A Break-even Analysis of RFID Technology for Inventory sensitive to Shrinkage

A Break-even Analysis of RFID Technology
for Inventory sensitive to Shrinkage
A.G. de Kok, K.H. van Donselaar, T. van Woensel ?
TU/e Eindhoven University of Technology
Department of Technology Management
Den Dolech 2, NL5600 MB Eindhoven, The Netherlands
Abstract
By embedding RFID tags onto their products, both manufacturers and retailers
try to control for shrinkage (e.g. due to theft). Current inventory control systems
do not take into account the disappearing inventory due to this shrinkage. As a
response, corrective actions are made by performing costly audits in which actual
inventory is counted. The research presented in this paper adapts the inventory
policy by including both the shrinkage fraction and the impact of RFID technology.
Accordingly, by comparing the situation with RFID and the one without RFID in
terms of costs, an exact analytical expression can be derived for the break-even
prices of an RFID tag. It turns out that these break-even prices are highly related
with the value of the items that are lost, the shrinkage fraction and the remaining
shrinkage after implementing RFID. A simple rough-cut approximation to determine
the maximum amount of money a manager should be willing to invest in RFID
technology is presented and evaluated.
Key words: Inventory control, Shrinkage, RFID, Break-even analysis
1
Introduction
More and more, RFID technology is expected to take the place of bar codes
in the supply chain allowing manufacturers and retailers to know the exact
location and quantity of their inventory without conducting time consuming
? Corresponding author
Email addresses: a.g.d.kok@tm.tue.nl (A.G. de Kok),
k.h.v.donselaar@tm.tue.nl (K.H. van Donselaar), t.v.woensel@tm.tue.nl (T.
van Woensel).
Preprint submitted to IJPE
25 July 2006

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audits at several points along the chain. Assuming that the detection equip-
ment is reasonable reliable, RFID should provide more accurate information
of the available inventories and its position throughout the chain. McFarlane
and She? (2003) reviewed some of the key challenges of RFID in supply chain
operations and introduced the main elements of using such a system. The prob-
lem is however that this technology is perceived as expensive and therefore not
(yet) feasible. This paper establishes a cost-bene?t trade-o?, generating ex-
act analytical expressions for the break-even RFID prices, as such facilitating
business case calculations.
Atali et al. (2005) distinguish in their paper between three main sources of
inventory discrepancies which are not taken into account in the classical in-
ventory models:
(1) Shrinkage: thefts are generally not captured by the inventory control. As
such, this leads to a system inventory which is higher than the actual
inventory.
(2) Misplacement of products: goods are not in the correct place and are
thus not available for customers. Consequently, inventory is correct but
partially not available, introducing an inventory deviation.
(3) Transaction errors: this is related to wrong scanning of products at the
check-out counters in retail outlets or switches of products in the suppliers
warehouse.
The standard way of identifying and remedying for the above inventory de-
viations is doing costly audits. As such, both physical errors (e.g. misplaced
items) as system inventory errors (e.g. due to shrinkage or transaction errors)
are corrected for. Complete and accurate information on the inventory sta-
tus in the supply chain is thus crucial. In this paper, we mainly focus on the
inventory inaccuracy caused by shrinkage.
Our application assumes that, depending upon the achieved read accuracy,
RFID enhances the accuracy of the information currently obtained through
bar code scanning which is more vulnerable to human error. Consequently, we
assume that RFID results in a better control of shrinkage. Shrinkage can then
either be completely vanished (i.e. 100% reliable RFID), or some fraction of
the shrinkage observed in the situation before RFID was used, is left (RFID
is less than 100% reliable, e.g. due to read errors). The latter case seems to be
more realistic: Lee and Ozer (2005) report that between 10% and 66% of the
original shrinkage observed is reduced after implementing RFID technologies.
