Production, Manufacturing and Logistics
Evaluation of cycle-count policies for supply chains with inventory inaccuracy and implications on RFID investments

https://doi.org/10.1016/j.ejor.2014.01.052Get rights and content

Highlights

  • We consider cycle-counts in supply chains with inventory inaccuracy.

  • We provide a recursion to evaluate cost and a heuristic to obtain base-stock levels.

  • It is more effective to conduct more frequent cycle counts at the downstream stage.

  • Location, error rates, and costs are primary factors for cycle-count allocation.

Abstract

Inventory record inaccuracy leads to ineffective replenishment decisions and deteriorates supply chain performance. Conducting cycle counts (i.e., periodic inventory auditing) is a common approach to correcting inventory records. It is not clear, however, how inaccuracy at different locations affects supply chain performance and how an effective cycle-count program for a multi-stage supply chain should be designed. This paper aims to answer these questions by considering a serial supply chain that has inventory record inaccuracy and operates under local base-stock policies. A random error, representing a stock loss, such as shrinkage or spoilage, reduces the physical inventory at each location in each period. The errors are cumulative and are not observed until a location performs a cycle count. We provide a simple recursion to evaluate the system cost and propose a heuristic to obtain effective base-stock levels. For a two-stage system with identical error distributions and counting costs, we prove that it is more effective to conduct more frequent cycle counts at the downstream stage. In a numerical study for more general systems, we find that location (proximity to the customer), error rates, and counting costs are primary factors that determine which stages should get a higher priority when allocating cycle counts. However, it is in general not effective to allocate all cycle counts to the priority stages only. One should balance cycle counts between priority stages and non-priority stages by considering secondary factors such as lead times, holding costs, and the supply chain length. In particular, more cycle counts should be allocated to a stage when the ratio of its lead time to the total system lead time is small and the ratio of its holding cost to the total system holding cost is large. In addition, more cycle counts should be allocated to downstream stages when the number of stages in the supply chain is large. The analysis and insights generated from our study can be used to design guidelines or scorecard systems that help managers design better cycle-count policies. Finally, we discuss implications of our study on RFID investments in a supply chain.

Introduction

Inventory record inaccuracy refers to the discrepancy between physical inventory held in stock and the record of inventory stored in the information system of a firm. Shrinkage, spoilage, misplaced inventories, and transaction errors (e.g., scanning errors and incorrectly counting products) contribute to inaccurate inventory information. Inaccurate inventory information leads to ineffective replenishment decisions, which, in turn, result in poor service levels and higher inventory costs. This is a major issue affecting supply chain performance in manufacturing, distribution and retail settings. For example, DeHoratius and Raman (2008) found records to be inaccurate 65% of the items stored at a publicly traded retailer. According to ECR ECR Europe (2003), the value of lost inventory due to shrinkage in 2000 was €13.4 billion for retailers and €4.6 billion for manufacturers in Europe.

A common method to mitigate the impact of inventory inaccuracy is to conduct cycle counts. Companies usually implement cycle-count policies according to an ABC classification scheme, i.e., classifying products into A, B, C classes based on product attributes, such as volume, error rate and value, and assigning a count cycle to each class (Jordan, 1994). Motivated by empirical studies and business practice, researchers recently have developed various analytical models, aiming to study this problem more rigorously (see Section 2 below). To our knowledge, all of the existing analytical results are on single-location models. Nevertheless, major apparel retailers and consumer-packaged goods companies have significant inaccuracy problems across their supply chains. Managers have limited knowledge of the extent of inaccuracy at different locations and their impact on overall supply chain performance (Delen et al., 2009, Hardgrave et al., 2009, Hardgrave et al., 2013). In this study, we investigate the impact of inventory inaccuracy on the supply chain performance. In particular, we aim to answer the following questions: (1) What is the impact of inventory inaccuracy at a location on the entire supply chain performance? (2) Given the fact that cycle counts are costly, which locations should have more frequent counts? (3) How should different product attributes and system characteristics be taken into account when designing cycle-count policies in a supply chain? The answers to these questions are not readily available in the academic and business literatures. While one may argue that record inaccuracy at downstream locations has a greater impact because of proximity to customers, inaccuracy at an upstream location affects the supply for all downstream locations. Similarly, one may argue that maintaining accurate records at a location with a longer lead time is more important because such locations are slower to respond to demand changes. On the other hand, such locations generally have more pipeline and safety stock, which implies that they would be affected less by record inaccuracy.

