Newsvendor Research Articles

End-to-End Learning for Optimization via Constraint-Enforcing Approximators

In many real-world applications, predictive methods are used to provide inputs for downstream optimization problems. It has been shown that using the downstream task-based objective to learn the intermediate predictive model is often better than using only intermediate task objectives, such as prediction error. The learning task in the former approach is referred to as end-to-end learning. The difficulty in end-to-end learning lies in differentiating through the optimization problem. Therefore, we propose a neural network architecture that can learn to approximately solve these optimization problems, particularly ensuring its output satisfies the feasibility constraints via alternate projections. We show these projections converge at a geometric rate to the exact projection. Our approach is more computationally efficient than existing methods as we do not need to solve the original optimization problem at each iteration. Furthermore, our approach can be applied to a wider range of optimization problems. We apply this to a shortest path problem for which the first stage forecasting problem is a computer vision task of predicting edge costs from terrain maps, a capacitated multi-product newsvendor problem, and a maximum matching problem. We show that this method out-performs existing approaches in terms of final task-based loss and training time.

A deep learning-based approach to a newsvendor problem considering uncertainty and time-varying costs

A deep learning-based approach to a newsvendor problem considering uncertainty and time-varying costs

Clustering retail stores for inventory transshipment

Rapid growth in the world of e-commerce is forcing traditional retailers to rethink their operational efficiency and revenue/cost streams. Retailers are facing increasing pressure to better utilize in-store inventory and reduce end-of-season markdowns. Transshipments between stores can re-balance inventory levels while preventing shortages and backorders. However, the joint inventory and transshipment problem is difficult to optimize in an extensive network, and many retailers lack the capital and managerial bandwidth required to create a system capable of transshipments between any two stores in a network of hundreds. We consider two multi-location newsvendor problems with reactive and proactive transshipments, respectively. We propose clustering stores into transshipment groups while considering both demand correlation and physical distance between locations. Since minimizing demand correlation does not follow the triangle inequality, we introduce two modified clustering algorithms that outperform existing algorithms for distance- and correlation-based clustering. For a given set of clusters, we mathematically model these two problems considering total system profit. In addition, we quantify the performance of distance-based and correlation-based clustering under several inventory ordering and transshipment policies to show the robustness of our results. To verify our methods, we test the proposed methodology using grocery sales data from IRi over three years in Houston and Dallas, TX and liquor licensee purchase information over three years from the Iowa state government. We present correlation, transshipment, and profitability analysis. We show that when demand correlation is present and stable over time, clustering based on demand correlation can maintain high transshipments and profits while decreasing solution complexity.

Cross-Border Capacity Planning in Air Traffic Management Under Uncertainty

In European air traffic management (ATM), it is an important decision how much capacity to provide for each airspace, and it has to be made weeks or even months in advance of the day of operation. Given the uncertainty in demand that may materialize until then along with variability in capacity provision (e.g., due to weather), Airspace Users could face high costs of displacements (i.e., delays and reroutings) if capacity is not provided where and when needed. We propose a new capacity sharing scheme in which some proportion of overall capacities can be flexibly deployed in any of the airspaces of the same alliance (at an increased unit cost). This allows us to hedge against the risk of capacity underprovision. Given this scheme, we seek to determine the optimum budget for capacities provided both locally and in cross-border sharing that results in the lowest expected network costs (i.e., capacity and displacement costs). To determine optimum capacity levels, we need to solve a two-stage newsvendor problem: We first decide on capacities to be provided for each airspace, and after uncertain demand and capacity provision disruptions have materialized, we need to decide on the routings of flights (including delays) as well as the sector opening scheme of each airspace to minimize costs. We propose a simulation optimization approach for searching the most cost-efficient capacity levels (in the first stage), and a heuristic to solve the routing and sector opening problem (in the second stage), which is [Formula: see text]-hard. We test our approach in a large-sized simulation study based on real data covering around 3,000 flights across Western European airspace. We find that our stochastic approach significantly reduces network costs against a deterministic benchmark while using less computational resources. Experiments on different setups for capacity sharing show that total variable costs can be reduced by more than 8% if capacity is shared across borders: even though we require that no airspace can operate lower capacities under capacity sharing than without (this is to avoid substitution of expensive air traffic controllers with those in countries with a lower wage level). We also find that the use of different technology providers is a major obstacle to reap the benefits from capacity sharing and that sharing capacities across airspaces of the same country may instead be preferred. History: This paper has been accepted for the Transportation Science Special Issue on Emerging Topics in Transportation Science and Logistics. Funding: This work was supported by the Horizon 2020 Framework Programme [893380]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.1210 .

