Linear Programming Approach Research Articles

English

English

Operational strategies and integrated design for producing green hydrogen from wind electricity

Realizing the potential of renewable hydrogen production requires flexible operation of electrolysis systems to integrate with intermittent power sources. This work develops an optimization model to assess flexible operational strategies for alkaline and proton exchange membrane (PEM) electrolysers powered by wind energy. The model quantitatively analyses trade-offs between electrolyser shutdown strategies, overloading capacities, and battery integration to identify optimal regimes balancing efficiency, flexibility, and economics. The results reveal a mixed-integer linear programming approach can optimize system configurations and control strategies to minimize the levelized cost of hydrogen production. Optimal near-minimum load operation is achieved by independently optimizing the load of each electrolyser block, while avoiding shutdowns above a critical load level. Strategic electrolyser overloading can provide economic benefits by reducing installed capital costs, if technical feasibility and accelerated degradation are addressed. Battery energy storage integration significantly improves economics by enhancing asset utilization, provided excess renewable energy is available. The model provides novel insights on integrating alkaline and PEM electrolysis with intermittent wind power to advance renewable hydrogen production. Quantifying trade-offs between operational flexibility and economics will help guide flexible design and control strategies for cost-optimal renewable electrolysis systems.

Application of Stochastic Programming in Agricultural and Newsvendor Problems and It's Application in Real Life

The study of making the best decision under risk management in a variety of areas of our lives is known as Stochastic Programming. We will go through two-stage Stochastic Linear Programming approaches for a variety of real-world choice issues, as well as how to solve them. We will achieve this by constructing stochastic linear programming models based on real-world situations like the well-known Farmer's situation and News Vendors problems. The influence of pricing, Stochastic Integer Linear Programming problem, second stage Stochastic Integer Linear Programming problem, first stage Stochastic Binary Linear Programming problem, risk aversion problem, and continuous function for random variables based on two-stage SLP with the aid of Farmer's problem will all be examined. We will address the Newsvendor’s problem with Deterministic Equivalent Stochastic Linear Programming, an extension of Deterministic Stochastic Linear Programming for risk aversion with a high number of decision variables and restrictions, utilizing the two-stage Stochastic Linear Programming approach once more. Hand calculation is a challenging way to acquire the solution to the problems. As a result, we will use the programming language AMPL to design computer solutions for tackling both farmer and newsvendor difficulties. We will also utilize MATLAB to create graphs for the farmer's problem's continuous function. Dhaka Univ. J. Sci. 72(1): 30-45, 2024 (January)

A New Method to Solve Matrix Game with Interval Payoffs and its MATLAB Code

Game theory is of substantial significance in diverse domains, acting as a potent instrument to comprehend and assess strategic engagements among rational decision-makers. It formulates mathematical models to represent strategic interactions among rational decision-makers in the competitive world. Due to ambiguity in the real-world problems, acquiring the precise payoff values of a matrix game proves challenging. However, in numerous scenarios, these payoffs fluctuate within specific ranges, making them suitable for consideration as interval numbers. This leads to the formulation of a special form of game problem known as the interval valued game problem (IVGP). Some methodologies exist in the literature to find the optimal strategies as well as the value of game for IVGP, but most of them possess some limitations, resulting in the need for proposing a new methodology to find the optimal strategies and value of game. Thus, in this paper, a new solution method for game problems with payoffs represented as interval numbers is presented, utilizing the fuzzy concept. The process begins by transforming the interval payoffs into fuzzy numbers using a ranking function. Subsequently, these fuzzy payoffs are converted into crisp values, leading to the formulation of the crisp matrix game. The resulting crisp matrix game is then solved using linear programming approach. Additionally, MATLAB code for the proposed method is developed and proposed to streamline the computation process, enhancing comparison and decision-making efficiency, particularly when dealing with large payoff matrices. Furthermore, three numerical examples are provided to illustrate the validity of the proposed approach as well as its MATLAB code. A real-life example of IVGP in the realm of tourism industry is also provided. Finally, a comparative analysis is conducted, comparing the proposed method with some existing methods.

