An economic production quantity model with backlogging and imperfect rework process for uncertain demand

Abstract

This paper deals with a lot-sizing problem in the economic production quantity model with imperfect production processes and failure in repair where a Brownian motion process governs the inventory level variation. We assume that the unsatisfied demand is fully backlogged. In addition, we assume that all imperfect items produced are stocked separately and then reworked. Reworking and shortage costs are included in the proposed mathematical modelling and analysis. The aim of this research is to determine the optimal production lot size and backorder level such that the long-run total expected cost of the system is minimised. For the proposed model, we prove closed-form expressions for the inventory process and for the backlog costs. Moreover, a computer code using software package for the numerical work is furnished to derive the optimal solution. Some numerical examples and sensitivity analysis are provided to illustrate the validity of the proposed model.