Linear Programming Method Research Articles

FUZZY LINEAR PROGRAMMING METHOD IN PRODUCTION PLANNING: AN APPLICATION IN THE METAL INDUSTRY

Günümüzde hızla artan rekabet ortamı işletmelerin sahip olduğu kaynakları daha verimli kullanması ihtiyacını ortaya çıkarmıştır. İşletmelerin sahip oldukları kaynakları maksimum kâr sağlayacak bir şekilde müşterinin talep ve istekleri doğrultusunda doğru zamanda ve doğru miktarda sağlayabilmeleri hayati önem taşımaktadır. Bu sebeple rekabet ortamında başarılı olmak ve kâr sağlamak amacıyla işletmeler üretim planlama alanına odaklanmışlardır. İşletmeler bu sayede üretim planlama ile olası talep artışlarına önceden çözüm bularak minimum maliyet ve maksimum kâr ile rakip işletmeler içerisinde en önde yer almaktadır. Üretim planlama konusu fazla kısıt ve kaynak bulundurması nedeni ile işletmelerin karar vermesi gereken önemli bir problemdir. Üretim planlama problemlerinde detaylı çözüme ulaşmak için en etkili ve hızlı yöntem yöneylem araştırmasının bir uygulaması olan doğrusal programlamadır. Doğrusal programlama ile işletmeler üretim planlama alanında karşılaştığı problemlere hızlı çözüm bularak karmaşık bir sistem de bile uygun optimal değere ulaşmaktadır. Bu çalışmada metal sektöründe faaliyet gösteren bir firmada üretim planlama problemi incelenmiş olup çalışmayı en iyi ifade eden model olan yöneylem araştırmasının bir yöntemi olan doğrusal programlama ile çözülmüştür. Model gerçek hayat problemlerinde verilerin kesin olmaması nedeniyle bulanık doğrusal programlamanın Verdegay yaklaşımı ile de çözülmüştür. Son olarak, Lingo bilgisayar programı yardımıyla çözüm sonucu bulunarak duyarlılık analizi yapılmıştır.

Integrated simulation and optimization framework for quantitative analysis of near-face stockpile mining

A new conceptual mining method called the near-face stockpile (NFS), which combines the in-pit crushing and conveying IPCC system with a pre-crusher stockpile, has recently been proposed for large open pits with sufficient pit bottom width. In the past, stockpiles mainly act as a "buffer" to improve the stability of the production system. However, in NFS ore will be dumped into the pre-crusher stockpile located at the bottom of the current pit and be fed into the crusher after blending to the desired head grade, instead of being dumped directly into the crusher. Theoretically, this design not only retains the high efficiency and high output of IPCC, but also endows the mining system with better quantity and quality stability. Verifying these advantages and objectively evaluating the NFS method has become a problem worth studying. Since the NFS method exhibits distinctive layout and feeding mechanisms, which distinguish it from other mining methods, a novel simulation model is required for the accurate modeling of the NFS method and quantitatively evaluating the performance of NFS methods. In addition, this paper also proposes an optimization model for short-term production scheduling for NFS method based on the mixed integer linear programming (MILP) method. An oil sands mine case study is implemented to verify the proposed simulation model. One year simulation results reveal that compared to the traditional mining method, the overall production increased by 5.06%, the transporting distance of minerals by trucks was reduced by 17.87%, and the shovels’ and crusher's utilization increased by 4.96% and 4.85%, respectively, when using NFS method.

Berth Allocation Considering Multiple Quays: A Practical Approach Using Cuckoo Search Optimization

Maritime container terminals (MCTs) play a fundamental role in international maritime trade, handling inbound, outbound, and transshipped containers. The increasing number of ships and containers creates several challenges to MCTs, such as congestion, long waiting times before ships dock, delayed departures, and high service costs. The berth allocation problem (BAP) concerns allocating berthing positions to arriving ships to reduce total service cost, waiting times, and delays in vessels’ departures. In this work, we extend the study of continuous BAP, which considers a single quay (straight line) for berthing ships, to multiple quays, as found in many ports around the globe. Multi-Quay BAP (MQ-BAP) adds the additional dimension of assigning a preferred quay to each arriving ship, rather than just specifying the berthing position and time. In this study, we address MQ-BAP with the objective of minimizing the total service cost, which includes minimizing the waiting times and delays in the departure of ships. MQ-BAP is first formulated as a mixed-integer linear problem and then solved using the cuckoo search algorithm (CSA), a computational intelligence (CI)-based approach. In addition, the exact mixed-integer linear programming (MILP) method, two other state-of-the-art metaheuristic approaches, namely the genetic algorithm (GA) and particle swarm optimization (PSO), as well as a first come first serve (FCFS) approach, are also implemented for comparison purposes. Several experiments are conducted using both randomly generated and real data from the Port of Limassol, Cyprus, which has five quays serving commercial vessel traffic. The comparative analysis and experimental results show that the CSA-based method achieves the best overall results in affordable time as compared to the other CI-based methods, for all considered scenarios.

