Simplex Method Algorithm Research Articles

Optimal profitable applications for web development companies using a linear programming approach

The consumed resources in web development companies are different and greatly affect a company’s profit or loss extent. We will utilize linear programming to measure that and maximize the company’s profit. Furthermore, we will apply the simplex method algorithm within certain constraints placed on different components of the company's different products. This problem can be solved with a trial and error approach but this requires great effort and time, which is a challenging thing to do on each product. We can employ different computer tools that calculate and solve these problems. Microsoft Excel is one of these tools that solve linear programming equations and provides accurate outputs; there are plugins such as (Solver) that work in integration with Excel. This paper’s main goal and purpose are to calculate and acquire the ideal products that maximize the company's profit under certain constraints. The best distribution and optimal use of resources to increase profit while maintaining quality and quantification of each project type with imposed restrictions and steps that the company must take to stop and reduce excess and unused resources. The simplex method algorithm is used because it is faster than other algorithms in solving linear programming problems, and it has high efficiency in reducing the needed resources for computer processing. On the other hand, the limitations of this algorithm manifested in its dependence on variables will increase the complexity of the problem, and this cannot be implemented accurately in all cases of linear programming problems.

Solving Linear Fractional Programming Problem in symmetric trapezoidal fuzzy environment

Fuzzy set theory has been applied on different important fields, such as managements, operations research, and control theory. In this paper, we provided a new algorithm to solving a fuzzy fractional linear programming problem (FFlPP) in full fuzzy environments. All the variables and coefficients of both the constraints and the objective function are symmetric trapezoidal fuzzy numbers. The fuzzy linear fractional programming problem (FLFP) has been switched to fuzzy linear programming (FLP) problems, where both of constraint and objective function involve fuzzy numbers as variables and coefficients. Further, using the fuzzy simplex method algorithm to get an optimal fuzzy solution. Finally, we provide illustrative numerical examples.

Improved Simplex Method Algorithm used in power Market Clearing

Electric power industry is the foundation of national economy and plays a key role in the development of human society. Traditional power industry is monopolized by industry and lacks market efficiency. In recent years, it is seeking breakthroughs in market-oriented reform. Although China’s electricity market reform has achieved some results, but there are still lacking of market players and regional transactions, excessive data management, concentration and other defects. This puts forward higher requirements for the system design of power market trade. It is facing the electricity market security and performance challenges, the goal is to improve the electric power market transaction mode and enhance transaction security, it studied different kinds of markets transaction model to construct a perfect competitive market trade system, which based on block chaining technique. The trade model adopted different levels of multi auction which integrated intra provincial trading and inter provincial trading parts in a system. The intra province trading part adopt the model of contact trading and bidding coexist, each province carried out trading for surplus-deficit electricity on the basement of intra province demand. Here, it constructed a competitive cross-regional power market which can realize the intra-provincial contract, bidding and inter-provincial trading in day power market. The simulation results based on six provinces to shown the different conditions, and operated by the intelligent contracts. It recorded the full trading information distributed through the inter-provincial power trading algorithm in the intelligent contracts, the results has presented the amount of electricity transaction and the corresponding trading volume. It has achieved fair resource scheduling and transaction information security.

A simplex method algorithm using a double basis

A simplex method algorithm not requiring explicit LU decomposition updating in the iterations is considered. The solutions obtained with fixed LU factors are corrected using small auxiliary matrices. The results of some numerical experiments are presented.

High-pressure phase behaviour of poly(d-lactic acid), trichloromethane, and carbon dioxide ternary mixture systems

The high pressure phase behaviour of poly(d-lactic acid) (Mw=359,000), trichloromethane, and carbon dioxide ternary mixture systems is presented in this study. Cloud and bubble point pressures were measured using a variable volume view cell at temperatures (313.15 to 363.15)K and pressures up to 33.6MPa. The hybrid equation of state for the polymer-carbon dioxide system was used to correlate the experimental results. The van der Waals one-fluid mixing rule with three adjustable binary interaction parameters was used for all correlations. The binary parameters were optimised using the simplex method algorithm.

High-Pressure Phase Behavior of Poly(l-lactic acid), Trichloromethane, and Carbon Dioxide Ternary Mixture Systems

In this study, the phase behavior of a poly(l-lactic acid) (M = 312 000, polydispersity 2.189)–trichloromethane–carbon dioxide ternary system was measured using a variable volume view cell at pressures up to 34.0 MPa and temperatures between (313.15 K and 363.15) K at an interval of 10 K. Bubble and cloud point pressures were determined as functions of the trichlomethane-to-carbon dioxide ratio, concentration of poly(l-lactic acid) (1.0, 2.0, and 3.0 wt %), and temperature. The hybrid equation of state for the supercritical CO2-polymer system combined with the van der Waals one-fluid mixing rule was used for correlation of the experimental results. The three binary parameters of this system were optimized by the simplex method algorithm.

Phase Behavior of Poly(d-lactic acid), Dichloromethane, and Carbon Dioxide Ternary Mixture Systems at High Pressure

The phase behavior of a poly(d-lactic acid) (Mw = 359 000 g/mol, polydispersity 1.7), carbon dioxide, and dichloromethane ternary system was measured by a variable-volume view cell. The experimental temperatures and pressures ranged from 313.15 to 363.15 K, up to 300 bar as various experimental conditions of the CO2/dichloromethane mass ratio and temperature, at poly(d-lactic acid) mass fractions of 1.0, 2.0, and 3.0%. The correlation results were obtained from the hybrid equation of state (Peng–Robinson equation of state + SAFT equation of state) using the van der Waals one-fluid mixing rule for the polymer–CO2–solvent system. The binary interaction parameters were optimized by the simplex method algorithm.

Taking account of height constraints in problems of optimizing the spatial energy distribution

The authors attempt to solve the problem of three-dimensional stabilization through stabilization of the spatial energy distribution by mathematical-programming methods. The method proposed calculates the optimal displacements of the control rods, on the basis of introducing into the simplex-method algorithm additional constraints, which are physically equivalent to the height constraints and also the corresponding modification of the criterion regarding the choice of column to be inserted in the basis. One version of this approach was considered for an algorithm of regulation of the energy distribution in an RBMK reactor. Calculations performed were introduced into experimental-commercial use at the second-unit reactor of the I.V. Kurchatov Beloyarskii atomic power plant, which confirmed the effectiveness of the given algorithm, showing that it is sufficiently efficient.