When having this shrinkage information, one however should take this infor-
mation into account when determining the stock levels. Traditional inventory
management literature assumes that inventory managers know exactly what
they are storing and that this information is 100% reliable. In reality, due to
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e.g. shrinkage inventory records are only rough estimates of the actual inven-
tory on the retail shelves or in the manufacturer’s warehouse. A contribution
of this paper is that we determine an inventory policy taking into account
shrinkage.
Today, a substantial amount of empirical research on inventory discrepancy is
available. DeHoratius et al. (2004) found that 65% of the inventory records at
one retailer were inaccurate. Along the same line, Kang and Gershwin (2005)
found that the best performing store in their sample study only had 70-75%
of its inventory record matching physical inventory during its annual inven-
tory audit. The overall average over all stores was 51%. Raman et al. (2001b)
reported that, at the stores of one retailer, two-thirds of the Stock Keeping
Units (SKUs) had inaccurate inventory records upon physical audits. Such
inaccuracies could have the potential of reducing pro?t by 10% due to higher
inventory cost and lost sales. Other studies report that the main cause of in-
ventory discrepancy is due to shrinkage: Fleisch and Tellkamp (2005) reported
that shrinkage accounted for 2-4% of sales in the US retail industry in 2001.
Alexander et al. (2002) at IBM reported that the amount of inventory shrink-
age rates are around 1.75% of 2001 sales in the US, Europe and Australasia.
ECR Europe (2003) found that, in Europe, the shrinkage rates were 1.75% for
retailers and 0.56% for manufacturers.
In general, literature on an analytical assessment of the RFID technology is
fairly limited. Atali et al. (2005) and Lee and Ozer (2005) mainly focus on the
inventory function and the e?ect of taking into account the inventory discrep-
ancy. It is however stated that a cost-bene?t trade-o? for RIFD tags is still
an open issue not tackled by their research. In another paper, Kok and Shang
(2005), assume in their model that inventory errors are i.i.d with a mean of
zero. In this setting, they model the transaction- and misplacement errors but
not the shrinkage errors. They state that the commonly practiced audit poli-
cies can only be e?ective if the right inspection cycle is chosen. They however
did not optimize on this inspection cycle length for the audits in their study.
Rekik et al. (2005) model the consequences of misplacement of inventory on
the retail shelf by comparing three alternatives. In the ?rst alternative, the
retailer is unaware of the misplacement and places his orders as if inventory
information is perfect. In the second case, the retailer is aware of the errors in
his inventory status information, and adjusts his ordering policy accordingly.
In the ?nal scenario, perfect inventory status information based on RFID
technology is assumed. The problem is modeled using a conventional news-
boy formulation with some modi?cations to adjust for the scenarios described
above. A numerical analysis demonstrates the limited bene?ts of RFID.
Our paper positions itself close to these literature contributions. More specif-
ically, it focuses on the cost-bene?t trade-o? between inventory costs and the
costs of RFID with regards to shrinkage (as such extending the analysis in
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Atali et al. (2005)). Next to this, the length of the inspection cycle is ex-
plicitly taken into account in the analysis. This was a parameter that needs
to be optimized as indicated by the research of Kok and Shang (2005) (they
considered in their paper the inspection cycle length as given). Compared to
Rekik et al. (2005) model, we use a more appropriate inventory model (i.e.
a periodic review base stock policy) rather than the single period newsboy
model of which the use is mainly limited to e.g. fashion products.
The overall objective of this paper is to determine the additional cost per
time unit caused by shrinkage. One might then consider RFID equipment and
tag investments that in principle allow to prevent shrinkage and to come to
(almost) perfect observation (i.e. bene?ts), yet at the expense of additional
investments in equipment and tags (i.e. costs). The insights in this paper are
not limited to RFID only but are also useful for any technology cost-bene?t
analysis with inventory implications.
This paper makes the following contributions:
• Current inventory base stock policies are augmented taking into account
inventory shrinkage. As such, we quantify the potential gains of using any
technology (e.g. RFID) leading to better knowledge on the actual inventory
status. The approach is ?exible as it also considers residual shrinkage after
implementing RFID. As such, it takes into account potential problems (e.g.
read errors) occurring after RFID implementation.
