Optimal Integrated inventory model with Lost Sale and Backordering

Rapid market changes, explosion of product varieties and short life cycles have increased competition in today´s global markets. It is obvious that in today´s competitive markets, collaboration between the vendor and the buyer is necessary to reduce the joint inventory cost and the response time of the vendor-buyer system. Joint Economic Lot sizing Problem has been extended in many different directions. Shortage is not allowed in the most of the previous researches. A few of them considered shortage backordering as a result of imperfect quality. The purpose of this paper is to recast the Joint economic lot sizing model to be more relevant to current situations, where lost sales and/or backorders are more probable and could be cost efficient.