Mixed-integer Linear Programming

Copyright © 2013 John Moussourakis, Cengiz Haksever. This is an open access article distributed under the Creative Commons Attri-bution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. One of the most important responsibilities of a supply chain manager is to decide “how much ” (or “many”) of inventory items to order and how to transport them. This paper presents four mixed-integer linear programming models to help supply chain managers make these decisions for multiple products subject to multiple constraints when suppliers offer quantity discounts and shippers offer freight discounts. Each model deals with one of the possible combinations of all-units, incremental quantity discounts, all-weight and incremental freight discounts. The models are based on a piecewise linear approximation of the number of orders function. They allow any number of linear constraints and de-termine if independent or comm...

The Indian share market has experienced substantial growth during 2025-2026 due to increased retail participation, digital trading infrastructure, foreign institutional investments, and rapid expansion in technology-driven industries. Portfolio optimization in such a volatile and diversified market environment requires mathematically rigorous models capable of incorporating realistic trading restrictions and sectoral dynamics. This study develops a mixed-integer linear programming (MILP) framework for portfolio optimization using current data from the National Stock Exchange (NSE) of India. Unlike traditional continuous portfolio models, the proposed framework incorporates practical financial constraints including integer share purchases, transaction costs, sectoral diversification, budget limitations, and exposure control across multiple industries. The analysis considers major Indian blue-chip companies from diversified sectors including information technology, banking, energy, automobile, pharmaceuticals, telecommunications, and infrastructure. Current market data from Reliance Industries, Tata Consultancy Services (TCS), Infosys, HDFC Bank, ICICI Bank, Larsen & Toubro, Sun Pharma, Bharti Airtel, and Tata Motors are utilized for comparative analysis. 1 Computational results demonstrate that the MILP approach generates practically implementable portfolios while maintaining balanced sectoral exposure and controlled investment risk. The results further reveal that the information technology and banking sectors continue to dominate expected returns during 2025-2026, whereas energy and pharmaceutical sectors provide portfolio stability under market uncertainty.

Decarbonizing biomethane facilities demands integrated electricity-heat strategies respecting land constraints. This study presents the first optimization framework integrating bifacial agrivoltaic systems with anaerobic digestion plants for biomethane production, addressing a critical gap in renewable energy system design. A multi-objective genetic algorithm coupled with Technique for Order Preference by Similarity to Ideal Solution ranking methodology was developed to simultaneously optimize economic performance and land utilization across three distinct agrivoltaic configurations including fixed vertical, 1-axis, and 2-axis tracking systems. The framework evaluates eight scenarios encompassing on-grid agrivoltaic systems with various heating technologies (biogas boilers, groundwater heat pumps, and biogas combined heat and power units), alongside benchmark alternatives including standalone combined heat and power unit (baseline), grid-dependent systems (without agrivoltaics), and off-grid agrivoltaic configurations. Results demonstrate that the on-grid 1-axis agrivoltaic system integrated with groundwater heat pump achieves superior techno-economic performance, delivering a net present value of 2.88 M€, representing a 4.1-fold improvement over conventional combined heat and power baseline systems. This configuration maximizes biomethane sales by electrifying thermal demands, avoiding biogas combustion and capitalizing on favorable biomethane-to-electricity price ratios. Heat pump electrification strategies consistently outperform biogas-combustion strategies (boiler or combined heat and power) in net present value, achieving up to 8.7 times higher performance through strategic biogas preservation for upgrading within the primary scenarios. Comparative analysis confirms the superior techno-economic and spatial performance of optimized on-grid systems, with 9.17-11.23 M€ higher net present value and 17-20 times lower land occupation than off-grid alternatives. Sensitivity analysis confirms the consistent superiority of on-grid 1-axis agrivoltaic systems paired with heat pumps, reflecting robust trade-offs between energy yield, cost, and land priorities. The developed framework offers a versatile approach for integrating renewable energy in agricultural systems, promoting a sustainable energy transition while maintaining agricultural productivity.

