# Integrating the Department of Defense Supply Chain: Techincial Report

By Eric Peltz; Marc Robbins | Go to book overview

APPENDIX B
Inventory Performance Analysis

Generalized Boosted Model

This analysis examines the effects of different factors on measures of inventory performance: material availability/backorder rate, inventory turns, maximum months of supply on hand, and maximum length of stock-out periods. Linear regression will not work well since the data do not fit the assumptions (e.g., linearity and normality), so another statistical technique, the Generalized Boosted Model (GBM), that does not face the same problems was employed.

The results that follow indicate the relative influence of the factors considered. The relative influence of a factor or covariate is the percentage reduction in absolute error attributable to that factor.

The population of items covered in the analysis consists of the top 20,000 NIINs (DVDs are excluded, based upon a July 2011 snapshot of what items are DVD versus DLA direct) in terms of the extended value of demand in CY 2010 that had four or more demands resulting in 16,469 items. The analysis is based on demands, backorders, and inventory levels for these NIINs between August 2008 and July 2011.

GBM Description

GBM adds together many simple functions of the covariates (usually piecewise constants or simple regression trees) to estimate a smooth function of a large number of covariates. GBM is an algorithm that at each iteration adds to the previous iteration model a simple regression tree model. At every step, the algorithm essentially looks for a small adjustment to the prior iteration model that improves the fit of the model to the data.

The number of iterations determines the model complexity, and it is derived from the data. Generally the best number of iterations is determined by stopping rules that choose the number of iterations that maximizes the predictive performance of the model on an independent data set. This analysis was run using a five-fold cross-validation. See Tables B.1 and B.2.

Because the final GBM model is a sum of regression trees, it has many of the good properties of regression trees. Trees can handle continuous, nominal, ordinal, and missing covariates. They are flexible because they can capture nonlinear effects and interaction terms. Trees are invariant to one-to-one transformation of the covariates and can handle large number of covariates even if correlated among each other.

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