scholarly journals Mathematical model and algorithm for solving the problem of planning the operation of multiphase systems with heterogeneous resources and time limits

2021 ◽  
pp. 35-45
Author(s):  
Ivan Alekseevich Selishchev ◽  
Svetlana Aleksandrovna Oleinikova
Keyword(s):  
Mathematical Model ◽  
Production Systems ◽  
Critical Path ◽  
Parallel Solution ◽  
Time Limits ◽  
Stochastic Nature ◽  
Optimization Task ◽  
Single Operation ◽  
Multiphase Systems ◽  
Algorithmic Software

The object of this research is the modern service and production systems, the specific functioning of which lies in a set of sequential and parallel operations with a random duration. A fundamental peculiarity of such systems is the stochastic nature of the duration of a single operation, which depends not only on the external random factors, but also on the choice of resources, and namely on the operator. This substantiates the parallel solution of the task on making a schedule of mutually dependent operations and the task on assigning the operators. In the conditions of resource and time limits, this task is NP difficult and requires the development of algorithms for developing the solution that is close to optimal in the limited time. For the development of mathematical and algorithmic software to solve this task, the author used the critical path method and PERT method, incident wave method, and methods for solving the assignment tasks. As a result, the author acquired a mathematical model that considers the stochastic nature of the duration of a single operation, which depends not only on random factors, but also on the operators. Based on such model, is formulated the optimization task that allows finding the launch time and the corresponding operators to gain the most profit. Based on the analysis of existing approaches and the specificity of the task at hand, the author proposes the algorithm for solving the task founded on successive refinement of the time characteristics of operations.

The substantiation of the formalized estimation of effectiveness of technological and production systems

2018 ◽  
Vol 15 (1) ◽  
pp. 169-181
Author(s):  
M. I. Sidorov ◽  
М. Е. Stavrovsky ◽  
V. V. Irogov ◽  
E. S. Yurtsev
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Production Systems ◽  
Van Der Pol

Using the example of van der Pol developed a mathematical model of frictional self-oscillations in topochemically kinetics. Marked qualitative correspondence of the results of calculation performed using the experimental data of researchers.

scholarly journals METHODS OF FORMULATING AND SOLVING OPTIMIZATION PROBLEMS OF CUTTING LOGS OF LARGE SIZE BY BAR-SAWING METHOD WITH CUTTING OUT ONE BAR AND FIVE PAIRS OF SIDE EDGING BOARDS WITH SUBSEQUENT SAWING LUMBER FOR EDGED BOARDS

2017 ◽  
Vol 7 (1) ◽  
pp. 137-150
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Target Function ◽  
Cross Sectional ◽  
Optimization Task ◽  
Cutting Out ◽  
The Mathematical Model ◽  
The Relationship

For the first time the mathematical model of task optimization for this scheme of cutting logs, including the objective function and six equations of connection. The article discusses Pythagorean area of the logs. Therefore, the target function is represented as the sum of the cross-sectional areas of edging boards. Equation of the relationship represents the relationship of the diameter of the logs in the vertex end with the size of the resulting edging boards. This relationship is described through the use of the Pythagorean Theorem. Such a representation of the mathematical model of optimization task is considered a classic one. However, the solution of this mathematical model by the classic method is proved to be problematic. For the solution of the mathematical model we used the method of Lagrange multipliers. Solution algorithm to determine the optimal dimensions of the beams and side edging boards taking into account the width of cut is suggested. Using a numerical method, optimal dimensions of the beams and planks are determined, in which the objective function takes the maximum value. It turned out that with the increase of the width of the cut, thickness of the beam increases and the dimensions of the side edging boards reduce. Dimensions of the extreme side planks to increase the width of cut is reduced to a greater extent than the side boards, which are located closer to the center of the log. The algorithm for solving the optimization problem is recommended to use for calculation and preparation of sawing schedule in the design and operation of sawmill lines for timber production. When using the proposed algorithm for solving the optimization problem the output of lumber can be increased to 3-5 %.

A Model for Shortening the Length of Activities in Construction and Overhaul Planning: UPROB

2002 ◽  
Author(s):  
Niko Majdandzˇic´ ◽  
Slavko Sebastijanovic´ ◽  
Gordana Maticˇevic´ ◽  
Nebojsˇa Sebastijanovic´
Keyword(s):  
Mathematical Model ◽  
Thermal Energy ◽  
Input Data ◽  
Critical Path ◽  
Planning System ◽  
Task Completion ◽  
Assembly Lines ◽  
Total Cost ◽  
Activity Cost ◽  
Optimal Variation

This paper presents a mathematical model of the UPROB (planning system for construction and overhaul) system that was developed for tank assembly lines, construction of thermal energy structures, and for performing an overhaul in complex plants. Planning technology includes utilizing linear diagrams with a direct usage of input data from a plant’s database. A model has been developed to determine the critical path and also, to define steps for the most economical shortening of the entire plan. Several plan variations are developed (according to specified goals) and the management determines the optimal variation. After selecting a plan, it is possible to control and create work orders for individual tasks in certain activities. Task completion percentage, activity cost, and the total cost of the plan are also provided.

