Optimal solution techniques to alternative vendor-buyer models in two-stage supply chains with a stochastic lead time for delivering batches of a lot

Vendor-buyer models have been developed assuming a stochastic lead time for delivering equal-sized batches (sub-lots) of a lot and backordering of shortages. The expected total costs for both the vendor and the buyer are minimized independently, as well as for the integrated system. The significant cost-reduction by the latter method is illustrated. However, these models appear to have some loopholes. First we demonstrate the loopholes and then develop alternative models considering lead time as a random variable while accounting for the loopholes. This follows the development of optimal solution techniques to the alternative models. Then we undertake comparative studies of our methods with the earlier ones on solutions to numerical problems. This comparison highlights the potential significance of the current method. Finally, the limitations of this study and the scope of future research are discussed.