Identification Shrinkage in Inventory Management: An RFID-based Solution Wei Zhou1,3 , Selwyn Piramuthu2,3,∗ 1 Information & Operations Management, ESCP Europe, Paris, France 2 Information Systems and Operations Management, University of Florida, USA 3 RFID European Lab, Paris, France ∗ corresponding author:
[email protected]
Abstract The identity of a product in a retail store setting is commonly represented by attached tag(s) and/or labels. This identification mechanism works reasonably well in practice. However, there are situations where such identification information may be intentionally or unintentionally separated from the associated item. While it is possible, in principle, to restore an item’s identification information based on its location, characteristics, among others, such attempts are not always successful. We consider a few scenarios where an item’s identification information is lost or switched with that from another item (ticket-switching) through intentional or unintentional means. We propose an RFID-enabled tracking/tracing system to address this with a knowledge-based self-adaptive mechanism. We consider three different scenarios to illustrate and estimate the underling value of such a system. Our results indicate that identification shrinkage could result in large losses that are associated with inventory cost due to both additional holding cost and inflated demand. We show how this can be addressed by utilizing an RFID-based tracking/tracing system. With limited resources and the presence of ticket-switching problem, our analyses indicate a counter-intuitive result that inventory managers should prioritize ‘cheap’ items.
Keywords: identification shrinkage, knowledge-based system, RFID, ticket-switching
1
Introduction
Identification information is extremely important for items that pass through a supply chain. This is especially critical when there are a large number of items that need to be identified at the instance-level or even the categorical- (or class-) level when items are transferred from one node to another in a supply chain. The concept of ownership of an item anywhere in the supply chain implicitly recognizes the fact that both the owner and the owned item have associated identification information. Without this information, possibly even at a crude or a higher-level of granularity (e.g., a case of red delicious apples), it becomes rather difficult to transfer ownership of an item between nodes as the item moves forward in its supply chain [6]. Sometimes, at the 1
store-level, an item is identified not at the instance-level but optionally at the class-level (e.g., an apple belonging to the type red delicious) and more by its unit price (e.g., $3.00/lb [of red delicious apples]). Among currently available auto-ID technologies, bar codes are very widely used in the retail industry. While they allow for identification of items at instance-levels, bar codes are commonly used to identify items at the class-level. Product/material/machinary/staff identification is traditionally accomplished by the use of bar codes. RFID (Radio-Frequency Identification) tags are increasingly being used for identification in the retail industry at the pallet level as well as, in a few instances, at the item-level (e.g., American Apparel, Trasluz). RFID has provided a unique way to identify as well as to track and trace products in a supply chain (e.g., [3], [4]). Although cost was purportedly an issue with RFID (vs. bar code) adoptions, recent research results[12] suggest that it may not necessarily be of concern in all cases. Despite its importance, to our knowledge and from our review of existing literature, the concept of identification in a supply chain context has not been studied in the past. We attempt to fill this gap in existing literature by investigating the characteristics of identification in supply chains and their practical implications. Automatic identification in supply chain [8] is used to improve logistics services including transportation, receiving and in-facility operations, especially in retail stores. Automatic identification provides more accurate and faster (even real-time) services and consequently reduces operational/transactional costs and lead time. It should be noted that both automated and traditional manual identifications are not always 100% accurate [7]. Along with other causes such as inventory misplacement and theft, identification errors (including natural detachment and intentional separation) contribute to inventory shrinkage especially in retail supply chains. Moreover, identification loss can result in a much larger problem than just inventory shrinkage, and can extend to marketing, customer relationship management[16] and supply chain coordination. Researchers have extensively studied inventory shrinkage in the past few decades. To our knowledge there is a lack of published research that specifically considers the statistical characteristics of inventory identification as well as addresses relevant issues such as tag-removal or ticket-switching in logistics channels or in retail stores. We contribute to existing literature in this area by studying this specific inventory shrinkage problem with the presence of the item in the inventory but with the item identification missing or switched. We propose an RFID-based solution to address this long-existing issue and evaluate its benefit by investigating the impact of such a phenomenon on inventory policy by detailing three possible identification shrinkage issues in supply chain management: identification detachment, ID sub-categorization, and ticket switching. The remainder of this paper is organized as follows: We present a brief overview of relevant background in Section 2. We then introduce the proposed RFID-based solution in Section 3. Sections 4 and 5 quantify the potential benefits of the proposed system by investigating statistical characteristics of various forms of identification shrinkage. Analysis and discussion of results are presented in Section 6. Section 7 concludes the paper with a brief discussion on the insights 2
garnered and their implications.