Data-driven energy management system for flexible operation of hydrogen/ammonia-based energy hub: A deep reinforcement learning approach

In the context of carbon neutrality, multi-energy systems are being designed to enhance the integration of renewable energy, and the deployment of large-scale energy storage solutions is vital to ensure a flexible and cost-effective system operation. Hydrogen and ammonia are two promising energy carriers that can serve as storage media, feedstock, and fuels. This study designed an energy hub that integrates multiple energy resources and energy storage methods. Two pathways, power-to-gas-to-power (P2X2P) and biomass-to-gas-to-power (B2X2P), which use hydrogen and ammonia as energy carriers, are proposed for the energy hub. Considering the flexibility and profitability of the energy hub, scheduling of the energy hub was controlled using model-based mixed-integer linear programming and model-free deep reinforcement learning methods. A modified double-deep Q-network framework was trained on a monthly dataset and executed on a yearly dataset. The results indicate that the B2X2P pathway outperforms the P2X2P pathway in terms of profitability, while the P2X2P pathway has greater operational flexibility. Because the optimal biomass-to-ammonia-to-power has a 550.76 MUSD net present value and a five-year discounted payback period, ammonia is best suited for mass production and storage. Moreover, the modified double deep Q network framework demonstrates superior generality for solving similar optimal scheduling problems.

A Linear Programming Method Based Optimal Power Flow Problem for Iraqi Extra High Voltage Grid (EHV)

The objective of an Optimal Power Flow (OPF) algorithm is to find steady state operation point which minimizes generation cost, loss etc. while maintaining an acceptable system performance in terms of limits on generators real and reactive powers, line flow limits etc. The OPF solution includes an objective function. A common objective function concerns the active power generation cost. A Linear programming method is proposed to solve the OPF problem. The Linear Programming (LP) approach transforms the nonlinear optimization problem into an iterative algorithm that in each iteration solves a linear optimization problem resulting from linearization both the objective function and constrains. A computer program, written in MATLAB environment, is developed to represent the proposed method. The adopted program is applied for the first time on Iraqi 24 bus Extra High Voltage (EHV) network (400 kV). The required are data taken from the operation and control office, which belongs to the ministry of electricity.

School and residential segregation in the reproduction of urban segregation: A case study in Buenos Aires

The link between residential and school segregation is widely recognised as a key to explaining urban inequalities. However, most studies have focused on countries of the Global North. This paper attempts to identify to what extent socio-economic residential segregation explains secondary school segregation in Buenos Aires (Argentina). Based on a linear programming method, the study proposes a hypothetical pupil allocation model that takes into account the capacity of schools and is used as an ideal typus to compare with the real socio-economic school composition. Using a ‘decompose method’ of segregation differences to analyse the differences in segregation indices and a local segregation analysis, this paper finds that in a residential context with low segregation but high social inequalities, school segregation is a social mechanism that allows maintaining spaces of differentiation and distancing between groups. In discussion with the idea of a ‘vicious circle of segregation’, this article argues for the potential of a multi-domain approach to segregation, to understand how different domains work in articulated and complex ways to reinforce urban segregation.

Optimization of heterogeneous capacities considering the profit margin per product

This paper aims to present a proposal to improve this methodology for the analysis of heterogeneous capacities based on the profit margin per product. Which was structured in three moments: development of the proposal, deployment in a business context, and validation of the results through the application of a linear programming method. This proposal considers the five initial steps of the existing tools as a starting point, taking as a reference the normal time available for each homogeneous group and introducing modifications in the steps. The application of the methodology in the conditions of SMEs demonstrated its ability to generate results superior to those of traditional methods and similar to those obtained by specific linear programming techniques.

