In this article we develop an Economic Production Quantity deteriorating inventory model for non random uncertain environment. This model includes rework process, screening of imperfect items. The items are partially serviceable as because at the time of production some items view as defective which are not recoverable/serviceable. Also the transportation cost has been incorporated to capture the actual cost of the commodity during selling period. At first we develop a cost minimization problem under several assumptions related to imperfect items and rework process under certain constraints. We solve the crisp model (primal non-linear problem) first, and then we transfer this model into equivalent game problem taking the help of the theories related to strong and weak duality theorem. However this game problem consists of the Lagrangian function that correspond a non-linear objective function subject to some linear constraints. Finally we solve both the problems to know the cost variation of the proposed model.