Revenue Management vs. Newsvendor Decisions: Does Behavioral Response Mirror Normative Equivalence?

We study and compare decision‐making behavior under the newsvendor and the two‐class revenue management models, in an experimental setting. We observe that, under both problems, decision makers deviate significantly from normative benchmarks. Furthermore, revenue management decisions are consistently higher compared to the newsvendor order quantities. In the face of increasing demand variability, revenue managers increase allocations; this behavior is consistent with normative patterns when the ratio of the selling prices of the two customer segments is less than 1/2, but is its exact opposite when this ratio is greater than 1/2. Newsvendors' behavior with respect to changing demand variability, on the other hand, is consistent with normative trends. We also observe that losses due to leftovers weigh more in newsvendor decisions compared to the revenue management model; we argue that overage cost is more salient in the newsvendor problem because it is perceived as a direct loss, and propose this as the driver of the differences in behavior observed under the two problems.     

Prices,Markups, and Trade Reform

This paper examines how prices, markups, and marginal costs respond to trade liberalization. We develop a framework to estimate markups from production data with multi‐product firms. This approach does not require assumptions on the market structure or demand curves faced by firms, nor assumptions on how firms allocate their inputs across products. We exploit quantity and price information to disentangle markups from quantity‐based productivity, and then compute marginal costs by dividing observed prices by the estimated markups. We use India's trade liberalization episode to examine how firms adjust these performance measures. Not surprisingly, we find that trade liberalization lowers factory‐gate prices and that output tariff declines have the expected pro‐competitive effects. However, the price declines are small relative to the declines in marginal costs, which fall predominantly because of the input tariff liberalization. The reason for this incomplete cost pass‐through to prices is that firms offset their reductions in marginal costs by raising markups. Our results demonstrate substantial heterogeneity and variability in markups across firms and time and suggest that producers benefited relative to consumers, at least immediately after the reforms.     

Demand Forecast Sharing in Supply Chains

This paper examines the incentives of a manufacturer and a retailer to share their demand forecasts. The demand at the retailer is a linearly decreasing function of price. The manufacturer sets the wholesale price first, and the retailer sets the retail price after observing the wholesale price. Both players set their prices based on their forecasts of demand. In the make‐to‐order scenario, the manufacturer sets the production quantity after observing the actual demand; in the make‐to‐stock scenario, the manufacturer sets the production quantity before the demand is realized. In the make‐to‐order scenario, we show that sharing the forecast unconditionally by the retailer with the manufacturer benefits the manufacturer but hurts the retailer. We also demonstrate that a side payment contract cannot induce Pareto‐optimal information sharing equilibrium, but a discount based wholesale price contract can. The social welfare as well as consumer surplus is higher under the discount contract, compared with under no information sharing. In the make‐to‐stock scenario, the manufacturer realizes additional benefits in the form of savings in inventory holding and shortage costs when forecasts are shared. If the savings from inventory holding and shortage costs because of information sharing are sufficiently high, then a side payment contract that induces Pareto‐optimal information sharing is feasible in the make‐to‐stock scenario. We also provide additional managerial insights with the help of a computational study.     

Combined Pricing and Portfolio Option Procurement

In this paper, we study a single‐product periodic‐review inventory system that faces random and price‐dependent demand. The firm can purchase the product either from option contracts or from the spot market. Different option contracts are offered by a set of suppliers with a two‐part fee structure: a unit reservation cost and a unit exercising cost. The spot market price is random and its realization may affect the subsequent option contract prices. The firm decides the reservation quantity from each supplier and the product selling price at the beginning of each period and the number of options to exercise (inventory replenishment) at the end of the period to maximize the total expected profit over its planning horizon. We show that the optimal inventory replenishment policy is order‐up‐to type with a sequence of decreasing thresholds. We also investigate the optimal option‐reservation policy and the optimal pricing strategy. The optimal reservation quantities and selling price are shown to be both decreasing in the starting inventory level when demand function is additive. Building upon the analytical results, we conduct a numerical study to unveil additional managerial insights. Among other things, we quantify the values of the option contracts and dynamic pricing to the firm and show that they are more significant when the market demand becomes more volatile.     

