Split: Sveuciliste u Splitu * Gradevinski Fakultet
This paper is concerned with the decision-making on the optimal production batch size and optimal number of shipments for a finite production rate model with random scrap rate. The classic finite production rate (FPR) model assumes a continuous inventory issuing policy for satisfying product demand and perfect quality for all items produced. However, in a real life vendor-buyer integrated production-inventory system, a multiple shipment policy is practically used in lieu of the continuous issuing policy, and it is inevitable to generate defective items during a production run. All nonconforming items produced are assumed to be scrap, and the finished (perfect quality) products can only be delivered to customers if the whole lot is quality assured at the end of the production run. The fixed-quantity multiple instalments of the finished batch are delivered to customers at a fixed interval of time. Mathematical modelling is employed and the renewal reward theorem is used to cope with the variable production cycle length. The long-run average cost for the proposed model is derived, and its convexity is proved by the use of the Hessian matrix equations. A closed-form optimal production-shipment policy for such an imperfect FPR model is obtained and a special case is discussed. Finally, a numerical example is provided to demonstrate the model’s practical usage.
International Journal for Engineering Modelling 22(1-4), pp.25-34