Mathematical modeling for production system with backlogging and failure in repair

This paper employs mathematical modeling to derive the optimal lot size for economic production quantity model with random defective rate, imperfect rework process, and backlogging. In real life manufacturing process, the generation of defective items is inevitable. In this study, random defective rate is assumed and all defective items are reworked when regular production ends. During the rework process, a random portion of reworked items fails and becomes scrap. Disposal and repair costs are included in the proposed mathematical modeling and analysis. The optimal production lot size and backordering level that minimize overall production costs are derived. Numerical example is provided to demonstrate its practical usage.

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