The emergence of electric vertical take-off and landing (eVTOL) aircraft—commonly
termed “flying cars”—operated by firms such as Joby Aviation and Archer Aviation introduces a novel class of fleet management problem that existing airline operations research
frameworks address only partially. Classical fleet assignment models, originally developed
for fixed-wing hub-and-spoke carriers, must be substantially extended to accommodate the
point-to-point, high-frequency, and geographically diffuse structure of eVTOL networks.
This paper formulates a master Mixed-Integer Linear Program (MILP) for global eVTOL
fleet management, integrating four coupled sub-problems: fleet assignment, vehicle routing,
charging infrastructure scheduling, and crew allocation. We define the index sets, decision
variables, and constraint families in full, derive a compact objective function that balances
revenue maximization against operational cost, and discuss the tractability of the resulting
formulation under realistic network sizes. Decomposition strategies—specifically Benders
decomposition and Lagrangian relaxation—are identified as the primary solution pathways.
The model is designed to be directly falsifiable against emerging operational data from
FAA-conforming eVTOL test programs.

In semiconductor manufacturing, furnaces are used for diffusion and deposition operations. A furnace is a batch processing machine, which can simultaneously process a number of lots together as a batch. Whenever a furnace becomes available, scheduling the next batch involves decisions on both which operation to process next (dispatching policy) and how many lots to put into the batch (loading policy). A simulation model of a wafer fabrication facility is used to examine the effects of different loading and dispatching policies for diffusion operations. Results indicate that the loading policy has a significant effect on the average diffusion flow time as well as the overall cycle time of the products, whereas dispatching policy has a less significant effect. We show that the production volume of a product should be considered in setting the minimum number of lots needed to start a batch. We suggest that the diffusion flow time for a low volume product can be reduced by releasing the product in batches or by setting the minimum batch size such that the work-in-process of the product can be moved faster.

The ratio of Earth's mean diameter to the Moon's mean diameter converges to approximately 108-a value that recurs independently across cosmological measurement, ancient calendrical systems, and biological constants. We propose this ratio is not coincidental but geometrically embedded: it represents a gravitational configuration that produces three simultaneous conditions favorable to biological complexity. We formalize these conditions as a falsifiable framework for ranking exoplanetary candidates by biological complexity potential, apply it to the NASA Exoplanet Archive, and identify three primary candidates for targeted biosignature observation: Kepler-62 e, Kepler-62 f, and Kepler-22 b. We further propose the Hill sphere radius as a tractable proxy for moon-stabilization potential when direct moon observation is unavailable. The framework generates specific, testable predictions about the relationship between planet/moon geometry and biosignature complexity detectable by current and near-future instrumentation. We further develop a communication protocol-pause-MILP-which proposes that the universal substrate for interstellar communication is not content but operation: the act of pausing to optimize under constraint, which any sufficiently advanced civilization must perform. The protocol collapses the Arecibo content-transmission problem and produces a structurally cooperative signal whose round-trip handshake does not require iterative dialog.

Call control features (e.g., call-divert, voice-mail) are primitive options to which users can subscribe off-line to personalise their service. The configuration of a feature subscription involves choosing and sequencing features from a catalogue and is subject to constraints that prevent undesirable feature interactions at run-time. When the subscription requested by a user is inconsistent, one problem is to find an optimal relaxation, which is a generalisation of the feedback vertex set problem on directed graphs, and thus it is an NP-hard task. We present several constraint programming formulations of the problem. We also present formulations using partial weighted maximum Boolean satisfiability and mixed integer linear programming. We study all these formulations by experimentally comparing them on a variety of randomly generated instances of the feature subscription problem.

Supply chain network design aims at the integration of the different actors of a supply chain within a single framework in order to optimize the total profit of the system. In this paper, we consider the integration of line balancing issues within the tactical decisions of the supply chain, and we offer a novel model and a solution approach for the problem. The new approach decomposes the problem into multiple line balancing problems and a mixed-integer linear model, which is easier to solve than the previously available nonlinear mixed-integer formulation. The results show that the new method is able to solve previously studied models within a fraction of the previously reported running times, and also allows us to solve larger instances than those reported by previous works. Finally, we also provide some analysis on the influence of the cost structure, the demand, and the structure of the assembly process on the final configuration of the assemblies and the distribution network.

