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2.1 LITERATURE REVIEW AND SURVEY OF
INVENTORY MODELS
Review of literature and survey of the developed inventory models
are being treated for consideration in this chapter. Although there is an
abundance of the literature of general inventory models, however an
attempt has been made to cover some of them which are related to our
problems. The aim of this chapter is to present a complete and update
picture of inventory theory related to the problems of the thesis. The
review of the related literature is an essential aspect of a research work.
2.1.1 Survey of Inventory Models with Inflation
In the classical inventory it is assumed that all the costs associated
with the inventory system remain constant over time. Since most decision
makers think that the inflation does not have a significant influence on the
inventory policy and most of the inventory models developed so far does
not include inflation and time value of money as parameters of the
system. But, due to large scale of inflation the monetary situation in
almost of the countries has changed to an extent during the last thirty
years. Nowadays inflation has become a permanent feature in the
inventory system. Inflation enters in the picture of inventory only because
it may have an impact on the present value of the future inventory cost.
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Thus the inflation plays a vital role in the inventory system and
production management though the decision makers may face difficulties
in arriving at answers related to decision making. At present, it is
impossible to ignore the effects of inflation and it is necessary to consider
the effects of inflation on the inventory system.
Buzacott (1975) developed the first EOQ (Economic Order
Quantity) model taking inflationary effects into account. In this model, a
uniform inflation was assumed for all the associated costs and an
expression for the EOQ was derived by minimizing the average annual
cost. Misra (1975-a, 1979) investigated inventory systems under the
effects of inflation. Bierman and Thomas (1977) suggested the inventory
decision policy under inflationary conditions.
Economic analysis of dynamic inventory models with non-
stationary costs and demand was presented by Hariga (1994). The effect
of inflation was also considered in this analysis. An economic order
quantity inventory model for deteriorating items was developed by Bose
et al. (1995). Authors developed inventory model with linear trend in
demand allowing inventory shortages and backlogging. The effects of
inflation and time-value of money were incorporated into the model. The
inventory policy was discussed over a finite time-horizon with several
reorder points. It was assumed that the goods in the inventory deteriorate
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over time at a constant rate. The results were discussed with a numerical
example and sensitivity analysis of the optimal solution with respect to
the parameters of the system was carried out. Several particular cases of
the model were discussed in brief.
Effects of inflation and time-value of money on an inventory model
was discussed by Hariga (1995) with linearly increasing demand rate and
shortages. Hariga and Ben-Daya (1996) then discussed the inventory
replenishment problem over a fixed planning horizon for items with
linearly time-varying demand under inflationary conditions. Ray and
Chaudhuri (1997) developed a finite time-horizon deterministic
economic order quantity inventory model with shortages, where the
demand rate at any instant depends on the on-hand inventory at that
instant. The effects of inflation and time value of money were taken into
account. A generalized dynamic programming model for inventory items
with Weibull distributed deterioration was proposed by Chen (1998). The
demand was assumed to be time-proportional, and the effects of inflation
and time-value of money were taken into consideration. Shortages were
allowed and partially backordered. The effects of inflation and time-value
of money on an economic order quantity model have been discussed by
Moon and Lee (2000). Authors have considered the normal distribution
as a product life cycle in addition to the exponential distribution. The
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two-warehouse inventory models for deteriorating items with constant
demand rate under inflation were developed by Yang (2004). The
shortages were allowed and fully backlogged in the models. Some
numerical examples for illustration were provided.
Chang (2004) proposed an inventory model under a situation in
which the supplier has provided a permissible delay in payments to the
purchaser if the ordering quantity is greater than or equal to a
predetermined quantity. Shortage was not allowed and the effect of the
inflation rate, deterioration rate and delay in payments were discussed as
well. Models for ameliorating / deteriorating items with time-varying
demand pattern over a finite planning horizon were proposed by Moon et
al. (2005). The effects of inflation and time value of money were also
taken into account. An inventory model for deteriorating items with
stock-dependent consumption rate with shortages was produced by Hou
(2006). Model was developed under the effects of inflation and time
discounting over a finite planning horizon. The results were discussed
with a numerical example and particular cases of the model were
discussed in brief. Sensitivity analysis of the optimal solution with
respect to the parameters of the system was carried out.
