Newsvendor Research Articles

On the optimal solution of a distributionally robust multi-product newsvendor problem

This paper derives the optimal solution for a distributionally robust multi-product newsvendor problem, in which different products are produced under a capacity constraint, while only the mean and variance of the product demand are known. The problem aims to find a capacity allocation scheme to minimize the system cost of the worst-case among all possible demand distributions. When the total capacity is among certain ranges, the optimal solution has a closed-form. For other ranges, the optimal solution can be derived by solving one equation. The solution shows that there exist a number of threshold values for the capacity, below which some products are neglected (allocated with zero capacity). Besides, in the optimal solution, which products are prioritized for production is determined by the order of an index measured by the unit production cost, unit shortage cost, demand mean, and demand variance. For a special case where the cost structures for different products are identical, a closed-form solution is derived for any total capacity value. For this special case, the index order is simply determined by the coefficient of variation of each product demand. Sensitivity analysis shows that when the capacity is abundant, a larger demand variability of one product may cause a higher production quantity for this product; while if the capacity is tight, a larger demand variability cause a lower production quantity. For a set of test problems, the performance of the robust optimization solution is quite close to that of the stochastic optimization solution.

Food Supply Chain Sustainability Strategy for Fresh Retailer and Multi-Output Random Fresh Suppliers after COVID-19

Feeding people sustainably during the COVID-19 pandemic remains a challenge, as food productivity is declining and there is a risk of chain breakage at any time. To maintain the core function of supplying food to end consumers, a new framework must be developed to investigate the strategies for coordinating a new supply chain comprised of multiple suppliers with random output. Thus, in both decentralized and centralized systems, this paper constructs a supply chain model of a retailer procuring from multiple suppliers and characterizes each party’s optimal decisions. These results show that: (1) the optimal order quantity, profit of each part, and overall profit of the supply chain in the concentrated situation are better than those in the decentralized situation, and the transmission mechanism is slightly different from the classic newsboy model; (2) a supply chain coordination contract consisting of price discounts and compensation is designed, which can realize the coordination of a retailer and multiple suppliers with random yield in the endogenous price situation. These results imply that managers can develop sustainable food supply chains during uncertain times by ordering from these multi-suppliers with random yield. This paper adds to the literature on random yield assembly systems by taking into account that multiple suppliers have random component distributions.

Digital Coupon Promotion and Inventory Strategies of Omnichannel Brands

This paper investigates when an omnichannel brand should offer digital coupons in the online and buy-online-and-pick-up-in-store (BOPS) channels and, if so, the joint decision of coupon face value and store inventory. The impact of a digital coupon promotion on store inventory is also explored. Two scenarios are considered, one where consumers’ costs in the online and store channels are homogeneous and another in which they are heterogeneous, and two newsvendor models, with and without a coupon promotion, are constructed under each scenario. The results show that the issuance of coupons improves the omnichannel brand’s profit when the price is high and the coefficient of the difference in valuation between two types of consumers is low in the homogeneous scenario. In the heterogeneous scenario, the brand prefers the coupon promotion when the price is high or moderate and the coefficient of the difference in valuation between two types of consumers is high. In addition, offering a coupon promotion yields a higher store inventory in most cases. However, store inventory is decreased in some special cases in the homogeneous scenario. Moreover, an increased hassle cost in the BOPS channel significantly lowers the offline demand and profit increase from a digital coupon promotion. Furthermore, a coupon promotion is more likely to benefit both the brand and consumers as the cross-selling revenue increases. These results provide guidance for omnichannel brands to implement coupon promotions and adjust store inventory with stochastic demand.

Marketing effort within the newsvendor problem framework: A systematic review and extensions of demand-effort and cost-effort formulations

This study deals with a generalization of the newsvendor problem with marketing efforts. Combining inventory and marketing decisions is currently a topic that has been widely studied. Various formulations of marketing efforts and their costs have been applied in the literature. Therefore, a systematic review was performed to identify existing formulations, especially those that deal with mathematical modeling and optimization. The findings observed on a wide set of marketing effort formulations are summarized, generalized, and applied in the newsvendor problem framework. It was found that the optimal marketing effort decision does not depend on the uncertainty involved in the model for the additive demand case under commonly used assumptions. Optimal marketing is equal to its deterministic equivalent, contrary to the multiplicative form, where the decision directly depends on uncertainty. Formulations of the demand-effort response function and the cost of marketing effort are generalized (to concave and convex functions, respectively) and extended to an S-shaped demand-effort response function. Assumptions and theorems that guarantee the uniqueness of optimal marketing efforts are established. Finally, the effects of price and cost parameter changes on optimal marketing effort decisions were analyzed.

