Variable selection framework for allocating products to recommended replenishment models in VMI applications

The purpose of this paper is to propose a multivariate-based method to classify products in replenishment categories based on principal component analysis (PCA) along with two classification algorithms, k-nearest neighbor (KNN) and linear discriminant analysis (LDA).

In the propositions, PCA is applied to data describing products’ features and demand behavior, and a variable importance index (VII) is derived based on PCA parameters. Next, products are allocated to inventory replenishment models applying the KNNs to all original variables; the classification accuracy is then assessed. The variable with the smallest VII is removed and a new classification is carried out; this iterative procedure is performed until a single variable is left. The subset yielding the maximum classification accuracy is recommended for future classification. The aforementioned procedure is repeated replacing the KNN by the LDA.

When applied to real data from a consulting company, the KNN classification technique led to higher performance levels than LDA, yielding 89.4 percent average accuracy and retaining about 80 percent of the original variables. On the other hand, LDA reached 87.1 percent average accuracy and retained 95 percent of the variables. Based on such results, the authors’ findings suggest that 14 out of the 24 variables are crucial in determining an inventory replenishment model for a product in a specific location replacement. Several of the retained variables were typically used in reorder point estimation or associated to market profile in specific locals.

The idea of this paper is to remove irrelevant and noisy market metrics that jeopardize the correct allocation of products to the most appropriate replenishment model.