Determining an optimal hierarchical forecasting model based on the characteristics of the data set: Technical note

• Date: 01 May 2016
• Author: Zlatana D. Nenova,Jerrold H. May
• DOI: http://doi.org/10.1016/j.jom.2016.04.001
• Published date: 01 May 2016

Short communication

Determining an optimal hierarchical forecasting model based on the

characteristics of the data set: Technical note

Zlatana D. Nenova

*

, Jerrold H. May

Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260,USA

article info

Article history:

Received 20 September 2015

Received in revised form

7 April 2016

Accepted 18 April 2016

Available online 28 April 2016

Accepted by: Daniel R. Guide

Keywords:

Forecasting

Hierarchical forecast aggregation

Supply chain management

abstract

The efficient flow of goods and services involves addressing multilevel forecast questions, and careful

consideration when aggregating or disaggregating hierarchical estimates. Assessing all possible aggre-

gation alternatives helps to determine the statistically most accurate way of consolidating multilevel

forecasts. However, doing so in a multilevel and multiproduct supply chain may prove to be a very

computationally intensive and time-consuming task. In this paper, we present a new, two-level oblique

linear discriminant tree model, which identifies the optimal hierarchical forecast technique for a given

hierarchical database in a very time-efficient manner. We induced our model from a real-world dataset,

and it separates all historical time series into the four aggregation mechanisms considered. The sepa-

ration process is a function of both the positive and negative correlation groups' variances at the lowest

level of the hierarchical datasets. Our primary contributions are: (1) establishing a clear-cut relationship

between the correlation metrics at the lowest level of the hierarchy and the optimal aggregation

mechanism for a product/service hierarchy, and (2) developing an analytical model for personalized

forecast aggregation decisions, based on characteristics of a hierarchical dataset.

©2016 Elsevier B.V. All rights reserved.

1. Introduction

Accurate products' demand forecasts facilitate the smooth

movement of goods through a supply network (Sanders and

Manrodt, 2003). Not surprisingly, there exists a nontrivial litera-

ture on the development of guidelines to improve firms' sales

forecasting methodologies (Moon et al., 2003). Such recommen-

dations are particularly useful when creating forecasts for hierar-

chically organized data, for which models are designed to address

managerial requests associated with a single or multiple levels of

the firm's hierarchies. Providing data to support decisions involving

multiple levels of a hierarchy typically requires consolidating hi-

erarchical estimates, such as products' demand forecasts.

To ensure the reliability of their consolidated multilevel fore-

casts, statisticians assess the accuracy of various aggregation al-

ternatives, because selecting an optimal consolidation method

could significantly improve the accuracy of the overallforecast. The

concept of aggregation bias was introduced by Theil (1954). Since

then, researchers have examined the performance of various

aggregation mechanisms. No consensus appears to have been

reached as to which one is optimal. Some authors argue in favor of

the top-down method (Fogarty et al., 1990; Grunfeld andGriliches,

1960; Narasimhan et al., 1995), while others support the use of the

bottom-up approach (Dangerfield and Morris, 1992; Schwarzkopf

et al., 1988). The inconsistent findings lead to the conjecture that

there exists some population of data sets for which top-down ag-

gregation is optimal, and a second population of data sets for which

bottom-up aggregation is optimal. Ideally, we would like to find a

way to describe and separate those two populations of data sets,

and to provide a theoretical justification as to why the data in each

population is best modeled using the particular aggregation tech-

nique. Within the academic community, the search for such de-

scriptors and separators of the two populations has led to the

examination of the association between bottom-level series cor-

relations and optimal forecast aggregations.

Schwarzkopf et al. (1988), limiting their discussion to two

products, note that estimation precision is a function of product

correlation. Estimates based on aggregated data may have a smaller

variance than those based on individual forecasts when the items

are independent, but they may have greater variance when the

items have a strong positive correlation, as well as a much smaller

variance if the items have a strong negative correlation. They

*Corresponding author.

E-mail address: zdn3@pitt.edu (Z.D. Nenova).

Contents lists available at ScienceDirect

Journal of Operations Management

journal homepage: www.elsevier.com/locate/jom

http://dx.doi.org/10.1016/j.jom.2016.04.001

0272-6963/©2016 Elsevier B.V. All rights reserved.

Journal of Operations Management 44 (2016) 62e68