Basis Of Linear Programming Research Articles

Aircraft fleet optimization by the simplex method

The transport system efficiency and the quality of its operation is organically connected with the improvement of air transportation technical means on the basis of modern science and technology. One of the directions of further aviation transport system development is the creation of methodological basis for optimal aircraft operation. Therefore, the increase in aircraft efficiency is one of the important tasks, as its improvement is associated with savings in material and financial resources, which affects the fleet structure and the process of passenger traffic. The article is intended to substantiate the method of optimizing the use of airline aircraft by means of mathematical apparatus. It has been found that the mathematical model structure is required to form an optimal aircraft fleet. A variant of aircraft fleet formation has been proposed taking into account the mathematical model, built on the basis of linear programming, namely, using the simplex method. It has been determined that the choice of optimal aircraft options is greatly influenced by the value of the parametric series. To obtain a reliable result, the aircraft loading must be 100%, otherwise the error grows due to coefficients at unknown target function. The proposed method of determining the optimal fleet with different types of aircraft and air traffic routes, taking into account the conditions of their usage, allows to recommend airlines to use aircraft with the highest efficiency.

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.

Finite-Time Control for Discrete-Time Positive Systems Subject to Event-Triggered Scheme and Markov Jump Parameters

This brief investigates the finite-time control problem for discrete-time positive systems subject to event-triggered scheme and Markov jump parameters. Switching transition probability is used to extend the fixed transition probability, which is more suitable to describe the performance of Markov jump systems (MJSs). On the basis of the 1-norm, a developed event-triggered scheme is proposed to be associated with the sample signal and the actual signal. Furthermore, a linear Lyapunov function and an average dwell time approach are adopted to obtain sufficient conditions for guaranteeing stochastic finite-time stability of the underlying systems. Additionally, a matrix decomposition strategy is constructed to design a finite-time event-triggered control law such that the corresponding MJSs are positive and stochastically finite-time bounded. All conditions are proposed on the basis of linear programming. Finally, a local railway transportation model is provided to verify the practicability of the strategy.

The Main Approashes for Increasing the Efficiency of the Rural School Network

The purpose of the article is to identify the main directions of improvement of the network of institutions of general secondary education in rural areas on the example of Ukraine. The authors developed an algorithm for research, consisting of four stages. During the study, the preconditions for forming a network of rural schools were considered. The following network parameters such as warehouse, spatial structure are found. Based on the analysis of modern socio-pedagogical requirements, the concept of promising organization of school services in rural areas has been developed. It is established that in conditions of rural settlements, it is advisable to form teams for teaching from pupils of different ages (multigrade classes). The authors provided suggestions on the formation of territorial educational districts as a promising direction for improving the network of rural schools. The perspective types of institutions of general secondary education, which are formed on the basis of interagency integration with other objects of cultural and household services of the population, are revealed. To improve the process of designing a network of village schools, the authors developed a methodology for optimizing the network of schools on the basis of linear programming.

MODEL FOR PREDICTIVE PURPOSE OF POPULATION BY MAJOR FOODS IN ACCORDANCE WITH RATIONAL NORMS OF ITS CONSUMPTION

Providing the population with affordable safe food is becoming increasingly important due to the growing population of the planet, the aggravation of socio-economic relations between states, the increase in the number of environmental problems and the replacement of natural organic food with snacks, products containing artificial components and GMOs, and functional foods. The article discusses the planning of measures taken by the regional authorities to provide the population with basic types of food, the calculation of the needs of which is compiled in accordance with rational norms for the consumption of food products that meet modern requirements for healthy nutrition. On the basis of linear programming, a model of predictive provision of the population with basic types of food products for the period 2018-2020 was compiled. The data on the compiled model can be prolonged and corrected when the statistical indicators of 2016, 2017 are obtained and the planned number of population in the period under review is specified. As a result of the study, the forecasted values of the required volume of food for the population of the Irkutsk region were obtained. The basic components of the mechanism of interaction of all interested subjects of the food market and a set of conditions for the implementation of promising directions of the mechanism for the formation and implementation of food policy in accordance with the stated goals are proposed. Social effectiveness in achieving the performance indicators proposed in the work will be determined by increasing the life expectancy of the population, reducing morbidity, improving the quality of life of those suffering from diseases associated with unsustainable nutrition, and the ratio of the resulting favorable social results to the costs to achieve them, while economic efficiency will be expressed by an estimate The impact of the results achieved in the implementation of program activities on the formation of the gross product, and Vyshen productivity and ensuring the dynamics of economic growth.

