A hierarchy preserving hierarchical compactor

On solutions and distribution problems of the linear programming with fuzzy random variable coefficients

Omah Jenang is one of the industries engaged in the production of traditional snacks. Currently Omah Jenang does not yet have guidelines for realizing the formation of the composition of production quantities correctly based on calculations that still use forecasting methods. Therefore Omah Jenang often experiences difficulties in providing raw materials and determining maximum profits. The purpose of this study was to de-termine the optimum yield of profits at Omah Jenang by using the simplex method linear program with the help of Lindo Software. The data used is food production data at the Omah Jenang Home Industry in 2022. The method used in this study is the Linear Pro-gramming simplex method and the Lindo Software application. The results of optimization calculations using the linear programming method and the help of Lindo Software are that the maximum profit in a month is IDR 20,000,000 in producing 800 packages of madumongso. Based on the calculation results it can be concluded that the benefits obtained by using the simplex method with the help of Lindo Software can be obtained maximum results.

Five problems of finding efficient vectors as a subset of a finite set of vectors are shown to be related and a common methodology based on the simplex method of linear programming is developed for solving all of them. Randomly generated problems for one of the five types are solved using the method, and the implications regarding computational requirements are discussed.

1. The use of the method of Latin squares, and specifying or excluding those alloying elements whose optimum content is known and is largely independent of the concentrations of the principal alloying elements makes it possible to reduce the number of investigated experimental melts in working out the composition of steel with the required properties. 2. We obtained multiple regression equations type "chemical composition-properties" for weldable low carbon alloy steel, heat-treated to the same strength (σ0 · 2 ⩾ 750 MPa). 3. The simplex method of linear programming as used to optimize the composition of steel with σ0 · 2 ⩾ 750 MPa according to the criteria of ductility, impact toughness, and crack resistance, with constraints on the chemical composition for obtaining satisfactory weldability. The devised weldable steel in sections up to 250 mm after hardening in water and temnering has good ductility, impact toughness, and crack resistance.

Agriculture in India is gradually tending to be less interesting and lucrative profession due to high risks and less reliability. In order to increase net return from agriculture, proper planning and consideration of prevailing constraints is essential. Bhagwanpur distributary command area-based problem, consisting of maximization of net return with available land, water, labour, energy and other affinity constraints was formulated and solved employing modified Simplex method of linear programming. The area allocated under different crops, land productivity and water productivity for various combinations of canal water and ground water use were computed. When more area was allocated under remunerative crops like maize and potato with 100 % tube well water and canal water use by the crops, maximum net return of `2.31× 108 could be obtained. Maximum land productivity for the command area, was 63826 `.ha-1 when 85 % canal water and 100 % ground water were used by the crops in total area of 3426.9 ha; while maximum water productivity of 25.66 `.m-3 was obtained when 100 % canal water and ground water were used. The results may be useful in suggesting farmers on allocation of their agricultural land under profitable interventions to maximize net return, water productivity and land productivity.

I describe a C++ program for computing the smallest enclosing ball of a point set in d-dimensional space, using floating-point arithmetic only. The program is very fast for d ? 20, robust and simple (about 300 lines of code, excluding prototype definitions). Its new features are a pivoting approach resembling the simplex method for linear programming, and a robust update scheme for intermediate solutions. The program with complete documentation following the literate programming paradigm [3] is available on the Web.

Given a directed network with two integer weights, cost and delay, associated with each link, quality-of-service (QoS) routing requires the determination of a minimum cost path from one node to another node such that the delay of the path is bounded by a specified integer value. This problem, also known as the constrained shortest path problem (CSP), admits an integer linear programming (ILP) formulation. Due to the integrality constraints, the problem is NP-hard. So, approximation algorithms have been presented in the literature. Among these, the LARAC algorithm, based on the dual of the LP relaxation of the CSP problem, is very efficient. In contrast to most of the currently available approaches, we study this problem from a primal perspective. Several issues relating to efficient implementations of our approach are discussed. We present two algorithms of pseudopolynomial time complexity. One of these allows degenerate pivots and uses an anticycling strategy and the other, called the NBS algorithm, is based on a novel strategy which avoids degenerate pivots. Experimental results comparing the NBS algorithm, the LARAC algorithm, and general purpose LP solvers are presented. In all cases, the NBS algorithm compares favorably with others and beats them on dense networks.

The full use of resource capacities of agricultural enterprises favorably affects the general increase in economic efficiency and rational production making them more competitive in the market. This creates the need for constant improvement of business strategies that uses all available resources to create the most profitable production. The main objective of this study was to find the ideal structure of production in agricultural enterprise and to enable the realization of maximum profit using the available production resources (land, mechanization, labor forces). As the basic method of planning, this study used the simplex method of linear programming which gives the most profitable sowing structure after detailed analysis of resources and achieved results, based on the limitations and gross margin. This work showed that the use of modern methods in production planning is one of the cheapest and safest methods for development of agricultural enterprises.

