A Coordinated Supply Chain Model for Imperfect Items under Power Function Lead Time Crashing Cost and Investment with a Service Level Constraint

Introduction

The coordinated vendor-buyer model on supply chain system received a lot of attention in recent years. As global markets became more competitive, critical information needs to be shared along the supply chain in order to satisfy customer demands. Close cooperation between the vendor and the buyer is necessary to find a more profitable joint production and inventory policy such that the joint total relevant cost for all stages could be optimized. Therefore, in today’s competitive business world, supply chain coordination is a key component for enhancing its responsiveness and profitability. Goyal (1976) first introduced the idea of optimizing the joint total cost in a single-vendor, single-buyer model. In this model, the demand for the item was assumed followed a uniform distribution and shortages were not permitted. Banerjee (1986) developed the Goyal’s (1976) model by assuming that a vendor has a finite production rate and considered a lot-for-lot policy. Goyal (1988) extended Banerjee’s (1986) model by relaxing the lot-for-lot policy to generalize the problem. A review of related literature was done by Goyal and Gupta (1989). Later, other related vendor-buyer coordination problems are investigated by academicians and practitioners, for example in Hill (1999), Goyal and Nebebe (2000), Wu et al. (2007), Mahdavi et al. (2008), Zavanella and Zanoni (2009), Hou et al. (2009), Nam et al. (2010), and Glock (2011). Further, a comprehensive review of vendor-buyer coordination problem which is referred to as the joint economic lot sizing (JELS) was done by Glock (2012a). Many earlier studies dealing with the coordinated (integrated) inventory-production model assumed that the production processes are perfect. Several researchers have demonstrated that defective items may occur caused by deterioration on production process. For example, Lin and Srivastava (2015) developed a two-warehouse inventory model with quantity discounts and imperfect production process. Yadav et al. (2015) studied EOQ (economic order quantity) model for imperfect items under the effect of inflation and learning with selling price dependent demand. Later, Lai et al. (2015) proposed two integrated optimization models of two-echelon for imperfect production system under quality competition environment.