Renewable energy technologies are becoming more and more relevant in a variety of engineering fields as a result of the move toward low-carbon, sustainable energy systems. Although research has historically concentrated on power generation, it now covers a broad range of applications, including precision agriculture, smart grids, energy storage, healthcare devices, and sustainable buildings. However, existing review studies are often limited to single disciplines or specific technologies, lacking a unified cross-disciplinary perspective that captures the interconnected nature of modern renewable energy systems. This gap motivates the need for a comprehensive review that bridges multiple engineering domains. This review provides a comprehensive synthesis of literature on renewable energy applications in electrical and electronics, computer, environmental, biomedical, architectural, and agricultural engineering. In electrical and electronics engineering, the use of renewable energy sources is largely based on the efficient generation of electricity from natural resources such as solar, wind, and ocean energy. Computer engineering contributes through artificial intelligence (AI), Internet of Things (IoT) architectures, digital twins, and cybersecurity solutions, optimizing energy management. Environmental engineering emphasizes life cycle assessment, carbon footprint reduction, and circular economy strategies. In biomedical engineering, energy harvesting and self-powered devices illustrate micro-scale applications of renewable energy. Architectural engineering integrates renewable systems through building-integrated photovoltaics, net-zero energy designs, and smart building management, while agricultural engineering uses solar-powered irrigation, biomass utilization, agrivoltaic systems, and other sustainable practices. To support a low-carbon future with integrated and sustainable engineering solutions, this study not only highlights innovations within individual fields but also showcases how different disciplines can connect and work together. Overall, the review offers a novel cross-disciplinary framework that advances the understanding of renewable energy systems beyond isolated applications and provides direction for future integrative research.

Electric vehicles (EVs) and distributed generation (DG) based on renewable energy sources (RES), mainly solar photovoltaics (PV) and wind, are the two main pillars of the current smart grid. EVs are growing in popularity. They promise improved resilience and sustainability through their synergistic combination. This review essay offers a thorough analysis of the opportunities and difficulties present in this pairing. We examine that managing the dual intermittency of renewable energy and EV mobility puts pressure on grid stability and power quality. This study carefully compares the performance, economic feasibility, and grid implications of several integration architectures, ranging from hybrid systems and vehicle-to-grid (V2G) ecosystems to solar and wind-powered charging stations. This work also analyzes the important trade-offs between grid hosting capacity (HC), cost vs reliability, and infrastructure centralization. According to the study, the main socioeconomic and technical obstacles to scalability are antiquated regulations, battery degradation issues, and a lack of standardized interoperability. To turn EVs from a grid burden into a versatile asset for a decarbonized energy future, the study concludes by outlining critical future research topics, highlighting the necessity of AI-driven energy management systems (EMSs), sophisticated vehicle-to-everything (V2X) services, and dynamic HC analysis.

The paper is devoted to optimal vaccination scheduling during a pandemic to minimize the probability of infection. The recent COVID-19 pandemic showed that the international community is not properly prepared to manage a crisis of this scale. Just after the vaccines had been approved by medical agencies, the policymakers needed to decide on the distribution strategy. To successfully fight the pandemic, the key is to find the equilibrium between the vaccine distribution schedule and the available supplies caused by limited production capacity. This is why society needs to be divided into stratified groups whose access to vaccines is prioritized. Herein, we present the problem of distributing protective actions (i.e., vaccines) and formulate two mixed-integer programs to solve it. The problem of distributing protective actions (PDPA) aims at finding an optimal schedule for a given set of social groups with a constant probability of infection. The problem of distributing protective act...

