Research on the Relationship between Economical Profit and Environmental Pollution of Imperfect Production Inventory Control Problem in Fuzzy-rough Environment

It is well known fact that a country's economic growth leans on its natural resources. But the support of environmental capacity stands as back up in the operation of country's economic growth. In order to study the inherent relationship between the economic profit and environmental pollution, we are putting forward a new practice in this research area. Also numerous strategies have been set up to reduce the amount of polluting gases such as reliability development by modern technology on production system, rework on imperfective item which reduce the waste of defective item and reduce the economic loses. The said parameters are imprecise in nature for the lack of precise numerical information. In this paper, the imprecise parameters are taken fuzzy rough numbers. Then, a multi-objective production control inventory problem is formulated where the first objective function is for economical profit in maximizing form and second objective function is for calculating the amount of polluting gases in minimizing form in fuzzy-rough environment. The said imprecise problem is converted into equivalent crisp multi-objective problem by using fuzzyrough mathematics. The said problem is converted into a single objective problem by weight sum method. Using optimal control theory, we have solved the optimal control problem and obtained the required optimal production and stock level in analytical forms. Then the numerical results of profit and amount of polluting gases are also obtained using MATHEMATICA software.