2
Background
Inventory shrinkage has been studied extensively in extant literature. In general, inventory shrinkage and information discrepancy between the physical stock and the database come from three major sources: loss, misplacement, and transaction errors. These result in the introduction of uncertainty in the actual physical inventory level. Elimination of inaccuracy in the inventory management system helps reduce supply chain costs and out-of-stock situations. Modern autoID technology helps achieve improvement in inventory accuracy through lower level (e.g., itemlevel) visibility[15]. Atali et al. [1] study the impact of RFID’s tracing/tracking capability when inventory information is imperfect and observe the benefits of information visibility on inventory management. Identification shrinkage is different from inventory shrinkage that is generally considered in the literature in that when an item’s identification is removed/switched, the associated item still exists at the retail store. In retailing, it signifies that id-lost items can not be sold and at the same time such items incur related inventory cost. To our knowledge, none of the existing literature specifically addresses identification shrinkage and its effect on inventory management. As one of the identification shrinkage types, ticket-switching arises from either operational error or theft when an ‘expensive’ ticket is replaced by a ‘cheap’ ticket at a retail store. In general, retailers carry a large number of items which renders it very expensive and difficult to prevent the occurrence of ticket-switching incidents. The consequence of ticket-switching on the inventory system include false-positives and false-negatives on the two ticket-switched items for every ticket-switching incident. In the retailing industry and among different item-identification technologies, price stickers are the easiest to switch since they generally don’t have any information on the associated item. On the other hand, bar codes have relevant information (e.g., the item’s identity) stored in database(s) that are readily accessible by the retail store check-out personnel. At this point in time, bar codes are the most commonly used technology for check-out information by retailers. Price stickers are not that uncommon while RFID (Radio-Frequency IDentification) tags are slowly being introduced, albeit primarily for inventory management purposes at present. Among ticket-switching incidents, a majority of cases go unreported. The news media generally pick up such incidents only when a large number of items, high monetary value, celebrity, or some bizarre person/modus operandi is involved. For example, a customer at a San Francisco Bay Area Target store was caught affixing home-made bar codes to packages of LEGO building sets that allowed him to purchase expensive sets at substantial discounts [10]. He apparently then sold these items on eBay and made about $30,000 per year from these sales. In another case, two couples were charged with defrauding Wal-Mart stores about $1.5 million across 19 states over the last decade where a home computer was used to print bar codes of cheaper items meant to be ticket-switched [13]. The suspects then allegedly either sold the merchandise elsewhere or returned them for store gift cards. These suspects apparently avoided detection 3
in part by visiting stores during the busiest periods. A Colorado University freshman used bar codes printed in his dorm room with ‘Barcode Magic’ to buy big-ticket electronic gadgets for cheap at a local Target store. For example, with a home-made bar code for a CD player that costs $4.99, he bought a system for using iPods that was valued at $149.99 [20]. A customer at a Leclerc supermarket in Tr´elisssac, Dordogne was caught during check-out for replacing the labels on two €2,300 bottles of Petrus with €2.50 labels [14]. To our knowledge, there are very few published research papers on ticket-switching and its effects on inventory management[17, 18]. Related research publications which discuss ticketswitching that we are aware of include [2], [5], [9] and [15]. All of these consider means to address ticket-switching through deterrence, prevention, or recognition as it occurs.