Power outages and bidirectional electric vehicle charging: Simulation of improved household energy resilience in subarctic conditions

In the highly digitalized and electrified modern world, blackouts and power outages cause significant disruptions to societies and to the normal daily life of individuals. The ongoing energy transition, climate change and energy crisis complicate grid dynamics, generate new forms of instability, and weaken the resilience of the electricity transmission grid leading to possible increases in power outages. Electric vehicles (EVs) with bidirectional charging points offer a convenient possibility for households to maintain electricity use during power outages through vehicle-to-home (V2H) operation. This study introduces a novel hybrid model that combines linear programming and deterministic approaches, considering ambient temperatures, to evaluate the efficacy of V2H for power outage prevention in subarctic detached households. The methodology includes a power outage response model that dynamically adjusts the EV’s SOC based on 5-minute interval household demand during sampled outage events. Utilizing real data, we simulate the energy resilience of V2H-equipped households during power outages, focusing on how this capability influences main customer objectives such as outage avoidance, electricity cost reduction, and EV state-of-charge (SOC). The approach provides insights into the system's performance across distinct EV-utilization cases and alternative customer preference assumptions. Based on our results, an EV could be used to fully prevent up to 98 % of all outages of the year occurring during EV plug-in. The average increased electricity costs resulting from outage response are less than 0.2€ if all outage types are considered. Overall, it can be stated that EVs can be effectively used to sustain household loads during power outages with V2H given EV availability, high SOC-level when the outage begins and if the EV is not needed for its primary purpose, mobility, during the outage.

A BI-OBJECTIVE COST MINIMIZATION MODEL FOR THE INSULAR TOUR ROUTE PLANNING PROBLEM

This article presents a study on the development of a bi-objective cost problem optimization model in planning tourist routes in the island zone. This problem is a new variant of the tour route plan problem. Bi-objective view of two cost components, namely maritime transportation costs and ground transportation costs. Two models were formulated using a mixed integer linear programming approach. The first model was designed to minimize one of the two cost components separately. The second model was bi-objective cost minimization based on the priority weights of the two costs. It was designed to determine minimum transportation costs based on priority weights. Model testing was carried out through numerical experiments on several cases that often occur in industries in Maluku, Indonesia, especially tourism and goods shipping. Each case has variations in the number of islands and nodes. As a result, the model can demonstrate its adaptability to changes in objectives and parameters. For cases that do not have a single solution, an increase in the network structure on the number of islands and nodes will increase the variety of efficient alternative solutions. The set of efficient solutions also shows an inverse relationship between MTC and GTC. The results also show that MTC minimization cannot be used as a reference for TC minimization in cases with many nodes and islands. Efforts to minimize MTC in the island zone impact reducing total costs but do not mean minimizing total costs. In addition, based on the exponential trend line of computing time, the number of nodes has a more significant influence on computing time compared to the number of islands.

Research on capacity optimization of new energy hybrid energy storage system of high-speed railway

With the fast expansion of electrified railways, the need for energy is growing. Thus, improving railway coupling and interconnection, new energy, and energy storage is critical to support low-carbon and green railway development. Therefore, this paper proposes an optimal configuration method for the access capacity of wind power generation system (WPGS), photovoltaic power system (PVPS), and hybrid energy storage system (HESS) in the traction power supply system (TPSS) of high-speed railways. Firstly, the HESS’s mathematical model is developed, then the high-speed railway TPSS’s economic optimization operating model is built, and a HESS energy management approach is presented, taking the energy management strategy parameters and model capacity configuration parameters as the optimization variables. The mixed integer linear programming approach is used to resolve the actual example with the least daily operational cost of the high-speed rail system as the optimization goal, and the optimal capacity of WPGS, PVPS, and HESS is obtained. Finally, through comparison and analysis, it is verified that the economic benefit is the highest when the distributed complementary energy system covering WPGS, PVPS, and HESS is connected to the traction substation, and 10.47% of the daily expenditure is saved.

Exploiting symmetry for the job sequencing and tool switching problem

The Job Sequencing and Tool Switching Problem (SSP), a well-known combinatorial optimization problem in the domain of Flexible Manufacturing Systems (FMS), is studied in this article. The aim of this research is to improve the currently known exact solution methodology for this NP-hard problem. We propose a new integer linear programming approach with symmetry-breaking and tightening cuts that provably outperformed the existing methodology described in the literature. The computational study conducted on a data set with 1,050 instances showed that the developed method can solve hard instances that were not solvable with the state-of-the-art methods presented in the literature.

