An assessment model for RFID impacts on prevention and visibility of inventory inaccuracy presence

Advanced Engineering Informatics 34 (2017) 70–79

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An assessment model for RFID impacts on prevention and visibility of inventory inaccuracy presence

MARK

⁎

W. Qina, , Ray Y. Zhongb, H.Y. Daic, Z.L. Zhuanga a b c

School of Mechanical Engineering, Shanghai Jiao Tong University, China Department of Mechanical Engineering, University of Auckland, New Zealand Business School, Central University of Finance and Economics, China

A R T I C L E I N F O

A B S T R A C T

Keywords: RFID Inventory inaccuracy Bullwhip effect Visibility Prevention

Bullwhip effect has been considered as one of major research topics in supply chain management. Most of the studies disregarded the mismatch between the recorded inventory and the reality. However, it is shown that the inventory inaccuracy under uncertainty is a widespread phenomenon in both retail and distribution centers. Due to the propagation of information distortion along the supply chain, the financial impacts of inventory inaccuracy include not only the cost of direct inventory loss but also the increasing holding and shortage cost at each stage. The emergence of RFID technology offers a possible solution to alleviate the growing cost of inventory inaccuracy. By making full use of RFID technology, this paper attempts to compare the inventory inaccuracy impact on bullwhip effect in terms of order variance amplification and supply chain performance under two scenarios: (1) all members are aware of the inaccuracy and optimize their operations; (2) all members deploy RFID technology to reduce inventory inaccuracy. Informed order policy is used as benchmark to capture the true RFID value and differentiate two types of RFID impacts, prevention and visibility, to provide more manageable insight. In particular, the incentive of sharing information in supply chain is also provided by comparing the cost of two supply chain settings.

1. Introduction

Misplacement relates to temporary inventory shrinkage and can be recovered by physical inventory audit [12]. Incorrect deliveries can also be called unreliable suppliers resulting in difference between received and stated product quantities. It was observed that the inventory shrinkage has the biggest impact on supply chain performance compared to other causes [10]. Since inventory inaccuracy incurs high inventory level and cost, low service level and lost sales, there is an increasing interest in investigating its impact on management performance of a supply chain. Atali et al. [2] explicitly modeled three kinds of demand stream: shrinkage, misplacement and transaction errors using dynamic programming (DP), and quantified the effect due to inventory inaccuracy based on different benchmarks under a given cycle count policy. Kök and Shang [16] proved that an inspection adjusted base-stock (IABS) policy for solving inventory inaccuracy is optimal for the single-period problem. Rekik and Dallery [26] analyzed the impact on retail stores due to product misplacement. Liu et al. [21] considered a retail environment in which a company needs to make both marking effort and stocking quantity decisions. However, the abovementioned works are restricted to a single stage in the supply chain. The first study of the

In real industry, the recorded and actual inventory in a supply chain may be quite different, but this inventory inaccuracy has not drawn much attention [25,7]. It is a widespread phenomenon in both retail and distribution environments. Iglehart and Morey [14] may be the first scholars to discuss this problem. Raman et al. [25] figured out that more than 65% of stock keeping units (SKU) in retail stores are inaccurate and the difference of recorded and actual inventory is on average 35% of the target inventory. For distribution and manufacturing industry, according to Kök and Shang [16], the inventory inaccuracy in most of distribution companies with an average inventory of US$3 billion, is 1.6% of the total inventory value, viz. 48 million, at the end of 2004. The above data indicates that the inventory inaccuracy may result in significant loss not only for the retailers but also for the whole supply chain. There are many causes of inventory inaccuracy. Fleisch and Tellkamp [9] characterized three key sources: theft and unsaleables, misplaced items, and incorrect deliveries. Theft and unsaleables refer to product shrinkage which results in permanent inventory shrinkage.

⁎

Corresponding author. E-mail address: [email protected] (W. Qin).

http://dx.doi.org/10.1016/j.aei.2017.09.006 Received 13 July 2016; Received in revised form 14 September 2017; Accepted 30 September 2017 1474-0346/ © 2017 Published by Elsevier Ltd.