Multi-Fluid Mathematical Model for Blast Furnace and its Parallel Solution

2014 ◽  
Vol 675-677 ◽  
pp. 1463-1472
Author(s):  
Jia Le Meng ◽  
Jian Hua Shao ◽  
Ai Min Zhao
Keyword(s):  
Heat Transfer ◽  
Fluid Dynamics ◽  
Mathematical Model ◽  
Computational Fluid Dynamics ◽  
Blast Furnace ◽  
Furnace Operation ◽  
Blast Furnace Operation ◽  
Computing Technology ◽  
Parallel Solution ◽  
Accelerate Convergence

Developing blast furnace model is benefit to understand, control and improve blast furnace iron making process. Multi-fluid blast furnace model was established on computational fluid dynamics, reaction kinetics, transport phenomena and other theories. In the model, complicated motion and heat transfer between phases of gas, liquid and solid were considered and numerous reactions in blast furnace were simplified. Because there were so many equations in the model and there were strong coupling relationships between phases, parallel computing technology using computer group was adopted to solve the model to accelerate convergence velocity of iteration. The model can provide versatile information, it is a useful tool to simulate blast furnace operation.

scholarly journals Simple mathematical model to predict the amount of energy produced in wind turbine - preliminary study

2021 ◽  
Vol 332 ◽  
pp. 01004
Author(s):  
Sylwester Borowski ◽  
Agnieszka Soltysiak ◽  
Klaudiusz Migawa ◽  
Andrzej Neubauer
Keyword(s):  
Mathematical Model ◽  
Wind Turbine ◽  
Production Systems ◽  
Renewable Energy Sources ◽  
Electricity Production ◽  
Decision Making Process ◽  
Simple Mathematical Model ◽  
Average Wind Speed ◽  
Average Wind ◽  
Preliminary Study

The manuscript presents a simple mathematical model for predicting the amount of energy produced in a wind turbine. As part of the own research, the data obtained from the SCADA program for the Enercon E-82 wind turbine was analyzed. It has been shown that it is possible to build a mathematical model to determine the amount of energy produced from the average wind speed. This method will be primarily useful for forecasting the volume of production as well as electricity demand, with particular emphasis on renewable energy sources. The application of the developed method in practice will facilitate and accelerate the implementation of the decision-making process in electricity production systems, while reducing the risk of error. This model can also be used to make repowering decisions.

scholarly journals Decomposition-Coordinating Method for Parallel Solution of a Multi-area Combined Economic Emission Dispatch Problem

2016 ◽  
Vol 6 (5) ◽  
pp. 2048
Author(s):  
Senthil Krishnamurthy ◽  
Raynitchka Tzoneva
Keyword(s):  
Power System ◽  
High Performance ◽  
Optimization Methods ◽  
System Control ◽  
Parallel Solution ◽  
Power System Control ◽  
Optimization Task ◽  
Tie Lines ◽  
Emission Dispatch ◽  
Economic Emission Dispatch

<p>Multi-area Combined Economic Emission Dispatch (MACEED) problem is an optimization task in power system operation for allocating the amount of generation to the committed units within the system areas. Its objective is to minimize the fuel cost and the quantity of emissions subject to the power balance, generator limits, transmission line and tie-line constraints. The solutions of the MACEED problem in the conditions of deregulation are difficult, due to the model size, nonlinearities, and the big number of interconnections, and require intensive computations in real-time. High-Performance Computing (HPC) gives possibilities for the reduction of the problem complexity and the time for calculation by the use of parallel processing techniques for running advanced application programs efficiently, reliably and quickly. These applications are considered as very new in the power system control centers because there are not available optimization methods and software based on them that can solve the MACEED problem in parallel, paying attention to the existence of the power system areas and the tie-lines between them. A decomposition-coordinating method based on Lagrange’s function is developed in this paper. Investigations of the performance of the method are done using IEEE benchmark power system models.</p>

Interactive Job Shop Experiments System on Education

2013 ◽  
Vol 411-414 ◽  
pp. 2938-2941
Author(s):  
Ning Zhao ◽  
Chuan Biao Xu
Keyword(s):  
Mathematical Model ◽  
Job Shop ◽  
Critical Path ◽  
Optimal Solution ◽  
Experiment System ◽  
Interactive Algorithm ◽  
Interactive Scheduling ◽  
Interactive Evaluation

In order to simplify teaching work and improve teaching effect for the education of the job shop problem (JSP), an interactive scheduling experiment system (ISES) is introduced. The system realizes interactive function through 3 modules (move interactive, algorithm interactive, evaluation interactive). Group adjustment and Critical path are built to ensure constraints and search the optimal solution in interactive way, Mathematical model and schedule algorithms are built to help teaching. A teaching example is showed at last.