A Mixed-Integer Linear Programming Approach to Optimize Tennis Regimens for Young Athletes in Korea

The popularity of tennis has been surging among young individuals in South Korea, as it offers an appealing alternative to other sports like golf. With this surge in popularity, there is a corresponding increase in competitive intensity, making the optimization of training regimens crucial for success. While athletes in this sport commonly engage in a variety of training activities there has been limited systematic research that offers a quantitatively validated approach for balancing these activities to maximize on-court performance. This study aims to fill this gap by providing an optimization model tailored to the specific requirements of tennis training. Through surveying 48 prospective athletes in South Korea, the study establishes upper and lower bounds for each of 4 activities: Serving Practice, Ground Strokes Practice, Physical Conditioning, and Mental Training. Multiple regression analysis is then used to calculate the weights of each training activity in an objective function, formulated to measure on-court performance. A Mixed-Integer Linear Programming (MILP) model is employed to allocate optimal weekly training hours to each activity, based on these weights and constraints. The study concludes by identifying an optimal training schedule that maximizes the value of the objective function, thereby optimizing on-court performance. The convergence of the objective and best bound at a low level further substantiates the optimality of the discovered solution.

Optimal dispatch of battery energy storage for multi-service provision in a collocated PV power plant considering battery ageing

This study explores how a battery energy storage system (BESS) can support photovoltaic (PV) power plant operation by simultaneously minimising the PV power plant (PVPP) clipping losses and providing grid ancillary services. For this purpose, a deterministic day-ahead control strategy is developed while considering both calendar and cycling battery ageing on the BESS multi-value stream. The battery degradation cost model has also been reformulated to integrate the proposed formulation and assess the impact of different ageing aspects. The dispatching problem is reformulated to implement a linear programming approach. It allows to optimally dispatch the power flow between the different system components and schedules the ancillary service provision. The Irish regulation for participating in the Renewable Electricity Support Scheme (RESS) and DS3 grid services markets is considered. A market participation framework has also been identified, and numerical analysis is performed while emulating a real case. The obtained outputs emphasise the value of PV-BESS in providing DS3 grid services and the potential of the multi-service provision to create an additional value from energy storage deployment. The proposed approach and control strategy can also be implemented for other BESS applications in different energy markets.

A mixed-integer linear programming approach for collateral management

Collateral management involves the efficient monitoring and allocation of assets to mitigate credit risk in financial transactions and is crucial for institutions such as commercial banks, investments banks, and central counterparties. It helps to ensure financial stability and compliance with regulatory requirements. This study is centered on a fundamental objective of collateral management, namely to collateralize as much as possible a set of transactions given a limited asset portfolio. In practice, an allocation is dynamic, necessitating periodic adjustments due to fluctuations over time in the asset pool, the transactions set, and asset value. Consequently, the objective is not merely the identification of an optimal allocation from zero but the optimization of an obsolete allocation in response to these fluctuations. The size and complexity of real-world problems often preclude direct resolution through conventional MILP solvers. In addition, each collateral adjustment movement incurs associated costs. In this research, a two-step method based on linear and mixed-integer linear programming formulations with ℓ1 penalties is devised, with the principal aim of minimizing under-allocation while simultaneously controlling the number of adjustment movements required. The method is tested on 20 real-world collateral givers and invariably reaches a good trade-off between solution quality, computational time, and the number of movements.

Novel Proportional–Integral–Derivative Control Framework on Continuous-Time Positive Systems Using Linear Programming

This paper considers the proportional–integral–derivative (PID) control for continuous-time positive systems. A three-stage strategy is introduced to design the PID controller. In the first stage, the proportional and integral components of the PID control are designed. A matrix decomposition approach is used to describe the gain matrices of the proportional and integral components. The positivity and stability of the closed-loop systems without the derivative component of PID control are achieved by the properties of a Metzler and Hurwitz matrix. In the second stage, a non-negative inverse matrix is constructed to maintain the Metzler and Hurwitz properties of the closed-loop system matrix in the first stage. To deal with the inverse of the derivative component of PID control, a matrix decomposition approach is further utilized to design a non-negative inverse matrix. Then, the derivative component is obtained by virtue of the designed inverse matrix. All the presented conditions can be solved by virtue of a linear programming approach. Furthermore, the three-stage PID design is developed for a state observer-based PID controller. Finally, a simulation example is provided to verify the effectiveness and validity of the proposed design.