An energy-aware combinatorial auction-based virtual machine scheduling model and heuristics for green cloud computing

Considering the increasing demand for cloud computing, and the financial and environmental impact of the increasing energy consumption trend of data centers, improving energy efficiency is vital for cloud service providers. In this study, an energy-aware virtual machine scheduling model is proposed which is based on the multi-unit nondiscriminatory combinatorial auction. The model includes a powerful bidding language that allows users to declare their complicated virtual machine requests using logical AND and OR relations along with the time constraints. The study also presents the formal definition of the model and the associated optimization problem for determining the optimum schedule and energy-efficient placement of VMs on physical servers. The optimization problem is formulated using integer linear programming and several heuristic solution methods including the Genetic Algorithm are proposed for this problem. The performances of the model and the proposed heuristics are assessed on a comprehensive test suite. The proposed model is estimated to provide approximately a 37% improvement in revenues, and the solution methods are estimated to provide high-quality solutions within only 5% of the optimum which enable the model to be deployed in large-scale clouds.

Control of Generalized Decoupled MIMO Systems Based on Linear Programming Method

In this work, a control method is suggested to generalize decoupled multi-input multi-output (MIMO) plant to get satisfactory results. The phenomena of decoupling converts a p × q MIMO plant to p number of equivalent single-input single-output (SISO) loops which enables one to control q number of outputs independently even due to the effect of coupling present in control inputs and outputs. The effect of these cross-couplings causes the disturbances. The decoupler aim is to eradicate the effect of these disturbances on outputs. In order to achieve it, this work proposed a novel generalized decoupling technique on the basis of linear programming. Infinity ( ∞ ) − norm method is considered to minimize the effect of decoupler gain of the cross-couplings of the MIMO system, over all frequencies, that minimizes undesired mutual couplings of the resulting decoupled plant also nullifying coupling effect completely at steady state as well. The proposed method of decoupling is compared with the relative gain array (RGA) and further modified RGA (MRGA) technique of decoupling which is also elaborated in this paper. To achieve the desired response from the decoupled plant proportional integral derivative (PID) control method is suggested using the Kharitonov theorem. The ensued technique is employed on different types of MIMO systems including square, non-square and time-delayed.

Impact of short-term and long-term energy storage units on power system operation economy: A parametric linear programming method

This paper evaluates the economic impact of short-term and long-term energy storage capacity on power system operation cost. First, the unit commitment (UC) model with short-term and long-term energy storage comprising a year-round hourly operation simulation is established to minimize the optimal operation cost. By introducing the convex hull of the original feasible region of decision variables, the integer variables in UC model are relaxed as continuous variables, transforming the UC problem as a linear programming (LP). Then, by regarding the power and energy capacities as parameters, the LP is cast as a multiparametric linear programming (mp-LP), where the optimal value function (OVF) is explicitly expressed as a piecewise linear function of the capacity parameters. An approximation method is used to calculate the analytical optimal value function and critical regions. The analytical expression of OVF contains rich sensitivity information. Finally, case studies validate our proposed method and provide visualization results. The sensitivity information of analytical OVF is exploited. As a potential application, the economic evaluation results could be applied in energy storage capacity sizing.

Marginal Carbon Dioxide Emission Reduction Cost and Influencing Factors in Chinese Industry Based on Bayes Bootstrap

Accurate measurement of the shadow price of carbon dioxide (CO2) is fundamental to the scientific assessment of the carbon emission reduction cost and the formulation and execution of China’s carbon emission mitigation policies. Underpinned by the directional distance function, this research uses a parametric linear programming method and a Bayes bootstrap estimation method to estimate the marginal CO2 emission reduction cost of the industrial sector in China and to quantify the related influencing factors. The results revealed that the marginal reduction cost of industrial CO2 is CNY 4565/ton. The marginal reduction cost of CO2 varies by industry, with the textile industry being the highest and the petroleum, coking and nuclear fuel processing industries the lowest. Meanwhile, an increasing number of industries are shifting to cleaner production. Furthermore, the marginal reduction cost of industrial CO2 has an “inverted U-shaped” relation with carbon intensity. Carbon emission reduction can be accomplished effectively if the carbon intensity is kept below the threshold value of 0.41 tons/CNY 10,000.

