Improved bid prices for choice-based network revenue management

One of the latest developments in network revenue management (RM) is the incorporation of customer purchase behavior via discrete choice models. Many authors presented control policies for the booking process that are expressed in terms of which combination of products to offer at a given point in time and given resource inventories. However, in many implemented RM systems—most notably in the hotel industry—bid price control is being used, and this entails the problem that the recommended combination of products as identified by these policies might not be representable through bid price control. If demand were independent from available product alternatives, an optimal choice of bid prices is to use the marginal value of capacity for each resource in the network. But under dependent demand, this is not necessarily the case. In fact, it seems that these bid prices are typically not restrictive enough and result in buy-down effects.We propose (1) a simple and fast heuristic that iteratively improves on an initial guess for the bid price vector; this first guess could be, for example, dynamic estimates of the marginal value of capacity. Moreover, (2) we demonstrate that using these dynamic marginal capacity values directly as bid prices can lead to significant revenue loss as compared to using our heuristic to improve them. Finally, (3) we investigate numerically how much revenue performance is lost due to the confinement to product combinations that can be represented by a bid price.The heuristic is not restricted to a particular choice model and can be combined with any method that provides us with estimates of the marginal values of capacity. In our numerical experiments, we test the heuristic on some popular networks examples taken from peer literature. We use a multinomial logit choice model which allows customers from different segments to have products in common that they consider to purchase. In most problem instances, our heuristic policy results in significant revenue gains over some currently available alternatives at low computational cost.     

Signaling Quality: Dynamic Price-Advertising Model

This paper extends the existing quality-signaling literature by investigating the roles of price and advertising levels as quality indicators in a dynamic framework. Considering perceived quality as a form of goodwill, we modify the well-known Nerlove-Arrow dynamic model to include price effects. In our model, price is used both as a monetary constraint and as a signal of quality, while advertising spending is used only as a signaling device, and thus purely as a dissipative expense. Utilizing optimal control, we determine optimal decision rules for a firm regarding both price and advertising over time as functions of perceived quality. The results indicate that, when prices act as monetary constraints and are reduced to increase demand, the firm should use the signaling role of advertising by increasing spending to accelerate perceived quality increases. In cases when the value of the perceived quality goes up together with the increase in the perceived quality by more than the demand, in percentage terms, the firm should increase the price (use its signaling role). At steady-state, we find that the level of optimal profit margin relative to price decreases with the elasticity of demand with respect to the brand price. However, higher elasticity of demand with respect to the firm’s perceived quality and/or a higher impact of price (advertising) lead/leads to a higher optimal profit margin (advertising spending) relative to price (revenue).     

考虑保质期的非即时易腐品最优订购与定价决策

针对有保质期约束的非即时易腐品,零售商可以在产品非腐败阶段和腐败阶段进行差异化定价来调整市场需求。即零售商可以调整产品非腐败阶段的定价策略,使得非即时易腐品在进入腐败阶段之前全部售出;或者在产品腐败阶段降低零售价格以刺激市场需求。因此,在需求依赖价格的假设下,本文研究了零售商关于有保质期约束的非即时易腐品的最优订购与定价决策。通过分析零售商单位时间利润函数的理论性质,得到了零售商的最优订购与定价策略。基于线性和指数型两种需求函数形式进行数值算例,可以发现针对保质期较长或者非腐败阶段较长的易腐品,零售商会延长订货周期来增加销售收入。特别是在指数型需求函数情境下,当市场需求与零售价格高度相关时,零售商更有意愿降价来刺激销量,从而使得易腐品在非腐败阶段内销售完毕。     

Dynamic zigzag pricing of resalable goods with no depreciation and intergroup externalities

This paper addresses the pricing policy of durable value goods that do not depreciate over time. This implies that demands for this type of goods fluctuate with respect to their market price and social interactions between customers rather than with respect to the time elapsed since they have been produced or created. We suggest an analytical approach for optimally setting durable value product prices with respect to the interdependency between two customer groups characterized by asymmetric intergroup externalities. We demonstrate that cyclic pricing policies of harmonic form become optimal when the company is prepared to compromise its short-run net profit to ensure its lasting reputation. Furthermore, we show that the greater the difference between the product of the price and the externality effect of the two customer groups, the greater the frequency of the harmonic fluctuation.     

Modeling of optimal investment in science and technology

The latest achievements in science and technology lead to the development of new and more productive capital that can essentially increase a company’s profit. On the other hand, companies should invest not only in the productive capital, but also in science and technology.