The global transition towards sustainable and resilient energy systems has emphasized the need for efficient utilization of renewable energy sources (RESs) and rapid electrification of transportation. However, smart grids must address the intermittency of solar and wind power while accommodating the growing demand from electric vehicles (EVs). Hence, in this paper, a data-driven energy management system (EMS) is proposed that combines multivariable forecasting, generation scheduling, and EV charging coordination in a dual-level decentralized framework to increase the efficiency, reliability, and scalability of modern power grids. First, short-term forecasts of solar irradiance, wind speed, and load demand are addressed via five machine learning models ranging from nonlinear to ensemble models. Accordingly, a unified CatBoost-based platform for forecasting these three variables is selected because of its better performance and accuracy. These forecasts are subsequently utilized in a mixed-integer linear programming (MILP) framework for optimal generation scheduling in the considered network, fulfilling load demand at reduced electricity and emission costs while maintaining grid stability. Finally, a priority-based scheme is proposed for charging/discharging coordination of the aggregated EVs, minimizing demand variability while fulfilling vehicles' charging needs and maintaining their batteries' lifetime. The superiority of the proposed method lies in integrating a multivariable forecasting pipeline, linear MILP generation scheduling, and battery-health-aware V2G coordination in a unified decoupled framework, unlike many recent frontier works that treat these capabilities independently. Simulation results, under different scenarios, confirm that the proposed intelligent EMS can significantly reduce operational fluctuations, satisfy load and EV demands, optimize RES utilization, and support system cost-effectiveness, sustainability, and resilience.

The Job Shop Scheduling Problem is a classic combinatorial optimization problem and one of the most well-studied scheduling problems. Several methodologies, both exact and metaheuristic, have already been proposed for the solution of this computationally difficult problem. This work presents for the first time a solution approach based on Variable Neighborhood Programming for the Job Shop Scheduling Problem. Variable Neighborhood Programming is a recent methodology which constitutes a combination of Genetic Programming and Variable Neighborhood Search. In addition, some encouraging comparative computational results are also shown against the state-of-the-art Gurobi optimization solver using medium-and large-scale benchmark instances. The findings of this work have a plethora of modern applications in Manufacturing-asa-Service online platforms. All experimental evaluations were performed on the Google Cloud Platform.

The general definition of the hybrid flow shop (HFS) environment is a set of S≥2 production stages where at least one of these stages includes more than one machine, which can process one job at a time. A job can be defined as several operations to be performed by none, one, or more machines at each stage. Usually, these jobs are completed in some sequence between the different production stages, and in the case of setup activities, products are grouped in batches with buffers of work in progress between different production stages. Today, flexible production systems permit in some instances to relax job precedence constrains with alternative process cycles and to group together different batches of similar products in order to reduce setup activity incidence. On the other hand, the availability of multiple parallel machines in a single production stage makes it possible to split the lot size between different resources. This paper aims to solve the HFS scheduling problem in a flexible multistage batch production system, offering a heuristic procedure, to minimize the production makespan and increase the productive capacity utilization using a batch aggregation/splitting strategy while introducing the "workload leveling function" concept. The results are compared with other important scheduling rules widely accepted in the industry and made part of an industrial application. The company used as a test sample is an Italian rotor shaft manufacturer. The final result is illustrated to validate the proposed heuristics.

We consider a continuous supply chain network consisting of buffering queues and processors first articulated by and analyzed subsequently by [1] and [4]. A model was proposed for such network by [23] using a system of coupling partial differential equations and ordinary differential equations. In this article, we propose an alternative approach based on a variational method to formulate the network dynamics. We also derive, based on the variational method, an algorithm that guarantees numerical stability, allows for rigorous error estimates, and facilitates efficient computations. A class of network flow optimization problems are formulated as mixed integer programs (MIP). The proposed numerical algorithm and the corresponding MIP are compared theoretically and numerically with existing ones , which demonstrates the modeling and computational advantages of the variational approach.