Jolai et al. (2006) presented an optimization framework to derive
optimal production over a fixed planning horizon for items with a stock-
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dependent demand rate under inflationary conditions. Deterioration rate
was taken as two parameter Weibull distribution function of time.
Shortages in inventory were allowed with a constant backlogging rate.
Two-warehouse partial backlogging inventory models for deteriorating
items were discussed by Yang (2006). The inflationary effect was
considered in the models. Deterioration rates in both the warehouses were
taken as constant. Some numerical examples for illustration were
provided and sensitivity analysis on some parameters was made.
Jaggi et al. (2007) presented the optimal inventory replenishment
policy for deteriorating items under inflationary conditions using a
discounted cash flow (DCF) approach over a finite time horizon.
Shortages in inventory were allowed and completely backlogged and
demand rate was assumed to be a function of inflation. Optimal solution
for the proposed model was derived and the comprehensive sensitivity
analysis has also been performed to observe the effects of deterioration
and inflation on the optimal inventory replenishment policies. Two stage
inventory problem over finite time horizon under inflation and time value
of money was discussed by Dey et al. (2008). Chern, Yang, Teng, and
Papachristos, (2008) developed an inventory lot-size model for
deteriorating items with partial backlogging and time value of money.
Roy, Pal and Maiti, (2009) developed a production inventory model
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with inflation and time value of money. Demand of the item was stock
dependent and lifetime of the product was taken as random in nature with
exponential distribution. Learning effect on production and setup cost
was incorporated. In their study, model was formulated to maximize the
expected profit during the whole planning horizon. Yang, Teng, and
Chern, (2010) developed an economic order quantity model, in which
shortages were allowed with partial backlogging. The effects of inflation
and time value of money were taken into consideration.
2.1.2 Survey of Inventory Models for Deteriorating Items
In recent years, mathematical ideas have been used in different
areas in real life problems, particularly for controlling inventory. One of
the important concerns of the management is to decide when and how
much to order or to manufacture so that the total cost associated with the
inventory system should be minimum. This is somewhat more important,
when the inventory under go decay or deterioration. Most of the
researchers in inventory system were directed towards non-deteriorating
products. However, there are certain substances, whose utility does not
remain same with the passage of time. Deterioration of these items plays
an important role and items cannot be stored for a long time.
Deterioration of an item may be defined as decay, evaporation,
obsolescence, loss of utility or marginal value of an item that results in
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the decreasing usefulness of an inventory from the original condition.
When the items of the commodity are kept in stock as an inventory for
fulfilling the future demand, there may be the deterioration of items in the
inventory system, which may occur due to one or many factors, i.e.,
storage conditions, weather conditions or due to humidity.
Commodities such as fruits, vegetables and foodstuffs suffer from
depletion by direct spoilage while kept in store. Highly volatile liquids
such as alcohol, gasoline etc. undergo physical depletion over time
through the process of evaporation. Electronic goods, photographic film,
grains, chemicals, pharmaceuticals etc. deteriorate through a gradual loss
of potential or utility with the passage of time. Thus, deterioration of
physical goods in stock is very realistic feature. As a result, while
determining the optimal inventory policy of that type of products, the loss
due to deterioration cannot be ignored. In the literature of inventory
theory, the deteriorating inventory models have been continually
modified so as to accumulate more practical features of the real inventory
systems.