Coping with Gray Markets: The Impact of Market Conditions and Product Characteristics

Gray markets, also known as parallel imports, have created fierce competition for manufacturers in many industries. We analyze the impact of parallel importation on a price‐setting manufacturer that serves two markets with uncertain demand, and characterize her policy against parallel importation. We show that ignoring demand uncertainty can take a significant toll on the manufacturer's profit, highlighting the value of making price and quantity decisions jointly. We find that adjusting prices is more effective in controlling gray market activity than reducing product availability, and that parallel importation forces the manufacturer to reduce her price gap while demand uncertainty forces her to lower prices. Furthermore, we explore the impact of market conditions (such as market base, price sensitivity, and demand uncertainty) and product characteristics (“fashion” vs. “commodity”) on the manufacturer's policy towards parallel importation. We also provide managerial insights about the value of strategic decision‐making by comparing the optimal policy to the uniform pricing policy that has been adopted by some companies to eliminate gray markets entirely. The comparison indicates that the value of making price and quantity decisions strategically is highest for moderately different market conditions and non‐commodity products.     

Price Manipulation and Quasi‐Arbitrage

In an environment where trading volume affects security prices and where prices are uncertain when trades are submitted, quasi‐arbitrage is the availability of a series of trades that generate infinite expected profits with an infinite Sharpe ratio. We show that when the price impact of trades is permanent and time‐independent, only linear price‐impact functions rule out quasi‐arbitrage and thus support viable market prices. When trades have also a temporary price impact, only the permanent price impact must be linear while the temporary one can be of a more general form. We also extend the analysis to a time‐dependent framework.     

Joint Ordering and Pricing Strategies for Managing Substitutable Products

Starr and Rubinson (1978) develop a model to establish the relationship between product demand and relative prices. The notion of relative prices motivates us to consider a situation in which a retailer would either charge the same retail price for all products if he adopts a ‘fixed’ pricing strategy or charge different prices for different products if he adopts a ‘variable’ pricing strategy. In this paper, we develop a base model with deterministic demand that is intended to examine how a retailer should jointly determine the order quantity and the retail price of two substitutable products under the fixed and variable pricing strategies. Our analysis indicates that the optimal retail price under the variable pricing strategy is equal to the optimal retail price under the fixed pricing strategy plus or minus an adjustment term. This adjustment term depends on product substitutability and price sensitivity. We also present two different extensions of our base model. In the first extension, our analysis indicates that the underlying structure of the optimal retail price and order quantity is preserved when there is a limit on the total order quantity. The second extension deals with the issue of retail competition. Relative to the base case, we show that the underlying structure of the optimal retail price and order quantity is preserved in a duopolistic environment. Moreover, our analysis suggests that both retailers would adopt the variable pricing strategy at the equilibrium.     

Dynamic Pricing to Minimize Maximum Regret

We consider a dynamic pricing problem that involves selling a given inventory of a single product over a short, two‐period selling season. There is insufficient time to replenish inventory during this season, hence sales are made entirely from inventory. The demand for the product is a stochastic, nonincreasing function of price. We assume interval uncertainty for demand, that is, knowledge of upper and lower bounds but not a probability distribution, with no correlation between the two periods. We minimize the maximum total regret over the two periods that results from the pricing decisions. We consider a dynamic model where the decision maker chooses the price for each period contingent on the remaining inventory at the beginning of the period, and a static model where the decision maker chooses the prices for both periods at the beginning of the first period. Both models can be solved by a polynomial time algorithm that solves systems of linear inequalities. Our computational study demonstrates that the prices generated by both our models are insensitive to errors in estimating the demand intervals. Our dynamic model outperforms our static model and two classical approaches that do not use demand probability distributions, when evaluated by maximum regret, average relative regret, variability, and risk measures. Further, our dynamic model generates a total expected revenue which closely approximates that of a maximum expected revenue approach which requires demand probability distributions.     