In this paper, we consider a periodic-review, N-stage serial supply chain with inventory record inaccuracy. Random customer demand arrives at stage 1. Stage 1 replenishes from stage 2, stage 2 from stage 3, and so on, and stage N from an outside supplier with ample supply. There are constant transportation lead times between stages. Record inaccuracy is caused by a random inventory loss that reduces physical inventory. (See Section 2 for a discussion on the other causes of inventory inaccuracy.) To describe inventory inaccuracy, we use the term “nominal” to signify inventory records stored in the computer system, and “actual” to signify the physical inventory levels. Each stage implements a cycle-count policy to correct the inventory records. A fixed stage-specific inspection cost is incurred for each cycle count. Errors at each stage are cumulative and they are not observed by the information system unless the stage conducts a cycle count. Thus, the discrepancy between the nominal inventory and the actual inventory equals the accumulated error since the last cycle count. The material flow is controlled by local base-stock policies. That is, if the local nominal inventory order position at a stage is less than a target base-stock level, the stage places an order to raise the nominal inventory position to the target level. Such a replenishment scheme is commonly seen in practice and most firms have computer systems automate this process. The objective is to minimize the actual average total supply-chain cost per period.

To evaluate the system cost, we derive the actual local inventory variables for any given cycle-count policy. However, obtaining these local inventory variables requires characterizing the local demand for each stage. One key contribution of this paper is that we provide a simple procedure to evaluate the system cost. This procedure recursively evaluates the cost for each echelon (a stage and all of its downstream stages) starting from echelon 1 to echelon N. Moreover, this recursion leads to a heuristic to find local base-stock levels. A numerical study suggests that the heuristic is effective. We then use these results to answer the research questions.

For two-stage systems, regarding the impact of errors, we show that it is more costly to have the same error occur at the downstream stage than at the upstream stage. Furthermore, regarding the cycle-count policies, we show that it is always a better strategy to assign more cycle counts to the downstream stage than to the upstream stage when both stages have identical errors and counting costs. For more general systems, we categorize system parameters into two groups in terms of their effect on cycle-count policy decisions. Primary factors determine which stages should get a higher priority when allocating cycle counts. They include location (position in the supply chain), error rate, and counting cost. All else being equal, downstream locations should be assigned more frequent counts. However, a significantly higher error rate or lower counting cost at an upstream stage may reverse the result. We observe that the marginal benefit of cycle counts is decreasing in its frequency. Thus, one should not allocate all cycle counts to a single location. We therefore suggest using secondary factors to determine whether the policy should strongly favor the high-priority stages or allocate counts in a more balanced way. The secondary factors include lead time and holding cost structure and the supply chain length. We find that more cycle counts should be allocated to a stage if the ratio of the stage’s lead time to the total system lead time is small and the ratio of the stage’s holding cost to the total holding cost is large. Furthermore, more cycle counts should be allocated to downstream stages if the supply chain is long (i.e., the number of stages in the supply chain is large).

Our research questions have implications for investment decisions on Radio Frequency Identification (RFID) systems. Specifically, if a location installs RFID readers, this will, in principle, eliminate inventory inaccuracy by continuously monitoring the inventory. This has the same effect as conducting a cycle count in each period in our model. In fact, many RFID applications in retail supply chains involve hand-held RFID readers, whose role is to facilitate cycle counting. Because RFID implementation can be very costly (Kearney, 2004), many industry practitioners are concerned about where RFID readers should be installed in a supply chain (Chappell et al., 2002). Labor savings and investment costs of RFID systems can be quantified in each stage in isolation from others (Chopra & Sodhi, 2007), but it is not clear how one can quantify the impact of reducing inaccuracy at a particular stage on supply chain performance. The guidelines developed in this paper have implications on how to prioritize RFID investments in a supply chain.

