knowledge of the complete operational profile. Since the global solution is not realizable in an onboard EMS, the main objective of this paper is to develop an algorithm for real-time application. A multi-horizon model predictive control (MH-MPC) algorithm is applied to a model of the power system to solve the optimization problem with a prediction mechanism over the entire route. This approach is benchmarked against the global LP solution to evaluate the effectiveness of the proposed EMS. The results highlight the potential of the MH-MPC approach for achieving a near-optimal EMS in a zero-emission HSPV.

A Linear Genetic Programming Approach for the Internet Shopping Optimization Problem with Multiple Item Units (ISHOP-U)

A Linear Genetic Programming Approach for the Internet Shopping Optimization Problem with Multiple Item Units (ISHOP-U)