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Dt = d + ρDt − 1 + εt

impact of inventory inaccuracy on the multi-stage supply chain may be conducted by Fleisch and Tellkamp [9]. They used a simulation model to capture the impact of inventory inaccuracy on bullwhip effect in a multi-stage supply chain. The relationships between the information inaccuracy and distortion, which cause the bullwhip effect [20], are still not well investigated. As inventory inaccuracy control plays a key role in achieving a high performance supply chain, how to improve inventory accuracy and reduce the cost simultaneously has attracted increasing investigation. Kök and Shang [16] provided a guideline to design effective cycle count programs to reduce the cost caused by inventory inaccuracy. The inventory inaccuracy can also be tackled by using benchmarking, awareness building, and process improvement [9]. All these approaches are termed as non-technology awareness. When contemplating technology solutions, radio frequency identification (RFID) could be possible due to its advanced identifying ability [28]. Recent study shows that due to RFID applications, shrinkage can be reduced by 67% of the current 0.22–0.73% of sales at manufacturers, and by 47% of the current 1.75% of sales at retailers [1]. According to Lee and Özer [19], the cost due to inventory inaccuracy can be reduced by information visibility [34]. The visibility provides accurate inventory information to align the recorded and actual inventory data in a timely manner [3,33]. Most of the studies claim the benefits from using RFID technologies [8,31,17,32], but RFID impacts on prevention and visibility of inventory inaccuracy presence is scarcely reported. To close the credibility gap, explicit analytical solutions are needed to concretely quantify the economic returns of RFID implementation. This paper is going to fulfill the gap by specifically addressing the following research questions: (1) What is the impact of RFID implementation on bullwhip effect when inventory inaccuracy exists in a supply chain? (2) How to quantify the benefits of RFID to reduce the inventory inaccuracy from visibility and prevention respectively in a multi-stage supply chain? To answer these questions, this paper examines a multi-stage supply chain subject to inventory shrinkage. A detailed model-based analysis is presented to identify the impact of reducing inventory inaccuracy on bullwhip effect due to RFID applications so as to reveal the specific RFID value. An analytical model is established at first and the order variance amplification with close form expressions is then quantified. Furthermore, some special insights of the supply chain performance (in terms of average cost and service level) are captured and summarized. The organization of this paper is as follows. Section 2 describes the modeling framework by specifying two scenarios under analysis. In Section 3, the analytical model of different scenarios is derived. In Section 4, the value of RFID implementation is justified by examing the supply chain performance. Numerical study of the two scenarios is given in Section 5 and conclusion is drawn in Section 6.

(1)

where Dt is the demand in period t , d > 0 is the stable demand in every period, −1 < ρ < 1 is the correlated factor and εt is normal distributed with zero mean and variance σd2 , which is dependent upon Dt while independent upon Dt − 1. We assume shrinkage exits in every stage of the supply chain and can be modeled as1:

St = st −ξt

(2)

where St is the order-up-to level in period t relating to the recorded quantity, and st is the inventory level without shrinkage. Since shrinkage never increases the product quantity, ξt should satisfy:

ξt =

2 2 ⎧ N(μs ,σs ),μs > 0 if N(μs ,σs ) ⩾ 0 ⎨0 if N(μs ,σs2 ) < 0 ⎩

(3)

where N(μs ,σs2) stands variance σs2 . According

for a normal distribution with mean μs and to Prob {μs −3σs < ξt < μs + 3σs} >90%, if ξt satisfies μs −3σs < ξt < μs + 3σs , a normal distribution with positive mean μs and variance σs2 could be determined. And we assume that ξt is dependent upon St while independent upon St − 1. The particular value of RFID technology is to provide accurate information timely, especially the visibility to the whole supply chain. In this paper, we assume that the end customer demand and inventory shrinkage information in every stage is shared in the whole supply chain, which is called centralized demand information. Therefore, each member in the supply chain is based on the end customer demand information to make decisions instead of the order quantity from its direct downstream. The ordering process of every stage in period t is: at the beginning of period t , t = 1,2,3,…, each stage reviews its inventory and places an order based on the predicted demand. At the end of this period, this order is received with the assumption that the delivery lead time is 1.2 In presence of inventory discrepancy, the supply chain may take different strategies based on the awareness of the existence of discrepancy for different parties. If they are unaware of the inventory discrepancy, it is assumed that the recorded inventory is as the same as actual, which is called ignorant policy Lee and Özer [19]. In this paper, we assume that the non-technology solution uses the informed policy which recognizes the existence of inventory discrepancy. The order quantity can be adjusted with the mean of shrinkage in each period under the precondition that the average shrinkage quantity in long run can be obtained. RFID technology is deployed to provide accurate inventory quantity timely or even catch some shrinkage and therefore reduce the shrinkage to ξt′. If ξt′ = ξt , RFID can only provide visibility to identify inventory shrinkage, which leads to no inventory discrepancy with inventory shrinkage. The other extreme case is ξt′ = 0 , which means it can not only identify inventory shrinkage, but also prevent it totally resulting in no inventory discrepancy and no shrinkage simultaneously. For 0 < ξt′ < ξt , RFID applications can provide both visibility and partial prevention, which is so called imperfect RFID

2. The modeling framework A K-stage serial supply chain with retailer, distributor, manufacturer and tires of suppliers suffering from inventory shrinkage is considered. Each stage has only one member who adopts the order-upto policy. This is an optimal policy that minimizes the holding cost h and shortage cost p over the infinite horizon [11]. These costs may be different for different stages but keep constant through time horizon for a given stage and the holding costs consist entirely of interest on money tied up with inventory [13]. The ordering decisions of every member are made within a Newsvendor framework [22]. The underlying assumption in typical Newsvendor model formulation is that the recorded and actual inventory are the same. Therefore, in presence of inventory inaccuracy, the Newsvendor model should be revisited. Suppose the external demand faced by the first stage of the supply chain (e.g. retailer) is an auto-correlated AR (1) process, which is borrowed from Lee et al. [20].

