Price-setting Newsvendor Model Research Articles

How Does Risk Hedging Impact Operations? Insights from a Price-Setting Newsvendor Model

If a financial asset’s price movement impacts a firm’s product demand, the firm can respond to the impact by adjusting its operational decisions. For example, in the automotive industry, automakers decrease the selling prices of fuel-inefficient cars when the oil price rises. Meanwhile, the firm can implement a risk-hedging strategy using the financial asset jointly with its operational decisions. Motivated by this, we develop and solve a general risk-management model integrating risk hedging into a price-setting newsvendor. The optimal hedging strategy is calculated analytically, which leads to an explicit objective function for optimizing price and “virtual production quantity” (VPQ). (The latter determines the service level—that is, the demand-fulfillment probability.) We find that hedging generally reduces the optimal price when the firm sets the target mean return as its production-only maximum expected profit. With the same condition on the target mean return, hedging also reduces the optimal VPQ when the asset price trend positively impacts product demand; meanwhile, it may increase the VPQ by a small margin when the impact is negative. We construct the return-risk efficient frontier that characterizes the optimal return-risk trade-off. Our numerical study using data from a prominent automotive manufacturer shows that the markdowns in price and reduction in VPQ are small under our model and that the hedging strategy substantially reduces risk without materially reducing operational profit. This paper was accepted by Kay Giesecke, finance. Funding: Financial support from the Hong Kong Research Grants Council [General Research Fund 17200521] is gratefully acknowledged. Supplemental Material: The data files and e-companion are available at https://doi.org/10.1287/mnsc.2023.4942 .

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 Does Risk Hedging Impact Operations? Insights from a Price-Setting Newsvendor Model

Financial asset price movement impacts product demand and thus influences operational decisions of a firm. We develop and solve a general model that integrates financial risk hedging into a price-setting newsvendor. The optimal hedging strategy is found analytically, which leads to an explicit objective function for optimization of pricing and service levels. We find that, in general, the presence of hedging reduces the optimal price. It also reduces the optimal service level when the asset price trend positively impacts product demand ("asset price benefits demand"), while it may increase the optimal service level by a small margin when the impact is negative ("asset price hurts demand"). We construct the mean-variance efficient frontier that characterizes the risk-return trade-off, and we quantify the risk reduction achieved by the hedging strategy. Our numerical case study using real data of Ford Motor Company shows that the markdown in price and decrease in service level are small under our model, and the hedging strategy substantially reduces risk without materially reducing operational profit.

The price-setting newsvendor with Poisson demand

The price-setting newsvendor (PSN) model has received considerable attention since it was first introduced by Whitin (1955). However, the existing publications that study this model consistently assume the existence of a continuous density function of demand. In this paper, we study the PSN model with Poisson demand — that is, a discrete demand distribution without density function. The Poisson PSN has an important property, it combines price-dependency of variance and coefficient of variation of the (standard) additive and multiplicative models: demand variance decreases and the coefficient of variation increases in the selling price. We develop an analytical solution approach that covers a broad class of demand models, including linear and logit demand, explain how to apply our approach to more general demand functions via piece-wise linear approximation, and develop analytical and numerical insights. We characterize the behavior of the optimal price and we analyze the performance gap of different price-setting heuristics. Among other insights, we observe some instances in which a significant share of profits would be lost if the discrete nature of demand were not modeled explicitly. To help companies overcome this risk, we present an easily applicable decision rule with which to determine when to use simple heuristics and when to solve the associated discrete optimization problem.

Pricing to the Scenario: Price-Setting Newsvendor Models for Innovative Products

In this paper, we consider a manufacturer who produces and sells a kind of innovative product in the monopoly market environment. Because the life cycle of an innovative product is usually shorter than its procurement lead time, one unique demand quantity (scenario) will occur in the selling season; thus, there is only one chance for the manufacturer to determine both optimal production quantity and optimal sale price. Considering this one-time feature of such a decision problem, a price-setting newsvendor model for innovative products is proposed. Different to the existing price-setting newsvendor models, the proposed models determine the optimal production quantity and sale price based on some specific state (scenario) which is most applicable for the manufacturer. The theoretical analysis provides managerial insights into the manufacturers’ behaviors in a monopoly market of an innovative product, and several phenomena in the luxury goods market are well explained.

