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In this paper an attempt is made to study n jobs over two machines where processing times are associated with respective probabilities with time delays known as arbitrary lags i.e. start lag or stop lag. The objective of the study is to develop an efficient algorithm in order to minimize the rental cost with different system parameters such as arbitrary lags and job weightage as well.. Further jobs are associated with weights to indicate their preference in production scheduling. The proposed algorithm is easy to understand and also provide an important tool for the decision making in the field of production.