1 This kind of shrinkage model is so called additive model. An alternative way to model the effect of inventory inaccuracy is a multiplicative model which implies the magnitude of shrinkage is dependent of the actual inventory quantity which is more realistic and complexity. One on hand, as our focus is to obtain manageable insights, we do not want to increase the complexity of the problem formulation; on the other hand, to be more realistic, we set the shrinkage quantity to be a given percentage of the actual inventory in our numerical study. 2 We assume the delivery lead time is 1 since this assumption may lead to close form solution for order variance in any given stage in multi-stage supply chain settings, otherwise, we cannot get close form solution for exponential growth complexity. Although lead time is a very important factor in bullwhip effect and people has done intensive analysis of lead time impact on bullwhip effect (see Chen et al. [5] and Kim et al. [15]). Whereas, our focus is the impact of inaccuracy not the lead time and lead time as a supply chain performance measure indicator is more suitable for different production and distribution processes not inventory inaccuracy problem [9]. Based on the abovementioned considerations, we hold that it is reasonable to set the delivery lead time 1.

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implementation.3 It is a conservative way to capture the RFID value by comparing the RFID-enabled policy with the informed policy other than with the ignorant policy. Therefore, we choose the informed policy as our comparative benchmark. Two scenarios are considered as follows:

Due to RFID implementation in the supply chain, the shrinkage quantity ξtk in stage k in time period t reduces to ξtk ′ which has the same format of ξtk , but with smaller mean μsk ′ and StD σsk ′. Noting that I,1 DtI,2 − 1 = Dt − 1, the demand in time period t for stage k is: k−1

Dtk,2 =

St

k−1

∑

μsi

∑

∗

Stk,1 = Mtk,1 + z kV k,1

∗

∗

∗

∗

k

∑ i=0

∑ i=0

ρi εt − 1 +

∑ i=1

μsi .

i=1

(σsi ′ )2

(12)

(13)

4. Supply chain performance Fleisch and Tellkamp [9] used two monetary and non-monetary measures to determine supply chain performance. In this paper, these indicators are improved to suit our supply chain settings. The two specifically designed monetary performance measures include cost components that are affected by shrinkage. Those costs that are not affected by shrinkage, such as fixed order cost and delivery cost, are omitted. The cost component of the first monetary performance indicator4 is the lost item value which is directly affected by inventory

μsi

k

k

ρi d + ρ k + 1DtI,1 −2 +

∑

Formula (13) implies that the order variance amplifications increase in each stage if the shrinkage quantity in every time period could be identified. And the more upstream the stage is, the more exaggerated the order variance will be. Since the cause of bullwhip effect is the information distortion from the downstream to the upstream in the supply chain, even if we know exactly the inventory shrinkage, this error item is also amplified. More upstream stages are tended to suffer more information distortion, which exaggerates the order variance. Studies about bullwhip effect relate bigger order variance amplification to worse supply chain performance [4]. However, the order variance amplification is exaggerated after implementing RFID technology [6].

i=1

=

k

i=1

k

∑

(11)

K

(6)

∗

ξti− 1′

i=1

K ΔV1,2 = Var (OtK ,1)−Var (OtK ,2) = − ∑ (σsi ′ )2 < 0.

The first two terms of formula (6) denotes the adjustment of expected demand while the last two terms are the one-for-one replenishment of the order quantity in stage k−1 plus the average lost quantity in one time period in stage k . By using the recursive relationship in formula (6), it can be shown that: ∗

i=0

∑

This section studies bullwhip effect in terms of order variance [20] and tries to capture the impact of inventory inaccuracy on bullwhip effect by comparing the differences of order variance from scenario 1 and 2. Observing from formula (8) and formula (12), the difference of order variance in scenario 1 and 2 is:

the standard normal distribution. The order quantity Otk,1 in stage k based on order-up-to policy is

I,1 Otk,1= Stk,1 −Stk−,11 + Stk − 1,1 −Stk−−11,1 +⋯+StI,1 −StI,1 − 1 + Dt − 1 +

k

ρi εt − 1 +

3.3. Bullwhip effect

), Φ(x ) is the cumulative distribution function of

∗

∑

i=0

(5)

Otk,1 = Stk,1 −Stk−,11 + Otk − 1,1 + μsk

k

ρi d + ρ k + 1DtI,1 −2 +

k

by [18]:

∗

by: (10)

Var (Otk,2) = ρ2(k + 1) σd2/(1−ρ2 ) + ( ∑ ρi )2σd2 +

k k−1 i with mean Mtk,1 = ∑i = 0 ρi d + ρ k DtI,1 − 1 + ∑i = 1 μs and standard deviation k − 1 2(k − 1 − i) 2 1/2 k ,1 σd ) . Then, the optimal order-up-to level (StD) V = (∑i = 0 ρ ∗ Stk,1 that minimizes the expected holding cost and shortage cost is given

pk + hk

(9)

with order variance:

