Hierarchical Forecasting with Polynomial Nets M.S. Lauretto, F. Nakano, C.A.B. Pereira, and J.M. Stern Abstract. This article presents a two level hierarchical forecasting model developed in a consulting project for a Brazilian magazine publishing company. The first level uses a VARMA model and considers econometric variables. The second level takes into account qualitative aspects of each publication issue, and is based on polyno- mial networks generated by Genetic Programming (GP). Keywords: Genetic programming, Functional trees, Forecasting, Logistics, Meta- control, Polynomial networks. 1 Introduction This article describes the authors’ consulting project for a leading Brazilian maga- zine publishing company, nicknamed ABC, and its associated distributor company, nicknamed DE. One of the major logistic challenges of this business is the classic newsstand, newsvendor or newsboy problem, asking for optimal inventory levels. The standard operations research models for this problem assume fixed prices and random demand, see Hadley and Whitin (1963) and Denardo (1982). The inventory levels are then optimized in order to minimize the costs of being either over or under stocked. The cost of overstock is captured by a well known Brazilian proverb stating that “a day-old newspaper is only good for wrapping fish”. Unfortunately, old magazines do not even have that use. In most cases, only the cover page of unsold magazines are stripped and sent back some way along the distribution channel for control purposes, while the rest is recycled at the nearest paper factory. The immediate cost of under stock is lost sales. The long term costs of under stock include customer frustration, possibly leading to permanent fidelity or loyalty transfer to another magazine, low visibility, loss of mind and market share, etc. M.S. Lauretto, F. Nakano, C.A.B. Pereira, and J.M. Stern University of S˜ ao Paulo, Brazil e-mail: {lauretto,nakano}@ime.usp.br K. Nakamatsu et al. (Eds.): New Advan. in Intel. Decision Techno., SCI 199, pp. 305–315. springerlink.com c  Springer-Verlag Berlin Heidelberg 2009