Optimal production, pricing and government subsidy policies for a closed loop supply chain with uncertain returns

<p style='text-indent:20px;'>This paper studies an original equipment manufacturer's (OEM's) optimal production and pricing decisions and the governments optimal subsidy level when the number of used products returning to the OEM is uncertain. The government aims to minimize its total expenditures but also attempt to achieve a given target collection level. We model the problem as an extended price-setting newsvendor model, which simultaneously incorporates supply uncertainty and external government influence. Moreover, we consider separately the cases of stochastic supplies with additive and multiplicative return uncertainty. We show that under the above settings, the governments optimal strategy is to provide only sufficient subsidies that cause its target to be met exactly. The government subsidies will mitigate the cost of remanufacturing and increase the total collection efforts of the government and the manufacturer. Moreover, the return uncertainty lowers both the manufacturers profits and selling price, whereas its effects on the governments optimal subsidies and the manufacturers optimal return efforts are insignificant. Therefore, the manufacturer is worse off but consumers are better off under the conditions of uncertain returns. By comparing the optimal decisions when the government is a central planner with the case of decentralized decision making, or comparing the arrangement in which the government provides subsidies directly to the manufacturer rather than to consumers, we find that the government subsidies would coordinate the supply chain only when its target collection level is high. Moreover, no essential differences exist between providing subsidies directly to the manufacturer and to consumers. Our results are robust under both the additive and multiplicative uncertainty models.

A study on the effect of yield uncertainty in price-setting newsvendor models with additive-multiplicative demand

Random yield and uncertain demand usually both exist in many industries, such as the semiconductor industry. In this paper, the price-setting newsvendor model is studied which involves a single manufacturer and a single retailer with random yield and uncertain demand respectively. Under the condition of additive-multiplicative demand, we investigate the varying effects of random yield on the optimal price, order quantity, and expected profit in two situations with different cost structures. The first case is an in-house production case where the firm pays for the raw material quantity it has ordered, and the second one is a procurement case where the firm pays for the real product quantity it receives only. By using the theory of stochastic comparisons, we find that a less variable and a stochastically larger yield rate both lead to a lower optimal price and a higher expected profit for the in-house production case. Moreover, a less variable yield rate also results in a lower optimal price and a higher profit for the procurement case, but this is not true for a stochastically larger yield rate. Numerical examples illustrate that the effect of yield randomness on the optimal order quantity is not general.

A numerical study on competing supply chains: a price-setting newsvendor model

Consider an industry with two competing two-echelon supply chains. Each supply chain consists of one manufacturer and one retailer. Each retailer is modelled as a price-setting newsvendor. That is, each retailer sets his inventory as well as retail price. In such a setting, we numerically study the impact of horizontal competition and demand uncertainty on wholesale and retail prices, inventories, manufacturer profit, retailer profit, and supply chain profit. Demand uncertainty is captured by an additive stochastic demand function in which the random shock is uniformly distributed. Three key findings are: 1) horizontal competition could be beneficial for both manufacturer and retailer; 2) it is possible for retailer to optimally keep less inventory when demand uncertainty increases, provided that horizontal competition is much intense; 3) inventory (and thus order quantity) is an effective tool for retailer to transfer much of demand risk to manufacturer.

A numerical study on competing supply chains: a price-setting newsvendor model

Consider an industry with two competing two-echelon supply chains. Each supply chain consists of one manufacturer and one retailer. Each retailer is modelled as a price-setting newsvendor. That is, each retailer sets his inventory as well as retail price. In such a setting, we numerically study the impact of horizontal competition and demand uncertainty on wholesale and retail prices, inventories, manufacturer profit, retailer profit, and supply chain profit. Demand uncertainty is captured by an additive stochastic demand function in which the random shock is uniformly distributed. Three key findings are: 1) horizontal competition could be beneficial for both manufacturer and retailer; 2) it is possible for retailer to optimally keep less inventory when demand uncertainty increases, provided that horizontal competition is much intense; 3) inventory (and thus order quantity) is an effective tool for retailer to transfer much of demand risk to manufacturer.

