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Impact of RFID technology on inventory control policy
Feng Tao
1
*, Tijun Fan
1
, Kin Keung Lai
2
and Lin Li
1
1
Department of Management Science and Engineering, East China University of Science and Technology, 130
Meilong Road, Xuhui District, Shanghai 200237, China; and
2
Department of Management Sciences, City
University of Hong Kong, Kowloon Tong, Hong Kong, China
RFID application can improve operation performance in a supply chain by reducing or eliminating inventory
misplacement and shrinkage. In this paper, we present a periodic review inventory model to investigate and
characterize the multiperiod inventory control policies in both non-RFID and RFID cases when the firm
encounters misplacement and shrinkage. The optimal inventory control policy is proved to be a two-control limit
policy. The control limits in both the non-RFID case and the RFID case are analyzed and examined, while
considering the impact of shrinkage and misplacement on inventory policies. A critical inventory level is
determined to identify the relationship of higher inventory level control limits between the RFID case and the
non-RFID case. An intensive numerical study with sensitivity analysis of selling price, misplacement rate,
shrinkage rate, inventory recovery rate, and tag price is conducted. We find that when RFID technology is
adopted, the inventory control policy in the RFID case is much more stable than that of the non-RFID case, as the
misplaced inventory can be recovered perfectly and instantly for sale and the inventory shrinkage can be reduced
by RFID technology. In addition, one of our intriguing findings is that when the shrinkage rate is below a
threshold value which is independent of parameters, RFID application has no effect on inventory control policy if
the misplaced inventory can be recovered in a timely manner by physical audit, which has not been revealed in
previous studies.
Journal of the Operational Research Society (2016). doi:10.1057/s41274-016-0030-5
Keywords: RFID; inventory control policy; misplacement; shrinkage; dynamic programming
1. Introduction
Inventory misplacement refers to placement of the product on
the wrong shelf by a customer or a salesperson, causing a
temporary loss which may be recovered by physical audit;
while inventory shrinkage is caused by damage or theft in the
store (such as customer shoplifting) so that the product cannot
be sold any more, which leads to permanent loss. These two
types of factors will definitely reduce the available inventory
for sale, although the records are kept unchanged accordingly
in the system (Atali et al,2004,2006; Kok and Shang, 2014).
As such, there exists discrepancy between inventory record
and the amount of product available for sale.
This phenomenon is prevalent in many industries, i.e., it is
reported by IBM that retailers suffer an inventory difference
rate of 1.75% of $58 billion in revenue, and manufacturers
suffer a rate of 0.22–0.73% (Alexander et al,2002). Dehor-
atius and Raman (2008) examined nearly 370,000 inventory
records from 37 stores of a large public retailer with annual
sales of approximately $10 billion; they found that 65% of the
records were not in accordance with the actual inventory level.
Kok and Shang (2007) examined a large distribution company
with an average inventory of $3 billion; the disparity is up to
1.6% of the total inventory value at the end of 2004.
Apparently, inventory misplacement and shrinkage bring
uncertainty in determining inventory control policy, and
weaken the performance of the supply chain. Concerning the
effects of these two factors, the retailer needs to increase its
inventory level in order to alleviate lost sales due to stock-out.
In turn, the excessive inventory will raise the inventory cost. It
has been estimated that, due to inventory misplacement and
shrinkage, lost sales and inventory costs will cut profit by
more than 10% (Alexander et al,2002; Raman et al,2001;
Heese, 2007).
Radio frequency identification (RFID) technology has been
publicized as an effective and promising solution to inventory
misplacement and shrinkage (Dai and Tseng, 2012; Camdereli
and Swaminathan, 2010; Fan et al,2014). With RFID
technology, the items can be tracked through the use of an
RFID tag. Therefore, two principal values of this technology
are observed: (1) providing product visibility that the manager
can identify the item and access information such as the
position status; and (2) helping the manager eliminate
*Correspondence: Feng Tao, Department of Management Science and
Engineering, East China University of Science and Technology, 130
Meilong Road, Xuhui District, Shanghai 200237, China.
E-mail: ftao@ecust.edu.cn
Journal of the Operational Research Society (2016) ª2016 The Operational Research Society. All rights reserved. 0160-5682/16
www.palgrave.com/journals
misplacement and shrinkage (Kok, 2008; Rekik et al,2008).
Thus, when misplacement and shrinkage are reduced or
eliminated by RFID application, what inventory control
policies will result? What is the impact of this technology
on inventory control policies? It is necessary to answer these
questions to uncover the benefits of RFID technology.
In empirical studies, shrinkage is found to be the dominant
factor, and misplacement is inevitable and occurs widely. In
this paper, we focus on the impact of these two factors on
inventory control policy and analyze the effectiveness of
applying RFID technology when the retailer encounters
misplacement and shrinkage. A large majority of recent
papers have considered the newsvendor solution to investigate
the effect of RFID on supply chain/partner decisions
(Camdereli and Swaminathan, 2010; Fan et al,2014,2015).
In these models, inventory is ordered only once at the
beginning of the planning horizon, and the unsold inventory is
salvaged at the end of the planning horizon. However, some
retailers need to periodically replenish inventory, and the
unsold inventory in the current decision period is kept for sale
in the next decision period. Based on these differences, we
formulate a dynamic programming model to further investi-
gate inventory control policies with RFID adoption. In general,
the research questions of this study are
(1) As a newsvendor solution has been widely studied, how
should we consider inventory misplacement and shrink-
age in multiperiod inventory control? What is the impact
of the related parameters on inventory control policies?
(2) Although RFID is a promising solution to misplacement
and shrinkage, is it always optimal to invest in this new
technology whenever these two factors exist?
Motivated by the issue of RFID technology adoption and
previous research, we formulate a dynamic programming
model for a finite planning horizon to investigate the
characteristics and differences of inventory control policies
by comparing a non-RFID case and an RFID case, respec-
tively. The corresponding inventory control policies in a
single-period decision epoch are characterized analytically;
while in a multiperiod decision epoch, an intensive numerical
study is conducted to examine the impact on inventory policy
with respect to selling price, misplacement rate, shrinkage rate,
and recovery rate of shrinkage. It is intriguing to find that
inventory control policy is more sensitive to these parameters
in the non-RFID case than in the RFID case. More impor-
tantly, there is a threshold value of inventory shrinkage below
which it is unnecessary to invest in RFID technology.
The remainder of this paper is organized as follows.
Section 2provides a brief literature review of related research.
In Section 3, we present the dynamic programming model for
both non-RFID and RFID technology when there are inventory
misplacement and shrinkage. In Section 4, we characterize the
inventory control policies with single-period and multiperiod
analysis. The numerical study is presented in Section 5
followed by the conclusion of this paper in Section 6.
