Electricity Time‐of‐Use Tariff with Stochastic Demand

In this article, we study the electricity time‐of‐use (TOU) tariff for an electricity company with stochastic demand. The electricity company offers the flat rate (FR) and TOU tariffs to customers. Under the FR tariff, the customer pays a flat price for electricity consumption in both the peak and non‐peak periods. Under the TOU tariff, the customer pays a high price for electricity consumption in the peak period and a low price for electricity consumption in the non‐peak period. The electricity company uses two technologies, namely the base‐load and peak‐load technologies, to generate electricity. We derive the optimal capacity investment and pricing decisions for the electricity company. Furthermore, we use real data from a case study to validate the results and derive insights for implementing the TOU tariff. We show that in almost all the cases, the electricity company needs less capacity for both technologies under the TOU tariff than under the FR tariff, even though the expected demand in the non‐peak period increases. In addition, except for some extreme cases, there is essentially no signicant reduction in the total demand of the two periods, although the TOU tariff can reduce the demand in the peak period. Under the price‐cap regulation, the customer may pay a lower price on average under the TOU tariff than under the FR tariff. We conduct an extensive numerical study to assess the impacts of the model parameters on the optimal solutions and the robustness of the analytical results, and generate managerial implications of the research findings.     

Pricing and Operational Performance in Discretionary Services

In many services, for example, website or landscape design, the value or quality derived by a customer depends upon the service time, and this valuation differs across customers. Customers procure the service based on the expected value to be delivered, prices charged, and the timeliness of service. We investigate the performance of the optimal pricing scheme as well as two commonly used pricing schemes (fixed fee and time‐based pricing) for such services on important dimensions such as revenue, demand served, and utilization. We propose a novel model that captures the above features and wherein both service rate and demand are endogenous and functions of the pricing scheme. In particular, service time is an outcome of the pricing scheme adopted and the heterogeneous valuations of customers, unlike in the queueing‐based pricing literature. We find that the service system may benefit from a greater variance in consumer valuations, and the performance of pricing schemes is impacted by the shape of the distribution of customers' valuation of service time and the responsiveness desired by customers. Both the fixed fee and time‐based schemes do well relative to the optimal pricing scheme in terms of revenue in many plausible scenarios, but there are substantial differences between the pricing schemes in some important operational metrics. For instance, the fixed fee scheme serves more customers and has higher utilization than the time‐based scheme. We also explore variants of the fixed and time‐based schemes that have better revenue performance and show that the two‐part tariff which is a combination of fixed and time‐based pricing can do as well as the optimal scheme in terms of revenue.     

Profitability of Service‐Level‐Based Price Differentiation with Inventory Rationing

In this paper, we study the profitability of service‐level‐based price differentiation (SLBPD) in an inventory‐rationing context. SLBPD implies that a company offers several combinations of prices and guaranteed service levels, from which customers self‐select; different customers choose different offerings because they incur different shortage costs if an order is not fulfilled immediately. We develop an analytical model for SLBPD and explore if and when such a service differentiation strategy yields higher profits than a single undifferentiated offering. The results of our analyses suggest that SLBPD is profitable only if a company faces pricing restrictions, e.g., because of competitive pressure or regulatory restrictions. We develop necessary and sufficient conditions under which a specific and relevant form of SLBPD (called “service‐level‐based upselling”) is profitable, and provide an algorithm to compute the optimal parameters of such a policy. Based on this algorithm we carry out numerical analyses that allow us to characterize the profit increment of service‐level‐based upselling. We derive managerial insights into the attractiveness of SLBPD and explain how our basic analytical framework can be extended to account for more complex practical features.     

