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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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This study considers an EOQ inventory model with advance payment policy in a fuzzy situation by employing two types of fuzzy numbers that are trapezoidal and triangular. Two fuzzy models are developed here. In the first model the cost parameters are fuzzified, but the demand rate is treated as crisp constant. In the second model, the demand rate is fuzzified but the cost parameters are treated as crisp constants. For each fuzzy model, we use signed distance method to defuzzify the fuzzy total cost and obtain an estimate of the total cost in the fuzzy sense. Numerical example is provided to ascertain the sensitiveness in the decision variables about fuzziness in the components. In practical situations, costs may be dependent on some foreign monetary unit. In such a case, due to a change in the exchange rates, the costs are often not known precisely. The first model can be used in this situation. In actual applications, demand is uncertain and must be predicted. Accordingly, the decision maker faces a fuzzy environment rather than a stochastic one in these cases. The second model can be used in this situation. Moreover, the proposed models can be expended for imperfect production process.

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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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In this study, a two-warehouse inventory model with exponentially increasing trend in demand involving different deterioration rates under permissible delay in payment has been studied. Here the scheduling period is assumed to be a variable. The objective of this study is to obtain the condition when to rent a warehouse and the retailer\'s optimal replenishment policy that minimizes the total relevant cost. An effective algorithm is designed to obtain the optimal solution of the proposed model. Numerical examples are provided to illustrate the application of the model.Based on the numerical examples, we have concluded that the single warehouse model is less expensive to operate than that of two warehouse model. Sensitivity analysis has been provided and managerial implications are discussed.

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This paper deals with a deterministic inventory model for deteriorating items under the condition of permissible delay in payments with constant demand rate is a function of time which differs from before and after deterioration for a single item. Shortages are allowed and completely backlogged which is a function of time. Under these assumptions, this paper develops a retailer\'s model for obtaining an optimal cycle length and ordering quantity in deteriorating items of an inventory model. Thus, our objective is retailer\'s cost minimization problem to nd an optimal replenishment policy under various parameters. The convexity of the objective function is derived and the numerical examples are provided to support the proposed model. Sensitivity analysis of the optimal solution with respect to major parameters of the model is included and the implications are discussed.

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This paper considers the fuzzy inventory model for deteriorating items for power demand under fully backlogged conditions. We define various factors which are affecting the inventory cost by using the shortage costs. An intention of this paper is to study the inventory modelling through fuzzy environment. Inventory parameters, such as holding cost, shortage cost, purchasing cost and deterioration cost are assumed to be the trapezoidal fuzzy numbers. In addition, an efficient algorithm is developed to determine the optimal policy, and the computational effort and time are small for the proposed algorithm. It is simple to implement, and our approach is illustrated through some numerical examples to demonstrate the application and the performance of the proposed methodology.