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Open accessJournal ArticleDOI: 10.1088/1757-899X/263/4/042152

An optimal EOQ inventory model for non-instantaneous deteriorating items with various time dependent demand rates and time dependent holding cost

01 Nov 2017-Vol. 263, Iss: 4, pp 042152
Abstract: An economic order quantity inventory model for non-instantaneous deteriorating items has been developed with cubic demand rate, cubic deterioration rate and time dependent holding cost. Shortages in inventory are allowed in this model. In shortage period, partial and complete backlogging cases are considered. The main objective of this model is to develop an optimal policy that minimizes the total average inventory cost and optimal order quantity. Numerical examples are used to illustrate the developed model

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Topics: Economic order quantity (65%), Holding cost (59%)
References
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Journal ArticleDOI: 10.1016/J.IJPE.2005.01.010
Kun-Shan Wu1, Liang-Yuh Ouyang1, Chih-Te Yang1Institutions (1)
Abstract: In this study, we consider a problem of determining the optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand. In the model, shortages are allowed and the backlogging rate is variable and dependent on the waiting time for the next replenishment. The necessary and sufficient conditions of the existence and uniqueness of the optimal solution are shown. As the special cases, the results for the models with instantaneous or non-instantaneous deterioration rate and with or without shortages are derived. Further, we analytically identify the best circumstance among these special cases based on the minimum total relevant cost per unit time. Sensitivity analysis of the optimal solution with respect to major parameters is carried out. Finally, four numerical examples are presented to demonstrate the developed model and the solution procedure.

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316 Citations


Journal ArticleDOI: 10.1016/J.CIE.2006.07.012
Liang-Yuh Ouyang1, Kun-Shan Wu1, Chih-Te Yang1Institutions (1)
Abstract: In this study, an appropriate inventory model for non-instantaneous deteriorating items with permissible delay in payments is considered. The purpose of this study is to find an optimal replenishment policy for minimizing the total relevant inventory cost. This mathematical model is a general framework that comprises numerous previous models such as in Ghare and Schrader [Ghare, P. M., & Schrader, G. H. (1963). A model for exponentially decaying inventory system. International Journal of Production Research, 21, 449-460], Goyal [Goyal, S. K. (1985). Economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, 36, 335-338], and Teng [Teng, J. T. (2002). On the economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, 53, 915-918] as special cases. We have developed some useful theorems to characterize the optimal solutions and provide an easy-to-use method to find the optimal replenishment cycle time and order quantity under various circumstances. Several numerical examples are given to test and verify the theoretical results. Finally, a sensitivity analysis of the optimal solution with respect to major parameters is also included. According to the results of numerical analysis, we provided several ways for the retailer to effectively reduce total annual relevant inventory cost.

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Topics: Economic order quantity (56%)

196 Citations


Journal ArticleDOI: 10.1016/J.IJPE.2003.12.006
Abstract: This paper deals with the problem of determining the economic order quantity under conditions of permissible delay in payments. The delay in payments depends on the quantity ordered. When the order quantity is less than the quantity at which the delay in payments is permitted, the payment for the item must be made immediately. Otherwise, the fixed trade credit period is permitted. The minimization of the total variable cost per unit of time is taken as the objective function. An algorithm to determine the economic order quantity is developed. The results obtained in this paper generalize some already published results.

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Topics: Economic order quantity (65%)

168 Citations


Open accessJournal ArticleDOI: 10.1016/J.CAM.2009.10.031
K. V. Geetha1, R. Uthayakumar1Institutions (1)
Abstract: In this paper, Economic Order Quantity (EOQ) based model for non-instantaneous deteriorating items with permissible delay in payments is proposed. This model aids in minimizing the total inventory cost by finding an optimal replenishment policy. In this model shortages are allowed and partially backlogged. The backlogging rate is variable and dependent on the waiting time for the next replenishment. Some useful theorems have been framed to characterize the optimal solutions. The necessary and sufficient conditions of the existence and uniqueness of the optimal solutions are also provided. An algorithm is designed to find the optimal replenishment cycle time and order quantity under various circumstances. Numerical examples are given to demonstrate the theoretical results. Sensitivity analysis of the optimal solution with respect to major parameters of the system has been carried out and the implications are discussed in detail. In the discussions, suggestions are given to minimize the total cost of the inventory system.

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Topics: Economic order quantity (58%), Total cost (51%)

108 Citations


Journal ArticleDOI: 10.1016/J.IJPE.2013.07.006
Abstract: This study is motivated by the paper of Chang et al. [International Journal of Production Economics 123 (2010) 62–68]. We extend their inventory model from two aspects. (1) The demand rate as multivariate function of price and level of inventory (2) Delay in payment is permissible. Under these assumptions, we first formulated a mathematical model and then some useful theoretical results have been derived to characterize the optimal solutions for non-zero and zero ending inventory system. Numerical examples are presented to illustrate the theoretical results. The sensitivity analysis of a suitable example is performed and some managerial insights are proposed. Our analysis revels that it is more beneficial to keep higher inventory level, hoping to stimulate more demand, even if it results in non-zero ending inventory.

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Topics: Perpetual inventory (64%), Inventory theory (64%)

78 Citations