An optimal policy for deteriorating items with time-proportional deterioration rate and constant and time-dependent linear demand rate

Journal of Industrial Engineering International, Apr 2017

In this paper, an economic order quantity (EOQ) inventory model for a deteriorating item is developed with the following characteristics: (i) The demand rate is deterministic and two-staged, i.e., it is constant in first part of the cycle and linear function of time in the second part.   (ii) Deterioration rate is time-proportional.   (iii) Shortages are not allowed to occur.   The optimal cycle time and the optimal order quantity have been derived by minimizing the total average cost. A simple solution procedure is provided to illustrate the proposed model. The article concludes with a numerical example and sensitivity analysis of various parameters as illustrations of the theoretical results.

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An optimal policy for deteriorating items with time-proportional deterioration rate and constant and time-dependent linear demand rate

An optimal policy for deteriorating items with time-proportional deterioration rate and constant and time-dependent linear demand rate Trailokyanath Singh 0 1 2 Pandit Jagatananda Mishra 0 1 2 Hadibandhu Pattanayak 0 1 2 0 Department of Mathematics, Ravenshaw University , Cuttack, Odisha 753003 , India 1 Department of Mathematics, C. V. Raman College of Engineering , Bhubaneswar, Odisha 752054 , India 2 Mathematics Subject Classification 90B05 In this paper, an economic order quantity (EOQ) inventory model for a deteriorating item is developed with the following characteristics: The optimal cycle time and the optimal order quantity have been derived by minimizing the total average cost. A simple solution procedure is provided to illustrate the proposed model. The article concludes with a numerical example and sensitivity analysis of various parameters as illustrations of the theoretical results. Constant and time-dependent linear demand rate Deteriorating items EOQ Time-proportional deterioration rate - The demand rate is deterministic and two-staged, i.e., it is constant in first part of the cycle and linear function of time in the second part. Deterioration rate is time-proportional. Shortages are not allowed to occur. & Trailokyanath Singh Introduction Most of the business organizations emphasize on inventory management and solving inventory problems because they want to obtain economic order quantity (EOQ) which minimizes the total average inventory cost. Over the last few decades, many researches have been done for controlling and maintaining the inventory. In real life situation, decay or deterioration of items is a natural phenomenon. Vegetables, fruits, foods, perfumes, chemicals, pharmaceutical, radioactive substances and electronic equipments, etc., are examples of deteriorating items, i.e., the loss characteristics of items at any time is regarded as deterioration. Therefore, it is not wise to ignore the factor deterioration while analyzing the model. Several inventory models for deteriorating items are developed to answer these questions: ??How much to order to replenish the inventory of an item?? and ??When to order so as to minimize the total cost?? (Gupta and Hira 2002). The classical inventory model for deteriorating items of Harris (1915) and Wilson (1934) states that the depletion of inventory is mainly due to the constant demand rate. Firstly, the effect of deterioration on fashion items after their prescribed date was studied by Whitin (1957). Later, a dynamic version of the classical EOQ model for deteriorating items was developed by Wagner and Whitin (1958). Ghare and Schrader (1963) studied the inventory model for deteriorating items with constant deterioration rate and constant demand rate with the help of the differential equation dId?tt? ? hI?t? D?t?; 0 t T where I?t?, D?t? and h represent the inventory level at any time t, the demand rate at time t and constant deterioration rate, respectively, during the cycle time T. Furthermore, the model for replenishment policies involving time-varying pattern has received much attention from several researchers. Donaldson (1977) examined the classical noshortage inventory model for deteriorating items with a linear trend in demand over a known and finite horizon by using calculus method. An order-level inventory model for deteriorating items having constant deterioration rate was studied by Shah and Jaiswal (1977). Aggarwal (1978) modified the work of Shah and Jaiswal by calculating the average holding cost. Dave and Patel (1981) developed the inventory model for deteriorating items with linear increasing in demand rate and deterioration rate which was a constant fraction of the on-hand inventory. All the models discussed above are based on the constant deterioration rate, constant demand rate, infinite replenishment and no shortage. Heng et al. (1991) proposed an exponential decay in inventory model for deteriorating items by assuming a finite replenishment rate and constant demand rate. The reviews of the advances of deteriorating inventory literature are presented by Raafat (1991); Goyal and Giri (2001); Li et al. (2010); Bakker et al. (2012) and Janssen et al. 2016). Goswami and Chaudhuri (1991) considered the replenishment policy for a deteriorating item with linear trend in demand rate. Xu et al. (1991) presented an inventory model for deteriorating items with linear demand rate over known and finite horizon. Chung and Ting (1994) proposed a heuristic inventory model for deteriorating items with time-proportional demand rate. Wee (1995) proposed a replenishment policy with exponential time-varying demand rate by extending the partial backlogging model. Benkherouf (1995) presented an optimal replenishment policy for a deteriorating item with known and finite planning horizon. The above models are based on constant deterioration rate and shortages. Srivastava and Gupta (2007) studied an EOQ model for deteriorating items with c (...truncated)


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Trailokyanath Singh, Pandit Jagatananda Mishra, Hadibandhu Pattanayak. An optimal policy for deteriorating items with time-proportional deterioration rate and constant and time-dependent linear demand rate, Journal of Industrial Engineering International, 2017, pp. 1-9, DOI: 10.1007/s40092-017-0198-6