The analysis of deteriorating inventory began with Ghare and
Schrader (1963), who established the classical no-shortage inventory
model with a constant rate of decay. However, it has been empirically
observed that failure and life expectancy of many items can be expressed
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in terms of Weibull distribution. This empirical observation has prompted
researchers to represent the time to deterioration of a product by a
Weibull distribution. Covert and Philip (1973) extended Ghare and
Schraders (1963) model and obtain an economic order quantity model
for a variable rate of deterioration by assuming a two-parameter Weibull
distribution. Philip (1974) presented an EOQ model for items with
Weibull distribution deterioration rate.
Pierskalla and Roach (1972) suggested optimal issuing policies
for perishable inventory. Misra (1975-b) presented a production lot size
model for an inventory system with deteriorating items with variable rate
of deterioration while rate of production was finite. An order level
inventory model for a system with constant rate of deterioration was
presented by Shah and Jaiswal (1977). Aggarwal (1978) and Aggarwal
and Jaggi (1989) presented inventory ordering policies for deteriorating
items. Goyal (1986) and Gupta and Vrat (1986) suggested inventory
models with variable rates of demand. Dave (1986) presented an order
level inventory model for deteriorating items. Model was continuous in
units but allowed discrete opportunities for replenishment. In this model,
demand kept on changing from time unit to time unit and occurs
instantaneously at the beginning of each time unit. Deterioration rate was
assumed to be constant and lead-time was zero.
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A deterministic inventory system with stock dependent demand
rate was formulated by Baker and Urban (1988). An inventory model
concerning a single item was suggested by Mandal and Phaujdar (1989)
for deteriorating items with a variable rate of deterioration. Model was
developed with stock-dependent consumption rate and uniform
production rate. Shortage was allowed and the excess demand was
backlogged as well. The rate of deterioration was assumed first as
constant and then variable. Dutta and Pal (1990) presented a note on an
inventory level dependent demand rate. Inventory model for deteriorating
items with stock dependent demand rate was proposed by Pal et al.
(1993). Inventory models for perishable items with stock dependent
selling rate were suggested by Padmanabhan and Vrat (1995). The
selling rate was assumed to be a function of current inventory level and
rate of deterioration was taken to be constant with complete, partial
backlogging and without backlogging. Balkhi and Benkherouf (1996)
presented a production lot size model for deteriorating items and arbitrary
production and demand rates. In this model demand and production were
allowed to vary with time in an arbitrary way and shortages were
allowed. The rate of deterioration was taken as constant and the method
was illustrated with the help of numerical example.
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Mandal and Maiti (1997) presented an inventory model for
damageable items with fully backlogged shortages for both linear and
non-linear damage and demand functions. The authors considered
production rate as finite and solved the model with profit maximization
criteria together with sensitive analysis. An economic order quantity
model for perishable products with nonlinear holding cost was proposed
by Giri and Chaudhuri (1998). The demand rate was taken as function
of on-hand inventory.
An EOQ inventory model with ramp-type demand rate for items
with Weibull deterioration was formulated by Wu et al. (1999).
An order level inventory model for deteriorating items was
proposed by Gupta and Agarwal (2000). The demand was taken as a
linear function of time and production rate was taken as demand
dependent. A production inventory model for deteriorating items with
exponential declining demand was discussed by Kumar and Sharma
(2000). Time horizon was fixed and the production rate at any instant was
taken as the linear combination of on-hand inventory and demand.
Aggarwal and Jain (2001) presented an inventory model for
exponentially increasing demand rate with time. The items were
deteriorating at a constant rate and shortages were allowed. The authors
solved the model by two methods. The first method was efficient for
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getting accurate results, although, lengthy and complicated while the
second method was faster than the first method and thus easy to apply.
Goyal and Giri (2001-a) presented a review of the advances of
deteriorating inventory literature since early 1990s. The models available
in the relevant literature have been suitably classified by shelf-life
characteristic of the inventoried goods. A single-vendor and multiple-
buyers production-inventory policy for a deteriorating item was
formulated by Yang and Wee (2002). Production and demand rates were
taken to be constant. A mathematical model incorporating the costs of
both the vender and the buyers was developed.