The optimal control of an economic system that divides its output among the production of consumption goods, the accumulation of new capital, and the contribution to science and technology is considered. The model is expressed as nonlinear integral equations with unknowns in the integrands and lower limits of integration. An optimization problem for the profit maximization is suggested. The necessary condition for an extremum and the second variation of the functional are derived. The structure of optimal solutions is analyzed. Interpretation of all results is provided.     

For what trading strategies is the tax payment stream of infinite variation?

For an Itô asset price process and under quite mild structural assumptions, we show that the accumulated payments of a linear tax on trading gains are of infinite variation if the quadratic covariation of the trading strategy and the asset price is negative. By contrast, if the strategy is a smooth function of the asset price and some finite variation processes with positive partial derivative with respect to the price variable, then accumulated tax payments are of finite variation. An interesting example are constant proportion portfolio insurance (CPPI) strategies which we extend to models with capital gains taxes. The associated tax payment stream is of finite variation if the tax-adjusted constant multiple of the cushion which is invested in the risky asset is bigger or equal to one. Otherwise, it is of infinite variation.     

An examination of the role of price insurance products in stimulating investment in agriculture supply chains for sustained productivity

This study examines how managing risk by introducing commodity price insurances may improve the likelihood of increased investment in agri-food supply chains. A model is introduced which shows how insurance products on index prices can reduce the uncertainty of the impact of investment, and also how lower investment can generate the same impact as a higher investment. To show our results, we use two different frameworks which include total profit (Pareto optimal) and Stackelberg game setups. The results demonstrate that in both frameworks the investment will have a greater impact when an insurance product is present. By implication, the study presents an encouraging message to the insurance industry to introduce products to secure supply chain actors’ revenue leading to an increase in investment rate. Consequently, the study offers insight into how the role of traditional government subsidies for protecting farmers, particularly the small to medium-sized farms, may be revisited by replacing some of the existing subsidisation policies with revenue insurance.     

Arbitrage and the tax code

We provide a detailed characterization of arbitrage-free asset prices in the presence of capital gains and income taxes. The distinguishing feature of our analysis is that we impose on the model two important features of the tax code: the limited use of capital losses and the inability to wash sell. We show that under remarkably mild conditions, the lack of pre-tax arbitrage implies the lack of post-tax arbitrage with the limited use of capital losses. The conditions are that the risk free interest rate be positive and that tax rates on interest income exceed capital gains tax rates. The result also holds when only a wash sale constraint is imposed and no investor holds a portfolio with a large capital loss. We allow investors to face different tax rates and have different bases for the calculation of capital gains taxes. The characterizations we provide have important implications for both asset pricing and portfolio choice. Our results imply that models that use arbitrage-free pre-tax models continue for derivative pricing and hedging are also arbitrage free in a world with taxes. Similarly, portfolio choice models with taxes typically specify pre-tax arbitrage free price processes and then analyze portfolio choice in the presence of taxes. In these models, it is unclear if portfolio recommendations are based on risk-return tradeoffs or on the arbitrage opportunities present in the model. Our results imply that if the above features of the tax code are modeled explicitly, then we can isolate the post-tax risk-return tradeoffs.     

A multi-item newsvendor problem with preseason production and capacitated reactive production

Given items with short life cycles or seasonal demands, one can potentially improve profits by producing during the selling season, especially when its production capacity is substantial. We develop a two-stage, multi-item model incorporating reactive production that employs a firm’s internal capacity. Production occurs in an uncapacitated preseason stage and a capacitated reactive stage. Demands occur in the reactive stage. Reactive capacities are pre-allocated to each item in the preseason stage and cannot be changed during the reactive stage. Reactive production occurs during the selling season with full knowledge of demands. The objective is expected profit maximization. Unsatisfied demand is lost. The revenue, salvage value, and production and lost sales costs are proportional. Assuming no fixed costs, we present a simple algorithm for computing optimal policies. For a model with fixed costs for allocating preseason stage production and reactive stage capacity to product families, we characterize optimal policies and develop optimal and heuristic algorithms.     

