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The expected total cost function is developed by using a Markovian approach. The imperfect production and inventory control model is considered and integrated with an irreducible discrete time Markov Chain. Two Markov Chain models are developed with/without time factor. The former model with time factor has higher accuracy in the expected total cost. The optimal total cost and detailed production plan for each state are accomplished. Two applications for the developed Markov Chain models aredoi:10.25417/uic.14134463.v1 fatcat:ua2mfza6gbfulpmmexldtb734m