Optimization of work performance of snow removal work trains on the basis of linear programming

The introduction of monitoring systems for the work performance of special rolling stock and monitoring the load of snow removal work trains revealed a number of shortcomings in the planning, organization, and recording of work performed by snow removal work trains. The elimination of the identified problems is possible on the basis of optimization of work performance, the implementation of which can be achieved on the basis of existing systems with appropriate additional functionality. For this purpose, in the framework of the theoretical studies presented in the paper, a methodology for optimization of work performance of snow removal work trains has been developed. Linear programming is adopted as a method of solving the optimization problem. On the basis of the algorithm for solving the transport problem, the problem of minimizing the cost of snow removal from various sections of the track by the existing park of work trains is formulated, for which a mathematical model is constructed that includes the objective function and the corresponding restrictions. The results of the study show that the widespread use of work planning on the basis of the presented optimization methodology will make it possible to make the most efficient use of snow removal equipment and, as a result, to reduce the cost of this type of railway track maintenance work.

全国の電力基幹系統を考慮した最適電源構成モデルの開発と太陽光・風力発電大量導入に関する分析

This paper develops an optimal power generation mix model considering nationwide high-voltage power grid in Japan and aims to analyze the massive deployment of variable renewable (VR) such as PV and wind. The model is developed on the basis of linear programming and includes 200 million constraints and 100 million endogenous variables. The highlight of the model consists in the detailed geographical resolution derived from 135 nodes and 166 high-voltage lines and in the detailed temporal resolution derived from 10 minutes in a whole year. As energy storage technology, the model explicitly incorporates the possible deployment of sodium-sulfur battery and Li-ion battery as well as pumped-storage hydro power plants. Active power flow of the grid is considered through a direct current (DC) method. Simulated results reveal that the considerable deployment of PV and wind does not necessarily require the large-scale installation of rechargeable battery, because the intermittency of PV and wind is controlled by the inter-regional power flow exchange, the flexible operation of ramp generators and pumped-storage hydro and the utilization of VR output curtailments. In Hokkaido area where a large installable potential of wind power is expected, the time interval when a system non-synchronous penetration (SNSP) ratio exhibits more than 50 percent amounts to 1320 hours per annum, implying the requirement of advanced grid operation for the sake of power system security.

Optimal design of urban water supply pipe networks

This paper approaches the optimisation of looped water distribution networks supplied from one or more sources, according to demand variation. The pipe networks have concentrated outflows or uniform outflow along the length of each pipe. An optimisation model coupled with a computational iterative procedure of optimal discharges through pipes is developed on the basis of linear programming for the design of new or partially extended water distribution networks. The optimum solution obtained by this model consists of one or two pipe segments of different discrete sizes between each pair of nodes. The improved linear optimisation model guarantees a high reliability. Also, it is possible to take into account the network pipes with variable discharge on route. Additionally, the paper compares the linear optimisation model to some others, such as the classic model of economical velocities, the Moshnin model and a nonlinear model. This shows a good performance of the proposed model.

All-integer column generation for set partitioning: Basic principles and extensions

Column generation, combined with an appropriate integer programming technique, has shown to be a powerful tool for solving huge integer programmes arising in various applications. In these column generation approaches, the master problem is often of a set partitioning type.The set partitioning polytope has the quasi-integrality property, which enables the use of simplex pivots for finding improved integer solutions, each of which is associated with a linear programming basis. By combining such pivots with column generation, one obtains a method where each found solution to a restricted master problem is feasible, integer, and associated with a dual solution that can be used in a column generation step.This paper presents a framework for such an all-integer column generation approach to set partitioning problems. We give the basic principles of all-integer pivots and all-integer column generation. We also state optimality conditions and introduce means for preserving a basis in the event that a heuristic is applied to the master problem. These extensions introduce flexibility in the design of a specific solution scheme of this kind, and with proper settings optimal or approximate solutions can be sought for.

