An Integrated Production-Inventory Model with Backorder and Lot for Lot Policy

In this paper, an inventory model for two-stage supply chain is investigated. a supply chain with single vendor and single buyer is considered. we assume that shortage as a backorder is allowed for the buyer and the vendor makes the production set up every time the buyer places an order and supplies on a lot for lot basis. with these assumptions, the joint economic lot size model is introduced and the minimum joint total relevant cost and optimal order quantity and optimal shortage quantity are obtained for both the buyer and the vendor at the same time. numerical example is given and then sensitivity analysis is performed to study the effects of changes in the parameters on optimum joint total relevant cost and optimal order quantity and optimal shortage quantity.