Hydrothermal operation planning (HTOP) is a complex, large-scale optimal control problem. Traditionally, mathematical programming is used to solve it; however, metaheuristic techniques have emerged as an alternative approach. However, even in the context of current technological developments, the models developed to date generally require simplifications in the formulation. In particular, in medium-term planning, they have used a deterministic model or simplified transmission lines into a single bus. However, this approach leads to conservative and unrealistic solutions that may result in either oversizing or underutilization of resources. Therefore, this work proposes a methodology for incorporating uncertainties into the HTOP problem with a multi-bus topology. It was tested in a threebus system, where linear functions are applied to simplify the production of hydroelectric plants and the cost of thermal units. The methodology incorporated well-established techniques in an implicit stochastic optimization (ISO) model, using a tree of 50 scenarios to model the hydrological series, which is solved with linear programming (LP). The results were validated with the costs of the 10000 generated series, showing an error of 5.07%. Additionally, the solutions were compared with an adapted metaheuristic technique for this problem to explore models applicable to more complex formulations.

and Microgrids (MG) achieve optimum and reliable integration of Distributed Generation (DG) units in the existing electricity distribution network. An AC/DC hybrid MG system is proposed in this paper in order to integrate the Photovoltaic (PV) home system, Micro Combined Heat and Power (mCHP) units with the appropriate size, a Boiler and Batteries within the power infrastructure. Furthermore, three different types of consumers with large, medium and small electrical and thermal demands are examined. The purpose of this paper is to draw conclusions from the application of control and energy management algorithms of DG units in an AC/DC Microgrid which mainly incorporated Photovoltaics Units (PV), mCHPs and Batteries. Especially, the main focus is on the energy control and management of the mCHPs system in order to meet the consumers' electrical and thermal needs and to minimize the power flow from the main power grid. The simulation scenario aims to highlight the characteristics and particularities of the AC/DC MG in different power generation conditions from PV systems and mCHPs, electrical and thermal consumptions as well as the power supplied by the external power grid. The AC/DC MG responds to the needs of its users for electricity and heat and also operates according to the needs of the market. Finally, the results show significant reduction of power flow from the electricity distribution network. All simulations have been implemented with the Matlab program.

Timetable generation is a very difficult task. It is a time consuming, and arduous process. To manually generate a timetable, takes a lot of time, effort, and manpower. However, a timetable scheduling system is designed for different purposes such as: organizing lectures in higher institutions, private organization, airlines, bus station, etc. This paper tries to minimize the difficulties in generating a timetable for academic purposes, using Logarithmic algorithm, to be precise the modified Quicksort algorithm for its design. The algorithm is designed to eradicate collisions on the timetable, and to run in parallel. This helps to minimize the human errors, improve the accuracy of the timetable scheduling process as well as the computation time. To this extent, a Paperless Master Timetable Scheduling System (PMTSS) was proposed and implemented tin this paper to achieve the said requirements. The system can be installed on any android or windows platform. The content of the design also provides exciting services such as: Live Chat for Administrators, Lecturers and Students, Timetable alertsetc. The paperless timetable scheduling system involves dynamic system utilization and modifications.

According to different needs of users, there are different consumption habits. Consumption habits of people, which have the same age group or the same professions, are similar. A type of internet usage habits of people in this way is one of these habits. In recent years, developments in technology, GSM, and especially with 4G mobile internet usage have found applications in many areas of daily life. Enter to internet, wherever users need to, creates freedom. Messaging, media, finance and many different needs can be met through this connection. Users' occupation, age, gender, location, usage patterns according to different characteristics such as income level and the relevant properties are similar to each other according to the amount of internet usage (in Mb Download) connected to internet and internet usage frequency and duration of exposure can be clustered. SOM type of study, personal internet usage by artificial neural networks (data of the CDR) process and their profession, age, gender, location is to cluster usage patterns according to the values.

The effort to continuously improve and innovate smart appliances (SA) energy management requires an experimental research and development environment which integrates widely differing tools and resources seamlessly. To this end, this paper proposes a novel Direct Load Control (DLC) testbed, aiming to conveniently support the research community, as well as analyzing and comparing their designs in a laboratory environment. Based on the LabVIEW computing platform, this original testbed enables access to knowledge of major components such as online weather forecasting information, distributed energy resources (e.g., energy storage, solar photovoltaic), dynamic electricity tariff from utilities and demand response (DR) providers together with different mathematical optimization features given by General Algebraic Modelling System (GAMS). This intercommunication is possible thanks to the different applications programming interfaces (API) incorporated into the system and to intermediate a...