(4)

i=1

∑ i=0

k

ρ k − 1 − i εt + i +

i=0

(

ξti+ k − i′

i=1

k−1 k i′ = ∑i = 0 ρi d + ρ k DtI,1 − 1 + ∑i = 1 μs k−1 k−1−i k 2 k = [(∑i = 0 ρ σd ) + ∑i = 1 (σsi ′ )2]1/2 . ∗ optimal order-up-to level Stk,2 is given

k

k

where z k = Φ−1

∑

= Mtk,2 + z kV k,2

Otk,2 =

i the demand Dtk,1 = DtI,1 + k − 1 + ∑i = 1 μs with the shrinkage mean information to compensate the shrinkage quantity. Using the recursive relationship, Dtk,1 can be expressed as:

pk

k

ρ k − 1 − i εt + i +

The order quantity Otk,2 in stage k is

Considering the lead time and make-to-stock policies in supply chain, the upstream stages have to forecast beforehand to fulfill the later demands [30]. If there is no inventory shrinkage problem, the end customer demand at the lowest stage of the supply chain is immediately transmitted to all upstream stages. The demand in time period t to be covered in stage k , k = 1,2,3,…,K relates to the first stage in time period t + k−1. If the supply chain suffers inventory shrinkage problem, the accurate shrinkage quantity in each time period ξtk is unknown without RFID implementation. With physical inventory audit, stage k knows the mean inventory shrinkage μsk . So, in time period t , stage k tries to cover

i=0

∑ i=0

Hence, the k ,2∗

3.1. Analysis of scenario 1

ρi d + ρ k DtI,1 −1 +

k−1

ρi d + ρ k DtI,1 −1 +

with mean Mtk,2 and StD V k,2

To identify the impact of inventory discrepancy on bullwhip effect and obtain the value of RFID from the above two scenarios, we first develop the closed-form expressions for ordering decisions.

k−1

∑ i=0

3. Ordering decisions

∑

(8)

3.2. Analysis of scenario 2

(1) There is inventory shrinkage and discrepancy in every stage of the supply chain and the informed policy is used to compensate the shrinkage; (2) There is less inventory shrinkage and no inventory discrepancy in every stage of the supply chain because of the deployment of RFID technology.

Dtk,1 =

2

k

⎞ ⎛ Var (Otk,1) = ρ2(k + 1) σd2/(1−ρ2 ) + ⎜∑ ρi ⎟ σd2. ⎝ i=0 ⎠

(7)

According to Lee et al. [20], Var (DtI,1) = σd2/(1−ρ) and noting the independence of DtI,1 − 2 and εt − 1, we can get:

4 We use this monetary performance indicator replaces the one in Fleisch and Tellkamp [9] which also include the holding and shortage costs, since these costs are already included in our second monetary performance indicator.

3

Imperfect RFID implementation here means the RFID implementations cannot catch all the shrinkage, but we assume it can provide accurate inventory quantity.

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4.2. Formulations of RFID value

shrinkage. The second monetary performance indicator includes the inventory holding and shortage costs which are indirectly affected by inventory shrinkage.

According to the beforehand analysis, scenario 2 has better performance due to lower cost, higher service level and lower inventory discrepancy. The specific RFID value based on the monetary indicators in stage k is given by:

4.1. Performance indicators 4.1.1. Expected lost cost As the shrinkage of scenario 1 in stage k is ξtk , the expected lost cost of scenario 1 ELCk,1 = E (r kξtk ) = r kμsk , where r k is the unit product purchase price in stage k . The shrinkage of scenario 2 reduces to ξtk ′, hence the expected lost cost of scenario 2 is:

Some managerial insights could be obtained by the following results (All the proofs are given in the Appendix A.):

ELCk,2 = E (r kξtk ′) = r kμsk ′ < ELCk,1

Proposition 1.

ΔP k= (ELCk,1−ELCk,2) + (ECk,1−ECk,2) = r k (μsk −μsk ′) + V k,1f (z k̂ )−V K ,2f (z k )

(14)

(1) (2) (3) (4) (5) (6)

4.1.2. Expected holding and shortage cost Without RFID implementation, the decision makers in scenario 1 can only forecast the demand based on the long run average shrinkage quantity. In fact, at the beginning of a time period, the true demand of stage k should cover not only the real demand of end-customer but also its own shrinkage quantity. Then k−1 downstream stages turn out to be k Dtk,1 = Dtk,1 + ∑i = 1 ξti+ k − i Mtk,1 = Mtk,1 with mean and StD

V k,1

[(V k,1)2

k ∑i = 1

= + The expected holding and shortage cost in period t of scenario1 is: ∗

∗

(15)

And according to Lee et al. [18], it can be rewritten as:

ECk,1 = V k,1f (z k̂ )

(16)

where f (x ) = (hk + pk ) L (x ) + hkx is convex in x and f (x ) ⩾ f (z k ) ⩾ 0 z k V k ,1

∞

when x < z k . L (x ) = ∫x (y−x ) d Φ(y ) and z k̂ = k,1 < z k . V Similarly, the expected holding and shortage cost in period t of scenario 2 is: ∗

∗

ECk,2= Eεt ,ξt [hk max((Stk,2 −Dtk,2),0) + pk max((Dtk,2−Stk,2 ),0)] = V k,2f (z k )

z k̂

zk,

(17)

(z k̂ )

(z k ) .

f ⩾f < As It can be explained as the critical ratio z k best balances holding and shortage cost rate hence leading to least cost, any other value will result in larger cost. Noting that V k,2 < V k,1, so we can get: (18)

ECk,1 > ECk,2

ΔPUk = r kμsk + V k,1f (z k̂ )−V k,1f (z k ).