2. Literature review
Our research pertains to inventory inaccuracy in a retail supply
chain, which is widely discussed in the literature (Raman et al,
2001; Fleisch and Tellkamp, 2005; Thiel et al,2010).
Typically, the classic inventory models are based on the
assumption of accurate inventory information; however, a
series of the research consider the problem of inventory
uncertainty (Heese, 2007; Rekik et al,2008). Kok (2008)
proposed a near-optimal joint inventory inspection approach to
deal with the inventory inaccuracy caused by random errors.
Further, Kok and Shang (2007) extended the work by
providing a simple recursion to evaluate the N-stage serial
supply chain cost when it suffered from inventory inaccuracy.
Rekik et al (2008) studied the impact of different types of
misplacement inventory for a supply chain under a newsven-
dor framework. Kang and Gershwin (Kang and Gershwin,
2004) investigated the problems resulting from information
inaccuracy in an inventory system by applying (Q, R) policy.
Recently, Mersereau formulated this kind of inventory
replenishment problem as a Markov decisions process using
a Bayesian Inventory Record (Mersereau, 2013). In that paper,
the inaccurate inventory record (or unobserved perturbation of
the true inventory in the paper) is referred as invisible demand,
which is randomly distributed and happens after satisfying the
demand. The difference is that, in our paper, the inventory
misplacement and shrinkage are assumed to be constant and
exogenous parameters before observing the demand, and they
can be recovered or eliminated (to some extent) at the end of
each decision period.
The research on RFID in the literature is also relevant to our
topic. This research focuses on the value of the visibility
(availability) provided by RFID in improving operational
performance (Lee and Ozer, 2007; Sarac et al,2010). Lee and
Ozer (2007) argued that there is a huge credibility gap in both
claims of RFID value and its actual value when utilized. Dutta
et al (2007) reviewed the value proposition of RFID in three
dimensions and attempted to recognize the problems for
further investigation. Bottani et al (2010) investigated the
impact of RFID on mitigating the bullwhip effect in the Italian
FMCG supply chain. Lee (2010) presented a Supply Chain
RFID Investment Evaluation Model, and provided a basis to
understand RFID value creation, measurement, and ways to
maximize the value of RFID technology. Hossain and
Prybutok (2008) investigated the factors that affect consumer
acceptance of RFID technology.
The third stream related to our work is the application of
RFID in inventory management. Some studies investigated
supply chain coordination when applying RFID technology
(Heese 2007; Rekik et al,2008; Gaukler et al,2007; Rekik,
2011; Lim et al,2013). Dai and Tseng (2012) presented a
systematic approach to quantify the extent of saving from
timely information and reduction in information distortion
when applying RFID to eliminate inventory inaccuracy. Sahin
et al (2004,2008,2009) assumed that the wholesaler is not
Journal of the Operational Research Society
aware of inventory errors or chooses to ignore them, and they
estimated the efficiency loss due to these errors. However,
studies related to RFID in inventory management are relatively
new. Rekik and Sahin (2009) analyzed the shoplifting issue by
optimizing the holding cost under a service level constraint.
They evaluated the use of RFID technology in an inventory
system, and analyzed the critical tag cost which results in cost
effectiveness of RFID technology. Metzger et al (2013)
developed an inventory control policy for RFID-enabled retail
shelf inventory management when considering false-negative
reads due to imperfect detection by the technology. Compared
with these studies, in our paper it is assumed that, in the non-
RFID case, the recovered inventory will be kept for sale in the
next decision period instead of being salvaged at the end of the
current decision period. Our work also differs from these
models in that we consider inventory decisions in a multi-
period horizon and present the inventory policy as a two-
control-limit strategy. In addition, in the numerical study, we
find that the impact of tag price on inventory control policy is
limited.
The works most related to our research are Camdereli and
Swaminathan (Camdereli and Swaminathan, 2010) and Fan
et al (2014,2015). The study by Camdereli and Swaminathan
(2010) solely considered inventory misplacement, in which the
misplaced products have positive salvage value at the end of
the planning horizon. In the study by Fan et al,(2014), the
newsvendor model is formulated to cope only with inventory
shrinkage, in which the lost products cannot be found at the
end of the sales season. They analyzed the effectiveness of
deploying RFID technology in terms of ordering fill rate,
RFID reading rate improvement, and tag price. Further, they
extended the model to consider both misplacement and
shrinkage simultaneously (Fan et al,2015). The differences
between our work and these papers are threefold: (1) a
multiperiod dynamic programming model is formulated to
consider the finite planning horizon inventory control strate-
gies in daily operations; (2) the misplaced inventory can be
recovered for sale in the next decision period in the non-RFID
case, but can be recovered instantly for sale in the current
decision period in the RFID case; and (3) we focus on both
non-RFID and RFID cases to uncover the impact on inventory
control policy, and find the critical value of shrinkage ratio to
adopt RFID technology in the numerical study.
3. Model
Before presenting the model, we define the notations as
follows:
cis the unit purchasing cost;
gis the unit tag price with RFID technology;
his the daily holding cost of unsold product, where hr;
pis the unit penalty cost when stock-out exists;
ris the unit sales revenue;
sis the unit salvage value;
tis the decision horizon, where t=1, 2 ,…,T;
xis the initial inventory level before replenishment;
yis the inventory level after replenishment;
ais the shrinkage ratio;
bis the misplacement percentage, where a?b\1;
dis the shrinkage recovery rate, where 0 \dB1. If d=1
the shrinkage rate can be eliminated completely. On one
hand, stolen or shoplifted inventory can be detected by
RFID technology so that it can be recovered for sale. On
the other hand, with the help of RFID, the retailer can
discover the product that is about to expire, which also can
increase the availability of on-hand inventory.
Unfortunately, however, RFID technology cannot
identify whether a product on the shelf or in the store is
damaged, so it cannot recover the damaged inventory.
Therefore, to be practical, we define the shrinkage
recovery rate to indicate that there are still a number of
products in the inventory that cannot be recovered and
sold. In this paper, we assume that the shrinkage recovery
rate is zero when we do not apply RFID.
cis the discount factor;
Dis the stochastic demand with density function f(x) and
cumulative distribution function F(x), where E(X)\?;
Kis the setup cost with RFID technology.
The decision sequence in a typical period is as follows:
(a) At the beginning of the period, take the left inventory
from previous period as the initial inventory level of
current period;
(b) Make a decision on whether salvaging the excessive
inventory or placing an order based on the inventory
control policy;
(c) When demand arrives, satisfy it or get punished for stock-
out;
(d) At the end of the period, left inventory, if any, is stored
for sale in the next period.
Assumption 1 (A.1) Inventory misplacement and shrinkage
occur as soon as the inventory level is determined. At the
end of each decision period, the inventory record is cor-
rected to be equal to the true inventory level.