Modeling for the Optimization Evaluation of Layout Scenarios of Subsea Cluster Manifolds Considering Three Connection Types

2014 ◽  
Vol 48 (6) ◽  
pp. 98-111 ◽  
Author(s):  
Yingying Wang ◽  
Honglin Zhao ◽  
Deguo Wang ◽  
Minghua Xu ◽  
Marcelo Igor Lourenço ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Numerical Simulations ◽  
Programming Problem ◽  
Production Systems ◽  
Connection Matrix ◽  
Ocean Engineering ◽  
Cost Matrix ◽  
Proposed Model

AbstractBased on a connection matrix and a cost matrix, a mathematical model is presented to describe the optimization evaluation of the layout scenarios of subsea cluster manifolds in ocean engineering at the lowest cost. The connection facilities are considered, including jumpers, pipeline end terminations (PLETs), and infield flowlines. The dedicated series-iteration algorithms programed by MATLAB are conducted to solve this complex nonlinear 0‐1 programming problem. Additionally, numerical simulations are performed to demonstrate the validity of the model and the performance of its algorithms. The results show that the proposed model can precisely describe the layout characteristics of cluster manifolds in engineering and the dedicated algorithms are quite robust. Possible layout scenarios with three-to-eight cluster manifolds for 22 subsea wells can be obtained, from which the optimal one with the lowest cost can be found by comparison. This approach can provide quantitative and efficient references to engineers to assist them in making their decisions in the layout of subsea production systems.

scholarly journals Worker Movement Diagram Based Stochastic Model of Open Paced Conveyors

2018 ◽  
Vol 46 (2) ◽  
pp. 55-62 ◽  
Author(s):  
Tamás Ruppert ◽  
János Abonyi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Human Resources ◽  
Stochastic Model ◽  
Manufacturing Systems ◽  
Production Systems ◽  
Benchmark Problem ◽  
Stochastic Nature ◽  
Moving Patterns ◽  
Open Nature

Abstract Human resources are still utilized in many manufacturing systems, so the development of these processes should also focus on the performance of the operators. The optimization of production systems requires accurate and reliable models. Due to the complexity and uncertainty of the human behavior, the modeling of the operators is a challenging task. Our goal is to develop a worker movement diagram based model that considers the stochastic nature of paced open conveyors. The problem is challenging as the simulator has to handle the open nature of the workstations, which means that the operators can work ahead or try to work off their backlog, and due to the increased flexibility of the moving patterns the possible crossings which could lead to the stopping of the conveyor should also be modeled. The risk of such micro-stoppings is calculated by Monte-Carlo simulation. The applicability of the simulator is demonstrated by a well-documented benchmark problem of a wire-harness production process.

scholarly journals Matheuristic Algorithm for Job-Shop Scheduling Problem Using a Disjunctive Mathematical Model

Computers ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 1
Author(s):  
Eduardo Guzman ◽  
Beatriz Andres ◽  
Raul Poler
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Open Source ◽  
Job Shop ◽  
Job Shop Scheduling ◽  
Production Systems ◽  
Machine Scheduling ◽  
Efficient Solutions ◽  
Point Of View ◽  
Sequencing Problems

This paper focuses on the investigation of a new efficient method for solving machine scheduling and sequencing problems. The complexity of production systems significantly affects companies, especially small- and medium-sized enterprises (SMEs), which need to reduce costs and, at the same time, become more competitive and increase their productivity by optimizing their production processes to make manufacturing processes more efficient. From a mathematical point of view, most real-world machine scheduling and sequencing problems are classified as NP-hard problems. Different algorithms have been developed to solve scheduling and sequencing problems in the last few decades. Thus, heuristic and metaheuristic techniques are widely used, as are commercial solvers. In this paper, we propose a matheuristic algorithm to optimize the job-shop problem which combines a genetic algorithm with a disjunctive mathematical model, and the Coin-OR Branch & Cut open-source solver is employed. The matheuristic algorithm allows efficient solutions to be found, and cuts computational times by using an open-source solver combined with a genetic algorithm. This provides companies with an easy-to-use tool and does not incur costs associated with expensive commercial software licenses.

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