Allocation of Returned Products among Different Recovery Options through an Opportunity Cost–Based Dynamic Approach*

In a make‐to‐order product recovery environment, we consider the allocation decision for returned products decision under stochastic demand of a firm with three options: refurbishing to resell, parts harvesting, and recycling. We formulate the problem as a multiperiod Markov decision process (MDP) and present a linear programming (LP) approximation that provides an upper bound on the optimal objective function value of the MDP model. We then present two solution approaches to the MDP using the LP solution: a static approach that uses the LP solution directly and a dynamic approach that adopts a revenue management perspective and employs bid‐price controls technique where the LP is resolved after each demand arrival. We calculate the bid prices based on the shadow price interpretation of the dual variables for the inventory constraints and accept a demand if the marginal value is higher than the bid price. Since the need for solving the LP at each demand arrival requires a very efficient solution procedure, we present a transportation problem formulation of the LP via variable redefinitions and develop a one‐pass optimal solution procedure for it. We carry out an extensive numerical analysis to compare the two approaches and find that the dynamic approach provides better performance in all of the tested scenarios. Furthermore, the solutions obtained are within 2% of the upper bound on the optimal objective function value of the MDP model.     

An Experimental Investigation of Pull Contracts in Supply Chains

In this study, I investigate supply chain contracts in a setting where a supplier uses its inventory to directly satisfy a retailer's demand. These “pull” contracts have increased in popularity in practice but have not been studied experimentally. In a controlled laboratory setting, I evaluate a wholesale price contract and two coordinating contracts. The data suggest that the benefit of the two coordinating contracts over the wholesale price contract is less than the standard theory predicts, and that retailers, in the two coordinating contracts, exhibit a systematic bias of setting the coordinating parameter too low, and the wholesale price too high, relative to the normative benchmarks. In an effort to explain this deviation, I explore three behavioral models and find that loss aversion and reference dependence fit the data well. I empirically test this result in a follow‐up experiment, which directly controls for loss aversion and reference dependence, and observe that retailers make significantly better decisions. Lastly, I administer a number of experiments which reduce the complexity of the problem, curtail the amount of risk, and increase the level of decision support, and find that none improve decisions relative to the treatment that controls for loss aversion and reference dependence.     

Joint Mail‐In Rebate Decisions in Supply Chains Under Demand Uncertainty

We study the joint decisions of offering mail‐in rebates (MIRs) in a single‐manufacturer–single‐retailer supply chain using a game theoretic framework. Either party can offer an MIR to the end consumer if it is in his best interest. The consumer demand is stochastic and depends on the product price and the amount of MIRs. When the retail price is exogenous, we show the existence of a unique Nash equilibrium under both additive and multiplicative demand functions and characterize it completely. We show that any of the following four scenarios can be the equilibrium: both parties offer MIR, only one party offers MIR, none offers MIR. When the retail price is a decision variable for the retailer and the rebate redemption rate increases with the amount of MIR, we once again prove the existence of a unique Nash equilibrium where both the retailer and the manufacturer offer MIRs. Using a numerical study, we show that the average post‐purchase price of the product is higher not only than the perceived pre‐purchase price but also than the newsvendor optimal price without an MIR. This implies that an MIR makes a product look cheaper while the consumers actually pay more on average.     

需求受销售价格与变质时间影响的时滞变质品供应链协调研究

在由单个生产商和单个销售商组成的两级时滞变质品供应链中，销售商面临的市场需求受销售价格和物品变质时间影响。分别建立分散决策与集中决策下的时滞变质品供应链定价与补货模型，得到两种决策模式下的销售价格与订货批量均衡解。通过比较两种决策模式发现，集中决策下的销售价格更低且订货批量和预期利润更高。引入数量折扣契约对时滞变质品供应链进行协调，并借助常相对风险规避型效用函数和纳什讨价还价理论来分配协调后的预期利润增量。通过数值算例演示了决策变量求解过程，敏感性分析给出了时滞变质品特性参数变动时对决策变量产生的影响。     