Optimal Uniform Pricing Strategy of a Service Firm When Facing Two Classes of Customers

When facing heterogeneous customers, how should a service firm make its pricing decision to maximize revenue? If discrimination is allowed, then priority schemes and differentiated pricing are often used to achieve that. In many applications, however, the firm cannot or is not allowed to set discriminatory prices, for example, list price in retail stores, online shopping, and gas stations; thus a uniform price must be applied to all customers. This study addresses the optimal uniform pricing problem of a service firm using a queueing system with two classes of customers. Our result shows that the potential pool of customers plays a central role in the firm's optimal decision. Depending on the range of system parameters, which are determined explicitly by the primitive data, the firm's optimal strategy may choose to serve only one class of customers, a subset of a class of customers, or a combination of different classes of customers. In addition, the optimal price is in general not monotonic with respect to the potential market sizes because their changes may lead to a major shift in the firm's decision on which customer class to serve. However, unless such a shift occurs, the optimal price is weakly decreasing in the potential market sizes.     

Static and Dynamic Pricing of Excess Capacity in a Make‐to‐Order Environment

We consider a make‐to‐order manufacturer that serves two customer classes: core customers who pay a fixed negotiated price, and “fill‐in” customers who make submittal decisions based on the current price set by the firm. Using a Markovian queueing model, we determine how much the firm can gain by explicitly accounting for the status of its production facility in making pricing decisions. Specifically, we examine three pricing policies: (1) static, state‐independent pricing, (2) constant pricing up to a cutoff state, and (3) general state‐dependent pricing. We determine properties of each policy, and illustrate numerically the financial gains that the firm can achieve by following each policy as compared with simpler policies. Our main result is that constant pricing up to a cutoff state can dramatically outperform a state‐independent policy, while at the same time achieving most of the increase in revenue achievable from general state‐dependent pricing. Thus, we find that constant pricing up to a cutoff state presents an attractive tradeoff between ease of implementation and revenue gain. When the costs of policy design and implementation are taken into account, this simple heuristic may actually out‐perform general state‐dependent pricing in some settings.     

电子市场中时间价格敏感需求下的交货期定价决策

电子市场中,如何通过交货期报价来增大需求、提高收益,对于网络营销企业来说是至关重要的.本文假定在一个包含网络营销企业与其客户的运作系统中,需求同时对价格与时间都敏感的条件下,以最优化自身收益为目标、以满足必须达到规定的服务水平为主要约束条件,构建了交货期定价决策模型.通过数值算例,探讨了在电子市场中消费者为价格敏感或交货期敏感时,网络营销企业的最优定价策略.上述结论可以为网络营销企业在电子市场中的定价决策提供有益的指导.     

Competitive Pricing in a Multi‐Product Multi‐Attribute Environment

We address the problem of simultaneous pricing of a line of several products, both complementary products and substitutes, with a number of distinct price differentiation classes for each product (e.g., volume discounts, different distribution channels, and customer segments) in both monopolistic and oligopolistic settings. We provide a generic framework to tackle this problem, consider several families of demand models, and focus on a real‐world case‐study example. We propose an iterative relaxation algorithm, and state sufficient conditions for convergence of the algorithm. Using historical sales and price data from a retailer, we apply our solution algorithm to suggest optimal pricing, and report on numerical results.     

基于异质性顾客心理期望等待时间的优先权服务定价研究

本文以非抢占式M/M/1排队系统为背景,以企业收益最大化为目标,基于顾客异质性(单位时间等待成本不同)将顾客分为两类,针对顾客的心理期望等待时间对服务提供商最优定价策略的影响进行研究。首先研究优先权顾客心理期望等待时间对企业收益的影响以及相应的优先权定价,然后研究优先权顾客和普通顾客同时存在心理期望等待时间对企业收益的影响和相应的优先权定价。研究表明:仅考虑优先权顾客的心理期望等待时间,企业应通过提高优先权定价来获得最优收益;当优先权顾客和普通顾客同时存在心理期望等待时间时,企业仍然采取提高优先权定价的策略,若普通顾客的价值大(获取服务的基本费用大),企业应对普通顾客提供一定的折扣来消除其心理期望等待时间增加企业收益;如果普通顾客的价值较小,企业应"有意"流失部分普通顾客,吸引更多顾客到优先权队列获取服务来获得更多收益。本文研究对于服务提供商在考虑顾客心理期望等待时间基础上设置最合理的队列机制有一定的指导意义和实际应用价值。     