Shipping before order making: Optimal shipping quantity and pricing decisions under uncertain demand

The innovative logistics mode of shipping before order making has been used by several leading online retailers, due to its advantage on enhancing consumer delivered value and promoting customer demand. This paper investigates the optimal shipping quantity and product pricing strategy of the online retailer that uses this logistics mode under a stochastic demand, which is shipping-dependent and price-dependent. First, we build an extended newsvendor model and explore the closed-form solutions of the optimal shipping quantity and optimal product pricing strategies under certain assumptions on the demand function. Then, we compare the differences of the optimal strategies under different risk attitudes and analyze the impact of key parameters on the optimal strategies. At last, we extend the basic model by considering a general demand function. We conduct numerical experiments to verify the theoretical conclusions and analyze the effect of parameters on online retailers’ optimal strategies and profits. The results show that the optimal shipping quantity first increases and then decreases with the increase of the price. This suggests that the online retailers should avoid blind price war under this logistics mode. The risk aversion degree slightly affects the optimal price, but significantly affects the optimal shipping quantity. Moreover, we find that parameters such as disposal cost and sensitivity of demand to shipping in advance significantly affect the optimal strategies of online retailers.

Multiproduct newsvendor with cross-selling and narrow-bracketing behavior using data mining methods

Behavioral studies have pointed out that in the face of two or more decision tasks, people tend to consider decision tasks separately and show narrow-bracketing characteristics, deviating from the rational decision maker’s overall consideration of multiple task combinations. We construct multiproduct newsvendor models with cross-selling under two dimensions: rational or narrow-bracketing newsvendors, with budget constraints or not. We first provide conditions for optimal order quantities, and obtain analytical results for model comparisons under a special case. We then examine the impacts of the cross-selling effect between products on decisions and profits across different models through numerical analysis. We further develop decision rule heuristics for the decision sequence of narrow-bracketing newsvendor with a budget constraint by employing classic data mining methods (i.e., Apriori and C4.5 algorithms) for the two-product settings. We find that: (1) The narrow-bracketing newsvendor orders no more product types than the rational newsvendor in the presence of cross-selling effects among products when there is a budget constraint. (2) In a complementary two-product setting for the rational or narrow-bracketing newsvendors, as the cross-selling effect caused by the shortage of one product increases, the optimal order quantity of this product increases, and the optimal order quantity of the other product decreases, leading to lower expected profits for both products, regardless of the budget constraint condition. (3) For the narrow-bracketing newsvendor with two complementary products and budget constraints, the product with lower cost or higher active cross-selling effect should be ordered first, and the product cost has higher priority in most cases. Robustness checks and managerial implications are also discussed.

Optimal ordering quantity under stochastic time-dependent price and demand with a supply disruption: A solution based on the change of measure technique

This paper presents a solution of a generalized newsvendor problem with supply disruption and dual sourcing, where the underlying product price and demand are correlated and evolve randomly over time. We contribute to the literature by employing a non-stationary model for demand, and proposing a novel solution methodology using the change of measure technique often applied for derivative pricing in the mathematical finance literature but not frequently considered in the management science and operations management literature. The application of this technique allows the non-linear expectation terms in the profit function, that are often computed numerically in the literature, to be determined analytically. This, in turn, leads to analytic solutions in special cases, and provides the foundations for a highly efficient numerical solution algorithm in general. A comparison against an alternative benchmark technique from the literature is provided to demonstrate the efficiency of our approach.

Non-parametric generalised newsvendor model

In the present paper we generalise the classical newsvendor problem for critical perishable commodities having more severe costs than its linear alternative. Piece wise polynomial cost functions are introduced to accommodate the excess severity. Stochastic demand is assumed to follow a completely unknown probability distribution. Non parametric estimator of the optimal order quantity has been developed from an estimating equation using a random sample. Strong consistency of the estimator is proved for unique optimal order quantity and the result is extended for multiple solutions. Simulation results indicate that non parametric estimator is efficient in terms of mean square error. Real life application of the proposed non-parametric estimator has been demonstrated with Avocado demand in the United States of America and Covid-19 test kit demand during second wave of SARS-COV2 pandemic across 86 countries.