An order level inventory model for deteriorating items with an
exponential increasing demand was proposed by Sharma and Singh
(2003). An order-level inventory problem for a deteriorating item with
time dependent quadratic demand was presented by Khanra and
Chaudhuri (2003). The inventory was assumed to deteriorate at a
constant rate and shortages were not allowed. A production-inventory
model for a deteriorating item over a finite planning horizon was
presented by Sana et al. (2004). Deterioration rate was taken as constant
fraction of the on-hand inventory. The demand was taken to be linear
time-varying function. An economic production quantity model for
deteriorating items was discussed by Teng and Chang (2005). Demand
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rate was taken as dependent on the display stock level and the selling
price per unit. A deteriorating multi-item inventory model with limited
storage capacity was suggested by Mandal et al. (2006). The demand
rate for the items was finite and deterioration rate was taken to be
constant. The replenishment rate was taken as constant. The problem was
supported by numerical examples. A note on the inventory models for
deteriorating items with ramp type demand was developed by Deng et al.
(2007). They have proposed an extended inventory model with ramp type
demand rate and its optimal feasible solution. Liao (2008) considered an
EOQ model with non-instantaneous receipt and exponentially
deteriorating items under two-level trade credit. Chung (2009) explored a
complete proof on the solution procedure for non-instantaneous
deteriorating items with permissible delay in payment.
2.1.3 Survey of Inventory Models with Permissible Delay in
Payments
There have been a lot of discussions in the existing literature for
the possible extension of the basic economic order quantity model to a
number of situations where its assumptions are not valid up to now. A
business either manufactures the products it sells or it purchases the
products to sell from other businesses. In either case, an increase in
inventory usually involves a corresponding increase in accounts payable.
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Raw materials used in the production process are purchased on credit, and
many other manufacturing costs are not paid for immediately. Products
from other businesses are bought on credit. Instead of making immediate
cash payment when inventory is increased, a business delays payment,
perhaps by a month or so.
that the customers are allowed some grace period before they settle the
account with the supplier. This gives a very advantage to the customers
due to the fact that they do not have to pay the supplier immediately after
receiving the product, but instead, they can delay their payment until the
end of the allowed period. The customer pays no interest during the fixed
period they have to settle the account, but if the payment is delayed
beyond that period, interest will be charged. The permissible delay in
payments brings some advantages to the buyer, as he would try to earn
some interest for the payment received during this period. When a
supplier allows a fixed time for settling the account, he is actually giving
a loan to the buyer without interest during this period. Therefore, it is
economical to delay in the settlement of accounts to the last moment of
the permissible delay in payments.
Inventory policy with trade credit financing was formulated by
Haley and Higgins (1973). The effect of payment rules on ordering and
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stock holding in purchasing was suggested by Kingsman (1983).
Different inventory policies with trade credit was developed by
Chapman et al. (1984) and Chapman and Ward (1988). Goyal (1985)
was the first to develop the economic order quantity under conditions of
permissible delay in payments. Author has assumed that the unit selling
price and the purchase price are equal. In practice, the unit selling price
should be greater than the unit purchasing price. Aggarwal and Jaggi
(1995) developed ordering policies of deteriorating items under
permissible delay in payments. The demand and deterioration were
exponentially deteriorating products under the condition of permissible
delay in payments was discussed by Hwang and Shinn (1997). Jamal et
al. (2000) presented optimal payment time for a retailer under permitted
delay of payment by the wholesaler. The wholesaler allowed a
permissible credit period to pay the dues without paying any interest for
the retailer. In the study, a retailer model was considered with a constant
rate of deterioration. An inventory model for initial-stock-dependent
consumption rate was suggested by Liao et al. (2000). Shortages were
not allowed. The effects of inflation rate, deterioration rate, initial stock-
dependent consumption rate and delay in payments were discussed.
