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As the benefits of adopting optimal inventory policies are realized as impressive in the supply chain, the research on developing inventory models for supply chain systems has achieved significance. The research effort stated in this thesis deals with (a) mathematical modeling for inventory control in supply chain systems under deterministic environments, (b) employing profit maximization (or cost minimization)as an economic performance criterion in decision making, and (c) analyzing the behaviour of the supply chain systems under various operating inventory parameters and modeling assumptions. In this thesis, various inventory models under various situations are studied. An optimal inventory policy for a deteriorating item with time-dependent quadratic demand, backlogged partially is developed under permissible delay in payments. An optimal inventory replenishment policy for a deteriorating item with stock-dependent demand and the time-dependent backlogging rate is considered.