A robust optimization method with successive linear programming for intensity-modulated radiation therapy

Intensity-modulated radiation therapy for cancer is considered to be effective when dealing with complicated tumour shapes because the dose distribution for each irradiation can be modulated. Fluence map optimization is often formulated as an optimization problem with dose volume constraints (DVCs). A linear programming (LP) method that approximated DVCs was proposed, and it was modified to the successive LP method (SLPM) to find a feasible treatment plan in a wider region. In the present paper, we propose a numerical method called SLPM-R (the SLPM with robustness) that enhances the SLPM using a robust optimization approach. We mathematically prove that the proposed method with extended LP problems has the favourable properties of the SLPM, even taking uncertainty in the influence matrix into consideration. In particular, when the optimal value of the LP problem is non-positive, the proposed SLPM-R guarantees that the output solution can satisfy all DVCs. Through numerical experiments, we observed that the proposed method found a feasible plan that the SLPM could not find. In addition, for a test case that even the SLPM-R failed, the largest deviations of 5.65 Gray in the SLPM was reduced to 3.15 Gray by the SLPM-R.

A review of reactive power optimization algorithm in power system

The paper analyses the significance of reactive power optimization, generalizes the current situation of power system development. Various optimization algorithms were introduced in this paper such as traditional optimization algorithm, intelligence optimization algorithm, including the methods of linear programming, Newtons method, heuristic optimization algorithm, etc. This research analyzes the advantages and disadvantages of each algorithm and its application direction by comparing their outstanding performance in solving discrete variables and continuous variables. The purpose of the research is to find the optimal solution of reactive power optimization algorithm, minimize the transport network loss of power system, and improve the quality of users.

Optimal and efficient planning of charging stations for electric vehicles in urban areas: formulation, complexity and solutions

The deployment of charging infrastructure for electric vehicles is crucial in extending their range. Many studies on the charging infrastructure deployment adopt the Mixed Integer Linear Programming (MILP) method to optimize various objectives. However, as the number of integer variables and constraints increases, the computational time and memory requirements of MILP models increase exponentially. This makes it impractical to use MILP models to solve large-scale optimization problems. In this paper, we formulate and prove that the Planning of Electric Vehicle Charging Stations (PEVCS) is an NP-complete combinatorial optimization problem. We also prove that PEVCS has a significant effect, that is, submodularity. Additionally, we propose two efficient methods that use submodularity to improve the conventional methodology for PEVCS. Furthermore, we provide a provable guarantee for the performance of our proposed methods. Our experimental results demonstrate the efficiency and effectiveness of these methods on small-scale and large-scale datasets, especially in realistic large-scale situations.

Optimizing the Use of Meninting Multipurpose Reservoir Water in West Lombok District

The construction of the Meninting Reservoir was planned with the objective of meeting the irrigation and domestic water demands on Lombok Island. It served as a multipurpose reservoir, with a maximum storage volume of 12.18 million m³, mainly for supplying irrigation and domestic water. The reservoir had considerable potential for water availability, which could be used to supply water to the South Lombok region with limited water availability but had agricultural land potential. Therefore, this study aimed to evaluate the potential of Meninting Reservoir water availability and its optimum utilization for irrigation and domestic purposes. The irrigation water demand for 1,559.29 ha and domestic water demand of 150 ls-1 was fulfilled by Meninting Reservoir. Water availability in this Reservoir was estimated with the F.J. Mock method of rainfall-runoff model using 25 years of daily rainfall data from Gunung Sari and Sesaot rain gauge stations. The calibration process of the rainfall-runoff parameters models employed observed discharge data from the Aiknyet water level gauge station. The formula for optimizing reservoir water release was prepared using the linear programming method based on operational water level limits, inflow discharge, irrigation, and non-irrigation water requirements, including domestic water. The optimal average annual cropping intensity was 203.96%, 215.87%, and 241.41% for dry, normal, and wet years, respectively. The service reliability of irrigation and domestic water demands reached 100% for all inflow discharge conditions. The k-factor value met the minimum limit of 0.70 and 0.85 for irrigation and domestic water demands, respectively.

Perencanaan Produksi Makanan Laut dengan Pertimbangan Permintaan dan Kapasitas

The sea holds many resources that are very important for life, and one of them is the potential of fisheries, which is a basic human need. Indonesia, as a maritime country whose waters cover 2/3 of its territory, most of its people who live in coastal areas have utilized this condition by conducting fisheries management activities. However, the process still needs technical support to optimize the results. This research will review the production planning process of processed marine products under demand uncertainty. This research will construct a model to minimize production costs by considering demand uncertainty. The model will be computed using Mixed Integer Linear Program (MILP) method to provide the decision of processed products produced and the amount of production.