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Chang and Dye (2001) developed an inventory model for
deteriorating items with partial backlogging and permissible delay in
payments. Chung et al. (2002) have discussed the inventory decision for
EOQ inventory model under permissible delay in payments. An EOQ
model for deteriorating items with credit policy was discussed by Chang
et al. (2003). Lot sizing decision policy was presented by Chung and
Liao (2004). In this policy trade credit was depending on the ordering
quantity. Teng et al. (2005) presented an optimal pricing and ordering
policy under permissible delay in payments. Deterioration rate was taken
as constant and shortages were not allowed in the study. The optimal
ordering policy in a DCF analysis for deteriorating items was suggested
by Chung and Liao (2006). In this policy trade credit was also
depending on the ordering quantity.
Huang (2007)
levels of trade credit policy within the economic production quantity
(EPQ) framework. Author has assumed that the supplier would offer the
retailer a delay period and the retailer also adopted the trade credit policy
replenishment model. Replenishment rate was taken as finite. Sana and
Chaudhuri (2008)
Increasing deterministic demands were discussed in the environment of
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permissible delay in payment and discount offer to the retailer. An
inventory model under two levels of trade credit policy was proposed by
Jaggi et al. (2008) with credit-linked demand.
2.1.4 Survey of Supply Chain Inventory Models
One of the most important topics in the study of the management
of contemporary manufacturing and distribution is supply chain
management (SCM). Inventory management is an essential process for all
parties engaged in supply chain activities, from the procurement of raw
materials through to the delivery of finished goods. The effective
execution of this process has a major influence on both the financial and
operational performance of an organization.
While many may argue that inventories are undesirable and should
be eliminated from the supply chain, the fact remains that organizations
require inventory in order to operate effective and to ensure the smooth
operation of their day-to-day business. Notwithstanding the critical
importance of inventories, companies have to keep in mind that
inventories can also cause adverse effects and often disguise other
underlying issues in the supply chain. Managing inventory can be both a
complicated and critical process given the conflicting business objectives
that can occur with in an organization and across multiple enterprises.
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Supply cha
management is the coordination of production, inventory, location and
transportation among the participants in a supply chain to achieve the best
mix of responsiveness and efficiency for the market being served
into widespread use in the 1990s. Prior to that time, business used terms
There is a difference between the concept of supply chain
management and traditional concept of logistics. Logistics typically refers
to activities that occur with in the boundaries of a single organization and
supply chains refer to networks of companies that work together and
coordinate their actions to deliver a product to market. Also, traditional
logistics focuses its attention on activities such as procurement,
distribution, maintenance and inventory management. Supply chain
management acknowledges all the traditional logistics and also includes
activities such as marketing, new product development, finance and
customer service.
In the wider view of supply chain thinking, these additional
activities are now seen as part of the work needed to fulfill customer
requests. Supply chain management views the supply chain and the
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organizations in it as a single entity. It brings a systems approach to
understanding and managing the different activities needed to coordinate
the flow of products and services to best serve the ultimate customer.
This systems approach provides the framework in which to best respond
in business requirements that otherwise would seem to be in conflict with
each other.
Taken individually, different supply chain requirements often have
conflicting needs. For instance, the requirement of maintaining high
levels of customer service calls for maintaining high levels of inventory,
but then the requirement to operate efficiently calls for reducing
inventory levels. It is only when these requirements are seen together as
part of a large picture that ways can be found to effectively balance their
different demands.
Effective supply chain management requires simultaneous
improvements in both customer service levels and the internal operating
efficiencies of the companies in the supply chain. Customer service at its
most basic level means consistently high order fill rates, high on-time
delivery rates and a very low rate of products returned by customers for
whatever reason. Internal efficiency for organizations in a supply chain
means that these organizations get an attractive rate of return on their
investments in inventory and other assets.
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The effective management of supply channel inventories is perhaps
the most fundamental objective of supply chain management.
Manufacturers procure raw material and process them into finished
goods, and sell the finished goods to distributors, then to retailer and/or
customer. When an item moves through more than one stage before
-
A large amount of researches on multi-echelon inventory control has
appeared in the literature during the last decades.
