Dynamic Procurement of New Products with Covariate Information: The Residual Tree Method

Abstract

Problem definition:We study the practice-motivated problem of dynamically procuring a new, short life-cycle product under demand uncertainty. The firm does not know the demand for the new product but has data on similar products sold in the past, including demand histories and covariate information such as product characteristics.Academic/practical relevance: The dynamic procurement problem has long attracted academic and practitioner interest, and we solve it in an innovative data-driven way with proven theoretical guarantees.This work is also the first to leverage the power of covariate data in solving this problem.Methodology: We propose a new, combined forecasting and optimization algorithm called the Residual Tree method, and analyze its performance via epi-convergence theory and computations. Our method generalizes the classical Scenario Tree method by using covariates to link historical data on similar products to construct demand forecasts for the new product.Results: We prove, under fairly mild conditions, that the Residual Tree method is asymptotically optimal as the size of the data set grows. We also numerically validate the method for problem instances derived using data from the global fashion retailer Zara. We find that ignoring covariate information leads to systematic bias in the optimal solution, translating to a 6-15% increase in the total cost for the problem instances under study. We also find that solutions based on trees using just 2-3 branches per node, which is common in the existing literature, are inadequate, resulting in 30-66% higher total costs compared with our best solution.Managerial implications: The Residual Tree is a new and generalizable approach that uses past data on similar products to manage new product inventories. We also quantify the value of covariate information and of granular demand modeling.for apparel articles may include the procurement cost, retail price, colour, item type (e.g., sweater, t-shirt, etc.), fabric, design style (e.g., sporty, classic), expert predictions of the product's popularity, etc. We refer to covariates tied to product attributes that do not change over time as "static." Our approach can also account for "dynamic" covariates-e.g., lagged demand observations included to naturally account for demand auto-correlations. Importantly, covariates are essential for accounting for product heterogeneity by providing a means for aligning demand observations across different products. This allows us to construct a large number of estimated demand trajectories relevant to the new product, which we can then use in a scenario-based model of forecast updating dynamics.Our method employs a new approach which we call the Residual Tree method, which can be used to solve general multi-stage stochastic programs where there is no information about the

Cross‐item learning for volatile demand forecasting: An intervention with predictive analytics

“…Although Alpha has no detailed knowledge about family structures of item sets used by EMS clients, or specific bills of materials, executives are adamant that they are required to supply all requested items that are part of manufacturing inventories and operationally-related (Hopp & Spearman, 2011;Orlicky, 1975). This suggests that realized demands across items and plants, in spite of individual differences, are likely to share some common patterns motivating a cross-item learning initiative (Ban et al, 2019;Bojer & Meldgaard, 2021). Hence, in addition to the item-wise temporal aggregation with a frequency of L weeks based on operational lead time, we performed cross-item aggregation by pooling temporarily aggregated observations of individual items into an n items by T/L blocks panel data set.…”

“…The resulting data structure enables learning algorithms (e.g., regression, tree, neural nets) to leverage multi-item information for cross-learning of demand patterns (Loureiro, Migueis, & da Silva, 2018;Ren, Chan, & Ram, 2017;Ren & Choi, 2016;Ren, Choi, & Liu, 2015). Cross-individual pooling has been found to be useful for prediction problems in retailing (Ban et al, 2019;Chuang, Oliva, & Perdikai, 2016), and has the added benefit of compensating for information loss in temporal aggregation, which reduces the number of available observations for model building at the item level (Petropoulos & Kourentzes, 2015).…”

“…This motivated us to reframe the prediction problem and pool demand data temporally and across items into a single model, as opposed to fitting individual-item models, to learn common functional relationships for the prediction tasks. The aggregation of items into a single model, that is, cross-item learning, is methodologically robust (Ban, Gallien, & Mersereau, 2019;Wu, Chen, Yang, & Tindall, 2021) and becoming increasingly popular (Bojer & Meldgaard, 2021). Our first iteration tested the single model approach using a machine learning algorithm to exploit data features from relevant demand forecasting theories.…”

Data Analytics in Operations Management: A Review

“…The paper shows how the approach is able to close the cost gap between the naive approach (which does not consider contextual data) and the perfect foresight approach (which knows demands before they are realized) by 88%. Ban et al (2018) consider the problem of dynamic procurement. In this problem, one has to decide how much of a product to order over a finite time horizon from different sources which have different lead times and different costs, so as to meet uncertain demand over the horizon.…”

Data Analytics in Operations Management: A Review

“…The paper shows how the approach is able to close the cost gap between the naive approach (which does not consider contextual data) and the perfect foresight approach (which knows demands before they are realized) by 88%. Ban et al (2018) consider the problem of dynamic procurement. In this problem, one has to decide how much of a product to order over a finite time horizon from different sources that have different lead times and different costs so as to meet uncertain demand over the horizon.…”