This paper is an extension of the work of Lin and Gong (2011) on Economic Production Quantity (EPQ) model on an imperfect production system over infinite planning horizon, where the production system is dictated by two
unreliable key production subsystems (KPS). While any shortage on the inventory of product was not allowed in the model of Lin and Gong (2011), planned shortage
backorders is considered in the model proposed in this paper. The mathematical model is developed in order to determine production run time (s) and production
time when backorder is replenished (T1) that minimizes the expected total cost per unit time including setup, inventory carrying, shortage, and defective costs.
Approaches to solve the model are also being proposed in this paper, altogether with some numerical examples.