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

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

Nughthoh Arfawi Kurdhi (Department of Mathematics, Sebelas Maret University, Surakarta, Indonesia), Livvia Paradisea Santoso (Department of Mathematics, Sebelas Maret University, Surakarta, Indonesia), Sri Sulistijowati Handajani (Department of Mathematics, Sebelas Maret University, Surakarta, Indonesia) and Titin Sri Martini (Department of Mathematics, Sebelas Maret University, Surakarta, Indonesia)
DOI: 10.4018/IJISSCM.2016070104
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Abstract

This paper presents a coordinated vendor-buyer supply chain model in two stages with imperfect quality items, lead time and ordering cost reduction, and service level constraint. It is assumed that each arrival lot received by the buyer contains a percentage of imperfect quality items which follows a uniform distribution. A 100% screening process for detecting the defective items is conducted. Lead time crashing cost and investment for ordering cost reduction follow power function distribution. The shortage during the lead time is permitted and backordered partially for the buyer. However, the level of shortage is limited by service level constraint policy. The optimal order quantity, reorder point, lead time, ordering cost, and the number of delivery are determined by the Lagrange method such that joint total cost of the system is minimized and the service level constraint is satisfied. An iterative procedure is developed to determine the optimal solution and a numerical example is presented to illustrate the result of the proposed model.
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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.

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