• The analysis presented gives a detailed cost-bene?t analysis focusing on the
most relevant factors (e.g. the cost of the technology, the inspection cycle
length, etc.). This results in exact analytical expressions for the break-even
RFID prices.
• The e?ect of the length of the inspection cycle is explicitly taken into ac-
count, quanti?ed and optimized. It is shown that the inspection cycle has
an important e?ect on the behavior of the break-even prices.
• Finally, it is shown that the value of the item, the fraction of demand that is
disappeared and the remaining shrinkage after RFID implementation have
the largest impact on the break-even prices for the RFID tags (when the
inspection cycle length is optimized). A simple rough-cut approximation is
presented to calculate the break-even prices.
This paper is organized as follows: in the next section the model is developed
and exact expressions for the break-even prices are derived, then computa-
tional results are presented for a complete experimental design; the last section
concludes the paper.
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2
Model development
Before starting with the analysis, we summarize in Table 1 the variables used
in the analysis.
We assume a periodic review base stock policy: every R periods, the inventory
is reviewed and raised to an order-up-to level S (see also e.g. Silver et al. (1998)
for more information on the stock policy used). Demand in subsequent periods
is i.i.d.; let E [D] denote the expected demand per period and assume that a
fraction of demand per period, ? disappears due to shrinkage, misplacement,
etc. The disappeared stock is lost. We assume that demand not met from the
shelf is backordered and assume that the process of disappearances is pure
Poisson with rate ?s = ?E [D]. Hence total consumption per time unit equals
(1 + ?) E [D].
At each review moment, the observation of the inventory takes place. We
assume that inventories are counted then for a random sample of stock keeping
units (SKUs). The probability that a particular SKU is in this sample is
set equal to p. Consequently, with this probability p the disappearance of
items is identi?ed correctly and with probability (1 ? p) the inventory is based
on the inventory at the last review moment minus observed demand plus
replenishment arriving between the last review moment and the current one.
De?ne C as the length of an observation cycle, i.e. the number of periods
between two review moments at which the inventory is observed correctly.
Then it follows that:
P (C = k) = p (1 ? p)k?1 , k = 1, 2, ...
(1)
Consequently, the expected observation cycle length E [C] is then equal to:
1
E [C] =
(2)
p
From renewal reward theory (Tijms Tijms (2003)), we ?nd the following iden-
tities:
?
p (1 ? p)k?1
k
E [X
E [X] =
k=1
j=1
jk]
(3)
E [C]
?
p (1 ? p)k?1
k
E [B
E [B] =
k=1
j=1
jk]
(4)
E [C]
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Table 1
List of variables used in the analysis
Variable
Description
C
Observation cycle length
1/p
Expected observation cycle length
1/pnoRFID
Expected observation cycle length without RFID
1/pRFID
Expected observation cycle length with RFID
E[D]
Expected demand per period
?
Disappearance fraction
?s
The rate of disappearances
Xjk
Physical inventory at the end of the j-th replenishment
cycle associated with observation cycle of length k, just
before the next order is delivered
Bjk
Amount of the demand backordered during the j-th
replenishment cycle associated with observation cycle of length k
X
Value of the physical inventory at the end of an
arbitrary period, just before an order is delivered
B
Value of the amount of demand backordered
during an arbitrary period
D1 (s, t]
Demand during the interval (s, t]
D2 (s, t]
Disappearances during the interval (s, t]
R
Length of the review period
Lj
Lead time for the j-th order in an observation cycle
S
Order-up-to level
Nr
Number of periods per year
v
Price per unit of the product sold
?
Auditing costs
r
Annual interest rate
?
Fraction of ? that cannot be prevented from disappearing
?