Clark and Scarf (1960) were the first to study the two-echelon
inventory model. They proved the optimality of a base stock policy for
the pure serial inventory system and developed an efficient decomposing
method to compute the optimal base stock ordering policy. Sherbrooke
(1968) considered an ordering policy of two-echelon model for
warehouse and retailer. It is assumed that stock-outs at the retailers are
completely backlogged. Van der Heijden et al. (1997) presented stock
allocation policies in general single-item and N-echelon distribution
systems, where it is allowed to hold stock at all levels in the network.
Diks and De Kok (1998) determined a cost optimal replenishment policy
for a divergent multi-echelon inventory system. A joint replenishment
policy for multi-echelon inventory control was proposed by Axsater and
Zhang (1999). A multi-echelon inventory model for a deteriorating item
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was developed by Rau et al. (2003). An optimal joint total cost has been
derived from an integrated perspective among the supplier, the producer
and the buyer. A deteriorating item inventory model in a supply chain
was proposed by Wu and Wee (2005). Shortages in inventory were
allowed and fully backlogged. Two-echelon inventory model with lost
sales was proposed by Hill et al. (2007). A two level supply chain in
which production interruptions for restoring of the quality of the
production process coordinated by Ahmed et al.(2008). Wong et al.
(2009) proposed a two-echelon supply chain with a single supplier
serving multiple retailers in vendor-managed inventory (VMI)
partnership.
2.1.5 Survey of Partial Backlogging Inventory Models
An important issue in the inventory theory is related to how to deal
with the unfulfilled demands which occur during shortages or stock outs.
In most of the developed models researchers assumed that the shortages
are either completely backlogged or completely lost. The first case,
known as backordered or backlogging case, represent a situation where
the unfulfilled demand is completely back ordered. In the second case,
also known as lost sale case, we assume that the unfulfilled demand is
completely lost.
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Furthermore, when the shortages occur, some customers are willing
to wait for backorder and others would turn to buy from other sellers. In
many cases customers are conditioned to a shipping delay and may be
willing to wait for a short time in order to get their first choice. For
instance, for fashionable commodities and high-tech products with short
product life cycle, the willingness of a customer to wait for backlogging
is diminishing with the length of the waiting time. Thus, the length of the
waiting time for the next replenishment would determine whether the
backlogging would be accepted or not. In many real life situations, during
a shortage period, the longer the waiting time is, the smaller is the
backlogging rate would be. Therefore, for realistic business situations the
backlogging rate should be variable and dependent on the waiting time
for the next replenishment. Many researchers have modified inventory
Some researchers have developed inventory models in which the
proportion of customers who would like to accept backlogging is the
reciprocal of a linear function of the waiting time up to the arrival of next
lot. Some researches have been done in which backlogging rate is taken
as exponential decreasing function of time. The inventory involving
backlogging and lost sales is called mixture inventory. Mixture inventory
means mixture of backorders and lost sales. Therefore, in the third case, it
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is assumed that a fixed fraction of the unfulfilled demand during the stock
out stage is back ordered while the remaining fraction is lost. Thus,
concept of partial backlogging should not be ignored in inventory models
of shortage.
Zangwill (1966) developed a production multi-period production
scheduling model with backlogging. Inventory models with a mixture of
backorders and lost sales were formulated by Montgomery et al. (1972).
Rosenberg (1979) presented the analysis of a lot-size model with partial
backlogging. Mak (1987) proposed optimal production-inventory control
policies for an inventory system. Shortages in inventory were allowed
and partially backlogged.
Economic production lot size model for deteriorating items with
partial backordering was suggested by Wee (1993). Abad (1996)
formulated a generalized model of dynamic pricing and lot-sizing for
perishable items. Shortage was allowed and the demand was partially
backlogged. The effects of lost sales on composite lot sizing were
discussed by Sharma and Sadiwala (1997).
