For new, short-life-cycle products such as fashion items, the selling seasons are short, but their order lead times are relatively long; hence, firms have no or limited replenishment opportunities. Moreover, there is no historical record of sales/demand for each new product, which poses a considerable challenge for firms in procurement decisions. However, a firm may have sold similar products in the past and maintain a good record of them. In addition to sale/demand figures, the data record may contain rich information about the attributes (covariate information) of those products, such as retail price, color, item type (e.g., shirt, pant), fabric, design style (e.g., casual, sporty), store type, season, etc., in the case of fashion clothing. Using covariate information, we attempt to link the new product to similar products that were sold historically via machine learning prediction models, such as k-nearest neighbors, classification and regression trees, and random forests. Motivated by real-world problems, two basic model settings are considered in Chapter 3 and Chapter 4. The first is a single-period (newsvendor) problem, and the second is a two-period problem, both of which we believe to be highly representative of realistic situations for many short-life-cycle products.

In Chapter 3, we employ a value-at-risk (VaR) constraint to the newsvendor model incorporating covariate information. Specifically, our approach uses predictive machine learning methods to weigh the relative similarity between the new product and historical products. The sample-dependent weights are embedded to approximate the true expected value in the profit function and the VaR constraint in our proposed data-driven formulation. We have some results: First, the resulting formulation can be transformed into a mixed integer program (MIP). Using the quantile structure allows us to convert the MIP into a linear program, which is computationally compatible with solving its risk-neutral counterpart. Second, we prove that the solution to our proposed approximation is asymptotically optimal with the sample-dependent approximation of the VaR constraint. Third, numerical experiments based on real data and synthetic data reveal a few interesting findings, e.g., countering our intuition that a risk constraint should trade off with profit, our experiments show that the VaR constraint to control profit risk can improve out-of-sample profits. In other words, by deploying the VaR constraint, the risk-averse retailer can earn more profit than the risk-neutral retailer. This is attributable to the hedging effect of the constraint against overfitting, which is a common issue in data-driven approaches. We also observe that the order quantity derived from our risk averse model could be either risk seeking or risk averse.

In Chapter 4, we consider a model of two-period dynamic procurement with percentile risk constraints incorporating covariate information and seek to maximize the joint profit while controlling joint-profit risk. We extend the data-driven nonparametric approaches for the dynamic objective function and percentile risk constraints. In particular, the weights in the second period will be adjusted after observing the first-period realized demand. An adaptive response to infeasibility, arising from downside risk concerns, is allowed in our model to avoid conservative planning. We prove that the proposed dynamic approximation is asymptotically optimal with the sample-dependent percentile risk constraints. The approximated formulation can be transformed into a tractable MIP, for which we also derive some dominance cuts to accelerate the computation. Across a series of tests on real data, we observe that forward-looking planning with downside risk awareness can benefit the firm, and as the first-period realized demand is informative, a risk-averse retailer would reduce the first order quantity and mitigate the joint-profit risk via risk-aversion adjustment and an accurate response in the second period.