The Impact of Demand Uncertainty on Consumer Subsidies for Green Technology Adoption

This paper studies government subsidies for green technology adoption while considering the manufacturing industry’s response. Government subsidies offered directly to consumers impact the supplier’s production and pricing decisions. Our analysis expands the current understanding of the price-setting newsvendor model, incorporating the external influence from the government, who is now an additional player in the system. We quantify how demand uncertainty impacts the various players (government, industry, and consumers) when designing policies. We further show that, for convex demand functions, an increase in demand uncertainty leads to higher production quantities and lower prices, resulting in lower profits for the supplier. With this in mind, one could expect consumer surplus to increase with uncertainty. In fact, we show that this is not always the case and that the uncertainty impact on consumer surplus depends on the trade-off between lower prices and the possibility of underserving customers with high valuations. We also show that when policy makers such as governments ignore demand uncertainty when designing consumer subsidies, they can significantly miss the desired adoption target level. From a coordination perspective, we demonstrate that the decentralized decisions are also optimal for a central planner managing jointly the supplier and the government. As a result, subsidies provide a coordination mechanism.This paper was accepted by Yossi Aviv, operations management.

Robust price-setting newsvendor model with interval market size and consumer willingness-to-pay

We consider a price-setting newsvendor problem with partial information. The newsvendor does not know the price-dependent probability distribution of demand, but is able to estimate lower and upper limits of the market size and consumer willingness-to-pay. The objective is to minimize the maximum loss in expected profit, or minimax regret. We derive closed-form expressions for optimal quantity and price and identify managerial insights.

The Impact of Demand Uncertainty on Consumer Subsidies for Green Technology Adoption

This paper studies government subsidies for green technology adoption while considering the manufacturing industry's response. Government subsidies offered directly to consumers impact the supplier's production and pricing decisions. Our analysis expands the current understanding of the price-setting newsvendor model, incorporating the external influence from the government who is now an additional player in the system. We quantify how demand uncertainty impacts the various players (government, industry and consumers) when designing policies. We further show that for convex demand functions, an increase in demand uncertainty leads to higher production quantities and lower prices, resulting in lower profits for the supplier. With this in mind, one could expect consumer surplus to increase with uncertainty. In fact, we show this is not always the case and the uncertainty impact on consumer surplus depends on the trade-off between lower prices and the possibility of under-serving customers with high valuations. We also show that when policy makers such as governments ignore demand uncertainty when designing consumer subsidies, they can significantly miss the desired adoption target level. From a coordination perspective, we demonstrate that the decentralized decisions are also optimal for a central planner managing jointly the supplier and the government. As a result, subsidies provide a coordination mechanism.

The Effect of Supply Uncertainty in Price-Setting Newsvendor Models

We consider a price-setting newsvendor model in which a firm needs to make joint inventory and pricing decisions before the selling season. The supply process is uncertain such that the received quantity is the product of the order quantity and a random yield rate. Two cost structures are investigated, the in-house production case in which the firm pays for the order quantity and the procurement case in which the firm pays for the quantity received only. Our objective is to investigate the effect of yield randomness on optimal decisions and expected profit. By using the theory of stochastic comparisons, we find that under both cost structures, a less variable yield rate leads to a lower optimal price and a higher expected profit. Moreover, we show that in the in-house production case, a stochastically larger yield rate also results in a lower optimal price and a higher profit, but this is not true in the procurement case. Examples show that the effect of supply uncertainty on optimal order quantity is not universal.

The effect of supply uncertainty in price-setting newsvendor models

We consider a price-setting newsvendor model in which a firm needs to make joint inventory and pricing decisions before the selling season. The supply process is uncertain such that the received quantity is the product of the order quantity and a random yield rate. Two cost structures are investigated, the in-house production case in which the firm pays for the input quantity and the procurement case in which the firm pays for the quantity received only. Our objective is to investigate the effect of yield randomness on optimal decisions and expected profit. By using the theory of stochastic comparisons, we find that under both cost structures, a less variable yield rate leads to a lower optimal price and a higher expected profit. Moreover, we show that in the in-house production case, a stochastically larger yield rate also results in a lower optimal price and a higher profit, but this is not true in the procurement case. Examples show that the effect of supply uncertainty on optimal order quantity is not universal.