3
RFID-enabled Inventory Management Framework
We propose a self-adaptive inventory process management system that is able to automatically adjust the inventory policy based on learned knowledge from historical data on inventory management and identity shrinkage. In the proposed framework (Figure 1), the inventory decision & control module makes various decisions on order quantity, space arrangement, and delivery route design using inputs that include demand, existing inventory information, incoming inventory, among others. These inventory management decisions generate outputs that include production or consumption and logistics service quality indicators. The service quality measurements are collected, measured, learned, and stored in a knowledge-base that can be further utilized to improve inventory process management towards better efficiency, lower cost, and better service quality, to compensate for inventory loss due to various types of identification shrinkage and other non-identification related shrinkage. Demand Ordering Quantity
Existing Inventory
Random Events
Inventory Decisions & Control
Knowledge Base
Learning
Production/ Consumption Service Quality
Evaluation
Adaptive Learning Module
Figure 1: Knowledge-based Inventory Management Process Framework In this framework (Figure 1), the knowledge-based learning module supports adaptive decision4
making[11] with changes in inventory dynamics, demand changes, identity detachment, other types of inventory shrinkage and related random events. In the next subsection we discuss dynamic inventory management policy followed by the knowledge-based adaptive learning component. The main component of inventory decision and control module is the problem solver that comprises a set of decision support tools that compute and deliver solutions to routine structured problems where all necessary inputs are deterministically known to fairly sophisticated ‘intelligent’ tools that pro-actively seek to provide appropriate support for making decisions in semi-structured or even unstructured environments. Dynamic environments that are essentially characterized by uncertainties in several dimensions necessitate a reasonably ‘smart’ decision support tool. These decision support tools are required to provide or assist in generating ‘good’ decisions in real-time. An example simplified scenario is when a certain level of service quality is received, the problem solver would approximate the influence of identity detachment, inventory space allocation, and other associated random events in order to fine-tune the inventory policy for the next time period. Problem-solving capability is an essential characteristic of an adaptive knowledge-based system since it is a requirement for supporting decision-making situations. Compared to humans, the relative speed at which computers are able to solve problems are measured in multiple orders of magnitude. This is beneficially utilized in the considered adaptive framework. The Problem Solver sub-component in this framework receives domain knowledge input indirectly from the Adaptive Learning component and item-level part information from supplier, and further includes two components: the knowledge-base and the Problem-solving component. The Adaptive Learning component provides the knowledge that is incorporated in the knowledgebase, which is a part of the problem-solving component. As knowledge in its knowledge-base becomes stale or when new knowledge or updates to existing knowledge become available, the Adaptive Learning component provides necessary knowledge input to bring the knowledge-base current. The other input to the Problem-solving component comes from the environment in terms of essential input data to address the associated decision problem. Essential characteristics of the Problem-solving component include the ability to update its knowledge-base using input from the Adaptive Learning component, appropriately invoking necessary knowledge from its knowledge-base and using it to address the input decision-making problem from the environment with the Problem Solver, and providing the most appropriate solution output for a given combination of existing knowledge and problem of interest. The dynamics in these systems necessitate the corresponding process of making decisions to be dynamic. The decision-making process cannot be truly dynamic when the source knowledgebase that it relies on remains static. Using input from recent performance of the system, the Performance Evaluation sub-component either assigns appropriate internal credit when the performance of the system was as expected or identifies deficits when the system performance is worse than expected. In the former case, the system identifies the parts of the knowledge-base that was used in the decision-making process and assigns (reinforcement) credit, which can then be used to efficiently fine-tune the knowledge-base for effective performance. In the latter 5
case, it identifies the source of the deficit. Specifically, the best course of action for a given decision-making scenario is identified. This is then incrementally learned and incorporated in the knowledge-base for later use. The learning sub-component is responsible for pro-actively keeping the knowledge-base from becoming stale. This is primarily done through indirectly monitoring the quality of the knowledgebase through the overall performance of the system. A poor system performance indicates incomplete or stale knowledge in the knowledge-base. If the knowledge-base is incomplete, there is a need to identify and generate the ‘missing pieces’ of knowledge. If the knowledge-base is found to have necessary knowledge albeit stale, either a complete overhaul of that part of the knowledge-base can be done or additional knowledge can be added to refresh the knowledge-base. Given these requirements, the necessary characteristics of this sub-component include the ability to identify staleness and incompleteness in the knowledge-base, and the ability to translate deficit identification to useable information that is incorporated in the updated knowledge-base. Learning is an important characteristic of any intelligent system. Learning from experience has several advantages. It enables a system