Supply Chain Coordination Under Service Level Constraint and Controllable Lead Time

Supply Chain Coordination Under Service Level Constraint and Controllable Lead Time

Prashant Jindal (Department of Applied Mathematics, Gautam Buddha University, Greater Noida, India) and Anjana Solanki (Department of Applied Mathematics, Gautam Buddha University, Greater Noida, India)
DOI: 10.4018/IJORIS.2016040105
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This paper investigates the coordination issue in a decentralized supply chain having a vendor and a buyer for a defective product. The authors develop two inventory models with controllable lead time under service level constraint. The first one is propose under decentralized mode based on the Stackelberg model, the other one is propose under centralized mode of the integrated supply chain. Ordering cost reduction is also including as a decision variable along with shipping quantity, lead time and number of shipments. Computational findings using the software Matlab 7.0 are provided to find the optimal solution. The results of numerical examples show that centralized mode is better than that of decentralized mode, and to induce both vendor and buyer for coordination, proposed cost allocation model is effective. The authors also numerically investigate the effects of backorder parameter on the optimal solutions. Benefit of ordering cost reduction in both models is also provided.
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1. Introduction

In modern competitive business situation, it is essential for businesses to continuously work on improving the performance of their supply chains. Accordingly, integrated supply chain decisions and coordination between supply chain’s members are frequently required for enhancing the performance of supply chains. The majority of the previous work on integrated vendor–buyer inventory systems does not think about ordering cost reduction. It has been a tendency for firms, to invest in logistics expertise and methodology development in order to increase competitive advantage from lowered logistics costs and customer fidelity. Porteus (1985) considered investment in reduced setups in the EOQ (Economic Order Quantity) model. Billington (1987); Kim, Hayya, & Hong (1992); Coates (1996) developed EPQ (Economic Production Quantity) models with setup cost reduction. However, these researchers investigated the advantage from order or setup cost reduction from a single party’s perspective. As shown by Gottardi & Bolisani (1996), the execution of logistics technology and methodology needs both trading partners to trade off transaction credentials, to regulate transaction measures, and to integrate linked applications.

The traditional EOQ/ EPQ model has numerous weaknesses. For instance, the traditional EOQ/EPQ models presume perfect quality of the product, whereas imperfect product quality is more likely and logical situation. These impractical assumptions open the corridor for many researchers to incorporate defective product in lot sizing decisions. Aderohunmu, Mobolurin, & Bryson (1995) analyzed the impact of transportation and delivery processing costs on the inventory costs. They examined the united supplier-buyer total inventory costs together with ordering, setup, transportation, and inventory holding for a durable supply chain partnership when the number of deliveries per shipment is fixed. Ha & Kim (1997) proposed an integrated policy in which once the product reaches the desired level, the product is shipped to the customer and which seems to be better than that of (Aderohunmu et al., 1995) because they provided a lower joint total relevant cost.

When the demand is stochastic, lead time becomes an essential matter of interest and its control leads to many benefits. Shorter lead time reduces the safety stock and the loss caused by stock-out, improves customer service level and increases the competitive advantage of business (Ouyang & Wu, 1997). An integrated vendor-buyer inventory model with controllable lead time in a JIT (Just in Time) environment was presented (Pan & Yang, 2002). They considered that lead time is a significant component which directly affects the customer service level, safety stock and competitiveness in any inventory control system. Ben-Daya & Hariga (2004); Chang, Ouyang, Wu, & Ho (2006); Ouyang, Wu, & Ho (2004; 2006) investigated the decision of lead time reduction in a framework of integrated inventory system in which a supplier and a retailer cooperate in operation’s improvement and share information to attain joint optimization. Ouyang, Wu, & Ho (2007) developed an integrated inventory model concerning imperfect production process with controllable lead time.

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