For ease of exposition, we assume that inventory misplace-
ment and shrinkage take place when the objective inventory
level is determined at the beginning of each decision period
(after salvaging and purchasing, but before demand arriving).
At the end of each decision period, inventory record is
corrected according to the true inventory level on hand. The
second part of this assumption ensures that the inventory
control policy is made on the true inventory data instead of
incorrectness inventory record. For example, assume the
inventory loss rate is 20%, at the end of current decision
period, if the record inventory level is 10, then the true
Feng Tao et al—Impact of RFID technology on inventory control policy
inventory level is 8 (=10 * 80%). At the beginning of next
decision period, if we decide to order up to 20 and take 10 as
the initial inventory level, according to A.1, the available
inventory level is 16 (=20 * 80%) when the replenishment is
determined. However, the true inventory level is 14.4
(=18 * 80%), which is less than expected.
Assumption 2 (A.2) When there is no RFID, misplaced
inventory can be recovered at the end of each decision
period, but shrinkage inventory cannot be recovered and
is lost permanently.
If RFID is not adopted, misplaced inventory can be found
and recovered by physical audit. However, it is infeasible or
costly to recover the inventory as soon as it is misplaced.
Thus,, it is reasonable to assume that the misplaced inventory
is recovered at the end of each decision period, so that it can be
salvaged (at the end of the planning horizon) or sold in the
next period. Concerning shrinkage, it consists of two types: (1)
theft or shoplifting—the stolen products are missing, but they
are in the record; and (2) damaged or expired products—this
type of product can no longer be sold. Therefore, these two
types of shrinkage reduce the available quantity of inventory.
It is noted that misplaced inventory and shrinkage inventory
may be found and monitored in a timely manner by
salespeople so that the inventories are recovered for sale in
the current decision period—we do not take these circum-
stances into account in this paper.
Accordingly, in each decision period, because of inventory
misplacement and shrinkage, the actual inventory that can be
sold after replenishment is (1 -a-b)y. The unmet demand
is lost. Consequently, without RFID, the retailer’s profit-to-go
function could be
PxðÞ
¼max
rE min yw;D
ðÞ
þsxy
ðÞ
þcyx
ðÞ
þpE D yw
ðÞ
þ
hE y min yw;DðÞðÞþcEPywDðÞ
þþby
()
;
ð1Þ
where y
w
=(1 -a-b)yis the actual inventory level after
replenishment. The first term in the maximum operator is the
expected revenue; the second term is the salvage value; the
next three expressions are the purchasing cost, the penalty cost
due to shortage, and the holding cost, respectively; and the last
term is the expected discount future profit.
Considering the salvage value, at the beginning of each
decision period, if the initial inventory level is higher than the
objective (optimal) level, the excess inventory will be
salvaged. In our model, the initial inventory levels of
the current and the next decision periods are xand
(y
w
-D)
+
?by, respectively. Therefore, the initial inven-
tory in any decision period (except the first one) consists of
the unsold inventory and the misplaced inventory recovered
at the end of the previous decision period. This is consistent
with assumption A.2. The salvaging activity as well as the
purchasing, if any, is triggered at the beginning of each
decision period before demand arrives such that we use the
difference between the initial inventory level xand the
objective inventory level yto calculate the salvage value and
procurement cost. At this point, the inventory level in record
is equal to the actual inventory level (according to A.1 and
A.2). However, just from this moment on (i.e., the excessive
inventory has been salvaged s(x-y)
+
or the order has been
placed c(y-x)
+
and the updated inventory level in current
decision period is realized), misplacement and shrinkage
occur. In addition, it is easy to understand that the misplaced
inventory incurs daily holding cost as it is recovered for sale
in the next decision period. Regarding damaged or expired
inventory, we consider the disposal cost as the daily holding
cost for ease of formulation. It is noted that we do not
consider the disposal revenue of this kind of inventory; that
is, we assume the salvage value of damaged or expired
inventory is zero. Finally, regarding stolen or shoplifted
inventory, we take the cost of identifying and auditing the
inventory as the holding cost. To this end, the holding cost is
hE(y-min (y
w
,D)). As the misplaced inventory bycan be
recovered for sale in the next decision period, we regard it as
expected future profit.
Assumption 3 (A.3) Misplaced inventory can be recovered
instantly and completely by means of RFID technology,
but shrinkage cannot be completely eliminated because of
inventory damage.
Analogous to the existing literature (Fan et al,2015), RFID
technology is assumed to perform so well that misplaced
inventory can be positioned and recovered entirely for sale
during the current decision period. However, when we
consider shrinkage, theft, or shoplifting can easily be detected
and recovered instantly, but RFID technology cannot recover
damaged products, which can no longer be sold. Therefore,
there is still a percentage of shrinkage (say 1 -din our paper)
that is lost permanently.
Before presenting the next assumption, let k
1
=1-a-b
and k
2
=1-(1 -d)aso that 0 Bk
1
Bk
2
B1, and
define the function Hk;aðÞ¼
krþpðÞ1F0ðÞðÞþa
1k1F0ðÞðÞ
; then we can
verify that H(k
2
,-c-g)BH(k
2
,s) and H(k
1
,-c)B
H(k
1
,s)BH(k
2
,s).
Assumption 4 (A.4) The parameters satisfy the following
condition:
s\h\min Hk1;cðÞ;Hk2;cgðÞ
fg
:
It is noted that the condition is unnecessary when formu-
lating the dynamic programming model, but it is sufficient in
proving the inventory control policies.
Based on the above assumptions, when RFID is adopted,
inventory can be tracked in real time so that the available
inventory increases as the misplacement is recovered and the
Journal of the Operational Research Society
shrinkage is decreased. Thus, the retailer’s objective profit-to-
go function could be
PRxðÞ
¼max
rE min yr;DðÞþsxyðÞ
þcþgðÞyxðÞ
þpE D yr
ðÞ
þ
hE y min yr;DðÞðÞþcEPRyrDðÞ
þ
()
ð2Þ
where y
r
=(1 -(1 -d)a)yis the inventory level under
RFID technology after replenishment. Here, the misplaced
inventory is recovered instantly and completely for sale, so
the expression does not contain b. The main difference
between the non-RFID case and the RFID case is that the
misplaced inventory is recovered for sale in the next
decision period (i.e., the term cEP((y
w
-D)
+
?by)in
Eq. (1)), but it is recovered for sale in the current decision
period in the RFID case (i.e., the term rE min (y
r
,D)in
Eq. (2)). Clearly and intuitively, the available inventory for
sale in Eq. (2) is larger than that in Eq. (1). However,
considering the cost of applying RFID technology, the
inventory control policy may not be easy to characterize in
a multiperiod planning horizon.
