A Monge Sequence-Based Approach to Characterize the Competitive Newsvendor Problem

Replicating cash flows of multiple agents in game-theoretic settings tends to be a challenging task. In this paper, we consider the competitive newsvendor game where multiple newsvendors choose inventory levels before demand arrival and the unmet demand of each newsvendor spills over to multiple other newsvendors. We show that this spillover behavior and the resulting cash flows of each newsvendor can be replicated within a transportation problem after assigning artificial costs on spillover behavior. This replication provides an opportunity to study structural properties of the problem, as well as determine the equilibrium of the game. This paradigm of using artificial costs within an optimization framework to replicate agents’ cash flows can be used in many other games as well.

Bartering: Price-Setting Newsvendor Problem with Barter Exchange

Barter exchange is a system of swapping goods or services for other goods or services in a moneyless and direct manner. Barter has become an effective model of a circular economy because it reduces the consumption impact. Bartering maximizes the utility of assets and existing resources, and can unleash the unspent social, economic, and environmental value of underutilized assets. The present article analyzes the price-setting newsvendor problem with a barter exchange option. The retailer facing a stochastic price-dependent demand sells a product on the market and, additionally, needs another product for its own purposes. Therefore, first, the retailer trades the unsold product for the product it needs by means of barter, and next disposes of the unsold product at a discounted price at the end of the selling season. The retailer’s optimal order quantity and optimal price are derived assuming additive uncertainty in demand. This type of demand function has special characteristics, for example, the actual demand may attain negative values in times of economic uncertainty. The possibility of negative demand realizations is taken into consideration in the study. It proves that, in certain cases, the optimal solution belongs to the set of high barter prices which implies that the actual demand may be negative.

A Prescriptive Machine-Learning Framework to the Price-Setting Newsvendor Problem

The approach to data-driven optimization described in this paper was developed when the authors were part of an IBM project team working with the U.S. Department of Energy, Pacific National Laboratory, and various energy utility partners on an initiative to develop a smart energy distribution infrastructure. Within this broader scope and based on the data collected in some initial controlled experiments, the paper specifically addresses the design and optimization of real-time price incentives to consumers to manage their electricity demand and determine the energy capacity to be provisioned by the utility. This latter problem fits into the well-known price-setting newsvendor problem framework, and our goal was to replace the simplistic methods in the literature by more realistic data-driven methods to take into account the data-collection capabilities and the modeling complexity of real-world applications. Our aspirations for the paper are (1) to introduce data-driven, distribution-free approaches to decision-making problems and (2) to motivate scalable conditional value-at-risk regression-based approaches for these problems.

A Robust Data-Driven Approach for the Newsvendor Problem with Nonparametric Information

Problem definition: For the standard newsvendor problem with an unknown demand distribution, we develop an approach that uses data input to construct a distribution ambiguity set with the nonparametric characteristics of the true distribution, and we use it to make robust decisions. Academic/practical relevance: Empirical approach relies on historical data to estimate the true distribution. Although the estimated distribution converges to the true distribution, its performance with limited data is not guaranteed. Our approach generates robust decisions from a distribution ambiguity set that is constructed by data-driven estimators for nonparametric characteristics and includes the true distribution with the desired probability. It fits situations where data size is small. Methodology: We apply a robust optimization approach with nonparametric information. Results: Under a fixed method to partition the support of the demand, we construct a distribution ambiguity set, build a protection curve as a proxy for the worst-case distribution in the set, and use it to obtain a robust stocking quantity in closed form. Implementation-wise, we develop an adaptive method to continuously feed data to update partitions with a prespecified confidence level in their unbiasedness and adjust the protection curve to obtain robust decisions. We theoretically and experimentally compare the proposed approach with existing approaches. Managerial implications: Our nonparametric approach under adaptive partitioning guarantees that the realized average profit exceeds the worst-case expected profit with a high probability. Using real data sets from Kaggle.com, it can outperform existing approaches in yielding profit rate and stabilizing the generated profits, and the advantages are more prominent as the service ratio decreases. Nonparametric information is more valuable than parametric information in profit generation provided that the service requirement is not too high. Moreover, our proposed approach provides a means of combining nonparametric and parametric information in a robust optimization framework.

Alterations of Cerebral Hemodynamics and Network Properties Induced by Newsvendor Problem in the Human Prefrontal Cortex

While many publications have reported brain hemodynamic responses to decision-making under various conditions of risk, no inventory management scenarios, such as the newsvendor problem (NP), have been investigated in conjunction with neuroimaging. In this study, we hypothesized (I) that NP stimulates the dorsolateral prefrontal cortex (DLPFC) and the orbitofrontal cortex (OFC) joined with frontal polar area (FPA) significantly in the human brain, and (II) that local brain network properties are increased when a person transits from rest to the NP decision-making phase. A 77-channel functional near infrared spectroscopy (fNIRS) system with wide field-of-view (FOV) was employed to measure frontal cerebral hemodynamics in response to NP in 27 healthy human subjects. NP-induced changes in oxy-hemoglobin concentration, Δ[HbO], were investigated using a general linear model (GLM) and graph theory analysis (GTA). Significant activation induced by NP was shown in both DLPFC and OFC+FPA across all subjects. Specifically, higher risk NP with low-profit margins (LM) activated left-DLPFC but deactivated right-DLPFC in 14 subjects, while lower risk NP with high-profit margins (HM) stimulated both DLPFC and OFC+FPA in 13 subjects. The local efficiency, clustering coefficient, and path length of the network metrics were significantly enhanced under NP decision making. In summary, multi-channel fNIRS enabled us to identify DLPFC and OFC+FPA as key cortical regions of brain activations when subjects were making inventory-management risk decisions. We demonstrated that challenging NP resulted in the deactivation within right-DLPFC due to higher levels of stress. Also, local brain network properties were increased when a person transitioned from the rest phase to the NP decision-making phase.