On a volume flexible inventory model for items with an imperfect production system

A mathematical model is developed for volume flexible production system taking into account the effect of imperfect quality products. At the start of the production of a lot, the whole system is adjusted so that the process is ‘in-control’ state and items produced are of acceptable quality. During high rate of production, the process shifts from the ‘in-control’ state to the ‘out-of-control’ state. In the ‘out-of-control’ state, the quality of products deteriorates resulting in defective items. The demand rate of some defective items which are suitable for sale at reduced price is considered as a function of reduction rate of selling price. The proposed model is graphically illustrated with numerical examples and optimised by Mathematica Software. Sensitivity analysis is undertaken and various issues regarding the sale of imperfect quality products are discussed.