to incrementally build and improve its knowledgebase when and where deficits are identified through continual feedback from the environment. Although it is not possible to begin with a ‘perfect’ or ‘complete’ knowledge-base containing all possible knowledge of the domain of interest in most applications, the capacity to learn over time alleviates this burden on the system. Without learning, a system is bound to repeat mistakes, which can prove to be expensive in monetary terms as well as in terms of resources including time, manpower, and materials. The knowledge-base of a system that does not have learning capability is bound to be static and hence become quickly stale in terms of knowledge in most dynamic environments that necessitate dynamic update of its knowledge-base to remain current. Static knowledge-bases are appropriate only in scenarios where the knowledge-base contains the complete domain knowledge that does not change with time and in static environments. Unless we are dealing with imaginary problems, it is hard to envision an application area where a static knowledge-base is appropriate. Learning is an important characteristic and the Learning component constitutes the core of the considered adaptive knowledge-based system framework since it is the primary source of knowledge. Although learning by itself can be accomplished through several means, we focus on machine learning as the mode of learning in the considered framework. The primary motivation behind this is the natural and seamless way in which such a learning can be incorporated with the rest of the framework to achieve improved performance results. Any of the several existing supervised machine learning algorithms such as decision trees, decision rules, feed-forward neural networks, genetic algorithms, etc. could be used in this component. Depending on the domain of interest, more specifically on the data characteristics including data types (e.g., numeric, alphanumeric, symbolic) and interactions among themselves in the domain of interest, an appropriate algorithm can be selected. For example, some algorithms such as those that are used in feed-forward neural network work better with real-valued data, while some others such as those used in inducing decision trees work better with symbolic data in general. Given the implications of the No Free Lunch (NFL) theorems, the criticality in selecting 6
the most appropriate algorithm as well as the ability to incorporate domain knowledge (in the form of hints) in the learning algorithm to avoid some of the problems associated with the NFL theorems cannot be overstated. Other considerations include the time taken to learn a concept of interest since an application might prove to be time-critical that necessitates learning concepts quickly in real-time. For example, genetic algorithms and the back-propagation algorithm and its variants used in feed-forward neural network are iterative in nature and could possibly take longer to learn a concept. Others such as decision trees or decision rules are one-pass algorithms that generally are fast learners. The quality of learned concepts is, of course, of paramount importance. The choice of algorithm used in the Learning component should, therefore, depend on several factors including data characteristics, learning accuracy, quality of learned concepts including representational conciseness, learning speed, among others. Regardless, as long as learning is achieved somehow, the framework is able to function without much degradation in its resulting performance. Essential characteristics of the Learning sub-component include the ability to (1) concisely, accurately, and quickly learn the concepts of interest, (2) accept necessary input data, and (3) generate learned concepts in a form that is required of the next component in the framework.
4
Categorical & Item-level Identification
Object identification is commonly operationalized through some variant of tag by either visual or non-visual means, such as bar code or radio frequency identification (RFID). ID tags can be applied at any node in the supply chain from raw material suppliers to the retailers as well as from either inside or outside the organization. ID tags are usually securely attached or sometimes printed on the items for identification. However, such attachments have the potential to be detached, damaged, or switched during everyday operations in the supply chain. We define and refer to this as the identification attrition problem. There is another dimension where identification in a supply chain management context is of interest. This refers to the classification hierarchy where each product and component in the supply chain are categorized by multiple features as related to the business objectives. For example, the same product with different origins can be grouped and categorized with the same identification, while at the same time, these can also be sub-categorized by their origins. While the products/items are generally indistinguishable despite the systematic minor differences (e.g., batch production date, origin, raw material supplier), supply chain practitioners do not have the incentive to sub-categorize these. Modern automatic identification technologies such as RFID have made it possible to systematically provide item-level identification for all the products and components in a supply chain. However, the necessity and the benefits of such identification has remained somewhat unknown to the industry. We define this as the identification sub-categorization problem. In what follows, we model and investigate the effects of this problem mostly in the context of inventory management.
7
4.1
Identification
Assume that we have an item x, with intrinsic identification IDx . We measure the possibility of true identification y of this item as P [y = idx |(x, idx )], where y represents the existence of item, x represents the presence, and idx represents item x’s unique ID as identified by a reader. In a perfect environment, P [y = idx |(x, idx )] = 1 and P [y = idx |x] = 0, assuming that the total number of items is large. Identifications are usually managed in a centralized fashion so that there exist a bank of component identities {id1 , id2 , · · · idN }.
