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In this paper, the study deals with the lead time and setup reduction problem in the vendor-purchaser integrated inventory model. The cost of capital (i.e., opportunity cost) is one of the key factors in making the inventory and investment decisions. Lead time is an important element in any inventory system. The proposed model is presents an integrated inventory model with controllable lead time with setup cost reduction for defective and non defective items under investment for quality improvement. In this analysis, the proposed model, we assumed that the setup cost and process quality is logarithmic function. Setup cost reduction for defective and non defective items, is the main focus for the proposed model. The objective of the proposed model is to minimize the total cost of both the vendor-purchaser. The mathematical model is derived to investigate the effects to the optimal decisions when investment strategies in setup cost reductions are adopted. This paper attempts to determine optimal order quantity, lead time, process quality and setup cost reduction for production system such that the total cost is minimized. A solution procedure is developed to find the optimal solution and numerical examples are presented to illustrate the results of the proposed models.

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The purpose of this article is to investigate a two-echelon supply chain inventory problem consisting of a single-vendor and a single-buyer with controllable lead time and investment for quality improvements. This paper presents an integrated vendor-buyer inventory model in order to minimize the sum of the ordering cost, holding cost, setup cost, investment for quality improvement and crashing cost by simultaneously optimizing the optimal order quantity, process quality, lead time and number of deliveries the vendor to the buyer in one production run with the objective of minimizing total relevant cost. Here the lead-time crashing cost has been assumed to be an exponentially function of the lead-time length. The main contribution of proposed model is an efficient iterative algorithm developed to minimize integrated total relevant cost for the single vendor and the single buyer systems with controllable lead time reduction and investment for quality improvements. Graphical representation is also presented to illustrate the proposed model. Numerical examples are presented to illustrate the procedures and results of the proposed algorithm. Matlab coding is also developed to derive the optimal solution and present numerical examples to illustrate the model.

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Coordinating the supply chain is among the most important subjects that is extensively addressed in the related literature. If a supply chain is to be coordinated, it is equivalent to say that we must solve a problem related to competition and cooperation. The game theory is obviously one of the most effective methods to solve such problems, in which the players of the supply chain are assumed to engage in cooperative and non-cooperative games. The current study aims to coordinate a two-level supply chain consisting of a manufacturer and a retailer. This will be achieved using cooperative advertisement along with pricing decisions such that the manufacturer offers a price discount to the retailer and the demand is affected by pricing and advertisement. Cooperative advertisement is a coordinated effort made by all the members of the supply chain to increase the customer demand, in which the retailer does the local advertisement and the manufacturer pays for a portion or all the costs of the retailer advertisement. We consider two models for manufacturer-retailer relation using the game theory: the manufacturer-Stackelberg and the retailer-Stackelberg games with asymmetric power distribution.