Multi-location newsvendor problem with random yield: Centralization versus decentralization

We study a multi-location newsvendor problem with an additive or multiplicative random yield assumption. We derive the expected cost and variance of cost under both centralized and decentralized systems. Given the additive random yield, we show that centralization is better than decentralization if demand is deterministic, or demand is uncertain and service level is 0.5. This result is driven by the risk pooling effect, where risk refers to supply risk. Given the multiplicative random yield, we show that decentralization is better than centralization if demand is deterministic. This result is driven by the risk diversification effect, where risk refers to supply risk. Through numerical experiments, we find that in general there is no risk pooling effect nor risk diversification effect if demand is uncertain. Specifically, under additive random yield the cost variance of centralized system can be either higher or lower than the decentralized system. Under multiplicative random yield, centralization is better than decentralization in terms of the expected cost, while decentralization is better than centralization in terms of the cost variance. Both the analytical and numerical results suggest that, when considering supply uncertainty, the comparison between centralization and decentralization highly depends on demand uncertainty.

Adaptive Discretization in Online Reinforcement Learning

Adaptive Discretization in Reinforcement Learning Performance guarantees for RL algorithms are typically for worst case instances, which are pathological by design and not observed in meaningful applications. Moreover, many domains (such as computer systems and networking applications) have large state-action spaces and require algorithms to execute with low latency. This phenomenon highlights a trifecta of goals for practical RL algorithms: low sample, storage, and computational complexity. In this work, we develop an algorithmic framework for nonparametric RL with data-driven adaptive discretization. Our framework has provably better sample, storage, and computational complexity than uniform discretization or kernel regression methods. Moreover, we highlight how the performance guarantees are min-max optimal with respect to a novel instance-specific complexity measure that captures structure in facility location and newsvendor models.

Time window optimization for attended home service delivery under multiple sources of uncertainties

We consider a vehicle routing problem variant to optimize time window assignments together with vehicle routing and scheduling decisions, under the uncertainties of trip time, service time and possible customers’ cancellations. We minimize the expected cost of vehicles’ overtime, idleness, and customer waiting, when also allowing to add new customers to existing schedules. We formulate a two-stage stochastic mixed-integer programming model using finite samples of the uncertain parameters, where in the first stage, we optimize vehicle routes and assign service time windows to customers, and in the second stage, we construct a linear program to compute the resultant undesirable cost given routes and time windows. We also propose a re-optimization method and an insertion-based linear program for accommodating real-time requests in a rolling horizon way for dynamic operations. To speed up computation, we further decompose the problem into three phases and propose Assignment–Routing–Scheduling heuristics. We first design three clustering algorithms based on spatial similarities to assign customers to vehicles, and then combine the nearest-neighbor and smallest-variance rules to decide the route for each vehicle. Finally, we cast the scheduling part as a Newsvendor problem variant and apply inventory approximations to derive closed-form solutions for determining time windows. We conduct numerical studies on diverse instances generated using both well-established benchmark data sets and Ford’s mobile service data, to compare different approaches and demonstrate the benefits of allowing flexible time-window assignments.

Application of the model combining demand forecasting and inventory decision in feature based newsvendor problem

This paper consider a one-step machine learning algorithm and propose a prediction technology using a large amount of relevant information. In the method proposed in this paper, the manager observed P features related to demand data n times, and established a prediction model through scikit-learn machine learning framework to study the data-driven newsvendor problem. In particular, the research method of this paper does not need to obtain the accurate demand distribution before optimization, and the data used by the algorithm is not limited to the historical sales data. We filter multiple characteristic variables related to the demand, substitute the filtered characteristic variable set into the model to predict the future demand, and make the order quantity decision of the newsvendor model according to the predicted demand. Finally, a case study was conduct to verify the effectiveness and feasibility of the proposed method. We find that using multiple characteristic information to predict the future demand has important guiding significance for the order quantity decision of newsvendor model, and this method can be applied to the inventory decision of many commodities.