ID 1 Item
Tag1
Figure 2: Item-level identification In practice, identifications are designated by the use of tags that are attached to the item or the packages that contain the item (Figure 2). The tags can themselves be a UPC bar code, an EPC RFID chip, or other identification technologies. Consequently, the bayesian probability of correctly identifying an item with an ID tag is P [idx |(x, tagx )] = σ(idx ), so PN i=0 P [idi |(x, tagx )] = 1, where id0 represents null reading that informs the system of itemP nonexistence. In general, if the attached tag is missing, N i=1 P [idi |x] = 1 and P [idx |x] = 1/N with uniform distribution assumption. When N is large, P [idx |x] approaches zero.
4.2
Identification Attrition
At the categorical level, the same identification is assigned to a group of items that share the same physical characteristics and criteria. Most UPC bar codes used in retail stores are categorical identifiers (e.g., bar codes on fresh milk, toys, furniture). With the presence of identification attrition, assume that the rate of tag detachment is 1 − R (Figure 3). With probability R, the item can be recognized based on its true identification. With 1 − R probability, however, correct identification is equally diluted by the total number of IDs such that P [idx |x] = 1/N . We define R as the retaining rate and 1 − R as the detachment rate. We also assume that R ≥ θ, where θ is the minimum rate of identification retainment. This realistically reflects reality whereby when there is some identification issue with certain product or component, it will be corrected to a satisfactory level before it reaches zero. The immediate consequence of identification attrition is value attrition of the product of interest. Consider an item x with a value of V and the true identity with this item idx . The item value discounted by the identification attrition V 0 is V 0 = V R + (1 − R)[V − C, 0]+ 8
(1)
Item
ID 1 tag
x
tag 1
ID 2
ID 3
ID i
tag 2
tag 3
tag i
ID j
tag j
ID n
tag n
Figure 3: Identification detachment
0
where we define the term VV = βid as the identification discount rate. C represents the cost to retrieve the identification, and C = P [idcx |x] with c representing the marginal operation cost (such as the cost to perform benchmark per unit). Consequently, only when V − C ≥ 0, it’s reasonable to invest in retrieving the ID back.
4.3
Identification Sub-categorization
In a product category with a total number of n items, it can be further sub-categorized to m groups with their unique sub-category IDs according to the non-critical differences that exist in the original category. The overall retaining rate R is based on all sub-categories such that R= where D =
5
P
Pm
i=i ri di
D
(2)
di is the total number of products and ri is the retaining rate for each sub-category.
Identification in Inventory Management
Identification detachment causes both inventory shrinkage and uncertainty in inventory management. Most identification shrinkages are caused due to the following three reasons: accidental detachment, tag removal, and tag switching. Accidental product identifier detachment occurs throughout the logistics operations in a supply chain, possibly due to unintended events. On the other hand, tag removal is an intentional separation of the identifier tag from the associated product/component by someone, resulting in the loss of its identification. Tag removal may involve malicious actions such as theft or non-malicious actions such as an accidental event caused by a line-side employee. Tag switching means that tags associated with different products are switched so the identity of these products of interest are consequently switched or lost. We use the classical EOQ model to illustrate the impact of identification shrinkage in different inventory management systems. We argue that other inventory models can be readily utilized for this purpose, but the EOQ model provides a simple yet straightforward means of investigation given the novelty of this topic. We consider an inventory system that continuously monitors the inventory level, which is driven by known demand that is constant and independent. Lead time is also assumed to be known and constant. 9
5.1
Notations
We base our analysis on the basic EOQ model, where we only consider the ordering cost and holding cost as given below: • Q = number of items per order • Q? = optimum number of items per order (EOQ) • D = Annual demand in units for the inventory item • S = Setup/ordering cost for each order • H = Holding/carrying cost per unit per year In this setup, only the annual ordering cost and the annual holding cost are considered so that the total annual cost is Q D (3) TC = S + H Q 2 Without taking into consideration the identification shrinkage, the optimal order quantity is found when the first order conditions are met such that − QD2 S + H2 = 0 and consequently, Q∗ =
q
2DS H .
The cycle time, which is the time between consecutive inventory replenishment, is
τ ∗ = Q∗ /D. The holding cost, which is the same as the ordering cost, equals
5.2
q
DSH 2 .