An Elasticity Approach to the Newsvendor with Price-Sensitive Demand

We introduce a measure of elasticity of stochastic demand, called the elasticity of the lost-sales rate, which offers a unifying perspective on the well-known newsvendor with pricing problem. This new concept provides a framework to characterize structural results for coordinated and uncoordinated pricing and inventory strategies. Concavity and submodularity of the profit function, as well as sensitivity properties of the optimal inventory and price policies, are characterized by monotonicity conditions, or bounds, on the elasticity of the lost-sales rate. These elasticity conditions are satisfied by most relevant demand models in the marketing and operations literature. Our results unify and complement previous work on price-setting newsvendor models and provide a new tool for researchers modeling stochastic price-sensitive demand in other contexts.

The effect of demand uncertainty in a price-setting newsvendor model

We study the effects of demand uncertainty on optimal decisions and the expected profit of a price-setting newsvendor who faces either additive or multiplicative stochastic demand. Our key findings are as follows. (1) A stochastically larger demand may even lead to a smaller order size and a lower profit when price is endogenous. (2) A stochastically larger demand will lead to a higher selling price in general for the additive demand case but to a lower selling price under certain mild conditions for the multiplicative demand case. Moreover, if the larger demand can be represented by a transformation of the lower one, it will lead to a higher expected profit for both demand cases. However, except for the setting with a zero shortage cost, a larger demand may not necessarily result in a higher expected profit in general. (3) Under mild conditions, a less variable demand will lead to a higher and lower selling price for the additive and multiplicative demand case, respectively, and a higher expected profit for both cases.

A price-setting newsvendor model under CVaR decision criterion with emergency procurement

In this paper, we consider a newsvendor model in which a risk-averse manager faces a stochastic price-dependent demand in either an additive or a multiplicative form. An emergency purchase option is allowed after the realization of demand to satisfy the units that are short. By adopting conditional value-at-risk (CVaR) as the decision criterion, we aim to investigate the optimal pricing and ordering decisions, and the effects of parameter changes in such a setting. We provide sufficient conditions for the uniqueness of the optimal policy for both demand models. We perform comparative statics analysis to show how the optimal pricing and ordering decision behaves when changing parameters. We also compare our results with those of the newsvendor with a general utility function and with CVaR criterion under lost sales assumption. Our key results include: (i) For both demand models, the optimal selling price is decreasing in risk aversion. Hence, the optimal price of a risk-averse newsvendor is not greater than the optimal price of a risk-neutral newsvendor. (ii) In contrary to the lost sales case, for the multiplicative demand model, the optimal order quantity may not be monotonic in risk aversion. Consequently, the optimal risk-averse order quantity may be lower or higher than the optimal risk-neutral counterpart. (iii) For the additive model, the optimal order quantity is strictly increasing in the emergency purchase price, while for the multiplicative model the optimal order quantity has no such a monotonic property. Some numerical examples are conducted to verify our claims and gain more insights about the risk-averse decision-making behaviors.

An Empirical Study on Demand Models for a Price-Setting Newsvendor

We consider the price-setting newsvendor model where the ordering and pricing decisions have to be made at the beginning of a selling period before demand is realized. Unsatisfied demand is lost and excess inventory has to be salvaged. The standard approach is to assume stochastic demand to be composed of deterministic functions decreasing in price and a stochastic error term. We present an empirical study which includes demand modelling as well as price and inventory optimization. Using the sales data of a retailing company, additive and multiplicative demand models are estimated and their adequacy of representing the data is assessed according to some statistical methods. Seeing the need and possibility of using a more general demand model we suggest estimating a more flexible demand distribution in a simple way. Applying the newsvendor problem formulation, the optimal policies under each of the three models as well as the policy under the sequential approach are calculated. The performance of each model is evaluated by simulating the corresponding policies using the same data set. We conclude that using a general model can increase the profits significantly.

An Elasticity Perspective to the Newsvendor with Price Sensitive Demand

We introduce a measure of elasticity of stochastic demand, called the elasticity of the lost sales rate, which offers a unifying perspective on the well-known newsvendor with pricing problem. This new concept provides a framework to characterize structural results for coordinated and uncoordinated pricing and inventory strategies. Concavity and submodularity of the profit function, as well as sensitivity properties of the optimal inventory and price policies are characterized by monotonicity conditions, or bounds, on the elasticity of the lost sales rate. These elasticity conditions are satisfied by most relevant demand models in the marketing and operations literature. Our results unify and complement previous work on price-setting newsvendor models, and provide a new tool for researchers modeling stochastic price-sensitive demand in other contexts.