Optimal shipping quantity, product pricing strategies and carbon emissions of online retailers under a new logistics mode

A new logistics mode has emerged in online retailing, which ships products before customers place orders online to reduce the waiting time for customers to receive them. The existing research on this logistics mode mainly focuses on the shipping quantity (i.e., the quantity of products to be shipped in advance from the order fulfillment center to the distribution center nearby customers before the order is placed online), while the product pricing problem and carbon emissions have not been studied comprehensively. Moreover, the risk attitudes of decision-makers have been ignored in the studies related to this new logistics mode. This paper builds an extended newsvendor model to explore the optimal joint decision problem of shipping quantity and product pricing under this new logistics mode and analyzes the carbon emissions of this new logistics mode compared with the traditional logistics mode. We consider decision-makers to be risk averse and take Conditional Value-at-Risk (CVaR) as the risk measure criterion. For both multiplicative and additive demand models, we obtain the closed-form solution of the optimal strategy. The differences between the optimal strategies of risk-averse and risk-neutral decision-makers and between the optimal strategies of this logistics mode and the traditional one have also been explored. Based on the optimal shipping quantity and product pricing strategies, we analyze the carbon emission variation of this logistics mode compared with the traditional one and provide sufficient conditions for reducing carbon emissions. Numerical experiments verify the theoretical conclusions and analyze the effect of some parameters on the optimal strategy, profit and carbon emission variation. The results show that online retailers should reduce product price in this new logistics mode compared with the traditional one. The risk-aversion degree slightly affects the optimal price but significantly affects the shipping quantity. Moreover, implementing this new logistics mode contributes to reducing carbon emissions compared with the traditional logistics mode in most cases. This study helps support online retailers in developing shipping quantity and product pricing strategies under this new logistics mode and helps the Environmental Protection Association to understand the carbon emissions under this new logistics mode so that relevant strategies can be developed.

Dynamic coordinated maintenance of wind-farms with risk-averse agents under CVaR criterion

We study a coordinated maintenance problem for multi-turbine offshore wind-farms. The deterioration of the turbines follows a Poisson process and the optimal order quantity for a single wind-farm, as well as for a coalition of wind-farms, is obtained using the analogy with the risk-averse newsvendor model considering the conditional value at risk (CVaR) criterion. We apply the theory of robust dynamic coalitional games to design a stable allocation mechanism that distributes the cost of the coalition among all the participants in a fair and stable way.

Optimal Purchasing Decisions with Supplier Default in Portfolio Procurement

As global public health events and regional conflicts have greater influence on supply chains nowadays, supplier default in procurement becomes more and more common in practice. However, there is less research on portfolio procurement purchasing decisions in the case of fixed-term contract supplier default. This paper focuses on the optimal purchasing decision of buyers by using a combination of fixed-term contracts and spot transactions, which is a beneficial extension of the classical newsvendor model. When supplier default is not considered, the optimal purchase quantity in the fixed-term contract is first obtained, which maximizes the buyer’s expected profits. Research shows that supplier default has an important impact on the optimal purchasing decision making in portfolio procurement. The optimal purchase quantity of the buyer in the fixed-term contract decreases with the increase in the default rate of the contract supplier, which implies that the default from the contract supplier inhibits a larger purchase quantity in the fixed-term contract. In addition, it is proved that the buyer’s expected profits from portfolio procurement increases with the decrease in the contract supplier’s default rate. Finally, numerical experiments and sensitivity analysis are conducted to prove the result, and some management opinions on the optimal decision-making in portfolio procurement with fixed-term contracts and spot transactions are put forward.

Nonlinear pricing for yield management and countering strategic consumer behavior

Many models assume that faced with excess inventory, retailers offer price discounts to increase sales. This discount is assumed to be a certain dollar amount or a certain percent of the regular price. However, many retailers use nonlinear pricing, e.g., “Buy one, get one for 50% off,” which we refer to as BOGO. We analyze BOGO within the newsvendor model and identify the reasons for its popularity. We describe the type of products for which BOGO is suitable, identify the optimal BOGO discount, and its effect on the retailer’s profit. We compare BOGO to straight price reduction and analyze the newsvendor’s optimal choice between them. We also examine the two promotions in the presence of strategic consumers. We find that for reasonable values of consumer marginal utility and a given order quantity, BOGO reduces strategic consumers’ chances of obtaining a unit at a discount and their incentive to wait. Therefore, the newsvendor orders a larger quantity with BOGO than with a price reduction. Thus, BOGO can be used to counter strategic consumer behavior. Also, we find that in the presence of strategic consumers, there are cases where it is optimal for the retailer to wait and offer a straight discount at the end of the season. However, with BOGO, it is always optimal to offer a BOGO at the start of the season if realized demand is low. We examine the robustness of our results to different arrival rates and positive salvage value and find that they qualitatively hold.