Identification Detachment
In the presence of identification shrinkage, when the item identifier is detached/removed/switched, inventory management would firstly suffer from increased inventory cost because the unidentifiable items take up space that could be used for identifiable items. Secondly, the system has to bear the costs associated with unsatisfied customers when shortage is incorporated in management policy decisions. Inventory shortage could also generate reorder costs. Moreover, the overall demand is inflated by identification shrinkage. In what follows, we investigate inventory policy with identification loss for the aggregated category case and the sub-categorization case. With pure identifier detachment, for each identification there exists a gap between the transactional information and the inventory record. Periodic inventory check informs the manager of any shortage and appropriate number of items can be ordered to address the shortage. Therefore, in calculating the revised inventory level, the annual demand would include both the actual demand and the one with tag detachment is given by R1 . In other words, the demand in the inventory system is inflated by R1 − 1. The holding/carrying cost is also increased by (1 − R) because of the excess unidentifiable inventory. As a result, the revised optimal ordering quantity becomes s 2DS/R Q∗ = (4) H + H(1 − R) Consequently, the optimal inventory policy with identification shrinkage can be determined, and the results are summarized in equations 5-8 below. 10
• The optimal quantity is s ∗0
Q =
2DS H
s
1 = Q∗ R(2 − R)
s
1 R(2 − R)
(5)
• The ordering cost: s ∗0
OC =
DSH 2
• The holding cost: s ∗0
HC =
DSH 2
s
s
(2 − R) = OC ∗ R
(2 − R) = HC ∗ R
• The delivery time:
s
τ
∗0
s
=τ
∗
(2 − R) R
s
(6)
(2 − R) R
(7)
R 2−R
(8)
Theorem 1: In the range R ∈ [θ, 1], where θ ∈ (0, 1), the optimal order quantity Q∗ monotonically increases with identification shrinkage 1 − R. Proof: The revised optimal quantity Q∗0 = Q∗ coefficient
q
1 R(2−R) ,
q
1 R(2−R)
is related to the original quantity with
which is monotonically increasing with (1 − R) in the range R ∈ [0, 1].
Theorem 2: The annual holding cost, ordering cost, and total inventory cost monotonically decrease with R. q q √ 2−R has a coefficient of Proof: The total annual inventory cost = 2DSH 2−R R R with the cost without shrinkage, which monotonically decreases with R.
5.3
Identification Detachment in Sub-categorization
When a category of products/components are further classified into multiple sub-categories, such as by their origin, supplier, logistic service provider, etc, we assume that the number of sub-categories is m. Each sub-category has its ownrretention rate ri , so the overall performance P is R =
m
rd i=i i i P and the optimal quantity is Q∗i = d i
2di S/ri H+H(1−ri )
As a result, the total ordering quantity is ∗
Q =
m X
s
i=1
2di S/ri H + H(1 − ri )
(9)
The results are summarized in equations 10-13 below. • The optimal quantity is Q∗0 =
m X i=1
s
2di S H
11
s
1 ri (2 − ri )
(10)
• The total ordering cost:
s
OC ∗0 = • The holding cost:
s
HC ∗0 =
m p SH X di 2 i=1
s
m p SH X di 2 i=1
s
2 − ri ri
(11)
2 − ri ri
(12)
• The delivery time of ith subcategory: τi∗0
=
τi∗
r
ri 2 − ri
(13)
Theorem 3: With or without identification shrinkage, the total inventory cost is higher with finer granular identification sub-categorization Proof Without identification shrinkage, the difference in total inventory cost between the one with a grouped category and the one with sub-categorization is ∗
TC − TC
∗0
=
r
2SH
X
di −
√
2SH
m p X
di
i=1
=
√
v um m p X uX 2SH t di − di 1
i=1
pPm Pm √ Since 1 di − i=1 di ≤ 0, sub-categorization increases the total inventory cost in a condition without stock shortage and without identification loss, such that T C ∗ − T C ∗0 ≤ 0. With identification shrinkage, the overall inventory is lowered by identification sub-categorization as s
T C ∗ − T C ∗0 = =
2SH
X
di
2 − R
R
−
√
2SH
m p X
s
di
i=1
2 − ri ri
v s um X m p √ uX 2 − R 2 − r i 2SH t di − di
R
i=1
i=1
ri
In the range of ri ∈ [θ, 1], R ∈ [θ, 1], T C ∗ − T C ∗0 ≤ 0 Theorem 4: The lead time is lower with finer granular identification sub-categorization In some extreme cases, the cause of most identification detachment is due to one source. With sub-categorization, the inventory system would be able to identify the problematic subcategory when the performance rate is below θ and, as a result, the total inventory cost would be improved.
