Optimal Pricing Model Research Articles

Optimal Opt-In Residential Time-of-Use Contract Based on Principal-Agent Theory

Installation of smart meters is increasing world-wide, opening the possibility to implement time-of-use (TOU) tariffs to moderate peak loads. This study is focused on the design of an optimal opt-in residential TOU tariff. Residential consumers are assumed to act in their private interests and maximize utility in response to tariffs. The regulated utility has a broader interest in maximizing societal welfare. However, the regulated utility cannot impose household behavior and cannot directly observe household type. Instead, the regulated utility must offer contract options including both a TOU tariff and current pricing to allow households to self-select the plan best suited to their interests. This paper proposes a simple flexible household utility function that can be calibrated with minimal data to describe diverse household behaviors and reveal household responses to different prices. An optimal pricing model is designed for the regulated utility, taking account of asymmetric information and potential household opportunistic behavior. Using economic constructs from principal-agent theory, the pricing model ensures participation among households most aligned with the regulated utility's desire. The pricing model can also be extended for competitive markets. A case study is performed to demonstrate the benefit the optional TOU tariff can realize.

Experimental Evidence on Transfer Pricing

Abstract We use incentivized economics experiments to test both the point predictions and comparative static predictions of optimal transfer pricing models, comparing behavior under varying conditions, including wholly versus partially-owned subsidiaries and different tariff and tax rates. As predicted, we find that transfer prices are responsive to relative tax and tariff rates as well as ownership proportions. Additionally, we examine convergence and learning in this setting. While individuals do not choose optimal transfer prices, their choices converge to optimal levels with experience. This paper thus makes two important contributions. First, by comparing behavior with theoretical predictions it provides evidence of whether (and when) individuals set transfer prices optimally. Second, by comparing behavior under conditions of full and partial ownership it provides evidence on the impact of policy interventions (like regulating ownership proportions by MNEs) on tax revenues.

A Profit Maximization Approach to Demand Response Management with Customers Behavior Learning in Smart Grid

In this paper, we propose a profit-maximization-based pricing optimization model for the demand response (DR) management with customer behavior learning in the context of smart grids. By recognizing the different consumption patterns between shiftable and curtailable appliances, two different and distinguished behavior models are proposed. For shiftable appliances whose energy consumption can be shifted from high price periods to low price periods but total energy consumption is fixed, a probabilistic behavior model and its learning algorithm are proposed to model an individual customer’s shifting probabilities dependent on different hourly prices. For curtailable appliances whose energy consumption cannot be shifted but total energy consumption can be adjusted, a regression model is proposed to model an individual customer’s usage patterns dependent on prices and temperatures. After proposing the learning algorithms to identify these proposed behavior models, this paper further develops a genetic algorithm-based distributed pricing optimization algorithm for DR management with the aim to maximize the retailer’s profit. Numerical results indicate the applicability and effectiveness of the proposed models and their benefits to the retailer by improving its profit.

Pricing Strategies for Hybrid Bundles: Analytical Model and Insights

Retailers are increasingly offering hybrid bundles—products that combine both good(s) and service(s). Some hybrid bundles, such as Lowe's flooring that combines flooring material (good) and flooring installation (service) are sold in traditional stores, while others, such as Best Buy's bundle that includes a computer (good) and tech support (service) are also offered online. The pricing strategy of a hybrid bundle is critical to its success. While pricing strategies for a goods bundle have been well-studied, those for a services bundle have been underexplored. Hybrid bundles, which fundamentally differ from bundles of goods or bundles of services, primarily with regard to quality variability and scalability, have received even less attention. Drawing from the pricing and bundling literatures for both goods and services, we develop an analytic model of optimal pricing for hybrid bundles by a monopolist retailer. We derive and illustrate many useful propositions, several of which are counter-intuitive. Our results show that an increase in quality variability of the service is associated with a higher optimal hybrid bundle price and a lower optimal price of the good, but a lower overall bundle profit. Our findings also reveal that the optimal price of the service (good) in a hybrid bundle is higher (lower) when the good has diminishing unit cost and the service has constant unit cost (i.e., the good is more scalable than the service). Our results also show that higher unit costs incurred to achieve lower service quality variability can result in higher (lower) profits when the cost increase is low (high). We discuss important implications of these insights for researchers and practitioners.

Price optimization – How to win a strategic whole

Tradition pricing efforts without specifying time span often attempt a short-term solution. A price optimization model factored in a customer lifetime value (LTV) study recently becomes a keen interest to many businesses striving for a long-term success. This article will discuss how to advance pricing models from a tactic focus to a strategic win. As such, two modeling steps will be covered thereby: (i) an intrinsic link between profit and price is first established with a contribution of LTV, particularly in direct marketing (DM) arena; (ii) a rigorous price equation is then migrated into a tabular simulation so that practitioners can alternatively resolve an optimization in either way.