Tag costs
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Suppose that at time 0 the inventory is perfectly observed, i.e. an observation
cycle starts. Suppose that this cycle has length k. Let us consider the j-th
review moment in this cycle 1 ? j ? k, with the ?rst review moment at time
0. Immediately after that moment the actual inventory position is equal to
S ? D2 (0, (j ? 1) R] , while the inventory control function assumes that the
inventory position equals S. The order generated at time (j ? 1) R is received
at time (j ? 1) R+Lj, with Lj the leadtime of the j-th order in the observation
cycle. Thus the actual net inventory at moment (j ? 1) R + Lj, immediately
after arrival of this order, denoted by Na
, equals:
j?1,k
Na
= S ? D
j?1,k
2 (0, (j ? 1) R + Lj ] ? D1 ((j ? 1) R, (j ? 1) R + Lj ]
Likewise, the actual net inventory just before the arrival of the next order
(placed at time jR and due at time jR + Lj+1), denoted by Nb is equal to:
j,k
Nb = S ? D
j,k
2 (0, jR + Lj+1] ? D1 ((j ? 1) R, jR + Lj+1]
Using the above expressions for the net inventory and the fact that Xjk =Max(Nb , 0)
j,k
and Bjk = (Max(?Nb , 0)?Max(?Na
, 0)), we ?nd the following equations:
j,k
j?1,k
E (Xjk) = E (S ? D2 (0, jR + Lj+1] ? D1 ((j ? 1) R, jR + Lj+1])+
E (Bjk) = E (D2 (0, jR + Lj+1] + D1 ((j ? 1) R, jR + Lj+1] ? S)+
?E (D2 (0, (j ? 1) R + Lj] + D1 ((j ? 1) R, (j ? 1) R + Lj] ? S)+
De?ne the following auxiliary variables to simplify the notation:
Zj1 = D2 (0, jR + Lj+1] + D1 ((j ? 1) R, jR + Lj+1]
Zj2 = D2 (0, (j ? 1) R + Lj] + D1 ((j ? 1) R, (j ? 1) R + Lj]
? E [Xjk] = E (S ? Zj1)+
? E [Bjk] = E (Zj1 ? S)+ ? E (Zj2 ? S)+
Then it follows that:
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?
k
E [X] = p
p (1 ? p)k?1
E [Xjk]
k=1
j=1
?
k
= p
p (1 ? p)k?1
E (S ? Zj1)+
k=1
j=1
?
?
= p
p (1 ? p)k?1 E (S ? Zj1)+
j=1 k=j
?
?
= p
E (S ? Zj1)+ p (1 ? p)j?1
(1 ? p)k
j=1
k=0
?
=
p (1 ? p)j?1 E (S ? Zj1)+
(5)
j=1
Similarly, the following expression for E [B] can be obtained:
?
E [B] =
p (1 ? p)j?1 E (Zj1 ? S)+ ? E (Zj2 ? S)+
(6)
j=1
We remark here that the expressions for E (Zj1 ? S)+ and E (Zj2 ? S)+
can routinely be calculated if Zj1 and Zj2 are assumed to be mixed-Erlang
distributed (see e.g. Tijms (2003)).
Let P2 be the long-run fraction of the demand ?lled directly from the stock
on-hand, then it follows that:
E [B]
P2 = 1 ?
(7)
E [D] R
Let Nr denote the number of periods per year. Let us assume that the price
of the product sold equals v and the annual interest rate equals r . So the
inventory holding costs are v × r (euro per unit per year) times the average
number of units in the pipeline or on hand. The cost of auditing the inventory
equals ?. Let E [L] be the expected leadtime of an order, then the total relevant
annual costs, T RCnoRFID, are equal to:
T RCnoRFID = vr (1 + ?) E [D] E [L] + vrE [XnoRFID]
+v?E [D] Nr + ?pnoRFIDNr
(8)
These costs are the sum of all the relevant cost components involved:
(1) Inventory costs, being the costs for the pipeline stock, vr (1 + ?) E [D] E [L]
and for the average inventory on hand, vrE [XnoRFID]
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(2) Shrinkage costs: v?E [D] Nr
(3) Audit costs: ?pnoRFIDNr
Similarly, we can construct the total relevant annual costs under RFID (de-
noted as, T RCRFID). Assume that RFID has the potential to eliminate shrink-
age but might leave some fraction ? of ? (0 ? ? ? 1) that cannot be protected
from shrinkage. In other words, the shrinkage left after implementing RFID
will be between 0 (? = 0, i.e. 100% reduction) and ? (? = 1, i.e. no reduction
of shrinkage through RFID). Using the ? factor we can thus control for the ex-
pected shrinkage when using RFID. The total relevant costs using RFID with
? the cost of the RFID tag is composed of the following cost components:
(1) Inventory costs, being the combination of costs for the pipeline inventory
vr (1 + ??) E [D] E [L] and for the average inventory on hand, vrE [XRFID].
