scholarly journals A Generalized MILP Formulation for the Period-Aggregated Resource Leveling Problem with Variable Job Duration

Algorithms ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 6 ◽  
Author(s):  
Ilia Tarasov ◽  
Alain Haït ◽  
Olga Battaïa
Keyword(s):  
Optimization Problem ◽  
Mathematical Formulation ◽  
Planning Horizon ◽  
Resource Leveling ◽  
Job Duration ◽  
Time Period ◽  
Decision Variables ◽  
Additional Costs ◽  
Flexible Resource ◽  
The Given

We study a resource leveling problem with variable job duration. The considered problem includes both scheduling and resource management decisions. The planning horizon is fixed and separated into a set of time periods of equal length. There are several types of resources and their amount varies from one period to another. There is a set of jobs. For each job, a fixed volume of work has to be completed without any preemption while using different resources. If necessary, extra resources can be used at additional costs during each time period. The optimization goal is to minimize the total overload costs required for the execution of all jobs by the given deadline. The decision variables specify the starting time of each job, the duration of the job and the resource amount assigned to the job during each period (it may vary over periods). We propose a new generalized mathematical formulation for this optimization problem. The formulation is compared with existing approaches from the literature. Theoretical study and computational experiments show that our approach provides more flexible resource allocation resulting in better final solutions.

scholarly journals A contact problem of bending of two beams with the internal joint

2021 ◽  
pp. 37-42
Author(s):  
Mikhail Osipenko ◽  
Keyword(s):  
Analytical Solution ◽  
Contact Problem ◽  
Composite Beam ◽  
Optimization Problem ◽  
Mathematical Formulation ◽  
Concentrated Force ◽  
Cubic Equation ◽  
Internal Joint ◽  
Uniqueness Of The Solution ◽  
The Given

The joint bending of two Bernoulli–Euler’s beams is considered. Each beam has one end fixed and the other free. The beams have the different lengths and thicknesses. The long beam is loaded by the concentrated force. This beam is composite as it includes the internal joint. There is the frictionless unilateral contact between the beams. The elastic lines of the beams are to be found. This problem is reduced to finding of the density of forces of interaction between the beams and the constant that describes the unknown term in the displacement of the unrestrained part of the composite beam. The mathematical formulation of this contact problem is propounded. The density is assumed to be the sum of piecewise continuous function and delta-functions describing the concentrated forces. The uniqueness of the solution of the problem is proved and the analytical solution is constructed. Two possible contact patterns are found out. The former is contact at one point at the end of the short beam. The latter is contact at the same point and at one more point located at the unrestrained part of the composite beam. The coordinate of this point is the root of the cubic equation. The obtained analytical solution is used for the optimization of the structure. The optimization problem is to find the beams thicknesses that minimize the maximum stress for the given loading, beams lengths and the overall deflection. This problem is solved numerically for some values of the given parameters. The hypothesis of the equal-stressed optimum structure is set up on the basis of the numerical results. This hypothesis enables to construct the analytical solution of the optimization problem.

The Ideology of Socialism and the Armenian Political Parties

wisdom ◽  
2020 ◽  
Vol 15 (2) ◽  
pp. 107-113
Author(s):  
Gegham HOVHANNISYAN
Keyword(s):  
Political Parties ◽  
Political Life ◽  
The Political ◽  
Political Organizations ◽  
Social Democrats ◽  
Time Period ◽  
The Social ◽  
Political Forces ◽  
The 19Th Century ◽  
The Given

The article covers the manifestations and peculiarities of the ideology of socialism in the social-political life of Armenia at the end of the 19th century and the beginning of the 20th century. General characteristics, aims and directions of activity of the political organizations functioning in the Armenian reality within the given time-period, whose program documents feature the ideology of socialism to one degree or another, are given (Hunchakian Party, Dashnaktsutyun, Armenian Social-democrats, Specifics, Socialists-revolutionaries). The specific peculiarities of the national-political life of Armenia in the given time-period and their impact on the ideology of political forces are introduced.