When considering the fixed setup cost with RFID invest-
ment, we have
WxðÞ¼KþPRxðÞ:
4. Analysis
In this section, we first analyze the one-period problem and
characterize the optimal inventory control policy. Next, we
consider the multiperiod model and discuss the intractability of
characterizing the optimal control policy analytically, leading
to a computational study in the next section.
4.1. Single-period analysis
For one period, when the retailer does not introduce RFID
technology, the single-period formulation could be
pxðÞ¼max sxyðÞ
þcyxðÞ
þþrEmin yw;DðÞ
pE D yw
ðÞ
þhE y min yw;DðÞðÞ
()
ð3Þ
As (D-y
w
)
+
=(D-y
w
)?(y
w
-D)
+
, the above func-
tion can be rewritten as
pxðÞ¼max
sxyðÞ
þcyxðÞ
þþrEmin yw;DðÞpE D yw
ðÞ
pE ywDðÞ
þhE y min yw;DðÞðÞ
()
Let k
1
=1-a-b; to obtain the optimal inventory
control limit, define two functions
uyðÞ¼k1rþpþhðÞ1Fk1yðÞ½hcð4Þ
and
vy
ðÞ
¼k1rþhþp
ðÞ
1Fk1y
ðÞ½
hþsð5Þ
It is easy to get
ouyðÞ
oy¼ovyðÞ
oy¼k2
1rþpþhðÞfk1yðÞ\0
The inequality holds as k
1
2
[0, r,p,h[0, f(k
1
y)[0, and
f(y)[0. Therefore, for Eq. (3), we have the following
conclusion.
Theorem 1 The optimal inventory policy for Eq. (3)is a two-
control limit strategy as
y¼
yL
;if xyL;
x;if yL\xyH;
yH
;if x [yH
:
8
<
:
where y
L
=arg {u(y)=0} and y
H
=arg {v(y)=0}.
Proof We resort to the proof in Eberly and Mieghem (1997)
by two steps: 1) to prove the continuity and concavity of
the right-hand side of Eq. (3) for any given xin the first
place; and 2) to obtain the expressions of the control limit.
(1) It is readily seen that s(x-y)
+
-c(y-x)
+
is
continuous and concave in yfor any given xas
sBc. In addition, rE min (y
w
,D) is continuous and
concave with respect to y;pE(D-y
w
)
+
and
hE(y-min (y
w
,D)) are both continuous and con-
vex with respect to y. Therefore, the right-hand side
of Eq. (3) is continuous and concave with respect to
yfor any given x.
(2) In terms of the control limit, we can see that when
x=0, the first derivative of Eq. (3) with respect to
yyields Eq. (4). With the first-order condition, we
get y
L
=arg {u(y)=0}. When xis sufficiently
large, the first derivative of Eq. (3) with respect to
yyields Eq. (5). With the first-order condition, we
get y
H
=arg {v(y)=0}. To prove the uniqueness
of the two-control limits, we resort to A.4. More-
over, with some algebra, it is easy to get u(0) =
k
1
(r?p?h)(1 -F(0)) -h-c[0, v(0) =k
1
(r?p?h)(1 -F(0)) -h?s[0 and lim
y??-
u(y)=-h-c\0, lim
y??
v(y)=-h?s\0,
which imply that there exist only one y
L
and y
H
such
that u(y
L
)=0 and v(y
H
)=0. It can be readily
verified that y
L
By
H
\?. The concavity of the
objective function yields that it is optimal to do
nothing on the inventory control policy whenever
the initial inventory level satisfies y
L
BxBy
H
.
Therefore, the optimal inventory control policy for
Eq. (3) is as follows: (i) to order up to y
L
when the initial
inventory level is below y
L
; (ii) to reduce the inventory
Feng Tao et al—Impact of RFID technology on inventory control policy
down to y
H
when the initial inventory level is above y
H
;
and (iii) to keep the inventory level unchanged if the
initial inventory level is between y
L
and y
H
. This com-
pletes the proof. h
Likewise, the single-period formulation with RFID technol-
ogy is
pRxðÞ¼max sxyðÞ
þcþgðÞyxðÞ
þþrEmin yr;DðÞ
pE D yr
ðÞ
þhE y min yr;DðÞðÞ
()
ð6Þ
Let k
2
=1-(1 -d)a, and define
uryðÞ¼k2rþpþhðÞ1Fk2yðÞðÞhþcþgðÞð7Þ
and
vry
ðÞ
¼k2rþpþh
ðÞ
1Fk2y
ðÞðÞ
hþsð8Þ
Theorem 2 The optimal inventory ordering policy for
Eq. (6)is a two-control limit as
y
r¼
yL
r;if xyL
r;
x;if yL
r\xyH
r;
yH
r;if x [yH
r:
8
<
:
where y
r
L
=arg{u
r
(y)=0} and y
r
H
=arg{v
r
(y)=0}.
The proof of Theorem 2 is analogous to that of Theorem 1;
therefore, it is omitted here.
Intuitively, if the retailer does not apply RFID when it
suffers from inventory misplacement and shrinkage, a higher
inventory level must be maintained in order to satisfy demand,
which leads to higher ordering levels in each decision period;
however, when the retailer implements RFID technology,
inventory levels can be reduced without decreasing the service
level (which can be defined as the availability of product).
Nonetheless, unfortunately, the relationships between corre-
sponding inventory levels are not that clear even though we
consider a single-period decision model, which is shown in
Lemma 1.
Lemma 1 Considering the inventory control policies with
RFID and non-RFID technology,
(1) Given parameters, there exist y*such that
v(y*) =v
r
(y*). If v(y*) =v
r
(y*) [0, then y
H
[y
r
H
;
if v(y*) =v
r
(y*) B0, then y
H
By
r
H
,the equality
only holds when v(y*) =v
r
(y*) =0.
(2) Given parameters, if g =0, there exist y* such that
u(y*) =u
r
(y*). If u(y*) =u
r
(y*) [0, then y
L
[y
r
L
;
if u(y*) =u
r
(y*) B0, then y
L
By
r
L
,the equality
only holds when u(y*) =u
r
(y*) =0; otherwise, the
relationship between y
L
and y
r
L
depends on the tag
price.
Proof By definition, it is easy to verify that
0\k
1
Bk
2
\1; the equality only holds when b=0 and
a=0, or b=0 and d=0.
