Linear Programming in Mathematics
The focus will be linear programming which fulfill the requirements of International/global market. The difficulty in designing and implementing global markets is oftentimes interdependence of technical and economic objectives ( 2006). From economic viewpoint, the global market must encompass common economic performance desiderata such as allocative efficiency. Thus, relying on existing market mechanisms known from other contexts when constructing new markets may result in poor efficiency (2005). The mechanism designer also has to account for the technical conditions of the target domain. Thus, for an example, in case of market for allocating Grid computing resources several conditions comprises of underlying environment in terms of Grid middleware and requiring potential Grid users and applications pointing to linear programs. The market should act as resource allocation manager, fulfilling requirements upon such manager as there allows introduction of precondition that international market apt for linear Grid has to be realized as global market, which the market cannot fulfill automated resource allocation as required by Grid resource management system. Different requirements from technical and economic viewpoints may lead to different and conflicting objectives as (2005) pointed out that “pure mechanism designer is likely to design an economic mechanism with high economic efficiency”.
Aside, when constructing electronic markets, it is essential to consider different influences that arise from technical fundamentals, potential user requirements, business constraints, economic objectives. Each of these influences has profound impact on the outcome on the acceptance of the market ( 2003).
Furthermore, methodology procedure is developed for representing competitive and noncompetitive market structures in linear programming models. Arbitrarily close approximations to nonlinear forms in both the objective function and constraint set can be made without much loss of the computational efficiency of the simplex algorithm. The noncompetitive market structure may be used for measuring income at endogenous prices in competitive model and may serve as a constraint on that measure of income to represent certain classes of economic policies. Product substitution effects in demand can be approximated by a linear program. The demand structure can be transformed to take account of any shift in demand which can be represented by a rotation of the demand function.
The research will be applied for market engineering and economic analysis, the need to formulate multi regional single time period linear goal programming model for agricultural planning in developing economy. In addition to specifying different levels of input and output for each activity, the need to describe explicit crop interdependencies which account for rotational requirements. Constraints are developed for land, labor, water, machinery, fertilizer and capital resources. Economic aspects are addressed through the use of different production functions and the incorporation of several objectives from conventional models which stress maximization of “economic welfare” defined as efficiency through maximum social product without consideration for income distribution. The emphasis on income distribution is reflected in our model in delineation of regional employment goals. In addition, foreign exchange expenditures and regional demand satisfaction goals reflect the importance of limiting foreign trade deficit and providing basic nutrition for the population, efficient and rigorous technique will be based on linear programming as readily accessible with the advent of computers. For this research, basic principles of linear programming will be briefly examined and some practical applications for formulating sound market economics recommendations in different contexts will be explained, the research should facilitate the adoption of the linear technique by international market and economic professionals. The proposed approach uses the strategy of simultaneously minimizing the most possible value of the imprecise total costs, maximizing the possibility of obtaining lower total costs, and minimizing the risk of obtaining higher total costs. Consequently, proposed linear programming approach yields an efficient solution and overall degree of decision maker satisfaction with determined goal values.
Particularly, several significant management implications and characteristics of linear programming approach that distinguish it from other decision models will be presented, has become increasingly common to use mathematical programming methods for deriving economic equilibrium of supply and demand. Well-defined approaches exist for the case of single firm and for the case of many firms leading to mathematical programming-based algorithm for determining market equilibrium. To present market engineering as holistic approach for designing, implementing and introducing electronic markets, services can then be composed to customized market processes. The market itself can then be provided as service and integrated into existing enterprise applications, explore several domains where markets should be increasingly employed in the future for resource allocation, to provide incentives for market participants or for risk management.
Credit:ivythesis.typepad.com
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