As

∗

z k̂

<

zk

(20)

ΔPpk = r kμsk + (V k,1−V k,1) f (z k )

and Φ(x ) is increasing in x , then

SLk,1 < SLk,2

Visibility value properties:

(21)

ΔPvk

and full prevention value

(26)

ΔPpk

have the following

Proposition 2. When hk , pk and r k , k = 1,2…,K are the same for all stages, we have:

4.1.4. Inventory discrepancy The inventory discrepancy level of scenario 1 is ID k,1 = E (ξtk ) = μsk > 0 and there is no inventory discrepancy of scenario 2 ID k,2 = 0 , thus:

ID k,1 < ID k,2

(25)

Formulas (24) and (25) show the lower bound and upper bound of RFID value respectively. The lower bound corresponds to RFID visibility value ΔPvk = ΔPLk . The difference of lower bound and upper bound reflects the RFID full prevention value:

(19)

= P k,2 (Dtk,2 < Stk,2 ) = Φ(z k )

(24)

The other extreme case is the RFID implementation can completely prevent shrinkage with ξtk ′ = 0 . So, it can provide both visibility and full prevention, which give the maximum RFID value:

Similarly, we can get the service level in scenario 2 as follows:

SLk,2

0; increasing in μsk ; increasing in σsi , i = 1,2…,k ; decreasing in μsk ′; decreasing in σsi ′ , i = 1,2…,k ; and increasing in pk .

ΔPLk = V k,1 [f (z k̂ )−f (z k )].

4.1.3. Service level According to the definition of service level, the probability that orders cannot be filled from the stock immediately in scenario 1 is given ∗ ∗ by SLk,1 = P k,1 (Dtk,1 < Stk,1 ) = G k,1 (Stk,1 ) = Φ(y k,1) , where P k,1 (x ) and k,1 G (x ) are the probability density function and cumulative distribution function of Dtk,1 respectively. It follows normal distribution ∗ y k,1 = (Stk,1 −M k,1)/ V k,1 = [Mtk,1 + z k̂ V k,1−Mtk,1]/ V k,1 = z k̂ , then

SLk,1 = Φ(z k̂ )

> is is is is is

Proposition 1. (1) shows that the expected lost cost as well as holding and shortage cost decrease after implementing RFID. Together with the results from formulas (21) and (22) suggesting higher service level and lower inventory discrepancy with RFID implementations, it could be observed that the supply chain performance becomes better after implementing RFID although the order variance in scenario 2 is bigger. Proposition 1. (2) and (3) show that, if the average lost quantity is large or the lost is uncertain, the cost saving due to RFID implementation tends to be larger. It implies that the supply chain with more serious shrinkage problem tends to have more cost saving potential by implementing RFID technology. Proposition 1. (4) and (5) imply that if the RFID implementation can reduce either the average quantity or the uncertainty of inventory shrinkage, the system will gain some positive benefits. And more shrinkage reduction leads to more cost saving. If a supply chain requires high service level, the shortage will be highly penalized. The shortage penalty is relatively high compared to the holding cost. The last proposition shows that this kind of supply chain benefits more from RFID implementations because it is more sensitive to information distortion. If the deployment of RFID technology can only identify discrepancies, but cannot prevent shrinkage, in other words, it can only provide visibility to supply chain with ξtk ′ = ξtk , the minimum RFID value will be given as follows:

(σsi )2]1/2 .

ECk,1 = Eεt ,ξt [hk max((Stk,1 −Dtk,1),0) + pk max((Dtk,1−Stk,1 ),0)]

ΔP k ΔP k ΔP k ΔP k ΔP k ΔP k

(23)

(1) ΔPvk is increasing in k ; (2) ΔPvk and ΔPpk are increasing in σsi,i = 1,2…,k ; (3) ΔPpk is increasing in μsk .

(22) 73

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5. Numerical study

Proposition 2. (1) implies that the upstream stages gain more visibility value than downstream stages as they suffer more serious information distortion. If hk , pk and r k are different in each stage, then, Proposition (2) may not be always held. As it is a value adding process from downstream to upstream stages, hk , pk and r k are larger in more downstream stages. Although the downstream stages benefit less in information distortion reduction, its impact on cost reduction may be more significant than the upstream stages due to the larger hk , pk and r k . Therefore, the RFID visibility value may be larger in downstream stages when their cost impacts are relatively larger than the upstream stages. If the uncertainty of the supply chain is bigger, both visibility and prevention value will increase. And the average amount of shrinkage has lineally impact on prevention value but no impact on visibility value. That is because the supply chain uses the informed policy, which takes the mean of shrinkage into consideration.

