Optimal Imperfect Production Inventory Model with Machine Breakdown and Stochastic Repair Time

Prasanta Kumar Ghosh, Jayanta Kumar Dey

This study develops an imperfect production inventory model with random machine breakdown and stochastic repair time. The model assumes that the production system produces mixture of perfect and imperfect items from the beginning of the production and the system shifts from 'in-control state' to 'out-control state' at random time and also machine repair time is independent of the machine break-down rate. Some portions of the acceptable imperfect products are sale at reduction price and a disposal cost is incurred for environmental protection to dispose the rest portion. Demand of the perfect items is constant and due to imperfect screening, the return items (which are sale as perfect items but originally they are imperfect) are replaced by the new perfect items. Here two cases discussed in comprising with stochastic machine repair time and production down time. MATHEMETICA is used to derive an optimal profit for both the cases. Sensitivity analysis are shown to betterunderst and the model.