A multi-objective two-stage stochastic programming approach for wind farms and demand side provider decisions using the weighted metric method

The rapid expansion of wind-based renewable energy sources highlights the critical need to enhance reserve capacity within power systems. This research aims to develop an effective model for harnessing the combined potential of flexible demand-side resources, acting as demand-side providers (DSPs), to address the inherent unpredictability of wind power. The DSP framework comprises three demand response aggregators: the capacity market program (CAP), energy storage systems (ESSs), and plug-in electric vehicle parking lots (PEVs PLs). To achieve this, a multi-objective two-stage stochastic programming model is introduced. It not only minimizes operational costs for system operators but also maximizes returns for demand-side resource owners supervised by DSPs in the energy and reserve market environment. The problem is tackled using a mixed-integer linear programming (MILP) approach employing a weighted metric methodology. Within this framework, the Weibull probability distribution function (WPDF) is utilized to model wind power uncertainty, while the truncated Gaussian distribution function (GDF) encapsulates the uncertainty regarding electric vehicle owner behavior. The results demonstrate that employing this method for simultaneous programming of energy and reserve not only reduces system operator costs but also enhances profits for resource owners.

A mixed integer linear programming approach for the design of chemical process families

The need for rapid and widespread deployment of new technologies to address climate change goals (e.g., deep, economy-wide decarbonization) presents new opportunities for advancing modular design strategies. Conventional engineering approaches focus on unique designs for each installation, while missing opportunities for manufacturing standardization. Extending insights from the automotive industry, we optimize a platform of common unit module designs while simultaneously designing an entire family of process variants that make use of that platform. This reduces engineering effort, deployment timelines, and manufacturing costs. We propose a nonlinear generalized disjunctive programming formulation and convert this to an efficient mixed-integer linear programming (MILP) formulation through discretization of the design space. We formulate our optimization in Pyomo with costing from IDAES, and we demonstrate the computational performance and solution quality on a water treatment desalination system from the PARETO framework and a carbon capture system built in Aspen Plus® as part of CCSI2.

A theory of stochastic fluvial landscape evolution

Geometries of eroding landscapes contain important information about geologic, climatic, biotic and geomorphic processes. They are also characterized by variability, which makes disentangling their origins challenging. Observations and physical models of fluvial processes, which set the pace of erosion on most continents, emphasize complexity and variability. By contrast, the spectral content of longitudinal river profiles and similarity of geometries at scales greater than approximately 100 km highlight relatively simple emergent properties. A general challenge then, addressed in this manuscript, is development of a theory of landscape evolution that embraces such scale-dependent insights. We do so by incorporating randomness and probability into a theory of fluvial erosion. First, we explore the use of stochastic differential equations of the Langevin type, and the Fokker–Planck equation, for predicting migration of erosional fronts. Second, analytical approaches incorporating distributions of driving forces, critical thresholds and associated proxies are developed. Finally, a linear programming approach is introduced, that, at its core, treats evolution of longitudinal profiles as a Markovian stochastic problem. The theory is developed essentially from first principles and incorporates physics governing fluvial erosion. We explore predictions of this theory, including the natural growth of discontinuities and scale-dependent evolution, including local complexity and emergent simplicity.

A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations Problems

AbstractWater distribution systems (WDSs) are critical infrastructure used to convey water from sources to consumers. The mathematical framework governing the distribution of flows and heads in extended period simulations of WDSs lends itself to application in a wide range of optimization problems. Applying the classical mixed integer linear programming (MILP) approach to model WDSs hydraulics within an optimization framework can contribute to higher solution accuracy with lower computational effort. However, adapting WDSs models to conform to a MILP formulation has proven challenging because of the intrinsic non‐linearity of system hydraulics and the complexity associated with modeling hydraulic devices that influence the state of the WDS. This paper introduces MILPNet, an adjustable framework for WDSs that can be used to build and solve an extensive array of MILP optimization problems. MILPNet includes constraints that represent the mass balance and energy conservation equations, hydraulic devices, control rules, and status checks. To conform to MILP structure, MILPNet employs piece‐wise linear approximation and integer programming. MILPNet was implemented and tested using Gurobi Python API. Modeling accuracy was shown to be comparable to EPANET, a public domain software for hydraulic modeling, and sensitivity analyses were conducted to examine the impacts of the modeling assumptions on the performance of MILPNet. Additionally, application of the framework was demonstrated using pump scheduling optimization examples in single and rolling horizon scenarios. Our results show that MILPNet can facilitate the construction and solution of optimization problems for a range of applications in WDSs operations.

