Using Queuing Approach for Locating the Order Penetration Point in a Two-Echelon Supply Chain with Customer Loss

An order penetration point (OPP) is the boundary between make-to-order (MTO) policy and make-to-stock (MTS) policy. This study is dedicated to OPP strategic decision making which is concerned with the upstream and downstream decisions of OPP in supply chains. In this paper, we consider a two-echelon production supply chain in which in first production stage, supplier manufactures the semi-finished products on a MTS policy for a manufacturer in second production stage that will customize the products on a MTO policy. The manufacturer desires to find the optimal fraction of processing time fulfilled by its supplier and its optimal semi-finished products buffer storage capacity in OPP. Also, impatient customers are considered in the study. In order to calculate system performance indexes, we employ matrix geometric method and queuing steady state equations. Afterward, optimal solutions are obtained applying an optimization mathematical model with enumeration an