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.