Several Methods of Inventory Control

This paper would firstly introduce the Single-Period Inventory Model, a basic method of inventory control. By analyzing the Newsvendor Problem which is a simplified situation of storing inventories, this paper would discover a method using normal distribution analysis to solve the problem. Then, the paper would promote the adoption of this method into realistic inventory problems and discuss its utility. Secondly, the topic is expanded to Multi-Period Inventory System. This system focus on a more sophisticated inventory situation, and it could be basically categorized into two models: fixed-order quantity model, and fixed time period model. The paper would discuss the methods of ordering determination of the two models respectively.

Omni channel Supply Chain Optimization and Mode Selection Based on Smart New Retail

Smart new retail mode has rapidly become the hot shopping mode. In order to develop vigorously in the new retail environment, it is urgent for merchants to set up supply chain network reasonably. This paper constructs a supply chain newsvendor model consisting of 1 wholesaler and N retailers. Analyse how channel conversion rate, negotiation ability of supply chain members, number of retailers, and other factors affect the balance among supply chain members when offline demand, online demand, and cross-channel demand exist simultaneously. Combined with the case data of two fast fashion brands, this paper compares and analyses the profit changes of decentralized supply chain and centralized supply chain under the influence of multiple factors. The study shows that there is no absolute optimal supply chain model and the choice of supply chain model will change with the change of influencing factors. However, no matter in which supply chain mode, improving channel conversion rate and controlling the number of retailers are beneficial. In addition, in decentralized supply chain, balance can be achieved among supply chain members so as to achieve Pareto optimality. Wholesalers should take the initiative to promote the transformation of demand among channels, and should not be too strong in member negotiations. This paper analyses the basic characteristics of the supply chain network under the new retail, and establishes the network optimization strategy that is easy to implement, which can help enterprises to carry out the supply network layout more effectively under the smart new retail mode.

Designing variable-sized block appointment system under time-varying no-shows

We consider the tactical problem of optimizing the capacity of a block appointment system with time-varying no-show and random service duration. The problem characteristics are motivated by a real-life case study of two outpatient specialty clinics in the US, where time-of-day variation in appointment attendance was observed. We aim to determine the block size (patients to be assigned in each time period) such that the weighted sum of block-wise waiting- and idle-times (or total cost) are minimized. First, we consider optimizing the capacity of a single block appointment system (SBAS) as a special case of the inverse newsvendor problem, and develop an analytical closed-form solution under the assumption of normally distributed service time. Also, a stochastic integer programming (SIP) model is developed to solve SBAS for any service time distribution. Subsequently, the SIP model is extended to determine the block size of the variable-sized multi-block appointment system (VSMBAS) by treating it as a sequential inverse newsvendor problem. Owing to the computational complexity of the SIP, we employ sample average approximation to estimate the expected total cost. Numerical studies considered several realistic clinic settings, and the results demonstrated that integrating time-varying no-shows for block size determination will considerably improve schedule efficiency as opposed to ignoring it. We also found the cost ratios (waiting-time to idle-time penalty), service time variation, and no-show pattern have a substantial influence on the block size of VSMBAS. Finally, we provide several practical implications based on our analysis.

Advance selling under uncertain supply and demand: a robust newsvendor perspective

AbstractConsidering the restriction of supply risk on optimal profit realization in advance selling, we discuss three selling strategies of a seller who produces and sells a seasonal product to a consumer under uncertain supply and demand: all advance selling, partial advance selling, and non‐advance selling. The robust newsvendor model is designed to solve the problem. Our results show that implementing an advance selling strategy is always beneficial from the demand uncertainty perspective to the seller. However, sellers should choose advance selling carefully from the standpoint of supply uncertainty: sellers will non‐advance selling under certain conditions. This condition is contingent on the market, capacity level, selling price, supply–demand correlation, consumer characteristics, and seller's pricing power. Interestingly, pricing power is the key driver to stimulate advance selling under supply uncertainty. In addition, the impact of supply and demand uncertainty and supply–demand correlation on these strategies are related to price discounts.