The rest of the paper is organized as follows. Section 2 discusses major causes of inventory inaccuracy in supply chains and reviews the literature related to each of the causes. Section 3 presents a single-stage model and discusses the model set-up. Section 4 introduces the serial system and provides a scheme to evaluate the average total cost per period. Section 5 presents the lower bound and the heuristic algorithm. Section 6 presents our analytical and numerical results and provide answers to the research questions. Section 7 concludes. All proofs are provided in Appendix A.

Section snippets

Causes of inventory inaccuracy and related literature

Empirical research and industry reports indicate that shrinkage, transaction errors, and misplaced items are the main reasons that cause inventory inaccuracy (ECR Europe, 2003, Raman and Ton, 2003, Sheppard and Brown, 1993). In the following, we describe each type of inaccuracy and its impact on the supply chain.

Shrinkage, also known as stock loss, may be due to theft by shoppers or employees, and spoiled and damaged inventory. The impact of shrinkage on the actual inventory is one-sided: it

Single-stage system

In this section we consider a single-stage system. We use this model to illustrate the assumptions and the concept of nominal and actual inventory variables. This discussion sets the stage for the serial system.

Consider a periodic-review inventory system that orders according to a base-stock policy. Time is divided into periods of length one and the periods are numbered 0,1,2,. There is a constant lead time of L periods. Customer demand follows a Poisson process with rate λ. Let [t,t+r) and [t,

An example

We use an example to illustrate the inventory dynamics under the nominal and actual inventory schemes. Consider a single-stage system with T=2, L=2, and s=10. Fig. 1(a) illustrates the dynamics of the nominal inventory order position and inventory level. Fig. 1(b) illustrates the corresponding actual inventory variables. The demand and error levels in each period are given in the figure. The system has conducted a cycle count at the end of period t-1, so there is no error in the system at the

Series systems

We now consider an N-stage series system. Customer demand occurs at stage 1. Stage 1 is replenished by stage 2, stage 2 by stage 3, and so on, and stage N by an outside source with ample supply. The lead time between stage j and j+1 is Lj periods. Let Lj=i=jNLi, the cumulative lead time from stage j to stage N. Each stage orders according to a local base-stock policy. At the beginning of a period, if stage j’s local inventory order position is lower than the base-stock level sj, the stage

Lower bound and heuristic

The above bottom-up recursion is similar to that for the classic multi-echelon inventory problem (e.g., Chen, 1999, Chen and Zheng, 1994). However, unlike the classic problem, the optimal solution cannot be obtained by minimizing (1/T)r=0T-1gj(Sj,r) recursively. The reason is as follows. In the first stage, each g1(y,r) function is convex, but we choose a single S1 that minimizes r=0T-1g1(S1,r). In the second stage, g2(y,r) calls g1(min{S1,y},r), and g2 is no longer convex, because S1 is not

Numerical study

This section provides a numerical study to investigate how system parameters affect cycle-count policies. These numerical observations will lead to guidelines for designing effective cycle-count policies.

We use our heuristic base-stock policy to answer these questions through a sensitivity analysis study. We focus our discussion on both two-stage and four-stage systems. The parameters we use in the sensitivity analysis are as follows: For the two-stage system, the parameters

Conclusion

Inventory record inaccuracy is a prevalent issue that affects supply chain performance. While common mitigation approaches such as conducting cycle counts and installing inventory tracking systems have been adopted by many firms, there are no clear guidelines in the literature on how to design cycle-count policies from the perspective of the entire supply chain. This paper aims to shed light on this issue.

For a two-stage system, we prove that with identical errors and counting costs at both

Acknowledgements

The authors would like to thank Zhijie Tao and Hang Bai for their help with computation, Bill Hardgrave for useful discussions and the Editor, and the anonymous reviewers for their helpful suggestions.

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