Some numerical studies are carried out to verify our theoretical analysis and to illustrate the inventory inaccuracy impact on bullwhip effect in terms of order variance and supply chain performance. Firstly, the magnitude of order variance increase and supply chain performance improvement for a given parameter set will be presented. Secondly, the impact on RFID value as a function of mean and variance of inventory shrinkage will be demonstrated. 5.1. Impact of inventory inaccuracy on bullwhip effect In our example, the supply chain has 7 stages and the end customer demand process is specified as d = 1000 , ρ = 0.7 and σd = 50 . Suppose the unit product cost at stage Ⅰ is $100 and decreases 2% every upstream stage. The annual interest is 20% and the monthly holding cost at stage k is 20%r k /12 . The shortage cost is 25hk . The mean of inventory shrinkage is 1.75% of inventory amount at stage Ⅰ (retailer) and decreases 0.1% every upstream stage while the shrinkage StD is μsk /3. If the supply chain implements RFID, then the shrinkage quantity reduces by 50% [1]. According to (8) and (12), Fig. 1 shows the order variance increases with RFID implementation. It could be observed that the values of order StD from scenario 2 is slightly bigger than that from scenario 1. Figs. 2 and 3 show the expected holding and shortage cost as well as lost cost of scenario 1 and 2 respectively. It is observed that the expected holding and shortage cost or the lost cost of scenario 2 is smaller than that of scenario 1, which is consistent with formulas (14) and (18). Compared with Fig. 3, expected holding and shortage cost in Fig. 2 are relatively small. They may contribute limitedly to the total cost because we assume the products are very valuable. The product lost costs will dominate the total cost. Any product lost reduction due to RFID implementation will lead to significant cost saving. As the RFID implementation reduces the shrinkage by 50%, the total cost reduction is approximate 50% for each stage. Figs. 4 and 5 illustrate the service level (SL) and discrepancy (ID) of each scenario. The average service level increases 8% after implementing RFID while the service level of scenario 2 is 96% constantly which is determined by the ration of the holing and shortage cost. And the discrepancy level of scenario 2 reduces to zero due to RFID implementation because real-time information could be shared among different echelons. According to previous analysis, the expected lost cost and discrepancy level are affected by the mean of shrinkage and the other two are affected by the variance. Therefore, the performance of lost cost and discrepancy in upstream stages are better due to the smaller mean of shrinkage while the performances of other indicators in upstream stages are worse due to suffering more information distribution for both scenarios. From the above figures, it is also observed that the performance of all indicators become better after implementing RFID. That validates the theoretical result that the larger order variance may not stand for worse supply chain performance in presence of inventory inaccuracy. This phenomenon can be explained as follows: if there is shrinkage, this uncertainty can be transferred to “true” demand uncertainty includes both end-customer demand uncertainty and inventory shrinkage uncertainty. In scenario 2, with RFID visibility, the order quantity covers both uncertainties, which leads to larger order variance, therefore, better supply chain performance is achieved.

4.3. Justification of RFID implementation This section is to find the answer to the question: in what conditions, RFID can bring sufficient economic impacts to justify its cost of implementation in a centralized serial supply chain? Suppose a supply chain with K stages wants to recover the RFID investment in N time periods, the fixed cost5 for every stage is W including the investment of middleware and readers, etc. We assume the RFID tags with unit price c are attached on each product in most upstream stage and are used by all downstream stages. In other words, the tagging costs are evenly shared by all the members in the supply chain. Hence, the RFID investments of the supply chain in N time periods are N [Eεt ,ξt (c·OtK ,2)] + KW . The K

corresponding benefits are N ∑i = 1 ΔP i . To balance the RFID investments and benefits of the whole supply chain, simple calculation may lead to the critical RFID tag price: K

cp =

N ∑i = 1 ΔP i−KW K

N [d/(1−ρ) + ∑i = 1 μsi ]

. (27)

If the RFID price is bigger than cp , there are no benefits for the whole supply chain. If the RFID price is smaller than cp , then the supply chain can gain some positive benefits from RFID implementations. For stage k , k = 1,2,…,K , the RFID investments in N time periods are N [Eεt ,ξt (c·OtK ,2)]/ K + W which is the same for each stage. The corresponding RFID benefits are N ΔP i . If the benefits can cover the investments in N time periods in stage k , it is worthy to invest on RFID implementation. As the benefits for each stage are different, some stages are willing to implement RFID and some are not due to the negative or minor benefits. Decision makers in stage k may forecast the demand based on the accurate information (shrinkage quantity in each past time period) of the downstream stages with RFID and the rough information (mean of the shrinkage quantity) of those stages without RFID implementations. Therefore, supposing set S stands for stages with RFID, we can obtain the order decision in stage k :

∼k Ot =

k−1

∑

k−1

ρi d + ρ k DtI,1 −1 +

i=0

∑

∑

ρ k − 1 − i εt + i +

i∈S&i
i=0

ξti− 1 +

∑

μsj

j∉S&j
(28) And the corresponding cost saving is:

∼k ΔP = r k (μsk −μsk ′) +

(VtK ,1)2 +

∑i ∈S&i < k

(σsi )2 f (z k̂ )−V K ,2f (z k ). (29)

Observing from formulas (23) and (29), the expected cost savings of stage k reduce if any of its downstream stage does not implement RFID. So, stage k may have some incentive to share some benefits to those stages without implementing RFID.

5.2. Value of RFID implementation Three types of RFID implementation are considered in this section: (1) the first one can totally prevent shrinkage and provide visibility; (2) the second one can partially prevent shrinkage, specifically, reducing shrinkage by 50%; and (3) the third one can only provide visibility. The

5 We suppose the fixed cost is the set up cost at the beginning of the implementation. During the use of RFID implementation, there is only tag cost.