Bayesian Inventory Control: Accelerated Demand Learning via Exploration Boosts

In the Bayesian newsvendor problem, it is known that the optimal decision is always greater than or equal to the myopic decision. As a result, the optimal decision can be expressed as the sum of the myopic decision plus a nonnegative “exploration boost.” In “Bayesian Inventory Control: Accelerated Demand Learning via Exploration Boosts,” Chuang and Kim characterize the form of the exploration boost in terms of basic statistical measures of uncertainty. This characterization expresses in clear terms the way in which the statistical learning and inventory control are jointly optimized; when there is a high degree of parameter uncertainty, inventory levels are boosted to induce a higher chance of observing more sales data to more quickly resolve statistical uncertainty, and as parameter uncertainty resolves, the exploration boost is reduced.

A co-opetitive newsvendor model with product substitution and a wholesale price contract

When an original equipment manufacturer (OEM) sources key components from one contract manufacturer (CM), the CM may produce its own-brand product to compete against the OEM. Therefore, these two firms have a co-opetitive relationship. We develop a co-opetitive newsvendor model in which two newsvendors (OEM and CM) compete against each other in the format of product substitution. Moreover, the CM also serves as the only supplier to the OEM. We find that whether the CM’s final product is substitutable for the OEM’s product is the prerequisite condition that allows the CM to utilize its monopoly power in the key component market and earn extra profits. This result implies that being the only key component supplier of another newsvendor cannot automatically bring extra profits to the CM, except that the CM’s final product has a reasonable competitive advantage against the OEM’s final product. Furthermore, relative to the output of the purely competitive supply chain, the co-opetitive supply chain can achieve higher joint profits if the CM can fully compete against the OEM, i.e., the CM’s product can be treated as a perfect substitute for the OEM’s product. We also find that in the traditional selling to the newsvendor setting, when effective demand increases, the retailer (OEM) could be less profitable. Furthermore, we extend the discussion to the cases of horizontal decentralization and Nash bargaining. A parallel Cournot competition case is also discussed.

Design and value analysis of the blockchain-based port logistics financial platform

ABSTRACT Time-consuming ocean transportation for international trades requires enterprises to advance payments for goods, which can be fatal for small and medium enterprises with insufficient self-owned capital. Logistics finance is an effective solution for tackling this problem. However, traditional logistics finance has long been plagued by information asymmetry, tremendous paperwork, and long financing cycles. As a distributed database with characteristics of transparency, traceability, and immutability, blockchain technology shows good potential in addressing pain points on traditional logistics financing platforms. This paper focuses on the operational mechanism and value analysis of the blockchain-based port logistics finance platform. The conceptual architecture of the blockchain-based port logistics finance platform is constructed, and a value analysis model based on the Newsboy Model is established for quantitatively analysing the platform’s value. The results revealed that the introduction of the blockchain into port logistics financing can significantly improve small to medium-sized enterprises’ profitability by providing reliable financing channels. The results also indicate that participants’ profit on the blockchain-based platform may be influenced by the speed of market expansion, initial capital size, and financing cost. This paper also discusses theoretical and managerial implications by providing insights into the participants’ decision-making on the platform under different constraints.

Pareto Optimal Solution of a Fuzzy Newsboy Problem

In this paper, a multi-item classical newsboy problem is formulated, occurring both fuzziness and randomness with floor space constraint. Here, the demand is considered as a random variable in fuzzy sense and also the purchase cost, salvage value, and selling price are fuzzy numbers. Initially, a method is explained for solving such a problem by using the minimization of a FN by Buckley [Buckley, JJ (2003). Fuzzy probabilities: New approach and applications]. Then the fuzzy programming technique, [Formula: see text]-constraint, and the weighted sum methods are applied to handle the multiobjective programming problem. The basic idea for transforming the fuzzy stochastic programming problem into a deterministic equivalent has been discussed. Finally, the deterministic model is solved by the LINGO package and is illustrated numerically.