Effect of multipath channel models to the recovery algorithms on compressed sensing in UWB channel estimation

Multipath arrivals in an Ultra-WideBand (UWB) channel have a long time intervals between clusters and rays where the signal takes on zero or negligible values. It is precisely the signal sparsity of the impulse response of the UWB channel that is exploited in this work aiming at UWB channel estimation based on Compressed Sensing (CS). However, these multipath arrivals mainly depend on the channel environments that generate different sparse levels (low-sparse or high-sparse) of the UWB channels. According to this basis, we have analyzed the two most basic recovery algorithms, one based on linear programming Basis Pursuit (BP), another using greedy method Orthogonal Matching Pursuit (OMP), and chosen the best recovery algorithm which are suitable to the sparse level for each type of channel environment. Besides, the results of this work is an open topic for further research aimed at creating a optimal algorithm specially for application of CS based UWB systems.

Entanglement witnesses and characterizing entanglement properties of some PPT states

On the basis of linear programming, new sets of entanglement witnesses (EWs) for 3⊗3 and 4⊗4 systems are constructed. In both cases, the constructed EWs correspond to the hyper-planes contacting, without intersecting, the related feasible regions at line segments and restricted planes respectively. Due to the special property of the contacting area between the hyper-planes and the feasible regions, the corresponding hyper-planes can be turned around the contacting area throughout a bounded interval and hence create an infinite number of EWs. As these EWs are able to detect entanglement of some PPT states, they are non-decomposable (nd-EWs).

A New Degeneracy Method and Steepest-Edge--Based Conditioning for LP

A new recursive method for resolving degeneracy in simplex-like methods for linear programming (LP) is described. The method provides a guarantee of termination, even in the presence of round-off errors, and is readily implemented. In contrast to a previous method of the author, this method works throughout in the primal space. One consequence is that the steepest-edge criterion can be used on all iterations and at all levels of recursion. It is also shown that the associated steepest-edge coefficients provide information from which the expected condition of the current LP basis can be calculated cheaply. This provides a more accurate indication of the actual condition of a system than is obtained from norm-based condition numbers. This idea also enables the condition of null space matrices to be estimated.

An LP-aggregation view on aggregationin multi-level production planning

Multi-level production planning systems often suppose a top level which anticipates alower level in terms of coarsened, i.e. aggregate information. Aggregation can occur withrespect to products, capacities, time and/or (sub-)projects. Since many of the underlyingmodels are constructed on the conceptual basis of linear programming, results from linearprogramming aggregation have to be regarded when generating and evaluating such asystem. A review of LP-aggregation is presented. Results are then transferred to productand resource aggregation with respect to the coordination of aggregate production planningand master production scheduling. In contrast to many other publications, the analysis doesnot interpret aggregation in production planning heuristically or as black-box, but explicatesaggregation in production planning in terms of LP-aggregation. Results can be transferredto several other aggregation approaches in production planning.

On geometric programming and complementary slackness

When the terms in a convex primal geometric programming (GP) problem are multiplied by slack variables whose values must be at least unity, the invariance conditions may be solved as constraints in a linear programming (LP) problem in logarithmically transformed variables. The number of transformed slack variables included in the optimal LP basis equals the degree of difficulty of the GP problem, and complementary slackness conditions indicate required changes in associated GP dual variables. A simple, efficient search procedure is used to generate a sequence of improving primal feasible solutions without requiring the use of the GP dual objective function. The solution procedure appears particularly advantageous when solving very large geometric programming problems, because only the right-hand constants in a system of linear equations change at each iteration.

Improved integer programming bounds using intersections of corner polyhedra

Consider the relaxation of an integer programming (IP) problem in which the feasible region is replaced by the intersection of the linear programming (LP) feasible region and the corner polyhedron for a particular LP basis. Recently a primal-dual ascent algorithm has been given for solving this relaxation. Given an optimal solution of this relaxation, we state criteria for selecting a new LP basis for which the associated relaxation is stronger. These criteria may be successively applied to obtain either an optimal IP solution or a lower bound on the cost of such a solution. Conditions are given for equality of the convex hull of feasible IP solutions and the intersection of all corner polyhedra.

The Structure of Integer Programs under the Hermitian Normal Form

This paper discusses the structure of integer programming under the Hermitian normal form. It shows that this formulation is akin to the simplex technique for linear programming in that there is a basis and a basic solution associated with each Hermitian normal matrix, and that this Hermitian basis forms a set of natural cutting planes; these cutting planes are strong in that they provide facets for at least one of the corner polyhedra associated with a linear programming basis B. In addition, the cofactors of the Hermitian basis are group elements under a homomorphism of the original group structure. The Hermitian basis also allows one to characterize the values of the right-hand side for which the present solution is feasible. Finally, for an optimal Hermitian basis, one can perform sensitivity analysis on the cost coefficients.