The Analysis of Zero Inventory Drift Variants Based on Simple and General Order-Up-To Policies

The Analysis of Zero Inventory Drift Variants Based on Simple and General Order-Up-To Policies

Jianing He (South China Normal University, China) and Haibo Wang (Texas A&M International University, USA)
Copyright: © 2010 |Pages: 16
DOI: 10.4018/jamc.2010070103
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In this paper, simple and general Order-Up-To (OUT) models with Minimum Mean Square Error (MMSE) forecast for the AR(1) demand pattern are introduced in the control engineering perspective. Important insights about lead-time misidentification are derived from the analysis of variance discrepancy. By applying the Final Value Theorem (FVI), a final value offset (i.e., inventory drift) is proved to exist and can be measured even though the actual lead-time is known. In this regard, to eliminate the inherent offset and keep the system variances acceptable, two kinds of zero inventory drift variants based on the general OUT model are presented. The analysis of variance amplification suggests lead-times should always be estimated conservatively in variant models. The stability conditions for zero inventory drift variants are evaluated in succession and some valuable attributes of the new variants are illustrated via spreadsheet simulation under the assumption that lead-time misidentification is inevitable.
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2. Literature Review

After searching papers concerning inventory drift, much fewer were found than we expected. Two seminal papers, written by John et al. (1994) and Disney and Towill (2005) respectively, both worked on APVIOBPCS model or OUT policy with independent and identically distributed (i.i.d.) demand and exponential smoothing forecasting. John et al. (1994) first examined the existence of inventory drift using the Final Value Theorem (FVT) when the lead-time estimation was not accurate. Then Disney and Towill (2005) presented a novel Estimated Pipeline Variable Inventory and Order Based Production Control System (EPVIOBPS) to eliminate the inventory drift instead of monitoring actual lead-times continuously. When facing different demand patterns or using different forecasting methods, sometimes the inventory deficit is inherent even though the accurate lead-time is known. Is the solution presented still effective? No clear answer has been found so far based on the literature. However, we prove the solution presented by Disney and Towill (2005) is not suitable for OUT policy with Minimum Mean Square Error (MMSE) forecast, which will be explained later in this article.

An outstanding order policy not just has zero inventory drift. As stated by Disney et al. (2006), inventory managers must balance two primary factors on making replenishments. One is the order variability measured by the bullwhip effect (i.e., the ratio of the variance of orders over the variance of demand). The other is the variance of the net stock measured by the net stock amplification (i.e., the ratio of net stock variance over the variance of demand). Trying to dampen the bullwhip effect may have a negative impact on net stock amplification and vice versa (Disney et al., 2006).

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