An integrated production-inventory model with backorder and lot for lot policy in fuzzy sense (Q1635435)

Summary: In this paper, an inventory model for two-stage supply chain is investigated in the fuzzy sense. 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. The decision variables are fuzzy order quantity and fuzzy shortage quantity which are expressed as triangular fuzzy numbers. After developing the mathematical model for the joint total relevant cost in fuzzy sense, its membership function is calculated and then defuzzified with the centroid method. The proposed model is solved and the amount of joint total relevant cost function in fuzzy sense is compared with the crisp one.