A Study on Environmental Management Utilizing the Sequential Unconstrained Minimization Technique
Yang, Wei-Tzen, Tsai, Ming-Liang, International Journal of Management
In this study we propose an emission-constrained economic production model utilizing the sequential unconstrained minimization technique (SUMT) to obtain the optimal solution of environment production system. We set up an iteration procedure of SUMT to simulate the model with numerical data. Comparing the simulation results of SUMT with traditional Kuhn-Tucker Optimization Method (IKTOM), we find that KTOM cannot provide solution subject to those from multiple constraints accurately and reliably, whereas SUMT demonstrates higher accuracy for pollution management problem.
In environment protection system, engineering making all production systems achieve the optimal economical operation under the pollution constraints is a very important problem. In general, pollution serves no influence to make production less economical provide that pollution is produced by the producer itself. Pollution will make less production and production less economical if pollution is from the different industry. Given an example, the polluted waste water from the chemical or textile dying industry will make the coastal fishery less and less economical because the fisherman should go far away in order to have same fish production.
In this study we propose a model of emission constrained economic production utilizing the sequential unconstrained minimization technique (SUMT) for optimal solutions. The model takes some nonlinearly equalities constraints on a nonlinearly inequality and transformed them into a series of unconstrained nonlinear programming problem. We can decide the optimal search direction using the Quasi-Newton Method, which does not need to specify initial values among the feasible regions. We can also approach the best answer by regularly adjusting the penalty parameter. Comparing with the traditional nonlinear programming techniques that are unable to provide solutions subject to multiple constraints accurately and reliably, this model becomes more popular because of its higher accuracy [1, 4, 11].
This paper is divided into five sections. The first is an introduction, the second is the mathematical model, the third deals with environment protective generation using of SUMT, the fourth is an iteration procedure of SUMT and the fifth shows simulation results and conclusion.
2. Mathematical Model