Quasi-Periodic Control Technique for Minimizing Fuel Consumption During Record Vehicle Competition

2013 ◽  
Vol 60 (2) ◽  
pp. 185-197 ◽  
Author(s):  
Paweł Sulikowski ◽  
Ryszard Maronski
Keyword(s):  
Fuel Consumption ◽  
Optimal Control Theory ◽  
Slope Angle ◽  
Control Technique ◽  
Decision Variables ◽  
Aeronautical Engineering ◽  
The One ◽  
Optimal Driving ◽  
The Given ◽  
Engine Power

The problem of the optimal driving technique during the fuel economy competition is reconsidered. The vehicle is regarded as a particle moving on a trace with a variable slope angle. The fuel consumption is minimized as the vehicle covers the given distance in a given time. It is assumed that the run consists of two recurrent phases: acceleration with a full available engine power and coasting down with the engine turned off. The most fuel-efficient technique for shifting gears during acceleration is found. The decision variables are: the vehicle velocities at which the gears should be shifted, on the one hand, and the vehicle velocities when the engine should be turned on and off, on the other hand. For the data of students’ vehicle representing the Faculty of Power and Aeronautical Engineering it has been found that such driving strategy is more effective in comparison with a constant speed strategy with the engine partly throttled, as well as a strategy resulting from optimal control theory when the engine is still active.

Utilization of remote sensing for estimation of scale of cutting and growing of forest zones

2017 ◽  
Vol 920 (2) ◽  
pp. 57-60
Author(s):  
F.E. Guliyeva
Keyword(s):  
Remote Sensing ◽  
Fixed Time ◽  
Time Interval ◽  
Time Points ◽  
Average Value ◽  
Time Period ◽  
Remote Estimation ◽  
The Given ◽  
Forest Cutting

The study of results of relevant works on remote sensing of forests has shown that the known methods of remote estimation of forest cuts and growth don’t allow to calculate the objective average value of forests cut volume during the fixed time period. The existing mathematical estimates are not monotonous and make it possible to estimate primitively the scale of cutting by computing the ratio of data in two fixed time points. In the article the extreme properties of the considered estimates for deforestation and reforestation models are researched. The extreme features of integrated averaged values of given estimates upon limitations applied on variables, characterizing the deforestation and reforestation processes are studied. The integrated parameter, making it possible to calculate the averaged value of estimates of forest cutting, computed for all fixed time period with a fixed step is suggested. It is shown mathematically that the given estimate has a monotonous feature in regard of value of given time interval and make it possible to evaluate objectively the scales of forest cutting.

scholarly journals The Model of Sociological Education in the USSR (the Late 1950s — Early 1980s)

2021 ◽  
pp. 112-117
Author(s):  
Sergei V. Kozin ◽  
Zhanna B. Litvinova
Keyword(s):  
Sociological Research ◽  
Scientific Publications ◽  
Mutual Exchange ◽  
Research Areas ◽  
Time Period ◽  
The Given ◽  
Soviet Sociology

The article provides an analysis of foreign and Soviet scientific publications devoted to the problem of sociological education, the “revival” of Soviet sociology, as well as to the role and place of sociology among the sciences, in society and education. The given study covers the time period of the late 1950s — early 1980s and briefly describes the education of the population of the USSR at that time. Looking through the works on Soviet sociology, the authors show that sociology was introduced not only into the research areas of specific universities and laboratories, but also into many other branches and spheres of activity, as well as into the authorities’ activity. The authors of the article purposefully focus on the role of consolidation and mutual exchange of sociological research from various sociological services.

scholarly journals THE WARSHIP ASSIGNMENT SCHEDULE USING INTEGER PROGRAMMING MODEL

JOURNAL ASRO ◽  
2019 ◽  
Vol 10 (3) ◽  
pp. 49
Author(s):  
Ahmadi Ahmadi ◽  
Benny Sukandari ◽  
Agus Mahrowi
Keyword(s):  
Integer Programming ◽  
Programming Model ◽  
Mathematical Formulation ◽  
Combinatorial Problem ◽  
Mathematical Methods ◽  
Alternative Scheduling ◽  
Integer Programming Model ◽  
Maintenance Schedule ◽  
Hard Constraints ◽  
Decision Variables

Scheduling is an assignment activity that deals with constraints. A number of events can occur in a period of time and location so that objective functions as close as possible can be fulfilled. In the hierarchy of decision making, scheduling is the last step before the start of an operation. Scheduling warship assignments in Kolinlamil are an interesting topic to discuss and find solutions to using mathematical methods. The process of the Kolinlamil warship assignment schedule was carried out to produce an annual shipbuilding schedule. This process not only requires fast follow-up, but also requires systematic and rigorous steps. Where the assignment schedule is a fairly complex combinatorial problem. While making the assignment schedule that is applied at this time is considered less accurate because it calculates the conventional method. The process of warship assignment schedule in this study using the Integer Programming model aims to obtain alternative scheduling operations. The schedule observed was 13 warships in carrying out N operations for 1 year (52 weeks). This research begins with determining the decision variables and limitations that existing constraints. Hard constraints include: maintenance schedule, time and duration of each task, warship class assigned to the task and the number of executing warships per task. While soft constraints are how long the warship performs its tasks in a row. The mathematical formulation of the Integer Programming model created consists of three indicator, one decision variables, two measuring parameters and five constraint functions. Furthermore, determining the best scheduling alternatives is completed using the Microsoft Exel Solver computing program.Keywords: Scheduling, Integer Programming, Solver.