12
5.4
Ticket-Switching
Another cause of identification shrinkage is ticket-switching. In simplest terms, tag or ticket switching involves two items A and B with different identifiers. Assume a scenario in an inventory system with perfect information and correctly identified items, where the identifier or at least the price tag from products A and B are switched. The tag switching rate is denoted by 1 − Rs . Item
ID 1 tag tag 1
ID 2
x
ID 3
ID i
tag 3
tag i
tag 2
ID j
ID n
tag j
tag n
Figure 4: Ticket-Switching s For item A: the annual demand in units is inflated by 2−R Rs because the system would record 2 − Rs sales, and there is another Rs rate of identification shrinkage. The holding cost per unit is inflated by 2 − Rs because the system stores more identity-less items without being able to locate them. On the other hand, for item B: the demand is inflated by (2 − Rs ) without unidentifiable items left in the inventory, and consequently the holding cost remains the same per unit. For both A and B, we have the following list of notations for tag switching:
0 = D (2−Rs ) • DA A Rs 0 = H (2 − R ) • HA s A 0 = D (2 − R ) • DB s B 0 =H • HB B
For item A: • The optimal quantity is
s
Q∗0 A = • The ordering cost:
s ∗0 OCA
=
• The holding cost:
s ∗0 HCA
=
2SDA HA
s
1 Rs
(14)
DA HA S 2
2 − Rs √ Rs
(15)
DA HA S 2
2 − Rs √ Rs
(16)
For item B: 13
• The optimal quantity is
s
Q∗0 B = • The ordering cost:
s ∗0 OCB =
• The holding cost:
s ∗0 HCB
=
2SDB (2 − Rs ) HB
(17)
D B HB S p 2 − Rs 2
(18)
DB HB S p 2 − Rs 2
(19)
Theorem 5: For the range R ∈ [θ, 1], where θ ∈ (0, 1), ticket-switching poses higher inventory cost on tag-detached item than on tag-attached item. ∗0 /T C ∗ = 2−R √ s . The same Proof: The coefficient of total inventory cost of item A is βA = T CA A Rs √ ∗0 /T C ∗ = coefficient for item B is βB = T CB 2 − R . β and β represent the rate of increasing s A B q B βA 2−Rs inventory cost for item A and item B respectively. Because βB = Rs ≥ 1 for Rs ∈ [0, 1], we show that tag switching deteriorates the inventory management cost of detached item A faster than attached item B.
5.5
With Back-order
In the previous section, we studied the general inventory policy with identification shrinkage but without inventory shortage. Now, we consider the case with shortages that are back-ordered at a given cost. We denote the maximum inventory level as M that occurs when the order arrives. Thus the maximum backorder level is M − Q. As a result, the total cost per unit time is given by: HM 2 P (Q − M )2 D + (20) TC = S + Q 2Q 2Q The first order condition,
and
∂T C ∂Q=0
∂T C ∂M =0 ,
yields the following results:
• The optimal quantity is s ∗0
Q =
2DS H
s
1 R(2 − R)
s
P + H(2 − R) H(2 − R)
(21)
• The maximum inventory level is s
M
∗0
=
2DS H
s
1 R(2 − R)
s
P P + H(2 − R)
(22)
• The ordering cost: s ∗0
OC =
DSH 2
s
2−R R
14
H(2 − R) P + H(2 − R)
(23)
• The holding cost: s ∗0
HC =
DSH 2
P 2−R
• The back-order cost: BC ∗0 =
s
1 RH[P + H(2 − R)]
(24)
P (Q∗ − M ∗ )2 2Q∗
(25)
• The delivery time: τ ∗0 = Q∗0 /D
5.6
Analysis
500 Total Inventory Cost w/o ID-Shrinkage Operational Cost w/o ID-Shrinkage Holding Cost w/o ID-Shrinkage Total Inventory Cost with ID-Shrinkage Operational Cost with ID-Shrinkage Holding Cost with ID-Shrinkage
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Figure 5: Analysis of Inventory Cost on ID-Shrinkage Figure 5 shows the impact of identification detachment. The vertical axis represents unit cost. In general, both holding cost and operational cost increase and consequently the total cost increases. With the presence of identification shrinkage, the optimal ordering quantity does change rightward but in a relatively small range according to our simulation results. We summarize detailed numerical analysis results of different scenarios in Figure 6 and Figure 7. Figure 6 summarizes the inventory policy with id detachment rate from 0% to 15%. In this simulation experiment with 10000 units of annual demand, $10 of setup cost, and $0.1 of holding cost, the consequent optimal order quantity doesn’t change dramatically (up to 1.15%) but the total inventory cost increases by up to 16.32%. This result is consistent with classical EOQ models that exhibit stable ordering quantity levels. In other inventory management schemes, possibility exists for larger inventory policy change due to id detachment. We leave it as an exercise for a future study. 15