(1) From Eqs. (5) and (8), we have
dv yðÞ
dy ¼k2
1rþpþhðÞfk1yðÞ\0 and dvryðÞ
dy
¼k2
2rþpþhðÞfk2yðÞ\0
Therefore, both v(y) and v
r
(y) are strictly decreasing
functions with respect to y. We have
vyðÞvryðÞ¼ rþpþhðÞk1k2
ðÞ½
k1Fk1yðÞk2Fk2yðÞðÞ
Thus, verifying v(y*) =v
r
(y*) converts to prove
k
1
-k
2
=k
1
F(k
1
y)-k
2
F(k
2
y). With some algebra,
we need to prove that there exists y* such that
1Fk2y
ðÞ
1Fk1y
ðÞ
¼k1
k2
:ð9Þ
The right-hand side of Eq. (9) satisfies 0\k1
k21, where
the equality only holds when k
1
=k
2
, while the left-hand
side of Eq. (9) holds for any y. Next, we prove that when
0\k1
k2
\1, Eq. (9) is valid. As a,b, and dare predeter-
mined parameters, k
1
,k
2
, and k
1
/k
1
k
2
.k
2
can be taken as
constant values. Here, F(•) is an increasing function
which implies that F(k
2
y)[F(k
1
y) for any given y.In
addition, lim
y!1
1Fk2yðÞ
1Fk1y
ðÞ
¼1 and 1Fk2yðÞ
1Fk1y
ðÞ
[0, and it is
easy to verify that GyðÞ¼
1Fk2yðÞ
1Fk1yðÞ
is a continuous
function with respect to y. Therefore, given a,b, and d,
there exists y* such that 1Fk2y
ðÞ
1Fk1y
ðÞ
¼k1
k2which ensures
v(y*) =v
r
(y*). In addition, as y
H
=arg {v(y)=0} and
y
r
H
=arg {v
r
(y)=0}, and v(y), v
r
(y) are both decreasing
functions with respect to y, when v(y*) =v
r
(y*) [0, we
have y
H
[y
r
H
[y*; when v(y*) =v
r
(y*) \0, we have
y
H
\y
r
H
\y*; and when v(y*) =v
r
(y*) =0, we have
y
H
=y
r
H
=y*. This completes the proof of the first
part.
(2) Similarly, we have
uyðÞuryðÞ¼ rþpþhðÞk1k2
ðÞ½
k1Fk1yðÞk2Fk2yðÞðÞþg
Therefore, if g=0, from the proof of part (1), we can
get the conclusion. Otherwise, given other parameters,
when g[0, the difference of u(y)-u
r
(y) depends on the
value of g, the tag price of RFID technology. That is, there
exists a value g*[0. If g[g*, then u(y)[u
r
(y), which
implies y
L
\y
r
L
regardless of y;if0BgBg*, then
Journal of the Operational Research Society
u(y)Bu
r
(y), which implies y
L
Cy
r
L
regardless of y. Intu-
itively, when the RFID tag price is large, compared with
the non-RFID case, the retailer becomes more conserva-
tive in ordering because of cost constraint, which increa-
ses the lower inventory control limit. Equivalently, when
the variable tag price increases, the marginal unit cost is
larger in the RFID case than the shortage cost because of
inventory misplacement and shrinkage in the non-RFID
case. This completes the proof. h
It is noted that, defining kas the available rate of
inventories, then 1 -F(ky) is the probability of lost sales.
When the proportion of available inventory in the non-RFID
case to that in the RFID case (namely, k
1
/k
2
) equals the
proportion of probability of lost sales in the RFID case to that
in the non-RFID case (namely, 1Fk2yðÞ
1Fk1yðÞ
), it determines a critical
value y*(v(y*)) which the relationship between upper level
inventory control limits in RFID and non-RFID cases can rely
on, which is illustrated in Figure 1.
Lemma 1 states that it is not easy to determine the
relationship between corresponding inventory control levels
with non-RFID and RFID cases. We believe that three reasons
may account for this: 1) unmet demand is lost; 2) the
misplaced inventory is recovered for sale in the next period in
the non-RFID case, but is recovered instantly for sale in the
RFID case; and 3) the procurement cost contains the variable
tag price of the new technology. The retailer needs to balance
the cost, or fiscal burden, resulting from RFID with the benefit
of more accurate inventory information. With the complexity
of the control limits, it is difficult to identify the relationship of
inventory control policies as Fan et al (2014,2015) did.
However, in the next section we conduct a detailed numerical
study to analyze the inventory strategies, revealing some
implications.
4.2. Multiperiod analysis
In this subsection, we extend the analysis to a multiperiod
case. In general, we count the time backward, and truncate
P(•) into P
t
(•), which refers to the period tprofit-to-go
formulation.
When there is no RFID technology, the profit-to-go
formulation could be
PtxðÞ
¼max
stxyðÞ
þctyxðÞ
þþrtEmin yw;Dt
ðÞptED
tyw
ðÞ
þ
htEyDt
ðÞ
þþcEPt1ywDt
ðÞ
þþby
()
ð10Þ
When RFID technology is applied, the profit-to-go model
could be
Similarly, if consider the fixed investment cost of RFID
technology, we have
WxðÞ¼KþPR
txðÞ
It is noted that, in multiperiod formulations, it is
intractable to verify the concavity of the objective functions
PR
txðÞ¼max stxyðÞ
þcþgðÞyxðÞ
þþrtEmin yr;Dt
ðÞptED
tyr
ðÞ
þ
htEyDt
ðÞ
þþcEPR
t1yrDt
ðÞ
þ
()
ð11Þ
Figure 1 Shape of V(y).
Feng Tao et al—Impact of RFID technology on inventory control policy
because of the terms (y
w
-D)
+
?byand (y
r
-D)
+
in the
expected future profit, so that it is infeasible to obtain the
analytical solution. However, the Value Iteration (VI) algo-
rithm can find a stationary q-optimal policy and an approx-
imation value to this dynamic programming, where qis
constant and q[0 (Puterman, 1994). In the numerical study,
we apply Policy Iteration (PI) algorithm to find the optimal
two-control limit policy as a representative example (Bert-
sekas, 1995) and the VI algorithm to find the q-optimal values.
Nonetheless, the policy may not be unique, as shown in
Figure 2. Again, this is mostly because of the maximum
expression in the expected future profit (Li et al,2012). When
we consider a multiperiod planning horizon, it is probable that
the objective function P
t
(•) is piecewisely concave (Xu and
Li, 2007), which is illustrated in Figure 3and intensively
examined in the numerical study.
5. Numerical study
In this section, we conduct a computational test to investigate
the optimal inventory control policies with inventory mis-
placement and shrinkage. All codes are written by MATLAB
software and available upon request; the presented numerical
results are only a small subset of the data.
We apply PI algorithm to find the optimal two-control limit
inventory management policy as an illustrated example for
finite planning horizon model and Gauss–Seidel Value Iter-
ation algorithm (Eberly and Meighem, 1997), which increases
the convergence to find the q-optimal approximation value,
where q=0.00001 in our test. For ease of computation, all
parameters are set to be independent of the decision period.
Without loss of generality, the demand is set to be binomial
distributed with n=40 and p=0.2, denoted by B(n,p). The
remaining parameters are s=1, c=6, p=4, h=2, g=0.5.