Optimal Dynamic Pricing of Perishable Items by a Monopolist Facing Strategic Consumers

We introduce a dynamic pricing model for a monopolistic company selling a perishable product to a finite population of strategic consumers (customers who are aware that pricing is dynamic and may time their purchases strategically). This problem is modeled as a stochastic dynamic game in which the company's objective is to maximize total expected revenues, and each customer maximizes the expected present value of utility. We prove the existence of a unique subgame‐perfect equilibrium pricing policy, provide equilibrium optimality conditions for both customer and seller, and prove monotonicity results for special cases. We demonstrate through numerical examples that a company that ignores strategic consumer behavior may receive much lower total revenues than one that uses the strategic equilibrium pricing policy. We also show that, when the initial capacity is a decision variable, it can be used together with the appropriate pricing policy to effectively reduce the impact of strategic consumer behavior. The proposed model is computationally tractable for problems of realistic size.     

Exploring the Impact of Delivery Performance on Customer Transaction Volume and Unit Price: Evidence from an Assembly Manufacturing Supply Chain

This study examines the effect of delivery performance on customer transactions. We propose that different delivery performance dimensions (on‐time delivery rate, early delivery inaccuracy, late delivery inaccuracy, and delivery speed) have varying impacts on future customer transaction quantities and unit prices. We further explore the effect of customer types on the proposed relationships. Trade customers (resellers) and Original Equipment Manufacturer (OEM) customers generally have different operational needs for deliveries and therefore may value these metrics differently. Using instrumental variable regression, we analyze a proprietary transaction‐level dataset. The information was compiled by a Fortune 500 manufacturer from its Heating, Ventilation and Air Conditioning (HVAC) control product supply chain, consisting of the manufacturer and its customers. The results indicate that measures of delivery performance affect customer transaction quantity and unit price differently. Furthermore, these impacts can differ significantly between trade customers and OEM customers. These findings provide fine‐grained insights about tuning delivery capabilities to increase sales volume or boost price.     

竞争环境下客户服务投入对企业利润影响的均衡分析

客户服务投入是企业吸引新顾客和维持现有顾客的重要手段之一。然而,服务投入究竟是否能给企业带来价值？对于这一问题,业界和学界都没有明确的答案。本文通过建模的方法研究在竞争的市场环境下,固有的市场因素对客户服务投入价值的影响。研究发现,服务竞争的市场均衡结构是两家厂商都投入客户服务。服务投入给企业带来的价值随着产品差异度的提高而提高,随着厂商自身市场份额的增加而增加。即,在产品差异度高的市场,服务投入更容易给企业带来价值。而在集中度高的市场,服务投入更容易给市场份额大的企业带来价值。     

Service Systems with Experience‐Based Anecdotal Reasoning Customers

The existing queueing literature typically assumes that customers either perfectly know the expected waiting time or are able to form rational expectations about it. In contrast, in this article, we study canonical service models where customers do not have such full information or capability. We assume that customers lack full capability or ample opportunities to perfectly infer the service rate or estimate the expected waiting time, and thus can only rely on past experiences and anecdotal reasoning to make their joining decisions. We fully characterize the steady‐state equilibrium in this service system. Compared with the fully rational benchmark, we find that customers with anecdotal reasoning are less price‐sensitive. Consequently, with a higher market potential (higher arrival rate), a revenue‐maximizing firm may increase the price if the service rate is exogenous, and it may decrease the price if the service rate is at the firm's discretion. Both results go against the commonly accepted pricing recommendations in the fully rational benchmark. We also show that revenue maximization and welfare maximization lead to fundamentally different pricing strategies with anecdotal reasoning, whereas they are equivalent in the fully rational benchmark.     