A laboratory exploration for multi-period perishable food pricing

Purpose – The purpose of this paper is to put forward a multi-period dynamic pricing strategy for perishable food considering consumers’ price fairness perception. The impacts of the multi-period retail price, food freshness and inventory shortage risk on consumers’ heterogeneous willingness to pay (WTP) and their strategic purchasing behaviours are studied. Design/methodology/approach – The authors present a price optimization model for perishable food, and conduct a laboratory experiment to justify the theoretical model. The data collected are analysed by correlation analysis and nonparametric test. Findings – The results obtained reveal, first, food freshness and inventory shortage risk have effect on consumers’ heterogeneous WTP. Second, different retail prices lead to consumers’ strategically purchasing behaviours. Finally, consumers’ intertemporal price fairness perception and the food retailer’s long-term utility maximization can be achieved by developing multi-period dynamic pricing strategy. Practical implications – This study suggests the perishable food retailer to apply a step-by-step price markdown strategy. It aims at eliminating price unfairness perceptions caused by loss of freshness and high shortage risk of the perishable food in the subsequent selling periods within the shelf life. Some valuable managerial insights towards perishable pricing for food retailers are discussed. Originality/value – This study serves as the first step to utilize a laboratory experiment to dig out consumers’ intertemporal WTP towards perishable food. It also presents a novel way for describing consumers’ intertemporal price fairness perception by equalizing consumers’ average utilities considering consumer surplus, food freshness and shortage risk at different selling periods. The line of research on dynamic pricing concerning consumers’ price fairness perception is quite new in academic research, and has arisen due to its importance for food retailers of maximizing their long-term revenues and also of constructing mutual benefit and lasting connections with the consumers.

Collaborative Optimal Pricing Model of Dual-Channel Supply Chain

Dual-channel not only provides reasonable products but also a large quantity of opportunities, where the mem- bers' attitude towards risk has a major impact on channel optimization. In this paper, risks are classified as general risk and interruption risk. As for general risk, combined with risk-aversion attitude, mean-variance method is used to build op- timal pricing model and expected utility model based on independent decision-making and collaborative decision-making mode. Besides, online channel substitution effect factor and ratio factor that manufacturer bears promotional cost for re- tailers are considered. For interruption risk, combined with risk-aversion attitude, optimal pricing model and expected utility model based on independent decision-making mode. Finally, through numerical analysis, it is proved that dual- channel collaborative pricing enables to avoid risks effectively, and the channel member with higher degree of risk aver- sion tends to take collaborative pricing strategy.

Monopoly Pricing and Diffusion of (Social) Network Goods

I present a new model of optimal dynamic pricing and diffusion of a network good sold by a monopolist. The good in this model is a social network good in that each consumer’s value of the good within a social network increases as more of her neighbors use the good. In each period, the monopolist sets a subscription price and consumers myopically optimize their choices after comparing the overall adoption and the current subscription price. Thus, in contrast with one-sided diffusion models in the social network literature, the diffusion process arises as an equilibrium behavior of both the monopolist and consumers. As a result, I characterize a unique equilibrium, in which the diffusion process stays at a certain point. The equilibrium is efficient in that it involves the highest adoption rate with respect to the equilibrium subscription price. I also present the deadweight loss in the equilibrium and show how it depends on the connectivity of the underlying social network.

Bid price optimization for truckload carriers in simultaneous transportation procurement auctions

Abstract We study simultaneous transportation procurement auctions from a truckload carrier’s perspective. We formulate a stochastic bid price optimization model aimed at maximizing the carrier’s expected profit. The model accounts for synergies among lanes and competing carriers’ bid patterns. We develop an iterative coordinate search algorithm to find high-quality solutions. The benefits of employing the bid price optimization technology are demonstrated through computational experiments involving a simulated marketplace.

Optimal dealer pricing under transaction uncertainty

Dealers in securities markets are standing ready immediately to trade certain amounts of securities at stated bid and ask prices. This paper assumes that the amount of transactions follows an uncertain mean-reverting process associated with the bid and ask prices. In order to maximize the dealer's total wealth, an optimal dealer pricing model under transaction uncertainty is established. And the optimal bid price and ask price over time are derived. Finally, the variations of the optimal bid and ask prices with different parameters are presented.