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Fig. 1. Order StD amplification of two scenarios.

Fig. 2. Expected holding and shortage cost of two scenarios.

Fig. 4. Service level of two scenarios.

first and third type correspond to upper and bound of RFID value respectively and the second type relates to imperfect RFID implementation. Based on formulas (24)–(26), the RFID value (with shrinkage reduction 50%) and its corresponding lower and upper bound are depicted in Fig. 6. The prevention value (the difference of upper and lower bound of RFID value) largely outweighs its visibility value (RFID value lower bound) due to lost cost reduction. The major composition of total cost reduction is only due to RFID prevention function. This result implies that the RFID implementation should be preferred because it is capable of catching shrinkage although it may incur bigger setup cost. However, the above conclusions are based on theoretical analysis. The performance of RFID implementation in a real situation will definitely reduce to some extent. To investigate this issue, we transform a prototype of intelligent manufacturing system in our laboratory to a RFID-enable 4-stage supply chain shown in Fig. 7. The tridimensional storehouse and 3 workstations which consist of the manufacturing system are reconstructed to be a retailer, a distributor, a manufacturer and a supplier. The ultra-high-frequency Alien RFID reader is utilized to capture the inventory in each stage. The following operational strategies of the supply chain are adopted in the testbed:

(1) All the members in the supply chain adopt the order-up-to policy. (2) For each stage the holding cost and shortage cost are different but keep constant. (3) The ordering decisions of each stage are made within a Newsvendor framework. The comparison between the scenario under the theoretical environment and the real case shows a certain degree of decline of RFID system’s performance. This is mainly due to the missed reading of the tags by RFID readers. For the 4-stage supply chain model with 1% missed reading rate, the value for implementing RFID technology suffers 5–6% reduction. Based on the testbed, the RFID visibility is achieved by visualizing the real-time captured data for different stages. Firstly, in the stage 1, retailors use RFID technology to manage their merchandise so that the replenishment plans could be automatically carried out according to the real-time sales data. Secondly, in stage 2, distributors are able to get the real-time replenishment plans from different retailors. Based on these plans, distributors are capable of making logistics schedules in a precise manner. Thirdly, manufacturers also get the information which is used for their production plans so that more reasonable and precise manufacturing could be realized. That will greatly decrease the WIP

Fig. 3. Expected lost cost of two scenarios.

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Fig. 5. Discrepancy level of two scenarios.

no impact on the main component of prevention value and lost cost saving. Keeping other parameters fixed, we vary μsI form 1% to 5% of shrinkage and decrease 0.1% every upstream stage, and then calculate the full prevention value based on formula (26). From Fig. 10, it is observed that the mean of shrinkage has a significant impact on the prevention value and the cost saving of each stage increases around $6800 as the mean of shrinkage increases 1% at the first stage. From Figs. 8–10, it is suggested that if the shrinkage mean or variance is large, that is, the supply chain suffers serious shrinkage problem, then, the RFID can provide more information and has larger cost reduction potential.

Fig. 6. RFID value of the supply chain.

inventory in their production lines or warehouses. Fourthly, suppliers get the production plans and carry out just-in-time (JIT) delivery for different manufacturers. Several types of logistics mode could be customized by manufacturers based on the real-time RFID data sharing and visibility, for example, JIT delivery to production lines, milk-run logistics, and on-demand delivery [27,23,24,29]. For further examination of the value of RFID implementation, more investigations are conducted. First we consider two extreme cases to study the impacts of inventory inaccuracy characteristics on RFID visibility and full prevention value. Keeping other parameters fixed, we vary σsk form μsk /9 to μsk 5/9 and calculate the visibility and full prevention value based on formulas (24) and (26) respectively. Fig. 8 shows that if the variance of inventory shrinkage is larger, which means the uncertainty of the supply chain is larger, then the RFID visibility leads to larger cost reduction. As can be seen from Fig. 9, the prevention value increases a small percentage as the shrinkage StD increases. It implies that shrinkage StD does not play a significant role in RFID prevention value because it has

5.3. RFID justification Supposing the fixed investments of the three type of RFID implementations are $150,000, $100,000 and $50,000 due to different requirement level respectively, the relationship between the critical RFID tag cost and the investment recover time based on formula (27) is depicted in Fig. 11. For each type of RFID implementation with given tag price and expected recovery period, the above corresponding curve is so called “feasible reign” referring to positive profit while the below corresponding curve is so called “infeasible reign” referring to no profit. As we can see from Fig. 11, it is difficult to take back investment for type three RFID implementation as all the critical RFID tag price is negative. Assume the current RFID tag in market is $1.5, it will take 1.58 and 2.62 years to take back investment for type one and two, respectively.

Fig. 7. RFID-enabled 4-stage supply chain.

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Fig. 8. Impact of StD of shrinkage on RFID visibility value.

Fig. 9. Impact of StD of shrinkage on RFID full prevention value.

Fig. 10. Impact of mean of shrinkage on RFID prevention value.

Fig. 11. RFID justification.