考虑计算资源容量的云服务垄断定价研究

云服务是针对虚拟计算资源的访问服务，客户价值差异与资源能力约束是影响云服务定价决策的重要因素。针对云服务市场中按固定价格和按用量定价两种常用定价方式，提出一般性假设并构建旨在最大化垄断利润的非线性定价模型，对模型求解并对模型解的含义进行揭示。给出数值算例，从市场覆盖、计算资源影子价格、厂商利润及客户剩余等方面对两种定价方法进行比较，结果表明：客户类型分布影响厂商利润、客户剩余及计算资源需求，厂商应努力掌握客户类型分布信息；计算资源充足时应采用按用量定价方法；市场覆盖与客户类型分布及可用计算资源量有关，按用量定价时市场覆盖更大；增加计算资源有利于提升社会福利。本文为云服务厂商定价决策提供理论与方法支持。     

TIME‐BASED PRICING AND LEADTIME POLICIES FOR A BUILD‐TO‐ORDER MANUFACTURER

We studied time‐based policies on pricing and leadtime for a build‐to‐order and direct sales manufacturer. It is assumed that the utility of the product varies among potential customers and decreases over time, and that a potential customer will place an order if his or her utility is higher than the manufacturer's posted price. Once an order is placed, it will be delivered to the customer after a length of time called “leadtime.” Because of the decrease in a customer's utility during leadtime, a customer will cancel the order if the utility falls below the ordering price before the order is received. The manufacturer may choose to offer discounted prices to customers who would otherwise cancel their orders. We discuss two price policies: common discounted price and customized discounted price. In the common discounted price policy, the manufacturer offers a single lower price to the customers; in the customized discounted price policy, the manufacturer offers the customers separately for individual new prices. Our analytical and numerical studies show that the discounted price policies results in higher revenue and that the customized discounted price policy significantly outperforms the common discounted price policy when product utility decreases rapidly. We also study two leadtime policies when production cost decreases over time. The first uses a fixed leadtime, and the second allows the leadtime to vary dynamically over time. We find that the dynamic leadtime policy significantly outperforms the fixed leadtime policy when the product cost decreases rapidly.     

A WTP‐Choice Model: Empirical Validation,Competitive and Centralized Pricing

Willingness To Pay (WTP) of customers plays an anchoring role in pricing. This study proposes a new choice model based on WTP, incorporating sequential decision making, where the products with positive utility of purchase are considered in the order of customer preference. We compare WTP‐choice model with the commonly used (multinomial) Logit model with respect to the underlying choice process, information requirement, and independence of irrelevant alternatives. Using WTP‐choice model, we find and compare equilibrium and centrally optimal prices and profits without considering inventory availability. In addition, we compare equilibrium prices and profits in two contexts: without considering inventory availability and under lost sales. One of the interesting results with WTP‐choice model is the “loose coupling” of retailers in competition; prices are not coupled but profits are. That is, each retailer should charge the monopoly price as the collection of these prices constitute an equilibrium but each retailer's profit depends on other retailers' prices. Loose coupling fails with dependence of WTPs or dependence of preference on prices. Also, we show that competition among retailers facing dependent WTPs can cause price cycles under some conditions. We consider real‐life data on sales of yogurt, ketchup, candy melt, and tuna, and check if a version of WTP‐choice model (with uniform, triangle, or shifted exponential WTP distribution), standard or mixed Logit model fits better and predicts the sales better. These empirical tests establish that WTP‐choice model compares well and should be considered as a legitimate alternative to Logit models for studying pricing for products with low price and high frequency of purchase.     

Newsvendor Pricing Problem in a Two‐Sided Market

We study the pricing problem of a “platform” intermediary to jointly determine the selling price of the platforms (hardware) sold to consumers and the royalty charged to content developers for content (software), when the demands for content and for platforms are interdependent. Our model elucidates the impact of supply chain replenishment costs and demand uncertainty on the strategic issues of platform pricing in a two‐sided market.     