Linear Programming Approach for Optimal Profit Mix of Cassava Grates and Flour

The research aimed to identify the optimal combination of cassava grates and flour to maximize the profit of a project initiated by the Philippine Root Crops Research and Training Center at Visayas State University. The findings revealed that the most profitable combination consisted of 125 kg of cassava grates and 25 kg of flour, resulting in an optimum profit of Php 4,250.00 for the entire production. The study highlighted that the project was constrained by limited inputs, preventing it from exceeding the optimal quantities of the two products. To enhance the profitability of both products, adjustments in the resources utilized during production were necessary. While the current production of cassava grates falls below the optimum quantity, indicating room for increased production with the existing inputs, the production of cassava flour had already reached its optimal level. To achieve optimal quantity and profit, the project must implement strategies to prevent resource wastage.

Theoretical solutions for the anchoring force of 3‐D anchored slope and optimization strategy for anchoring force distribution

AbstractBased on the three‐dimensional limit equilibrium method with modifying normal stress over the slip surface, this study presents a theoretical solution for the anchoring force of three‐dimensional slopes and proposes a new optimization strategy for anchor force distribution. The method employed the Boussinesq solution from the field of elasticity. It led to the derivation of an equilibrium equation set, which incorporated the anchoring force increment. As a result, the approach yielded a more accurate theoretical value for a three‐dimensional anchoring force. In practical engineering applications, the prestress of anchor cables is often uniformly set, which may lead to discrepancies in the anchoring force requirements at different locations on the slope, potentially resulting in resource waste. The research introduces a linear programming approach to optimize resource allocation, aiming to minimize the total anchoring force under fixed anchor cable quantities, installation angles, and locations. Nevertheless, the results from the Simplex Method could lead to an overly concentrated distribution of anchoring force. Therefore, the study further employs the normal distribution theory to reallocate anchoring forces, thus achieving a more reasonable distribution. The proposed method has been validated through three example studies and a practical engineering case study, resulting in significant reductions in the total anchoring force following optimization. Moreover, such an approach allows for optimized handling of the anchoring force for each anchor cable. The work provides a new perspective and tool for practical engineering applications.

Integrating Minimum Spanning Tree and MILP in Urban Planning: A Novel Algorithmic Perspective

This paper presents a novel eight-step iterative algorithm for optimizing the layout of a neighborhood, focusing on the efficient allocation of houses to strategically placed facilities, herein referred to as ’points of interest’. The methodology integrates a mixed integer linear programming (MILP) approach with a heuristic algorithm to address a variant of the facility location problem combined with network design considerations. The algorithm begins by defining a set of geographic coordinates to represent houses within a predefined area. It then identifies key points of interest, forming the basis for subsequent connectivity and allocation analyses. The methodology’s core involves applying the Greedy algorithm to assign houses to the nearest points of interest, subject to capacity constraints. The method is followed by computing a Minimum Spanning Tree (MST) among these points to ensure efficient overall connectivity. The proposed algorithm’s iterative design is a key attribute. The most promising result of this approach is its ability to minimize the distance between houses and points of interest while optimizing the network’s total length. This dual optimization ensures a balanced distribution of houses and an efficient layout, making it particularly suitable for urban planning and infrastructure development. The paper’s findings demonstrate the algorithm’s effectiveness in creating a practical and efficient neighborhood layout, highlighting its potential application in large-scale urban planning and development projects.

An efficient procedure for optimal maintenance intervention in partially observable multi-component systems

With rapid advances in technology, many systems are becoming more complex, including ever-increasing numbers of components that are prone to failure. In most cases, it may not be feasible from a technical or economic standpoint to dedicate a sensor for each individual component to gauge its wear and tear. To make sure that these systems that may require large capitals are economically maintained, one should provide maintenance in a way that responds to captured sensor observations. This gives rise to condition-based maintenance in partially observable multi-component systems. In this study, we propose a novel methodology to manage maintenance interventions as well as spare part quantity decisions for such systems. Our methodology is based on reducing the state space of the multi-component system and optimizing the resulting reduced-state Markov decision process via a linear programming approach. This methodology is highly scalable and capable of solving large problems that cannot be approached with the previously existing solution procedures.