不同权力结构和联盟策略下风险规避型闭环供应链决策

本文旨在探讨不同渠道权力结构和联盟策略下风险规避型闭环供应链的决策问题。考虑到产品需求和废旧产品回收的不确定性及决策者的风险规避特性,在制造商主导、零售商主导及制造商和零售商势力均衡三种情形下,分别构建了制造商和零售商联盟与不联盟时的闭环供应链博弈模型,获得了六个博弈模型下的均衡解,对比分析了不同模型下产品定价、废旧产品的最优回收价格和供应链及其成员的期望收益。研究结果表明,在制造商和零售商不联盟的情形下,决策者的风险规避程度增加能够缓解双重边际效应,供应链期望收益与风险规避程度正相关,而在制造商和零售商联盟的情形下,供应链期望收益与风险规避程度负相关;制造商和零售商不联盟时,制造商和零售商势力均衡的渠道权力结构对消费者最有利,而制造商和零售商联盟时,制造商和零售商势力均衡的渠道权力结构对消费者最不利;制造商和零售商权力结构不对等时最优价格决策之间的关系与制造商和零售商的风险规避程度有关;供应链期望收益在制造商和零售商势力均衡下最大,制造商期望收益在制造商主导的渠道权力结构下最大,零售商期望收益在零售商主导的渠道权力结构下最大。     

BlueLinx can benefit from innovative inventory management methods for commodity forward buys

Commodity prices often fluctuate significantly from one purchasing opportunity to the next. These fluctuations allow firms to benefit from forward buying (buying for future demand in addition to current demand) when prices are low. We propose a combined heuristic to determine the optimal number of future periods a firm should purchase at each ordering opportunity in order to maximize total expected profit when there is uncertainty in future demand and future buying price. We compare our heuristic with existing methods via simulation using real demand data from BlueLinx, a two-stage distributor of building products. The results show that our combined heuristic performs better than any existing methods considering forward buying or safety stock separately. We also compare our heuristic to the optimal inventory management policy by full enumeration for a smaller data set. The proposed heuristic is shown to be close to optimal. This study is the first to decide both the optimal number of future periods to buy for uncertain purchase price and the appropriate purchasing quantity with safety stock for uncertain demand simultaneously. The experience suggests that the proposed combined heuristic is simple and can be very beneficial for any company where forward buying is possible.     

Durable goods pricing with reference price effects

A price benchmark shaped by consumers on the basis of their perception of past prices is known as a reference price. Behavioral decision research suggests that consumers are likely to be backward-looking in that they make purchase decisions based not only on the current price but also on the reference price. It is evident that the reference price effect, which has significant impact on consumer demand, exists for both consumables and durables. Yet, how this effect works has only been investigated in relation to the pricing of consumables, and thus the corresponding results are unable to yield normative implications for durable goods pricing where the saturation effect must enter the picture. This study aims to provide marketers of durables with relevant insights that can be practically used to guide their design of pricing strategies in the presence of the reference price effect. Specifically, we develop a dynamic pricing model which incorporates both the reference price effect and the saturation effect into a framework to broaden our understanding on the durable goods pricing problem. As the internet technology and social media have enhanced consumers’ ability to recall and compare past prices, the need for such a pricing model with backward-looking consumer behavior is increasingly compelling. Our results indicate that while it is optimal for a myopic seller to adopt the skimming pricing strategy, either the price skimming strategy or the penetration strategy is optimal for a forward-looking seller, contingent on the potential market and consumers’ reference price effects.     

Price-setting newsvendor with strategic consumers

We consider a newsvendor who sells a single product over a single season with the objective of determining both the selling price and stock quantity to maximize the expected profit. The customers are strategic and we consider two demand cases: additive and multiplicative. For each case, we derive the newsvendor׳s optimal decisions and demonstrate that neglecting the price-sensitivity of demand leads the newsvendor to make sub-optimal decisions. Moreover, we show that under certain conditions, strategic consumer behavior may positively affect the newsvendor׳s optimal expected profit in the additive demand case.     