Simplifying Production Capacity and Workforce Planning for Firms in Ghana’s Distillery Industry: A Simplex Linear Programming Illustration

The convoluted operational nature of the distillery industry has left production managers battling with their planning needs. Meanwhile competition in the industry is nurtured around efficient and effective production facility and workforce configurations. Using a hypothetical dataset, this paper demonstrates how firms in Ghana’s distillery industry can apply plant capacity utilization and efficiency measures, financial cost and volume analysis, and machine hour measuring techniques to plan their production configurations at optimal cost and profit levels. The paper also designs a workforce re-engineering model for firms using a Simplex Linear Programming (LP) Method. Firms are now assured of an effective strategy for decision-making on the type of production plant to install the quantity of products to produce in a particular period and the maximum cost and profit levels to produce at. In addition, firms can also determine labor-hours and overtime schedules that would be required for a particular production period accurately.

Co-optimization of decarbonized operation of coal-fired power plants and seasonal storage based on green ammonia co-firing

Coal-fired power plants (CFPP) can provide significant inertia and flexibility support for power systems with a high share of renewable energy (RE). The ammonia–coal co-firing technology can effectively reduce carbon emissions (CE) from CFPP. We propose a low-carbon power supply and multi-timescale energy storage system in combination with this technology. The system consists of batteries, fuel cells and the CFPP equipped with the ammonia–coal co-combustion module. It can also cope with short and long term fluctuations in RE. We use the Mixed Integer Linear Programming method to construct an optimization model for this system. We then set up six sub-cases according to the power systems in Texas, USA. Based on weekly and annual simulations of these cases, we analyze the economic and environmental performances of the proposed system with different RE shares, as well as exploring the characteristics of different energy storage methods. Compared to batteries or fuel cells only scenarios, CFPP configured with green ammonia co-firing can significantly reduce the total operating cost (TOC), CE and RE curtailment. We use the rolling horizon optimization method to simulate and calculate the distribution of ammonia storage levels throughout the year. The ammonia storage levels are high in spring and autumn and low in summer. Finally, the sensitivity and efficiency analysis of the proposed system is carried out. As far as ammonia co-firing technology allows, the higher the maximum ammonia–coal mixing ratio, the lower TOC, CE and RE curtailment. This phenomenon is more significant at a higher RE share. The overall efficiency of green ammonia synthesis and combustion for power generation is around 13.92%. It can work in synergy with batteries and fuel cells to improve efficiency and reduce the marginal cost of long-term energy storage.

Multi-Objective Optimal DG Placement Approach Using Analytical Hierarchy Process

Distributed generation (DG) has been increasingly integrated into distribution systems in the last decade. The selection of the optimal location and capacity of these DGs is an important issue. This selection is based on minimizing losses, reducing emissions, reducing voltage deviation, and much more. This paper proposes a new optimization approach with a multi-objective function for maximizing DG capacities and minimizing both system losses and voltage deviation, which are subject to system constraints. The weight of each attribute of the multi-objective function is estimated using the analytical hierarchical process (AHP). The optimal DG size is calculated for all possible buses, and hence, the optimal bus can be located. Moreover, an algorithm is introduced to decrease the number of iterations when integrating more than one DG. The proposed method is an iterative linear programming method based on the familiar Newton-Raphson sensitivity matrix. The proposed approach has been tested on 69 and IEEE 33 bus systems. The simulation results are compared with previous literature results.

AN ANALYSIS OF GOMORY CUTTING PLANE METHOD APPLICATION IN THE OPTIMIZATION OF PRODUCTION PROFIT: A CASE STUDY OF GRIYA BATIK NOTONEGORO JEMBER

Gomory cutting plane method is one of the methods in linear programming that is needed to solve integer programming when the decision obtained is in the form of fractions with the addition of constraint known as gomory constraint. The purpose of this research is to determine the best optimum solution by maximizing the profit of batik production using the gomory cutting plane method. This type of research is applied research using a quantitative approach. Data collection methods used are interviews and documentation. This research is focused on four kinds of Jember batik motifs which are the best-selling, namely mbako semak batik cloth; sekar jagad batik cloth; kopi daun batik cloth; and parakopi batik cloth. The results showed that there was an increase in profit of or per production when using the simplex method assisted by QM for Windows V5 software. Meanwhile, to make batik cloth, integer values are needed in the form of integers. Therefore, the application of gomory cutting plane method in optimizing the profit of batik production is very appropriate to use with the obtained maximum settlement of which occurs when sheets, sheets, sheets, and sheets.