Supply chain price variability under the buyback contract

ABSTRACT Supply chain price variability, also known as the “Bullwhip effect in Pricing (BP),” refers to the absorption or amplification of the variability of prices from one stage to another in a supply chain. This article derives analytical conditions that result in BP considering a buyback contract and conducts numerical simulations to gain further insights. For this, a joint price and replenishment setting newsvendor model with a wholesale-Stackelberg game is considered. Two demand types (linear and isoelastic) are analyzed along with uniformly and normally distributed additive and multiplicative uncertainties. The outcome of this research reveals that the main influential factors that affect BP are the structure and error type of the demand functions. Absorption (amplification) in price fluctuations occurs for linear (isoelastic) demand cases. Moreover, the price variances and BP ratios differ under the buyback and wholesale-price-only cases. The overall results help understand the fluctuation of market prices under various conditions.

How Big Should Your Data Really Be? Data-Driven Newsvendor: Learning One Sample at a Time

We study the classical newsvendor problem in which the decision maker must trade off underage and overage costs. In contrast to the typical setting, we assume that the decision maker does not know the underlying distribution driving uncertainty but has only access to historical data. In turn, the key questions are how to map existing data to a decision and what type of performance to expect as a function of the data size. We analyze the classical setting with access to past samples drawn from the distribution (e.g., past demand), focusing not only on asymptotic performance but also on what we call the transient regime of learning, that is, performance for arbitrary data sizes. We evaluate the performance of any algorithm through its worst-case relative expected regret, compared with an oracle with knowledge of the distribution. We provide the first finite sample exact analysis of the classical sample average approximation (SAA) algorithm for this class of problems across all data sizes. This allows one to uncover novel fundamental insights on the value of data: It reveals that tens of samples are sufficient to perform very efficiently but also that more data can lead to worse out-of-sample performance for SAA. We then focus on the general class of mappings from data to decisions without any restriction on the set of policies and derive an optimal algorithm (in the minimax sense) and characterize its associated performance. This leads to significant improvements for limited data sizes and allows to exactly quantify the value of historical information. This paper was accepted by David Simchi-Levi, data science. Supplemental Material: The data files and online appendix are available at https://doi.org/10.1287/mnsc.2023.4725 .

Supermodularity in Two-Stage Distributionally Robust Optimization

In this paper, we solve a class of two-stage distributionally robust optimization problems that have the property of supermodularity. We exploit the explicit worst case expectation of supermodular functions and derive the worst case distribution for the robust counterpart. This enables us to develop an efficient method to obtain an exact optimal solution to these two-stage problems. Further, we provide a necessary and sufficient condition for checking whether any given two-stage optimization problem has the supermodularity property. We also investigate the optimality of the segregated affine decision rules when problems have the property of supermodularity. We apply this framework to several classic problems, including the multi-item newsvendor problem, the facility location problem, the lot-sizing problem on a network, the appointment-scheduling problem, and the assemble-to-order problem. Whereas these problems are typically computationally challenging, they can be solved efficiently under our assumptions. Finally, numerical examples are conducted to illustrate the effectiveness of our approach. This paper was accepted by Chung Piaw Teo, optimization. Funding: This work was supported by the National Natural Science Foundation of China [Grant 71971187], and Hong Kong Research Grants Council [Collaborative Research Fund (C6103-20GF), General Research Fund (14210821, 16204521, 16212419)]. Supplemental Material: The online appendix and data are available at https://doi.org/10.1287/mnsc.2023.4748 .