It should be noted that all the tests are conducted with a number
of parameter values to make sure that the conclusion is
independent of a specific value. As the fixed investment cost
Kcan only impact on the total profit, we omit it in the numerical
study.
5.1. Inventory control policy for finite planning horizon
In this subsection, we apply PI algorithm to illustrate the
optimal two-control limit policy as an example. Specifically,
we choose misplacement rate b=0.2 in non-RFID case, and
select inventory recovery rate d=0.85 in RFID case to find
the policy when change the value of shrinkage rate afrom 0.1
to 0.5 discretely.
The worst case in PI algorithm is to enumerate all the
possible actions in action space to find the optimal policy.
Theoretically, if the maximum demand is n, to satisfy the
demand, the system state can be any value between 0 and n
(both inclusive) as we consider lost sales model (in backlogged
model, the state can be negative in each decision period). On
the other hand, there are n?1 actions need to calculate in
each state. For example, if the maximum demand is 5, the state
space is {0, 1, 2, 3, 4, 5}. Given a state, say 3, the action can
be reducing to 0, 1, 2, or increasing to 4, 5, or keeping
unchanged (=3). Therefore, the action space is {-3, -2, -1,
0, 1, 2}. Namely, it is necessary to test 6 actions in each state.
In this case, the finite number of iterations in PI algorithm may
reach as much as (n?1)
n+1
. To simplify the calculation, we
focus on the updated inventory levels after the action is taken
when consider the pattern of two-control limit policy. We
know that the updated lower (y
L
) and upper (y
H
) bound
inventory levels can be any value in {0, 1, 2 ,…,n} satisfying
y
L
By
H
. Given a pair of values of lower bound and upper
bound, the action in each state is determined accordingly,
which generates a new subset action space. It is surely that the
optimal control policy is included in this new defined subset
action space. However, in this setting, the maximum number
of iterations is reduced to nþ2ðÞnþ1ðÞ
2, which is much less than
the original case. The outcome is summarized in the following
Table 1.
From Table 1, we can see that the two-control limit policy
may not be unique when we extend our analysis to finite period
model, which is also an evidence of piecewise concavity of the
objective function as mentioned in Section 4.2.
In terms of the piecewise exhibition of two-control limit
policy, there are two further explanations. 1) The control
Figure 2 Shape of the control policy.
Figure 3 Shape of the optimal value.
Journal of the Operational Research Society
policy may degenerate after several decision periods. For
example, taking a look at the control policy in RFID case when
a=0.3, if the inventory level exceeds 19 after satisfying the
demand, it is optimal to slash the inventory level down to 19
by salvaging some product. After that, demand in the next
decision period arrives, if the left inventory level is less than
11 after satisfying the demand, then it is optimal to order up to
11. From this period on, it is optimal to keep the inventory
level with 11 at the beginning of each decision period after
conducting inventory control policy. Therefore, the initial
inventory level determines the specific policy among the
optimal policies. 2) Sometimes, the two-control limit may
converge to only one point such that it is better to keep the
inventory level steadily during the planning horizon, i.e., if the
inventory level is in [0,21] after satisfying the demand in non-
RFID case with a=0.4, it is always optimal to keep the
inventory level at 19 when conducting the inventory control
policy. However, it is noted that this convergent two-control
limit policy is essentially different from the base-stock
inventory control policy as the latter is an order-up-to policy,
while the former does not only include order-up-to decision
but also contains salvaging the excessive inventory.
5.2. Sensitivity analysis
In this subsection, we conduct a sensitivity analysis on the
parameters to investigate the impact of different parameters on
the inventory control policies.
On selling price test. In this test, we aim to find the
relationship between the selling price and the inventory control
policies. The results are shown in Figure 4, where
a=0.1, b=0.1, d=0.9.
It is noted that, as the planning horizon is extended to a
finite period and the objective function is piecewisely concave,
the inventory control policy may not follow a unique interval
as analyzed in one period. It may be a consecutive multi-
interval policy, which is shown in Table 1. Therefore, for ease
of comparison, in this test we calculate the average inventory
levels instead of the control limits. The numerous original data
will be provided upon request.
In Figure 4, the horizontal axis is the selling price r, while
the vertical axis is the average inventory level (hereafter AIL
in short). The solid line represents the average inventory level
when the inventory record is accurate; the dash line refers to
the average inventory level if RFID technology is applied
when inventory misplacement and shrinkage emerge; and the
dash-dot line stands for the average inventory level with
corresponding non-RFID case.
From Figure 4, we see that the selling price has very little
impact on the inventory control policy, although intuitively, it
can influence the profit directly. Because of misplacement and
shrinkage, the retailer needs to keep a high level of inventory
to satisfy the demand, which is the increment part shown in the
figure with the dash-dot-two-arrow line. By means of RFID
technology, the retailer can reduce the average inventory level,
which is the decrement part shown in the figure with the dot-
two-arrow line. The discrepancy between the increment and
decrement is the gap, which is shown in the figure with the
dash-two-arrow line, that is, Increment =Decrement ?Gap.
Three main reasons can account for the gap:
(1) Inventory recovery rate—the existence of unrecoverable
products leads to a rise in inventory levels, which will
enlarge the gap.
(2) Misplaced inventory—note that in the non-RFID case the
misplaced inventory can be recovered at the end of each
decision period. Therefore, it will increase the amount of
available inventory at the beginning of the next decision
period and incur holding cost. However, in the RFID
case, it can be found instantly and be for sale in the
current decision period, which reduces the gap.
(3) The tag price of RFID—because of the tag price, the unit
procurement cost increases, which increases the cost of
identifying the missing inventory and the average
inventory level as well. This will be examined further
in the following.
We know that when the selling price increases, the cost of
stock-out increases accordingly. Thus, the average inventory
Table 1 A representative example of two-control limit policy
with increment of a
aNon-RFID (b=0.2) RFID (d=0.85)
0.1 [15]
[16],[17]
[18] [11, 20]
0.2 [16],
[17]
[18]
[19, 20]
, [21]
[22]
, [23] [11, 16]
0.3 [18]
[19]
, [20]
[21]
, [22, 24] [11]
[12, 13]
,
[14, 19]
0.4 [19]
[20, 21]
,
[22, 23]
[24] [12, 22]
0.5 [15],
[16, 18]
[19],
[20, 21]
[22],
[23, 24]
[25] [12, 20]
[.]
[A, B]
[..]
means if the inventory level lies in [.], raise it to A; if the
inventory level lies in [..], slash it down to B; if the inventory level lies in
[A, B] (inclusive), keep it unchanged.
Figure 4 Inventory on selling price r.
Feng Tao et al—Impact of RFID technology on inventory control policy
levels in all cases increase, which is clearly demonstrated in
the figure. However, in general, the significance of this impact
is limited.
On misplacement rate. The test of misplacement ratio b
without RFID technology is conducted. The results are shown
in Figures. 5and 6.