多重参照点、公平偏好和三级供应链协调机制设计

在“单个制造商—单个分销商—单个零售商”三级供应链框架下,考察零售商依赖于多重参照点的公平偏好对于供应链运作造成的偏差,并在此基础上设计一个能够实现供应链整体协调的利润共享组合契约。研究发现:零售商对分销商利润和制造商利润的公平感知影响批发价格和分销价格变动的机制具有差异性;零售商的公平偏好不影响供应链的整体利润,但是会引起利润在各厂商间的重新分配;通过实行一个合理的利润共享组合契约,可以在零售商具有公平偏好的情形下达到供应链全局最优。最后用数值仿真验证了该利润共享组合契约作为协调机制的可行性。     

Optimal admission and pricing control problem with deterministic service times and sideline profit

We consider a discrete-time admission control problem in a company operating in service industries with two classes of customers. For the first class of customers, the company then (1) has an option to accept or reject him/her (admission control), or (2) decides on an offering price (pricing control). The second-class (sideline) customers are only served if no first-class customers are in the system, and this yields the sideline profit. In this paper, we discuss both admission control and pricing control problems within an identical framework, and we examine the properties of the optimal policies to maximize the total expected present discounted net profits. We show that when the sideline profit is large, the optimal policies may not be monotone in the number of first-class customers in the system.     

A pricing model for clearing end-of-season retail inventory

The problem of setting prices for clearing retail inventories of fashion goods is a difficult task that is further exacerbated by the fact that markdowns enacted near the end of the selling season have a smaller impact on demand. In this article, we present discrete-time models for setting clearance prices in such an environment. When demand is deterministic, we compute optimal prices and show that decreasing reservation prices lead to declining optimal prices. When demand is stochastic and arbitrarily correlated across planning periods, we obtain bounds on the optimal expected revenue and on optimal prices. We also develop a heuristic procedure for finding near-optimal prices and test its accuracy through numerical experiments. These experiments reveal new insights for practitioners. For example, the penalty for choosing clearance price once and keeping it unchanged for the remainder of the selling season is found to be small when either the mean reservation prices do not change appreciably over time or when they drop sharply after the first period.     

Risk-averse order policies with random prices in complete market and retailers’ private information

We consider a retailer who orders products before the price for them becomes known. The price is an outcome of perfect competition in a complete market. Since the demand is price sensitive, the uncertainty in prices induces uncertain profits and associated risks. In this paper we show that if the retailer is risk averse and, as a result, selects a utility function of profit to maximize, then his subjective assessment of future prices is affected by the risk attitude. This, in turn, introduces a bias in retailer’s ordering policies. By considering coordinated pricing and ordering policies we derive a relationship between risk aversion, retailer’s subjective (private) assessment and the market implied, risk neutral forecast. This relationship and the induced bias are then illustrated for two typical operations management strategies which involve either inventory considerations or promotions avoiding accumulation of stocks.     

Firm and industry level profit efficiency analysis using absolute and uniform shadow prices

We discuss the nonparametric approach to profit efficiency analysis at the firm and industry levels in the absence of complete price information. Two new insights are developed. First, we measure profit inefficiency in monetary terms using absolute shadow prices. Second, we evaluate all firms using the same input–output prices. This allows us to aggregate firm-level profit inefficiencies to the overall industry inefficiency. Besides the measurement of profit losses, the presented approach enables one to recover absolute price information from quantity data. We conduct a series of Monte Carlo simulations to study the performance of the proposed approach in controlled production environments.     

Optimal pricing and inventory policies with reliable and random-yield suppliers: characterization and comparison

In this paper, we study the joint pricing and inventory replenishment problem for a periodic-review inventory system with random demand and dual suppliers, one of the suppliers is reliable but more expensive, the other supplier is less expensive but is unreliable with random yield. We characterize the firm’s optimal policies that simultaneously determine the optimal ordering and pricing decisions in each period over a finite planning horizon, and investigate the impacts of supply source diversification and supplier reliability on the firm and on its customers. We show that having source diversification or higher reliability of suppliers not only increases the firm’s expected profit, but also results in a lower optimal selling price, thus they benefit both the firm and its customers.     

Dynamic inventory system with pricing adjustment for price-comparison shoppers

With numerous price-comparison websites and applications, consumers today are frequently conducting price-comparison shopping. As a result, retailers face an increasing challenge in predicting consumer demand and determining the optimal product price and inventory level accordingly. To address this issue, this paper proposes an inventory model with joint decisions of price and inventory to optimize the retailer's long-run average profit under price-comparison consumer shopping. We first formulate the demand arrival process for a retailer under price-comparison shopping to be affected by not only its own price but also its competitors'. Based on this demand arrival process, we then formulate the retailer's long-run average profit and derive properties of its optimal solution. Our model focuses on capturing the impact of price-comparison consumers on a retailer's optimal price and inventory decisions. In particular, we allow competitors' prices to affect the retailer's demand via two key factors: the manufacturer's suggested price and the variability of the outside lowest price. According to our results, when the suggested price increases, the retailer should lower its price to obtain more price-comparison customers from competitors, whereas when the variability of outside lowest price increases, the retailer should raise its price to increase per unit profit from nonprice-comparison customers.     