Estimating flight-level price elasticities using online airline data: A first step toward integrating pricing, demand, and revenue optimization

We estimate flight-level price elasticities using a database of online prices and seat map displays. In contrast to market-level and route-level elasticities reported in the literature, flight-level elasticities can forecast responses in demand due to day-to-day price fluctuations. Knowing how elasticities vary by flight and booking characteristics and in response to competitors’ pricing actions allows airlines to design better promotions. It also allows policy makers the ability to evaluate the impacts of proposed tax increases or time-of-day congestion pricing policies. Our elasticity results show how airlines can design optimal promotions by considering not only which departure dates should be targeted, but also which days of the week customers should be allowed to purchase. Additionally, we show how elasticities can be used by carriers to strategically match a subset of their competitors’ sale fares. Methodologically, we use an approach that corrects for price endogeneity; failure to do so results in biased estimates and incorrect pricing recommendations. Using an instrumental variable approach to address this problem we find a set of valid instruments that can be used in future studies of air travel demand. We conclude by describing how our approach contributes to the literature, by offering an approach to estimate flight-level demand elasticities that the research community needs as an input to more advanced optimization models that integrate demand forecasting, price optimization, and revenue optimization models.

Estimation of Choice-Based Models Using Sales Data from a Single Firm

We develop a parameter estimation routine for multinomial logit discrete choice models in which one alternative is completely censored, i.e., when one alternative is never observed to have been chosen in the estimation data set. Our method is based on decomposing the log-likelihood function into marginal and conditional components. Our method is computationally efficient, provides consistent parameter estimates, and can easily incorporate price and other product attributes. Simulations based on industry hotel data demonstrate the superior computational performance of our method over alternative estimation methods that are capable of estimating price effects. Because most existing revenue management choice-based optimization algorithms do not include price as a decision variable, our estimation procedure provides the inputs needed for more advanced product portfolio availability and price optimization models.

Pricing strategy for product reuse with multiple quality levels and price- and availability-dependent demand

The study deals with optimal pricing model for recycling products, which are returned, recovered, and shipped into a secondary market for resale. The selling probability of recycling products is sensitive to their price and availability. This assumption is rational because price and availability often influence customer demand. The study also assumes that the three quality levels of collected returns exist, which affect the price they are sold for. This paper determines optimal selling prices for re-manufacturers. The exact closed-form solution is then derived and total profit is maximized to create the remanufacturing model. A numerical example and sensitivity analysis are conducted to demonstrate the model. The study provides managerial insights on the benefits of revenue management for product reuse. For example, if manager can develop an incentive return-subsidy policy to encourage consumer to offer better or more returns, the profits will increase more.

Modeling of Incentive Interruptible Load Contract for Practical Application

Interruptible load contract is an important means of demand side management, but its existing models cant coordinate practicality with efficiency. Based on the curtailment cost function of consumers, this paper proposes an optional interruptible load contract and builds an optimal curtailment amount and compensation pricing model by introducing information display and incentive mechanism. The model can guide consumers voluntarily disclose the information on their true cost, and achieve the optimal allocation of load interruption. It is better to coordinate the relationship between utility and economic efficiency, which is more efficient than the traditional practical optional contract for interruptible load, and more practical than the theoretical model of interruptible load contract of fully nonlinear pricing. Numerical examples verify the effectiveness of the proposed model.

Mathematical Model for Revenue Management with Overbooking and Costly Price Adjustment for Hotel Industries

Revenue management (RM) has been widely used to model products characterized as perishable. Classical RM model assumed that price is the sole factor in the model. Thus price adjustment becomes a crucial and costly factor in business. In this paper, an optimal pricing model is developed based on minimization of soft customer cost, one kind of price adjustment cost and is solved by Lagrange multiplier method. It is formed by expected discounted revenue/bid price integrating quantity-based RM and pricing-based RM. Quantity-based RM consists of two capacity models, namely, booking limit and overbooking. Booking limit, built by assuming uncertain customer arrival, decides the optimal capacity allocation for two market segments. Overbooking determines the level of accepted order exceeding capacity to anticipate probability of cancellation. Furthermore, pricing-based RM models occupancy/demand rate influenced by internal and competitor price changes. In this paper, a mathematical model based on game theoretic approach is developed for two conditions of deterministic and stochastic demand. Based on the equilibrium point, the best strategy for both hotels can be determined.

Solving Optimal Pricing Model for Perishable Commodities with Imperialist Competitive Algorithm

The pricing problem for perishable commodities is important in manufacturing enterprise. In this study, a new model based on the profit maximization principle and a discrete demand function which is a negative binomial demand distribution is proposed. This model is used to find out the best combination for price and discount price. The computational results show that the optimal discount price equals the cost of the product. Because the demand functions which involves several different distributions is so complex that the model is hard to solve with normal numerical method. Thus we combine the model with exterior penalty function and applied a novel evolution algorithm-Imperialist Competitive Algorithm (ICA) to solve the problem. Particle Swarm algorithm (PSO) is also applied to solve the problem for comparison. The result shows that ICA has higher convergence rate and execution speed.

