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
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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)