Another look at the integrated models for shipping a vendor s final production batch to a single buyer under linearly decreasing demand

Integrated production-inventory problem for a single-vendor single-buyer with a constant demand rate have been studied extensively by a number of researchers. Goyal (1977) was probably one of the first papers to investigate this problem. Banerjee (1986) considered the vendor manufacturing for stock at a finite rate and delivering the whole batch to the buyer as a single shipment -a lot for lot model. Goyal (1988) demonstrated how lower cost policies generally result from allowing a production batch to be split and delivered as a number of shipments. Lu (1995) set out the optimal production and shipment policy when the shipments sizes are all equal. Goyal (1995) demonstrated how lower cost policies sometimes result when successive shipment sizes increase by a ratio which is equal to production rate divided by the demand rate. Hill (1999) derived the form of the optimal policy if shipment sizes may vary. This consists a number of shipments which increase by the ratio used in Goyal (1995) followed by a number of equal-sized shipments.A common assumption in these model is the unit holding cost is more expensive for the buyer than for the vendor. However, research on consignment stock policies by Braglia and Zavanella (2003) and Valentini and Zavanella (2003) suggests that there are some situation where the reverse is true. According to Hill and Omar (2006), the underlying principle of consignment stock is that the vendor takes responsibility for managing stock. In order to minimise the stock held at the vendor, the vendor will ship all the stocks available whenever a delivery is ready for shipment.In the all above models, the demand rate is constant over an infinite time horizon. In a recent paper, Omar [Mohd Omar, An integrated equal-lots policy for shipping a vendor s final production batch to a single buyer under linearly decreasing demand. International Journal of Production Economics 118(2009) 185-188 presented an integrated production-inventory policy for periodically ship a single vendor s final production to a single buyer with equal-lot when the demand rate is linearly decreasing over a finite time horizon. By revising Omar s model, in this paper we shown that a better cost model is achieved when the shipments size and periods are varies. Further more we also propose a Consignment Model for this problem. Finally, we illustrate these models with numerical examples.

Keywords:

: single-vendor , single-buyer , integrated policy , consignment , vary demand