For the past four decades the integrated vendor and buyer supply chain inventory model has been an interesting topic, but quality improvement of defective items in the integrated inventory model with backorder price discount involving controllable lead time has been rarely discussed. The aim of this paper is to minimize the total related cost in the continuous review model by considering the order quantity, reorder point, lead time, process quality, backorder price discount and number of shipment as decision variables. Moreover, we assume that an investment function is used to improve the process quality. The lead time demand follows a normal distribution. In addition, the buyer offers backorder price discount to motivate the customers for possible backorders. There are some defective items in the arrival lot, so its treatment is also taken in account in this paper. We develop an iterative procedure for finding the optimal values of decision variables and numerical example is presented to illustrate the solution procedure. Additionally, sensitivity analysis with respect to major parameters is also carried out.

In the global critical economic scenario, inflation plays a vital role in deciding optimal pricing of goods in any business entity. This article presents two single-vendor single-buyer integrated supply chain inventory models with inflation and time value of money. Shortage is allowed during the lead time and it is partially backlogged. Lead time is controllable and can be reduced using crashing cost. In the first model, we consider the demand of lead time follows a normal distribution, and in the second model, it is considered distribution-free. For both cases, our objective is to minimize the integrated system cost by simultaneously optimizing the order quantity, safety factor, lead time and number of lots. The discounted cash flow and classical optimization technique are used to derive the optimal solution for both cases. Numerical examples including the sensitivity analysis of system parameters is provided to validate the results of the supply chain models.

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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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