Random sampling is an efficient method to deal with constrained optimization problems in computational geometry. In a first step, one finds the optimal solution subject to a random subset of the constraints; in many cases, the expected number of constraints still violated by that solution is then significantly smaller than the overall number of constraints that remain. This phenomenon can be exploited in several ways, and typically results in simple and asymptotically fast algorithms.Very often the analysis of random sampling in this context boils down to a simple identity (the sampling lemma ) which holds in a general framework, yet has not been stated explicitly in the literature.In the more restricted but still general setting of LP-type problems , we prove tail estimates for the sampling lemma, giving Chernoff-type bounds for the number of constraints violated by the solution of a random subset. As an application, we provide the first theoretical analysis of multiple pricing , a heuristic used in the simplex method for linear programming in order to reduce a large problem to few small ones. This follows from our analysis of a reduction scheme for general LP-type problems, which can be considered as a simplification of an algorithm due to Clarkson. The simplified version needs less random resources and allows a Chernoff-type tail estimate.

Time Preference, Firm Growth, and Programming Models††Research on this topic was supported in part by a grant from the Halliburton Education Foundation.

Rural Distribution Systems (RDSs) are expanding abruptly day by day. With this continuous expansion, the distribution loss is increasing deliberately as a coherent parameter. Constructing single phase HT (high tension) line, it becomes more alarming with respect to loss as well as system management. This paper highlights the advantages of three phase tap lines for the reduction in line loss compared to single phase. A cost analysis is carried out by designing all HT lines of RDSs with three phase taps instead of single phase taps and the obtained result is compared with the single phase tap line. Then, an optimum length of single phase tap line is determined using simplex method for linear programming considering the cost of three phase tap line as a standard. The results show that more area can be electrified using three phase tap lines compared to the single phase tap line with the same cost.

A basis-deficiency-allowing variation of the simplex method for linear programming

We present three new pivot rules for the Simplex method for Linear Programs over 0/1-polytopes. We show that the number of nondegenerate steps taken using these three rules is strongly polynomial, linear in the number of variables, and linear in the dimension. Our bounds on the number of steps are asymptotically optimal on several well-known combinatorial polytopes. Our analysis is based on the geometry of 0/1-polytopes and novel modifications to the classical steepest-edge and shadow-vertex pivot rules. We draw interesting connections between our pivot rules and other well-known algorithms in combinatorial optimization. Funding: A. E. Black and J. A. De Loera are grateful for the support received through the National Science Foundation [Grants DMS-1818969 and NSF GRFP]. L. Sanita is grateful for the support received from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant VI.Vidi.193.087].

This paper evaluates the efficiency level of medical spa businesses operating in Slovakia. The research aims to compile an efficiency ranking of these specific healthcare facilities to apply both methods and analyze their alternative use within the efficiency level measurement. The object of research is the Slovak spa businesses over the years 2014-2018. The study involved the Simplex Method of Linear Programming and the selected Data Envelopment Analysis model. In the study frame, the authors quantified the efficiency of medical spa businesses as the optimization task of SMPL and BCC input-oriented DEA model to identify prosperous businesses from non-prosperous ones. The study applied the Spearman rank correlation to reveal a potential degree of association of business rankings. The calculations were provided by the MS Excel, MS Excel Solver package, and the statistical program Gretl. The findings indicated that the business efficiency measured by SMPL provided similar results to the DEA model. These methods could be considered equivalent. Therefore, their alternative use was confirmed. The obtained results showed that both methods almost equally divided the businesses into two groups: 1) with efficiency score above (10 DMUs) and 2) below the overall achieved average (11 DMUs). According to the average results of both applied methods, the most efficient DMUs were DMU09 (Spa Lúcky, j.s.c.) and DMU03 (Spa Bojnice, j.s.c.), vice versa, the lowest efficiency score was achieved by DMU04 (Spa Brusno, j.s.c.). This research could be considered an important opportunity to identify new gaps in the prior literature and present the need for further development in these specific healthcare facilities, not only in Slovakia. The presented research findings are also beneficial for practice as they may lead to the formulation of recommendations for improvement of the current state of Slovak spa tourism and the spa businesses themselves.

Linear algebra and its applications : D.H. Griffel, Ellis Horwood Ltd., Chichester, 1989. Vol. 1: ISBN 0-85312-946-0, XIII + 289 pages, £29.95. Vol. 2: ISBN 0-7458-0581-7, X + 233 pages, £29.95