Fractional Price Matching Policies Arising from the Ocean Freight Service Industry

We consider a situation in which shippers (customers) can purchase ocean freight services either directly from a carrier (service provider)in advance or from the spot market just before the departure of an ocean liner. The price is known in the former case, while the spot price is uncertain ex‐ante in the latter case. Consequently, some shippers are reluctant to book directly from the carrier in advance unless the carrier is willing to “partially match” the realized spot price when it is lower than the regular price. This study is an initial attempt to examine if the carrier should bear some of the “price risk” by offering a “fractional” price matching contract that can be described as follows. The shipper pays the regular freight price in advance; however, the shipper will get a refund if the realized spot price is below the regular price, where the refund is a “fraction” of the difference between the regular price and the realized spot price. By modeling the dynamics between the carrier and the shippers as a sequential game, we show that the carrier can use the fractional price matching contract to generate a higher demand from the shippers compared to no price matching contract by increasing the “fraction” in equilibrium. However, as the carrier increases the “fraction,” the carrier should increase the regular price to compensate for bearing additional risk. By selecting the fractional price matching contract optimally, we show that the carrier can afford to offer this price matching mechanism without incurring revenue loss: the optimal fractional price matching contract is “revenue neutral.”     

Optimizing Customer Forecasts for Forecast‐Commitment Contracts

We study a “Forecast‐Commitment” contract motivated by a manufacturer's desire to provide good service in the form of delivery commitments in exchange for reasonable forecasts and a purchase commitment from the customer. The customer provides a forecast for a future order and a guarantee to purchase a portion of it. In return, the supplier commits to satisfy some or all of the forecast. The supplier pays penalties for shortfalls of the commitment quantity from the forecast, and for shortfalls of the delivered quantity from the customer's final order (not exceeding the commitment quantity). These penalties allow differential service among customers. In Durango‐Cohen and Yano (2006), we analyzed the supplier's problem for a given customer forecast. In this paper, we analyze the customer's problem under symmetric information, both when the customer is honest and when he strategically orders more than his demand when doing so is advantageous. We show that the customer gains little from lying, so the supplier can use his control over the contract parameters to encourage honesty. When the customer is honest, the contract achieves (near‐)coordination of the supply chain in a great majority of instances, and thus provides both excellent performance and flexibility in structuring contracts.     

A Choice‐Based Dynamic Programming Approach for Setting Opaque Prices

Opaque pricing is a form of pricing where certain characteristics of the product or service are hidden from the consumer until after purchase. In essence, opaque selling transforms a differentiated good into a commodity. Opaque pricing has become popular in service pricing as it allows firms to sell their differentiated product at higher prices to regular brand loyal customers while simultaneously selling to non‐brand loyal customers at discounted prices. We use a nested logit model in combination with logistic regression and dynamic programming to illustrate how a service firm can optimally set prices on an opaque sales channel. The choice model allows the characterization of consumer trade‐offs when purchasing opaque products while the dynamic programming approach allows the characterization of the optimal pricing policy as a function of inventory and time remaining. We compare optimal prices and expected revenues when dynamic pricing is restricted to daily price changes. We provide an illustrative example using data from an opaque selling mechanism ( Hotwire.com ) and a Washington DC‐based hotel.     

考虑退货风险的制造商双渠道供应链定价决策研究

针对事前不确定性导致的退货问题,从消费者行为出发,建立考虑定价差异和退货风险双重因素的市场需求函数,通过Stackelberg博弈模型研究四种不同市场需求情形在不同定价模式下双渠道供应链的最优决策。在数值仿真部分,对不同情形决策之间比较、供应链收益进行比较分析。研究表明：电子渠道销售价格与电子渠道的市场基本需求成正比,批发价和传统渠道销售价格与传统渠道的市场基本需求成正比,实体店体验服务水平和传统渠道的市场基本需求的关系（线性关系）则根据某些条件而定;退货风险对供应链决策的影响与定价模式、市场需求影响因素相关;制造商偏好于定价不相等模式,零售商偏好于定价相等模式;退货风险与定价差异对供应链成员收益的影响与定价模式相关,对整体供应链收益的影响与定价模式和退货率大小有关。