scholarly journals CULTURAL HERITAGE MONUMENT DOCUMENTATION THROUGH ADAPTIVE PARAMETRIC DESIGN PROCESS

2021 ◽  
Vol XLVI-M-1-2021 ◽  
pp. 769-776
Author(s):  
G. Tryfonos ◽  
M. Ioannides ◽  
A. G. Anastasi ◽  
V. A. Apostolou ◽  
P. P. Pieri ◽  
...  
Keyword(s):  
Cultural Heritage ◽  
Parametric Design ◽  
3D Models ◽  
Building Information Modelling ◽  
3D Data ◽  
Time Period ◽  
Building Information ◽  
Game Developers ◽  
The Given ◽  
The City

Abstract. The paper presents a novel adaptive parametric documentation, modelling and sharing methodology, which aims to achieve a continuous holistic documentation, data processing and sharing process for cultural heritage community, such as architects, engineers, archaeologists, conservators, programmers, fabricators, contest creators, game developers, scholars and common citizens. Thus, the use of advance parametric and building information modelling software allows the processing and specification of all data by creating the 3D models needed for the multidisciplinary experts. Two Cypriot case studies from the medieval time period have been chosen for the development, and evaluation of our proposed methodology in order to investigate the process of modelling and sharing all the given metadata and 3D data. The first one is the Asinou Church, a UNESCO Heritage stone monument in the Troodos Mountains with a unique interior and the Kolossi Castle, a former Crusader stronghold on the west of the city of Limassol on the island of Cyprus.

Feeder Ship Size Optimization in Maritime Markets with Uncertainty

2021 ◽  
Vol 38 (03) ◽  
pp. 2040014
Author(s):  
Hongtao Hu ◽  
Jiao Mo ◽  
Lufei Huang
Keyword(s):  
Dynamic Programming ◽  
Stochastic Dynamic Programming ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Planning Horizon ◽  
Dynamic Programming Method ◽  
Size Optimization ◽  
Stochastic Dynamic ◽  
Shipping Company ◽  
Decision Behaviors

This paper considers the ship size optimization problem for a liner shipping company that provides feeder service between one hub port and one feeder port. In the maritime market with uncertainty, this problem becomes more challenging. This research first analyzes the decision behaviors of the shipping company. Then, a stochastic dynamic programming method is proposed to calculate the expected total volume of containers transported within the planning horizon. Using the calculated volumes as input parameters calculate the profit of each ship sizes and then determine the suitable ship size for the feeder route. Numerical experiments are performed to validate the effectiveness of the proposed method and the efficiency of the proposed algorithm.

scholarly journals Heat transfer from convecting-radiating fin through optimized Chebyshev polynomials with interior point algorithm

2019 ◽  
Vol 9 (1) ◽  
pp. 102-110
Author(s):  
Elyas Shivanian ◽  
Mahdi Keshtkar ◽  
Hamidreza Navidi
Keyword(s):  
Heat Transfer ◽  
Chebyshev Polynomials ◽  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problem ◽  
Mathematical Formulation ◽  
Interior Point Algorithm ◽  
Equivalent Problem ◽  
One Dimensional ◽  
Fin Efficiency

AbstractIn this paper, the problem of determining heat transfer from convecting-radiating fin of triangular and concave parabolic shapes is investigated.We consider one-dimensional, steady conduction in the fin and neglect radiative exchange between adjacent fins and between the fin and its primary surface. A novel intelligent computational approach is developed for searching the solution. In order to achieve this aim, the governing equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem. Additionally, heat transfer rate and the fin efficiency are reported.

scholarly journals A Knowledge-Based Simulated Annealing Algorithm to Multiple Satellites Mission Planning Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Da-Wei Jin ◽  
Li-Ning Xing
Keyword(s):  
Simulated Annealing ◽  
Optimization Problem ◽  
Simulated Annealing Algorithm ◽  
Mission Planning ◽  
Knowledge Based ◽  
Combination Optimization ◽  
Annealing Algorithm ◽  
The Given ◽  
Planning Problems ◽  
Annealing Method

The multiple satellites mission planning is a complex combination optimization problem. A knowledge-based simulated annealing algorithm is proposed to the multiple satellites mission planning problems. The experimental results suggest that the proposed algorithm is effective to the given problem. The knowledge-based simulated annealing method will provide a useful reference for the improvement of existing optimization approaches.

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