Joint inventory-production inventory model with defective items, uncertain demand and allowable shortage (Q2204325)

Summary: Due to uncertain demand observed in the industries, it is important to investigate on the effect of this crucial issue on integrated vendor-buyer inventory model. Hence, in a specific imperfect manufacturing system, this paper, presents an integrated vendor-buyer inventory model wherein buyer's lead time demand is follows a normal distribution. As a consequence of demand uncertainty, a full backorder system for allowable shortage is considered. A solution procedure is proposed to find optimal joint strategy of both vendor and buyer and numerical example is presented to illustrate the results of the proposed model. This study, also, shows a respective probabilistic inventory model to be minimised is jointly convex in the decision variables. The proposed algorithm is coded by MATLAB 2012b.