From our assumption, the misplaced inventory rate bdoes
not have an impact on the RFID case. Here, we examine the
impact of misplaced rate bon the inventory control policy in
the non-RFID case. According to the discussion, the misplaced
inventory can only be recovered for sale in the next decision
period by physical audit. In other words, the misplaced
inventory can be taken as storage to the next decision period.
Hence, when the misplacement rate is large, it is natural to
increase the reorder point because more inventories are stored
for the future selling period. In addition, in the multiperiod
planning horizon of the non-RFID case, the misplaced
inventory not only incurs shortage cost, but also results in
increased holding cost. Therefore, we conduct a numerical
study on the holding cost (Figure 5) and penalty cost
(Figure 6), respectively, to exactly reveal the impact of
misplacement rate on the inventory control level.
From the figures, we see that as the misplacement rate
increases, the inventory levels increase accordingly (mostly),
which is evident. Given a misplacement rate, when holding
cost decreases, say from h=4toh=2, the average inventory
levels increase as it is less costly to hold more inventories.
However, in regard to penalty cost, the inventory levels do not
present a significant decrement with the decreasing of penalty
cost, say from p=7top=2. Thus, the holding cost plays a
more important role when determining the inventory policy
with misplacement rate. A retailer who suffers from a high rate
of misplaced inventory needs to recover the inventory in a
timely manner, or reduce the holding cost if the inventory
cannot be recovered for sale in the current selling period. It is
worthy of reminding that the average inventory level increases
(decreases) as the lower threshold of inventory control policy
increases (decreases), which leads to ordering of more (less)
inventories in the decision horizon.
On shrinkage rate and recovery rate test. We conduct the
test with different aand dwhen RFID technology is applied.
The impact of shrinkage rate aon the optimal solution is
examined here, where aincreases from 0.05 to 0.5 uniformly
with 10 values. The results are shown in Figures. 7and 8.
From Figure 7, we see that when there is no RFID
technology, the inventory control policy becomes more
sophisticated as aincreases. As mentioned, in a multiperiod
planning horizon, the inventory control policy consists of
several consecutive two-control-limit intervals, i.e., Example
1. In general, we can view the inventory control policy as an
enlarged two-control-limit policy where the lowest level of the
control limits is regarded as the new lower level (12 in
Example 1) and the highest level of the control limits is
defined as the new upper level (25 in Example 1). This new
defined two-control-limit policy provides the lower bound and
upper bound of the inventory control policy. We examine
these two thresholds in this test.
It is readily seen that, excluding the exceptional two points
(a=0.05, 0.40), the lower threshold is nonincreasing with
increasing of the shrinkage rate. This is mainly because the
missing inventories caused by shrinkage cannot be recovered
and are permanently lost; therefore, in order to satisfy the
demand, it is better to raise the lower inventory level to cover
the lost inventory. However, the upper threshold value is much
more sensitive to shrinkage rate than the lower threshold. This
can also be observed in the tests with other parameters, which
are not presented here. Remember that in the formulation, we
assume that the salvage value is incurred when the inventory
level exceeds the threshold in each decision period, which is
different from the assumption that the leftover inventories are
salvaged as in the newsvendor model. When RFID technology
is implemented, the inventory control policy is much more
stable than that of the non-RFID case, as the misplaced
inventory can be recovered perfectly and instantly for sale and
the shrinkage inventory can be reduced by RFID technology.
As the recovery rate is predetermined, when the shrinkage
becomes larger, the lost inventory in the current decision
epoch plays a role in the inventory policy; but the impact is
Figure 5 Inventory levels on band h.
Figure 6 Inventory levels on band p.
Journal of the Operational Research Society
limited, as the two thresholds do not change too much except
when a=0.35.
From Figure 8, the average inventory level in the non-RFID
case is generally increasing with respect to a. However, in the
RFID case, the average inventory level is much more stable;
the retailer can keep the inventory control policy unchanged
regardless of the shrinkage rate. Note that when aincreases
from 0.05 to 0.20, the average inventory level does not change.
This finding results in further investigation of the relationship
between aand d.
Intuitively, when the shrinkage rate is large, it is better to apply
the RFID technology with high performance. After conducting
an intensive numerical study, we find that, given a, there exists a
critical value d*(a); when dCd*(a), the inventory control
policies do not change anymore, which means there is no need to
implement RFID technology (from the inventory point of view).
Figure 9illustrates this finding. The non-RFID and RFID cases
are divided by d*(a) so that if the values of (a,d) are in the left-
hand part of Figure 9, it is unnecessary to apply RFID; while, if
the values are in the right-hand part of Figure 9,itisbetterto
introduce this new technology.
The curve d*(a) represents that, given the shrinkage rate,
when RFID is adopted, it is better to recover d*(a)9100%
proportion of the shrinkage product so that the optimal revenue
is achieved. The factors that affect inventory recovery rate can
be categorized into three types:
(1) Nature of the product. A perishable product, such as
seafood, vegetables, and some fruits, has a short life
cycle, and it may deteriorate easily and lose its value.
Fragile products, such as glass, china, and pottery, may
easily be broken in transportation. If these kinds of
products decay or are damaged and can no longer be
sold, the recovery rate decreases. From the inventory
side, retailers selling these types of products may not be
eager to apply RFID technology.
(2) Theft. Shoplifting results in permanent inventory loss if it
cannot be detected in real time, which decreases the
recovery rate.
(3) Performance of RFID technology. Most of the existing
papers contain the implicit assumption that RFID
performs so well that it can eliminate misplacement
and shrinkage perfectly, except for physical damage.
However, technological demerits and incorrect operation
will lead to malfunction, which results in decreasing of
the recovery rate.
Laying aside the performance of RFID, damage of perish-
able or fragile products and shoplifting are two main factors
that reduce the available items in store. Therefore, if the
misplaced and shoplifted products can be recovered and
monitored quite well by salespeople and the proportion of
damaged products is small, considering the inventory control
policy, the RFID technology seems less intriguing.
On tag price test. We reset some parameters as a=0.2,
d=0.8, and the tag price is increasing from 0 to 2 uniformly
with 21 values.
From Figure 10, it is surprising to find that the average
inventory level is (almost) increasing with respect to tag price.
Apparently, when tag price increases, the procurement cost
increases, which therefore leads to a reduction in the order
quantity. As in the multiperiod decision model, the inventory
control policy is a two-control-limit policy; the lower inven-
tory level decreases and/or the upper inventory level increases
Figure 7 Control limits on a.
Figure 8 Inventory on a.
Figure 9 Relation of aand d.
Feng Tao et al—Impact of RFID technology on inventory control policy
will result in a decrease of the average ordering quantity.