Deteriorating inventory model with quantity discount, pricing and
partial backordering was developed by Wee (1999). In this study, demand
was assumed to decrease with the increment in price for the product. The
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numerical example was also given to illustrate the model. Optimal price
and order size inventory policy for a reseller under partial backlogging
was proposed by Abad (2000-a). The problem of determining the lot size
for a perishable good under finite production was formulated by Abad
(2000-b). Shortage in inventory was allowed with partial backordering
and lost sale. Author has taken a problem of determining the production
lot size of a perishable product that decays at an exponential rate. Wu
(2000) developed inventory model for items with Weibull distribution
deterioration rate, time dependent demand and partial backlogging.
An EOQ inventory model for items with Weibull distribution
deterioration rate and ramp type demand was formulated by Wu (2001).
Shortages in inventory were allowed and assumed to be partially
backlogged. Ouyang and Chang (2002) presented stochastic continuous
review inventory model with variable lead time and partial backorders to
capture the reality of uncertain backorders. An EOQ model for
deteriorating items with time-varying demand and partial backlogging
was suggested by Teng et al. (2003). Papachristos and Skouri (2003)
considered a model where the demand rate was a convex decreasing
function of the selling price and backlogging rate was a time dependent
function. The time of deterioration of the item was distributed as two
parameter Weibull distribution function of time.
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A general time-varying demand inventory lot-sizing model with
waiting-time-dependent backlogging and a lot-size-dependent
replenishment cost was developed by Zhou et al. (2004).
An EOQ model with time varying deterioration and linear time
varying demand over finite time horizon was proposed by Ghosh and
Chaudhuri (2005). Shortages in inventory were allowed and partially
backlogged with waiting time dependent backlogging rate. Ouyang et al.
(2005) discussed an EOQ inventory mathematical model for deteriorating
items with exponentially decreasing demand. The shortages were allowed
and partially backordered. The backlogging rate was variable and
dependent on the waiting time for the next replenishment.
Pal et al. (2006) have developed an inventory model for single
deteriorating item by considering the impact of marketing strategies such
as pricing and advertising as well as the displayed stock level on the
demand rate of the system. Shortages were allowed and the backlogging
rate was dependent on the duration of waiting time up to the arrival of
next lot. An economic production lot size model for deteriorating items
with stock-dependent demand was produced by Jolai et al. (2006) under
the effects of inflation. Shortages were allowed and partially
backlogged.
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A deterministic inventory model for deteriorating items with price
dependent demand was developed by Dye et al. (2007-a). The demand
and deterioration rates were continuous and differentiable function of
price and time, respectively. Shortages for unsatisfied demand were
allowed and backlogging rate was taken as negative exponential function
of the waiting time. Numerical example was also used to study the
problem numerically. Dye et al. (2007-b) presented a deterministic
inventory model for deteriorating items with two warehouses. The
deterioration rate in both the warehouses was taken as different.
Shortages in OW were allowed and the backlogging demand rate was
dependent on the duration of stockout. Authors have used numerical
example to illustrate the model and conclude the paper with suggestions
for possible future research.
An inventory lot-size model for deteriorating items with partial
backlogging was formulated by Chern et al. (2008). Authors have taken
time value of money in to consideration. The demand was assumed to
fluctuating function of time and the backlogging rate of unsatisfied
demand was a decreasing function of the waiting time. The effects of
inflation and time value of money were also considered in the model.
Thangam and Uthayakumar (2008) presented a two-level supply chain
model with partial backordering and approximated Poisson demand.
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Skouri et al. (2009) developed an inventory model with general ramp
type demand rate, time dependent (Weibull) deterioration rate and partial
backlogging of unsatisfied demand.
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REFERENCES
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system with constant rate of deterioration. Opsearch, 15, 184-187.
[2] Aggarwal S.P. and Jaggi C.K. (1989). Ordering policy for decaying
inventory. International Journal of System Science. (I.J.S.S.), 20, 151-
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