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Simulation-based problems involving mixed-variable inputs frequently feature domains that are hierarchical, conditional, heterogeneous, or tree-structured. These characteristics pose challenges for data representation, modeling, and optimization. This paper reviews extensive literature on these structured input spaces and proposes a unified framework that generalizes existing approaches. In this framework, input variables may be continuous, integer, or categorical. A variable is described as meta if its value governs the presence of other decreed variables, enabling the modeling of conditional and hierarchical structures. We further introduce the concept of partially-decreed variables, whose activation depends on contextual conditions. To capture these inter-variable hierarchical relationships, we introduce design space graphs, combining principles from feature modeling and graph theory. This allows the definition of general hierarchical domains suitable for describing complex system architectures. Our framework defines hierarchical distances and kernels to enable surrogate modeling and optimization on hierarchical domains. We demonstrate its effectiveness on complex system design problems, including a neural network and a green-aircraft case study. Our methods are available in the open-source Surrogate Modeling Toolbox (SMT 2.0).

This paper presents a mixed-integer linear programming model for volt-var optimization considering the chronological operation of distribution systems containing distributed energy resources (DERs). The proposed model describes the operation problem of capacitor banks (CBs) and voltage regulators (VRs), and it is further based on the steady-state operation during each time interval contained in typical scenarios of distribution systems. A procedure using a K-means clustering algorithm is used to select the scenarios, thus preserving the simultaneity and chronological combination of different loads and DERs. According to the formulation that we developed, the regulation devices become sensitive to downstream load variations, since we use explicit current variables to control automatic CBs, and since we include means to compensate voltage drops along distribution lines in the control of VRs. The model is validated by comparing the results obtained during several tests of two typical cases with those obtained through nonlinear power flow. The typical case studies presented in the paper highlight the good agreement between the results obtained with the linearized model and with power flow method; further, the practical results confirm that the use of typical scenarios allows representing different levels of loads and DERs, while keeping the validity and performance of the proposed model.

Efficient and sustainable municipal waste collection is a critical challenge in urban management, requiring datadriven strategies that align operational performance with environmental objectives. Despite the increasing use of clustering and routing techniques in waste management, current approaches often fail to fully integrate spatial clustering with optimization models that account for real-world constraints such as vehicle capacities and workload balancing. This paper addresses that gap by proposing a novel framework that combines clustering algorithms with mixed-integer linear programming (MILP) to optimize the division of a city into sustainable municipal solid waste collection sectors. Using real-world data from Tarnów, Poland, we apply the k-means algorithm to generate spatially and quantitatively balanced clusters of over 10,000 collection points. These clusters serve as input to a MILP model that solves the Sustainable Sectorization of Municipal Solid Waste Collection Problem (SSMSWCP), aiming to minimize disparities in either route lengths or collected waste volumes across a heterogeneous vehicle fleet, including diesel and electric trucks. The proposed method supports strategic decisionmaking by enabling planners to evaluate alternative sector layouts, fleet configurations, and environmental tradeoffs. Computational experiments demonstrate the feasibility and flexibility of the approach and highlight how operational constraints and balancing criteria affect service equity and environmental outcomes. The entire methodology is implemented in open-source software and is transferable to other municipalities facing similar planning challenges.

Municipal Solid Waste Management (MSWM) represents a complex, multi-level decision domain that involves strategic, tactical, and operational planning under economic, environmental, and social constraints. This paper reviews the state of Operations Research (OR) applications to MSWM. The analysis encompasses optimization, simulation, metaheuristic, and hybrid approaches that address decision problems ranging from facility siting and capacity expansion to routing and scheduling. The study classifies OR contributions across decision levels, identifying methodological patterns and dominant model types such as mixed-integer programming, metaheuristics, and simulation-optimization frameworks. Despite significant progress in optimization and the integration of sustainability, critical gaps remain in uncertainty modeling, system-wide integration, and data-driven decision support. Deterministic formulations prevail at the strategic and tactical levels, while uncertainty is mainly explored in operational routing. Cross-level coordination among infrastructure planning, fleet design, and daily operations remains underdeveloped. Furthermore, persistent data scarcity and the limited incorporation of behavioral factors constrain the practical applicability of OR models. The review concludes with a research agenda that advocates for multi-level, uncertainty-aware, and dynamic optimization frameworks, supported by standardized data infrastructures and behavioral insights.