R 100.00% 98.50% 97.00% 95.50% 94.00% 92.50% 91.00% 89.50% 88.00% 86.50% Q* 0.00% 0.01% 0.04% 0.10% 0.18% 0.28% 0.41% 0.56% 0.73% 0.93% OC 0.00% 1.51% 3.04% 4.60% 6.19% 7.80% 9.44% 11.11% 12.82% 14.55% HC 0.00% 1.51% 3.04% 4.60% 6.19% 7.80% 9.44% 11.11% 12.82% 14.55% TC 0.00% 1.51% 3.04% 4.60% 6.19% 7.80% 9.44% 11.11% 12.82% 14.55%
85.00% 1.15% 16.32% 16.32% 16.32%
Figure 6: Numerical Analysis of Inventory Cost on ID-Shrinkage
In the presence of ticket-switching, Figure 7 summarizes the findings with different levels of id switch rate that ranges from 0% to 15%. The overall impact on optimal quantity is not negligible compared to a simple identification detachment scenario. More interestingly, the impact of ticket-switching on the inventory system is much greater for the cheap items (with tag removed) than from the expensive items. This result is consistent with Theorem 5 presented in the previous section. It is also somewhat counter-intuitive because the traditional pareto inventory analysis would put the more expensive items at higher priority. Our finding suggests that in the presence of ticket-switching, the inventory managers should pay relatively more attention to the cheap items. R Qa* Qb* TCa TCb
100.00% 98.50% 97.00% 95.50% 94.00% 92.50% 91.00% 89.50% 88.00% 86.50% 85.00% 100.00% 0.76% 1.53% 2.33% 3.14% 3.98% 4.83% 5.70% 6.60% 7.52% 8.47% 100.00% 0.75% 1.49% 2.23% 2.96% 3.68% 4.40% 5.12% 5.83% 6.54% 7.24% 100.00% 2.27% 4.58% 6.93% 9.33% 11.77% 14.26% 16.80% 19.39% 22.04% 24.74% 100.00% 0.75% 1.49% 2.23% 2.96% 3.68% 4.40% 5.12% 5.83% 6.54% 7.24%
Figure 7: Numerical Analysis of Inventory Cost on Tag-Switch
6
Conclusion
The cause of inventory shrinkage, its operational impact, and possible solutions have remained largely unknown to researchers. We investigated this specific problem of identification shrinkage from an inventory management perspective. We first considered identification detachment and the ticket-switching problem. We proposed a solution based on modern RFID-based tracking/tracing system. In order to examine its benefits and utilization, we then used a model to determine the corresponding inventory policy and the cost structure in the presence of identification shrinkage. Our results indicate that identification shrinkage has the potential to burden the inventory system through both increased holding cost and ordering cost. This issue is amplified when identifications are switched due to intentional or random causes. In the presence of ticketswitching, our results show that the inventory manager should pay more attention to the cheap items in order to reduce loss associated with inventory cost. We believe that this study contributes to extant inventory management literature by introducing the concept of item-level/categorical/sub-categorical inventory identification and identifier shrinkage. Further research can be directed to study the impact of identifier shrinkage 16
in different inventory management environments with context-specific information. Given the growth in usage of auto-id technologies, such as RFID, we foresee this research to be extended to address issues related to RFID read errors from the perspective of inventory management and other related applications.
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