Solving a Distribution-Free Multi-Period Newsvendor Problem With Advance Purchase Discount via an Online Ordering Solution

In this paper, we study a distribution-free multi-period newsvendor problem with advance purchase discount (APD). In addition to the regular-order placed at the beginning of each period, a decision-maker (DM) can also commit to an advance-order from the upstream supplier and receive discounts. The goal of the DM is to maximize total profits, and in this problem, the DM only has access to past demand data. To solve this problem, we apply an online method based on the theory of prediction and learning with expert advice to propose an explicit online ordering solution by using the fixed-stock policy as expert advice. With the properties of the gain function, we derive a theoretical result that guarantees, for any given advance-order quantity, the newsvendor’s cumulative gains achieved by the proposed online ordering solution converge to those from the best expert advice in hindsight for a sufficient large horizon. In addition, we extend the problem to the discrete case and obtain the corresponding explicit strategy and performance guarantee. Finally, numerical studies illustrate the effectiveness of the proposed solution, and the newsvendor’s total profits are comparable to the best expert advice. Sensitivity analysis also shows the robustness of the proposed solution.

A Newsvendor Problem Considering Decision Biases of Strategic Customers with Private Product Value Information

In this paper, we consider a newsvendor system with strategic customers, who are boundedly rational and risk averse in terms of buying during the selling season or waiting for a clearance sale with price discounts. The newsvendor’s decision is to determine the optimal stock quantity. An optimization problem is formulated with the incorporation of competition among strategic customers with private product value information. We embed risk aversion within the quantal response equilibrium to characterize the strategic customer behavior. The influences of the decision biases of strategic customers on the newsvendor’s decision and profit are discussed. We find that the risk aversion considered alone always benefits the newsvendor. However, the bounded rationality considered alone benefits the newsvendor conditionally. Combining the two behavioral factor influences, the decision biases cause the newsvendor to order more and be better off when the critical fractile is high but to order less and be worse off when the critical fractile is low.

Research on Pricing Decision Considering Advertising Benefit and Consumer Psychological Benefit

For perishable goods, the optimal pricing models studied by current scholars seldom consider price effect, psychological benefit and consumption time. Based on the current basic newsboy model, this paper focuses on the price characteristics and consumer psychology of perishable products under the background of single dealer, in order to build a complete optimal price decision model of perishable products. According to the two-stage ladder pricing of perishable products in the pricing stage, this paper constructs the optimal price decision model of dealers in different sales stages by representing consumer demand and dealer profit equation, so as to provide enterprises with the maximum optimal strategy. Moreover, sensitivity analysis of parameters in the model is carried out to ensure the stability of the model.

Transportation Asset Acquisition under a Newsvendor Model with Cutting-Stock Restrictions: Approximation and Decomposition Algorithms

Logistics service providers use transportation assets to offer services to their customers. To cope with demand variability, they may acquire additional assets on a one-off (spot) basis. The planner’s problem is to determine the optimal level of assets acquired upfront, such that their cost is minimized, for a given planning horizon. Our formulation captures a nontrivial complication: Although ordering quantities are pertinent to asset acquisition, customer demand is in the form of service requests. Not only does each request have a stochastic duration, but also the total number of requests per customer is uncertain. We introduce a two-stage newsvendor model where demand for spot assets is derived through optimal cutting-stock patterns. Leveraging results from bin-packing, we propose polynomial algorithms that have worst-case guarantees for upper and lower bounds. Our method finds optimal solutions to instances intractable by commercial solvers. We investigate demand variability by means of a factorial experiment. We find that, whereas variability in the number of requests leads to higher costs, variability in each request’s duration can reduce costs. Finally, we demonstrate the modularity of our approach with two extensions: asset routing and outsourcing. Our results provide a practical approach to transportation asset acquisition and offer insights on the differing impact of demand uncertainty on the total acquisition cost. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.1201 .

