Enterprise Decision-Making Oriented LP Model Parameter Estimation&Optimization

Enterprises often have difficulties in using the theory of linear programming (LP) to solve the actual management problems. Sometimes it’s not easy for the enterprise to determine the technological structure or design the production program by using input-output unit, sometimes there exists the problem to make the forecast target of the market demand be the optimal decision of the production planning model, and sometimes on the basis of the optimal schedule of transportation problem, there may occur the more-for-less phenomenon that increasing the supply with less total freight and so on. As all of these problems arise, the emphasis of the research on LP has been put on from modeling to model parameter estimation and optimization. Only estimating model parameters as accurate as possible, can we improve the accuracy of the optimal decision. And only by elimination of paradox phenomenon is the optimal decision effective. In order to provide useful dynamic information to solve corresponding actual economic management problems, the main research and contributions of this dissertation on the LP model parameter estimation and optimization can be summarized as follows:Firstly, a special kind of LP model parameters estimation called linear programming system identification, which seeks to estimate the technological coefficient matrix and the objective function coefficient vector with the given input-output data, is considered in this dissertation. The row estimation model and the modified row estimation model are constructed to estimate the technological coefficient matrix, and the improved maximum decisional efficiency approach, based on the maximum decisional efficiency approach proposed by Troutt, is constructed to estimate the objective function coefficient vector. To verify the accuracy of the proposed estimation methods by us, the subsequent validation criterion is put forward. Through studying and solving the linear programming system identification, we provide managers with an important way to analyze the input-output data, and offer help in linear programming system identification way to some undefined internal structure in the system.Secondly, in view of the existing paradox research focusing on the right side, we point out that the reason why the paradox occurs in LP is the unreasonable linear programming system consisting of the technological coefficient matrix and the objective function coefficient and the right-hand side. First, through changing the objective function coefficient, the method called the optimal structure of the objective function coefficient and the method based on the dual model are proposed. Second, the inverse optimal value method is provided to judge and solve the paradox, including the original-dual model which is constructed to judge whether there exists the paradox and two models, constructed to solve the paradox by changing the objective function coefficient and the technological coefficient matrix. Then the advantages and economic significance of the method is described.Lastly, the dual programming condition and the D-value of objective function model are given to judge whether the more-for-less paradox occurs in transportation problems. The maximum amount of supply and demand model is constructed to achieve the maximum adjustment scheme while increasing the supply with no freight increasing. And the reasonable pricing method is proposed to solve the paradox by changing the unreasonable transportation price and proved to be true. It is found that the proposed model and method exhibit excellent face validity for a numerical example.