(2) Shrinkage costs: v??E [D] Nr
(3) Tag costs: ?E [D] Nr
(4) Audit costs: ?pRFIDNr|(?=0)
As one can see, the costs depend on the value of ?: if ? = 0, then RFID is
100% reliable so that audit costs can be dropped. If ? = 0, then audits are still
necessary to periodically correct the inventory records. This might be due to
e.g. read errors with the RFID equipment, etc. Note that the speci?c physical
inventory depends on the use of RFID (E [XRFID]) or not (E [XnoRFID]) and
on ?. The inventory level (E [XRFID]) needed to guarantee the service level
will be higher (compared to the ? = 0 case). On top of this inventory increase,
we will face extra costs due to shrinkage at a rate of ??.
The total relevant annual costs under RFID are then equal to:
T RCRFID = vr (1 + ??) E [D] E [L] + vrE [XRFID]
+v??E [D] Nr + ?E [D] Nr + ?pRFIDNr|(?=0)
(9)
If ? = 0 (i.e. assuming 100% reduction of shrinkage), Equation (9) reduces to:
T RCRFID = vrE [D] E [L] + vrE [XRFID] + ?E [D] Nr
(10)
Comparing Equations (8) and (9), we ?nd that the no-RFID situation is more
costly than the RFID situation (in the case that the observation cycle length
is the same in both situations) if and only if:
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T RCnoRFID > T RCRFID
(11)
?
vr (1 + ?) E [D] E [L] + vrE [XnoRFID] + v?E [D] Nr + ?pnoRFIDNr
>
vr (1 + ??) E [D] E [L] + vrE [XRFID] + v??E [D] Nr
+?E [D] Nr + ?pRFIDNr|(?=0)
(12)
Or equivalently:
vr (1 ? ?) ?E [D] E [L] + vr (E [XnoRFID] ? E [XRFID]) + v (1 ? ?) ?E [D] Nr
??E [D] Nr + ?pnoRFIDNr ? ?pRFIDNr|(?=0) > 0
(13)
Again if ? = 0, then the term ?pRFIDNr|(?=0) equals zero and can be dropped;
in the other case where the fraction ? = 0, some residual shrinkage is left from
? after RFID implementation and we again have to take into account the audit
costs under RFID. Expressing this inequality as a constraint on ?, we ?nd that
RFID is pro?table if the following condition holds:
vr (1 ? ?) ?E [L]
vr (E [X] ? E [X
v (1 ? ?) ? +
+
RF ID])
Nr
NrE [D]
?p
?p
+
noRF ID ? RFID |
E [D]
E [D] (?=0) > ?
(14)
If ? = 0, then the term ?pRFIDNr|(?=0) equals zero and can be dropped. Note
that the pRFID is not necessarily the same as the pnoRFID. In Section ?? we
will look more closely on the optimal p for each of the two situations. If RFID
is 100% reliable then the above equation reduces to:
vr?E [L]
vr (E [X] ? E [X
?p
v? +
+
RF ID]) + noRFID > ?
(15)
Nr
NrE [D]
E [D]
In the next section, the exact analytical expression for the break-even prices
in Equation (14) will be evaluated for a large number of settings.
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