考虑消费者具有质量和价格偏好的双渠道供应链最优决策

产品价格和质量是消费者永恒的关注点。虽然多渠道给消费者带来了便捷的购物途径, 但是不同渠道的产品存在质量和价格分差异, 消费者在购买时须面对一个渠道、价格和质量的协调选择问题。本文提出了消费者对产品质量和价格偏好的双渠道定价决策模型, 并讨论了以制造商为领导者的分散决策和集中决策情形下的最优策略。比较了消费者偏好及产品质量水平对不同决策情形下的供应链决策的影响, 并通过设计收益共享契约机制实现了渠道的协调并证明了其有效性。研究表明:当产品质量在一定范围内时, 制造商和零售商可以获得最大利润;当消费者对质量的偏好逐渐增加时, 制造商的利润和零售商的利润随着消费者对质量的偏好提高而下降;制造商和零售商可以通过协调销售价格消除供应链的双重边际效应,从而实现供应链的协调。最后利用算例分析了消费者的质量、价格偏好对总利润的影响并给出了相应的管理启示。     

The acquisition of new technology and its impact on a firm's competitive position

The strategic decision concerning the optimal and dynamic acquisition of new technology is examined. The model focuses on a profit maximizing firm that optimally derives its price, level of output, and its level and composition of productive capacity over time. The acquisition of new technology and reduction of existing capacity may occur simultaneously, so that the composition of the firm's productive resources may be upgraded over time. It is assumed that the acquisition of new technology causes a reduction in production costs and a direct increase in the firm's demand. The demand experienced by the firm may be directly increased as a result of acquiring new technology due to benefits such as expanded product-mix or volume capabilities, improved quality of output, or improved customer service (shorter production lead time). In addition, it is shown that demand is indirectly increased due to the reduced production costs that enable the firm to charge a lower price. Therefore, the strategic impact of acquiring new technology is captured, since its effect on future demand and the firm's ability to meet the demand are considered. The importance of capturing the increased demand potential offered by the new technology is demonstrated through the analysis of numerical examples. In addition, the effect on the optimal solution caused by a variety of environmental conditions is examined. For example, the impact of technological innovation is observed by defining (i) the cost of acquiring technology as a decreasing function of time, and (ii) the effectiveness of new technology on reducing operating costs as an increasing function of time.     

Sharp distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios

We derive in closed form distribution free lower bounds and optimal subreplicating strategies for spread options in a one-period static arbitrage setting. In the case of a continuum of strikes, we complement the optimal lower bound for spread options obtained in [Rapuch, G., Roncalli, T., 2002. Pricing multiasset options and credit derivatives with copula, Credit Lyonnais, Working Papers] by describing its corresponding subreplicating strategy. This result is explored numerically in a Black-Scholes and in a CEV setting. In the case of discrete strikes, we solve in closed form the optimization problem in which, for each asset S₁ and S₂, forward prices and the price of one option are used as constraints on the marginal distributions of each asset. We provide a partial solution in the case where the marginal distributions are constrained by two strikes per asset. Numerical results on real NYMEX (New York Mercantile Exchange) crack spread option data show that the one discrete lower bound can be far and also very close to the traded price. In addition, the one strike closed form solution is very close to the two strike.     

Channel coordination through a revenue sharing contract in a two-period newsboy problem

This paper studies channel coordination through revenue sharing contract between a single retailer and a single wholesaler in a two-period newsboy problem. Two models are discussed, a single-buying-opportunity model and a two-buying-opportunity model. We discuss how the revenue sharing ratio and the wholesale prices are to be determined in order to achieve channel coordination and a win–win outcome. We find that the wholesale prices are set to be lower than the retail prices and the optimal revenue sharing ratio is linearly increasing in the wholesale prices. The proposed revenue sharing contract has more flexibility than price protection, in that the optimal revenue sharing ratio can be settled reasonably through negotiation between the retailer and wholesaler.