Dynamic ordering and buyer selection policies when service affects future demand

Make-to-stock suppliers selling to regular buyers must balance the cost of overstocking against the cost of buyers’ reactions when items become unavailable. In selecting which buyers to satisfy when shortages occur, they must weigh the current revenue from the satisfied buyers against the loss in future demand from the dissatisfied buyers. To provide insight and decision support on these trade-offs, we (i) develop a novel newsvendor model of a firm with heterogeneous buyers with service-dependent demand, (ii) provide properties of the optimal ordering and buyer selection decisions of the firm, and (iii) derive a novel Lagrangian Relaxation (LR)-based index policy for selecting buyers and compare it with two other LR-based index policies. The model concerns a firm that orders items for a group of repeat buyers who generate different revenues and visit the firm with different average rates that depend on whether they are satisfied or dissatisfied with their last visit. The firm selects which buyers to serve if the demand exceeds the order quantity (current capacity). For two buyers, we show that a fixed order quantity (FOQ) policy and an index buyer selection policy are optimal. For more buyers, the optimal policy involves overstocking (understocking) when the overall buyer satisfaction is high (low) and selecting buyers that maximize the current revenue (future demand) when the overall buyer satisfaction after the demand is high (low). To tackle the problem, we derive three LR-based index policies: a Lagrangian index policy that uses a uniform capacity price, a Whittle index policy that uses a discriminatory capacity price and is myopically optimal, and a novel “active-constraint” index policy that uses a discriminatory capacity price when the capacity constraint is active. Numerical results indicate that the latter policy is near-optimal and outperforms the other two and that combining it with the right FOQ policy can be very efficient.

Analyzing learning effects in the newsvendor model by probabilistic methods

In this paper, we discuss discrete choice theory and show how this theory can be used to quantify learning effects in experimental studies. We argue why the ordering quantities in newsvendor experiments should follow a multinomial logit distribution. We provide a robustness analysis to explain that the standard conditions for logit distributions can be relaxed considerably. A main finding is that when optimal parameter values are inferred from the empirical data, the model predicts observed orders well. This provides empirical evidence for a multinomial logit distribution in such experiments. Finally, we analyze the learning effect using the experimental data collected by Bolton et al. (2012).

Distributionally Robust Trading Strategies for Renewable Energy Producers

Renewable energy generation is offered through electricity markets, quite some time in advance. This then leads to a problem of decision-making under uncertainty, which may be seen as a newsvendor problem. Contrarily to the conventional case for which underage and overage penalties are known, such penalties in the case of electricity markets are unknown, and difficult to estimate. In addition, one is actually only penalized for either overage or underage, not both. Consequently, we look at a slightly different form of a newsvendor problem, for a price-taker participant offering in electricity markets, which we refer to as Bernoulli newsvendor problem. After showing that its solution is consistent with that for the classical newsvendor problem, we then introduce distributionally robust versions, with ambiguity possibly about both the probabilistic forecasts for power generation and the chance of success of the Bernoulli variable. Both versions of the distributionally robust Bernoulli newsvendor problem admit closed-form solutions. We finally use simulation studies, as well as a real-world case-study application, to illustrate the workings and benefits from the approach.

A Newsboy Model for Cross-Selling Products with Demand Impacted by Price

Cross-selling refers to the fact that customers may purchase another product related to them while purchasing one product, or the loss of sales opportunities for another product due to the shortage of one product. Considering the impact of price and cross-selling products on demand, the newsboy problem in the centralized decision-making environment is studied. In the centralized decision-making environment, consider a single retailer, pay attention to the sum of expected returns of all products, and propose the first-order necessary condition for the existence of the maximum value of the return function, which provides the basis for retailers to make decision-making strategies.

Data-driven risk-averse newsvendor problems: developing the CVaR criteria and support vector machines

Incorporating decision-makers' risk preferences into data-driven newsvendor models and developing machine learning methods to solve the models are the challenging problems addressed in this study. To consider different distributions and decision-makers' different risk preferences for the two losses of the total cost newsvendor model, the symmetrical, the partial symmetrical and the asymmetrical CVaR criteria are introduced. The regularisation, the primal-dual approach and the kernels in support vector machines are used to transform the data-driven risk-averse newsvendor problems under the CVaR criterion into the convex quadratic programming problems with good theoretical properties. Computational experiments are conducted on a real-world dataset. The models under the partial symmetrical and the asymmetrical CVaR criteria obtained good performances, but that under the symmetrical CVaR criterion suffered the underfitting problem. Two factors including the degrees of risk aversion for the two losses in the total cost newsvendor model and the empirical errors of data-driven models affect order decisions. The degrees of risk aversion for the two losses have anti-directional effects on order quantities. The introduction of asymmetrical CVaR criterion paves a new way to reveal the effects of different risk references for different losses on order decisions, and has the potential to improve newsvendor decisions.