The Model of Optimal Non-Queuing Pricing for Port Container Yard

As there are limited space and hardware equipment of Port Container Yard, export containers have to queue outside for entry if the container yard reaches its capacity saturation. Therefore, some containers probably could not be completed the loading preparation on time, which would cause great damage to the shipper. In order to solve this problem, this research establishes a queuing pricing model for port container yards. After implementation of this toll scheme, it will be effective in dispersing containers’ arriving time, and so as to eliminate the queuing phenomenon outside the entrance of container yard.

A joint optimal pricing and order quantity model under parameter uncertainty and its practical implementation

We consider a robust optimization model of determining a joint optimal bundle of price and order quantity for a retailer in a two-stage supply chain under uncertainty of parameters in demand and purchase cost functions. Demand is modeled as a decreasing power function of product price, and unit purchase cost is modeled as a decreasing power function of order quantity and demand. While the general form of the power functions are given, it is assumed that parameters defining the two power functions involve a certain degree of uncertainty and their possible values can be characterized by ellipsoids. We show that the robust optimization problem can be transformed into an equivalent convex optimization which can be solved efficiently and effectively using interior-point methods. In addition, we propose a practical implementation of the model, where the stochastic characteristics of parameters are obtained from regression analysis on past sales and production data, and ellipsoidal representations of the parameter uncertainties are obtained based on a combined use of genetic algorithm and Monte Carlo simulation. An illustrative example is provided to demonstrate the model and its implementation.

Strategic price positioning for revenue management: The effects of relative price position and fluctuation on performance

Emerging price optimization models systematically incorporate competitor price information into the derivation of optimal price points. While consideration of competitor pricing at this tactical level is essential to maximizing short-term revenues, the long-term impact of competitive price positioning on revenue performance should not be overlooked. This study examines the effect of two key dimensions of strategic price positioning – relative price position and relative price fluctuation – on the revenue performance of 6998 US hotels over an 11-year period. It finds that revenue performance is strongest for hotels that price higher than the competition and maintain a consistent relative price over time. Implications for revenue management practitioners are discussed.

스마트 그리드 환경의 전력소매시장을 위한 최적의 실시간 가격결정 모형에 대한 연구

최근 지구 온난화와 에너지 고갈 및 환경파괴로 인한 환경 문제에 대하여 세계 각국에서 심각하게 고민하고 있으며, 전기자동차의 상용화를 앞두고 이산화탄소 배출의 저감 및 효율적인 에너지 사용이 중요시 되고 있다. 또한, IT 기술의 발달과 함께 독점적인 전력공급에서 수요자가 참여하는 양방향 커뮤니케이션의 스마트 그리드의 개념이 도입되었다. 주요 국가들에서는 스마트 미터의 보급과 함께 에너지 사용의 효율성 개선을 위하여, 전력 경쟁시장에서 소비자의 수요반응의 활성화를 위한 인센티브의 지급 등의 정책도입이 요구되고 있다. 이에, 본 연구에서는 머지않아 등장할 소매전력시장에서 소비자의 수요반응을 증진하여 소비자의 전기 사용 비용을 절감하며 소매사업자의 이익을 최대화하는 전력 가격결정 모델을 제시하였다. 소비자 수요반응 참여율과 가격 탄성률에 따른 시뮬레이션을 시행하여 수요 반응을 나타내는 소비자 별 탄성률을 모든 소비자가 시간대별 고정 값을 사용하는 것과 소비자 별 탄성률을 예측하는 것을 비교하였다. 이를 통하여 전력 소매 시장에서 소비자의 에너지 사용을 줄이고 소매업자의 이익을 최대화할 수 있음을 밝혔다. Recently, global warming, energy shortage, and environmental disruption have been serious problems in every nation. It became more and more important to reduce the emission of CO2 and to use of energy efficiently. Smart grid was also introduced using the rapidly developing information technology. It deployed the mutual communication concept between customers and the suppliers in the electricity supply. There were increasing demands to adopt the smart meter and to present incentive for efficient energy usage in many developed countries. The objective of this research was to develop the optimal real time pricing model which maximized the profit of the power retailer and reduced the usage of energy. The simulation study was given to show the usefulness of the model. Simulation considered the customer demand response rate and price elasticity rate. The price elasticity rate was compared in the condition of fixed value according to time and variable value according to the customers. The optimal price model could maximize the profit of the power retailer and reduce the energy usage of the consumers.