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6. Conclusion

quantitative returns of a certain investment is important for practitioners to choose the most suitable RFID applications. Third, visibility value of RFID is preferable to members in a multistage supply chain with higher uncertainty of inventory discrepancy. While prevention is preferable to industries with higher value of products. There are several future research directions that remain to be investigated. First, this paper only considers the inventory inaccuracy coming from shrinkage. However, inventory inaccuracy source may include misplacement, unreliable delivery or transaction errors. This model could be extended to investigate all the errors. Second, different stage in a supply chain may obtain different RFID value under the same investment and some stages may have no incentive to implement RFID. How to increase the overall benefits of a supply chain deserves further study. Third, more real cases of RFID implementations need to be investigated and compared with the analytical models. The quantitative relations between the missed reading rate and the performance of RFID implementation need to be further studied. Finally, in order to fully validate the proposed model, an empirical study would be conducted by collecting the data from a typical supply chain which has used RFID technology in different echelons. A case study paper is under planning so as to show the feasibility and practicality of this approach.

Currently, industrial practitioners are exposed to increasing dynamics and complexity of global supply chain. How to make the right decisions for the investment of RFID technology becomes more and more challenging. In this paper, a centralized supply chain subject to inventory inaccuracy problems caused by shrinkage is investigated to help practitioners to understand: (1) the impacts of inventory inaccuracy on the supply chain performance in terms of information distortion and growing costs; (2) the impacts of RFID visibility and prevention on the extent, amount and economics of inventory inaccuracy, respectively; and (3) the larger scope of RFID benefit by including information distortion amplification in the overall benefit calculation with consideration of multi-stage settings. These contributions may shed some new light on framing the discussion of investing in RFID technology. An analytical model is presented to capture the inventory inaccuracy impact on bullwhip effect and to quantify the RFID value. In particular, two types of RFID value: visibility and prevention are differentiated. The proposed analytical models and numerical results also imply some important managerial insights in terms of investing in RFID technology as follows. First of all, RFID benefits in the downstream transfer to and accumulate in the upstream stages. According to this effect, the value of implementing RFID technology is more significant when the whole supply chain is considered. Second, different RFID applications result in different investments and lead to different benefits. Understanding how RFID technology creates values, like through visibility or prevention, and the

Acknowledgement Authors would like to acknowledge the financial support from National Science Foundation of China – China (No. 51775348) and National Key Technology R & D Program of China (No. 2015BAF12B02).

Appendix A Proof of proposition 1. (1) According to (14) and (15), ΔP k = (ELCk,1−ELCk,2) + (ECk,1−ECk,2) > 0 (2) As ∇μ k P k = r k > 0 , ΔP k is increasing in μsk . s

(3) It is obvious z k̂ = ∂f (z k̂ ) ∂σsi

z k V k ,1 (V k ,1)2 + ∑ik= 1 (σsi )2

is decreasing in σsi and z k̂ < z k , and f (x ) is decreasing in x when x < z k . Thus, f (z k̂ ) is increasing in σsi , that is, k

k

> 0 . As ∇σsi P k = [(V k,1)2 + ∑i = 1 (σsi )2]−1/2 σsi f (z k̂ ) + [(V k,1)2 + ∑i = 1 (σsi )2]1/2

∂f (z k̂ ) ∂σsi

> 0 , ΔP k is increasing in σsi,i = 1,2…,k .

(4) As ∇μ k ′ P k = r k > 0 , ΔP k is increasing in μsk ′. s

k

(5) As ∇σsi ′ P k = −[(V k,1)2 + ∑i = 1 (σsi ′)2]−1/2 σsi ′ f (z k ) < 0 , ΔP k is decreasing in σsi ′, i = 1,2…,k . (6) As L (x ) is decreasing in x , so, when z K > z K̂ , L (z K ) < L (z K̂ ) , we can get k

k

∇ pk P k = [(V k,1)2 + ∑i = 1 (σsi )2]1/2 L (z k̂ )−[(V k,1)2 + ∑i = 1 (σsi ′)2] L (z k ) > 0 . ΔP k is increasing in pk . □ Proof of proposition 2. Given hk , pk and r k , k = 1,2…,K are the same for all stages: (1) It is obvious V k,1 is increasing in k and z k̂ is decreasing in k which leads to f (z k̂ ) is increasing in k . According to (24) ΔPvk is increasing in k . (2) As z k̂ < z k , f (z k̂ ) > f (z k ) ,

⎡ ∇σ i Pvk = ⎢(V k,1)2 + s ⎣

∇σsi Ppk

=

[(V k,1)2

k

∑ i=1

+

−1/2

⎤ (σsi )2⎥ ⎦ k ∑i = 1

⎡ σsi [f (z k̂ )−f (z k )] + ⎢(V k,1)2 + ⎣

(σsi )2]−1/2 σsi f

(z k )

> 0,

ΔPvk

and

ΔPpk

k

∑ i=1

1/2

⎤ (σsi )2⎥ ⎦

∂f (z k̂ ) >0 ∂σsi

are increasing in σsi,i = 1,2…,k .

(3) As ∇μsi Ppk = r k > 0 , ΔPpk is increasing in μsk . □

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