Retailer's Response to Alternate Manufacturer's Incentives Under a Single‐Period,Price‐Dependent,Stochastic‐Demand Framework*

This article considers the joint development of the optimal pricing and ordering policies of a profit‐maximizing retailer, faced with (i) a manufacturer trade incentive in the form of a price discount for itself or a rebate directly to the end customer; (ii) a stochastic consumer demand dependent upon the magnitude of the selling price and of the trade incentive, that is contrasted with a riskless demand, which is the expected value of the stochastic demand; and (iii) a single‐period newsvendor‐type framework. Additional analysis includes the development of equal profit policies in either form of trade incentive, an assessment of the conditions under which a one‐dollar discount is more profitable than a one‐dollar rebate, and an evaluation of the impact upon the retailer‐expected profits of changes in either incentive or in the degree of demand uncertainty. A numerical example highlights the main features of the model. The analytical and numerical results clearly show that, as compared to the results for the riskless demand, dealing with uncertainty through a stochastic demand leads to (i) (lower) higher retail prices if additive (multiplicative) error, (ii) lower (higher) pass throughs if additive (multiplicative) error, (iii) higher claw backs in both error structures wherever applicable, and (iv) higher rebates to achieve equivalent profits in both error structures.     

Up Then Down: Bid‐Price Trends in Revenue Management

In the classic revenue management (RM) problem of selling a fixed quantity of perishable inventories to price‐sensitive non‐strategic consumers over a finite horizon, the optimal pricing decision at any time depends on two important factors: consumer valuation and bid price. The former is determined exogenously by the demand side, while the latter is determined jointly by the inventory level on the supply side and the consumer valuations in the time remaining within the selling horizon. Because of the importance of bid prices in theory and practice of RM, this study aims to enhance the understanding of the intertemporal behavior of bid prices in dynamic RM environments. We provide a probabilistic characterization of the optimal policies from the perspective of bid‐price processes. We show that an optimal bid‐price process has an upward trend over time before the inventory level falls to one and then has a downward trend. This intertemporal up‐then‐down pattern of bid‐price processes is related to two fundamental static properties of the optimal bid prices: (i) At any given time, a lower inventory level yields a higher optimal bid price, which is referred to as the resource scarcity effect; (ii) Given any inventory level, the optimal bid price decreases with time; that is referred to as the resource perishability effect. The demonstrated upward trend implies that the optimal bid‐price process is mainly driven by the resource scarcity effect, while the downward trend implies that the bid‐price process is mainly driven by the resource perishability effect. We also demonstrate how optimal bid price and consumer valuation, as two competing forces, interact over time to drive the optimal‐price process. The results are also extended to the network RM problems.     

Impact of Price Postponement on Capacity and Flexibility Investment Decisions

Investments in dedicated and flexible capacity have traditionally been based on demand forecasts obtained under the assumption of a predetermined product price. However, the impact on revenue of poor capacity and flexibility decisions can be mitigated by appropriately changing prices. While investment decisions need to be made years before demand is realized, pricing decisions can easily be postponed until product launch, when more accurate demand information is available. We study the effect of this price decision delay on the optimal investments on dedicated and flexible capacity. Computational experiments show that considering price postponement at the planning stage leads to a large reduction in capacity investments, especially in the more expensive flexible capacity, and a significant increase in profits. Its impact depends on demand correlation, elasticity and diversion, ratio of fixed to variable capacity costs, and uncertainty remaining at the times the pricing and production decisions are made.     

Dynamic Competition With Random Demand and Costless Search: A Theory of Price Posting

This paper studies a dynamic model of perfectly competitive price posting under demand uncertainty. Firms must produce output in advance. After observing aggregate sales in prior periods, firms post prices for their unsold output. In each period, the demand of a new batch of consumers is randomly activated. Existing customers who have not yet bought and then new customers arrive at the market in random order, observe the posted prices, and either purchase at the lowest available price or delay their purchase decision. We construct a sequential equilibrium in which the output produced and its allocation across consumers is efficient. Thus consumers endogenously sort themselves efficiently, with the highest valuations purchasing first. Transaction prices in each period rise continuously, as firms become more optimistic about demand, followed by a market correction. By the last period, prices are market clearing.