Due to dramatic increase in the number of product variants, line balancing has become a critical aspect of production systems aimed at improving efficiency and productivity. It involves distributing workstation in a way that minimizes idle time, maximizes resource utilization, and ensures smooth workflow. Although numerous research have been done on assembly line balancing problem (ALBP) to achieve optimal work distribution by minimizing bottlenecks and reducing production cycle times, insufficient emphasis is given to line target. This study aims to find out optimum line target which gives the minimum total idle time. The process begins with numerical example of a ready-made garment assembly line with seven operations and three types of machines. Line target acts as a variable function between two limiting values between 1000 pieces to 2500 pieces in an eight hour shift. Instead of treating ALBP in traditional manner, this paper formulates a mathematical model through integer programming method. This approach finds the optimum line target values of 1200 pieces which gives total idle time of 168 minutes. This model allows parallel workstation and has practical implications to the production engineers, managers and top management to maintain the efficiency and productivity of the assembly line.

In this paper, Label Setting Algorithm and Dynamic Programming Algorithm had been critically examined in determining the shortest path from one source to a destination. Shortest path problems are for finding a path with minimum cost from one or more origin (s) to one or more destination(s) through a connected network. A network of ten (10) cities (nodes) was employed as a numerical example to compare the performance of the two algorithms. Both algorithms arrived at the optimal distance of 11 km, which corresponds to the paths 1→4→5→8→10 ,1→3→5→8→10 , 1→2→6→9→10  and  1→4→6→9→10 . Thus, the problem has multiple shortest paths. The computational results evince the outperformance of Dynamic Programming Algorithm, in terms of time efficiency, over the Label Setting Algorithm. Therefore, to save time, it is recommended to apply Dynamic Programming Algorithm to shortest paths and other applicable problems over the Label-Setting Algorithm.

This book provides an overview of power transformer infrastructure and computer aided design with numerical solutions. Currently, a variety of design methodologies are available to perform the transformer infrastructure perfectly in the power grid. However, there is still a significant amount of work to develop these techniques for transformer design, to improve both cost and efficiency. Therefore, we can design additional methods to enhance efficiency and decrease manufacturing
costs. To ensure the reliability of the entire power system, it is necessary to examine various issues related to transformer design and explore potential solutions within the power transformer infrastructure. We have prepared the algorithms to follow a step-by-step procedure for transformer design. We validate the suggested algorithms on Mathematical Laboratory (MATLAB) software.

This book provides a comprehensive overview of both conventional and research advancements in power transformer design, along with numerical solutions. Innovative analysis techniques and evolutionary algorithms optimize the design of three phase core-type power transformers. It is crucial to analyze and reduce stray losses,
as they are related to the raw material. Any decrease in these losses will directly  reduce the transformer’s overall cost.

This paper introduces a sequential decomposition strategy based on a rigorous mixed-integer linear programming (MILP) model to address the integrated Production Routing Problem (PRP) of large-scale industrial gas supply chains. Solving the PRP in real-world instances represents a significant challenge due to the high combinatorial complexity involved. To effectively tackle this issue, a three-step sequential approach (TSSA) is proposed. In each step of the procedure, different assumptions are applied to manage the scalability of the resulting problem. Specifically, in Steps 1 and 2, the model size is controlled by allowing a reduced number of routes. In Step 3, a larger set of routes is considered, but the days on which they can be used are restricted. In each phase, the MILP model is solved to minimize either the cost of external purchases of product (Step 1) or the total operating cost (Steps 2 and 3), with the aim of sequentially finding feasible solutions and progressively improving them. To assess its performance, the TSSA procedure is compared with instances where the MILP model is solved monolithically. Two case studies are solved for this analysis: one small-sized and one industrial-scale problem. In the illustrative case, the proposed procedure found near-optimal solutions in a small fraction of the CPU time, in comparison to the monolithic MILP model. For the industrial case, the superior performance of the TSSA approach is more evident, achieving higher-quality solutions with shorter CPU times for a real-world problem.

