A Queueing-Game Model for Making Decisions About Order Penetration Point in Supply Chain in Competitive Environment

This study is dedicated to Order Penetration Point (OPP) strategic decision making which is the boundary between Make-To-Order (MTO) and Make-To-Stock (MTS) policies. This paper considers two competing supply chains in which a manufacturer produces semi-finished items on a MTS basis for a retailer that will customize the items on a MTO basis. The two-echelon supply chain offers multi-product to a market comprised of homogenous customers who have different preferences and willingness to pay. The retailer wishes to determine the optimal OPP, the optimal semi-finished goods buffer size, and the price of the products. Moreover, the authors consider both integrated scenario (shared capacity model) and competition scenario (Stackelberg queueing-game model) in this paper. A matrix geometric method is utilized to evaluate various performance measures for this system and then, optimal solutions are obtained by enumeration techniques. The suggested queueing approach is based on a new perspective between the operation and marketing functions which captures the interactions between several factors including inventory level, price, OPP, and delivery lead time. Finally, parameter sensitivity analyses are carried out and the effect of demand on the profit function, the effect of prices ratio on completion rates ratio and buffer sizes ratio and the variations of profit function for different prices, completion percents, and buffer sizes are examined in both scenarios.