According to dynamic programming theory, when the system
reaches a steady state so that a static two-control-limit policy
can be applied in daily operations, if the interval of keeping the
inventory unchanged is enlarged because the lower level
decreases and/or the upper level increases, much more
stable states emerge so that the average inventory level
increases. Further, in our test, we find that the upper inventory
level is much more sensitive to tag price than the lower
inventory level, which implies that when the tag price
decreases, the retailer needs to reduce the upper inventory
level first in order to modify the inventory control policy and
reduce the inventory cost. On the other hand, Fan et al
(2014,2015) in their study investigate a threshold value of tag
price to determine the order quantity with RFID adoption by a
newsvendor solution. However, when we extend the model to
a finite planning horizon and concentrate on the inventory
control policy, the firm can keep the policy unchanged if the
tag price varies in a small interval.
5.3. Remarks
In this paper, we assume that RFID technology performs
perfectly so that misplaced inventory can be recovered
instantly for sale and the shrinkage resulting from theft or
shoplifting can be detected in a timely manner. In practice,
RFID may make a mistake, i.e., misreading or missing the
signal, dropping of the tag, or malfunction of the technology.
However, we can modify the parameters to fit these situations.
Defining gas the performance of RFID technology, the
recovered misplaced inventory now is gbyinstead of by, and
the detected shrinkage inventory now is gd(1 -a)yinstead of
d(1 -a)y. This modification does not change the concavity or
convexity (as mentioned before, it is intractable to identify the
concavity or convexity) of the profit function in the multi-
period analysis. Therefore, our conclusions can be extended,
with slight modifications, to this situation, except that we need
to conduct additional sensitivity analysis on RFID perfor-
mance. For example, using the parameters in previous
subsections and assume g=0.9 in the first place to investigate
the impact of shrinkage rate on inventory control policy, and
then select a=0.2 to illustrate the impact of RFID perfor-
mance on inventory control policy. The results are concluded
in Table 2.
Table 2informs us that, compared with the well-performing
case of RFID technology (right-side column of Table 1), the
inventory interval between lower bound and upper bound
when RFID does not perform perfectly narrows down in
general (except the case when a=0.2). On the other hand, we
can see from Table 2that the lower bound of inventory control
policy is nonincreasing with respect to the performance of
RFID technology, which will directly reduce the order
frequency due to much more inventories that are recovered
for sale instantly by this new technology during each decision
period.
In addition, in the test of shrinkage and shrinkage recovery
rate, we find that there exist threshold values (a,d) that
determine RFID adoption. Further, we find that there is a
threshold value a* (equals 0.025 in this paper) at which it is
unnecessary to implement RFID technology when the shrink-
age is no larger than the threshold value. Based on numerous
computational tests, a* is independent of selling price,
procurement cost, salvage value, holding cost, even tag price
of RFID and demand pattern. This may explain why some
small retailers and perishable product retailers do not have the
incentives to apply RFID technology as their shrinkage is
much smaller and their misplacement can be recovered by
salespeople.
It is noted that we only consider the inventory control policy
when we present our conclusions. We do not intend to ignore
or depreciate the benefits of this new technology, such as
providing product life condition in quality management,
Figure 10 Sensitivity test on tag price.
Table 2 A test of two-control limit policy on RFID performance g
aInventory policy
a
gInventory policy
b
0.1 [11, 14] 0.8 [12, 17]
0.2 [12, 22] 0.85 [12, 21]
0.3 [12, 18] 0.9 [12, 22]
0.4 [12, 14]
[15, 18]
, [19, 22] 0.95 [11]
[12, 13]
, [14, 19]
0.5 [13, 19] 1.0 [11, 16]
a
With shrinkage awhen g=0.9.
b
With performance gwhen a=0.2.
Journal of the Operational Research Society
identifying position messages in transportation design, labor
reduction, and improving supply chain efficiency.
6. Conclusion
In this paper, we consider a multiperiod model with imple-
mentation of RFID technology when considering inventory
misplacement and shrinkage. A dynamic programming model
is formulated to investigate the inventory control policies
under both non-RFID and RFID cases. Rather than analyzing
the impact on profit when implementing RFID technology, we
focus on analyzing and investigating the impact on the
inventory control limits with selling price, misplacement rate,
shrinkage rate, shrinkage recovery rate, and tag price. The
optimal inventory control policy is proven to be a two-control-
limit policy. A critical inventory level is determined to identify
the relationship of upper inventory level control limits between
an RFID case and a non-RFID case. The numerical results
show that, given the parameters, the inventory control policy
of the non-RFID case is more sensitive to these parameters
than that of the RFID case. When RFID is applied, the retailer
can keep the inventory control policy unchanged or only
slightly changed, regardless of the inventory misplacement and
shrinkage.
Specifically, in the non-RFID case, the retailer needs to pay
more attention to holding cost rather than penalty cost when
deciding the inventory control policy. Compared with the
misplacement rate, the shrinkage rate plays a more important
role in determining the inventory control policy. In the RFID
case, the lower control limit is nonincreasing with increasing
of the shrinkage rate. The upper control limit and the average
inventory level are more sensitive to the shrinkage rate than
the lower control limit. Given a shrinkage rate, if the inventory
recovery rate exceeds a critical value, implementation of RFID
technology will have no impact on inventory control policy. In
addition, the numerical study reveals that when the shrinkage
ratio is below an independent threshold value (equal to 0.025
in our test), it is unnecessary to apply RFID technology, which
is not observed in current studies. Thus, from an inventory
control standpoint, the retailer does not have the incentive to
apply RFID technology if the shrinkage is small and the
misplacement can be recovered by physical audit. The test on
tag price reveals that when the tag price increases, it is better
to adjust the upper inventory control limit first, although the
retailer can keep the ordering quantity unchanged when tag
price varies by a small interval.
Finally, as with other studies of this topic, our research is
not without limitations. First, we only consider the benefit for
retailer by applying RFID technology, the benefit for supply
chain is beyond the scope of the current paper. Second, in our
paper, retailer is responsible for the tag price. It is surely that
sharing the RFID tag price as others did will definitely
increase the availability and applicability of this new technol-
ogy, which will in turn increase the benefit of this technology.
Third, in a competing market, accurate information provided
by RFID technology will improve the operational performance
and the competitive power, which is also beyond the scope of
the present study. Finally, we do not distinguish the misplace-
ment and shrinkage between shelf and warehouse. However,
these limitations should be regarded as opportunities for future
research in this area.
Acknowledgements—We thank Professor Thomas Archibald and Professor
Jonathan Crook, the editors of the journal, and two anonymous reviewers
for their valuable comments and suggestions that helped improve the
model and analysis presented in this paper. The work described in this
paper was supported by the National Natural Science Foundation of China
(71201059, 71171082, and 71431004).
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Received 27 April 2015;
accepted 6 July 2016
Journal of the Operational Research Society