A multi-product model for the design of global supply chains with reverse flows is proposed. Two levels of decisions are considered, one strategic and one tactical. The first is modelled through a macro perspective of time where the determination of the network structure and flows is accomplished. At tactical level, a micro perspective of time is considered, where production planning

A multi-product model for the design of global supply chains with reverse flows is proposed. Two levels of decisions are considered, one strategic and one tactical. The first is modelled through a macro perspective of time where the determination of the network structure and flows is accomplished. At tactical level, a micro perspective of time is considered, where production planning and inventory management are addressed in detail. A mixed integer linear programming formulation is developed which is solved with standard Branch and Bound techniques. The model accuracy and suitability are studied using a case study.

The multi-resource generalized assignment problem (MRGAP) is an assignment problem in which each agent has more than one capacity-constrained resource. Although each agent cannot perform each job in real life, in the MRGAP literature it is generally assumed that each job can be assigned to each agent. In addition, working with as few agents as possible can create significant advantages, as each new agent creates audit tracking difficulties and additional costs. For this reason, in this study, the MRGAP problem, in which eligibility constraints are taken into account, has been addressed in a bi-objective manner. The objectives are to minimize the total load squares and the total number of agents. The objective of minimizing the total number of agents has been discussed for the first time in the MRGAP literature. These two objectives considered were scalarized by using the weighted sum method. A simulation annealing algorithm has been developed to solve large-scale problems. Randomly ...

Globally, there is an increase in the proportion of renewable sources for electricity generation. Among renewable sources, hydropower is the most widespread. For this reason, the improvements of their applications have been the focus of researches. Hydroelectric power plants have numerous aspects which might represent several economic advantages, if they are operated efficiently. Mathematical optimization models are interesting tools that help in the decision-making processes. In this context, this paper introduces a new Mixed Integer Lineal Programming model that determines the most convenient combination of units to operate a large-scale hydro power plant. Several aspects of reality are taken into account, which are sometimes not considered, such as the variation of the hydraulic head and the performance of other elements besides the turbines, as floodgates. To prove the effectiveness of the new model, the Itaipú Power Plant is selected as a case study. It has an installed power capacity of 14,000 MW and holds the world record in terms of annual generation with 103 million MWh. Three possible scenarios are evaluated in order to analyze the behavior of this plant in normal and extreme situations. The results indicate that the model effectively reduces computational times, and that power generation is influenced by market price variations and reservoir limitations.

In this letter we investigate link scheduling algorithms for throughput maximization in multicast wireless networks. According to our system model, each source node transmits to a multicast group that resides one hop away. We adopt the physical interference model to reflect the aggregate signal to interference and noise ratio (SINR) at each node of the multicast group. We present an ILP formulation of the aforementioned problem. The basic feature of the problem formulation is that it decomposes the single multicast session into the corresponding point-to-point links. The rationale is that a solution algorithm has more flexibility regarding the scheduling options for individual nodes. The extended MILP problem that also considers power control is solved with LP relaxation. Performance results for both the ILP and MILP problems are obtained for different traffic loads and different number of nodes per multicast group.

In this letter we investigate link scheduling algorithms for throughput maximization in multicast wireless networks. According to our system model, each source node transmits to a multicast group that resides one hop away. We adopt the physical interference model to reflect the aggregate signal to interference and noise ratio (SINR) at each node of the multicast group. We present an ILP formulation of the aforementioned problem. The basic feature of the problem formulation is that it decomposes the single multicast session into the corresponding point-to-point links. The rationale is that a solution algorithm has more flexibility regarding the scheduling options for individual nodes. The extended MILP problem that also considers power control is solved with LP relaxation. Performance results for both the ILP and MILP problems are obtained for different traffic loads and different number of nodes per multicast group.