This paper addresses a bi-criteria scheduling problem with deteriorating jobs on a single machine. We develop a model for a single machine bi-criteria scheduling problem (SMBSP) with the aim of minimizing total tardiness and work in process (WIP) costs. WIP cost increases as a job passes through a series of stages in the production process. Due to the uncertainty involved in real-world scheduling problems, it is sometimes unrealistic or even impossible to acquire exact input data. Hence, we consider the SMBSP under the hypothesis of fuzzy L-R processing time's knowledge and fuzzy L-R due date. The effectiveness of the proposed model and the denoted methodology is demonstrated through a test problem.