Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly

This paper analyzes the impact of dynamic and fixed-ratio pricing policies on firm profits and equilibrium prices under competition. Firms that have equal inventories of perfectly substitutable and perishable products compete for customer segments that demand the product at different times. In each period, customers first purchase from the low price firm and then from the high price firm up to their inventories, provided the prices are lower than the maximum they are willing to pay. The main conclusions of this paper are as follows: although dynamic pricing is a more sophisticated policy than fixed-ratio pricing, it may lead to decreased equilibrium profits; under both pricing policies, one firm assumes the role of a low-cost high-output firm while the other assumes the role of a high-cost low-output firm; and, the supply demand ratio has more impact on the outcome of the competition than the heterogeneity in consumer reservation prices.     

Retail store location and pricing within a competitive environment using constrained multinomial logit

The purpose of this paper is to report a pricing and retail location model using the constrained multinomial logit (CMNL), which takes into account customers’ utility and maximum willingness to pay via cut-off soft-constraints. The proposed model is probabilistic and non-linear, therefore a PSO metaheuristic approach was designed to determine the most suitable price, store locations and demand segmentation. The results obtained in test-cases showed a close relationship between price and location decisions. In addition, the results suggest that not only price, but also location decisions are affected when the consumers’ maximum willingness to pay is considered.     

A simulation of the impacts of dynamic price management for perishable foods on retailer performance in the presence of need-driven purchasing consumers

Numerous studies have investigated dynamic pricing for perishable products. The models have been designed to determine an optimal pricing structure and improve retailer performance. Previous studies on pricing models for perishable products have considered various assumptions of consumer demand and purchasing behaviour from deterministic and stochastic price-dependent demands to myopic and strategic consumer purchasing behaviour. They have not, however, considered consumer demand in reaction to a situation where the display stock of a particular product has different qualities (such as shelf-life) and prices available at the same time. This is particularly applicable in the analysis of dynamic pricing models for perishable foods. In this paper, we investigate the impact of frequency of discount during a product’s selling period on retailer performance, by considering changes in consumer purchasing behaviour in response to the display stock of a particular food product having different remaining shelf-life and prices. On the basis of a literature review and data obtained from interviews with food retailers, a simulation study is performed to compare the performance of different pricing policies. The results demonstrate the benefits gained by adopting more dynamic price policies.     

Structural Electricity Models and Asymptotically Normal Estimators to Quantify Parameter Risk

ABSTRACT

We estimate a structural electricity (multi-commodity) model based on historical spot and futures data (fuels and power prices, respectively) and quantify the inherent parameter risk using an average value at risk approach (‘expected shortfall’). The mathematical proofs use the theory of asymptotic statistics to derive a parameter risk measure. We use far in-the-money options to derive a confidence level and use it as a prudent present value adjustment when pricing a virtual power plant. Finally, we conduct a present value benchmarking to compare the approach of temperature-driven demand (based on load data) to an ‘implied demand approach’ (demand implied from observable power futures prices). We observe that the implied demand approach can easily capture observed electricity price volatility whereas the estimation against observable load data will lead to a gap, because – amongst others – the interplay of demand and supply is not captured in the data (i.e., unexpected mismatches).     

Channel Coordination with Cooperative Advertising Considering Effect of Advertising on Willingness to Pay

In this paper, cooperative advertising in a manufacturer–retailer supply chain is studied. Advertising can enhance willingness to pay (WTP) of customers. This trade-off between the benefits of increasing WTP of customers and the advertising expenditure is a key to understanding the retailers optimal advertising decision. On the other hand, it is interesting to understand in which condition supporting the retailer for his advertising expenditure is beneficial for the manufacturer. In this study, in order to capture pricing and advertising strategies of the channel member, three non-cooperative games including Nash, Stackelberg retailer and Stackelberg manufacturer game-theoretic models are established. In spite of the related studies which restrict price in order to prevent negative demand, the proposed model allows channel members to increase their prices by enhancing WTP of customers. In this study, contrary to similar additive form demand functions applied in the co-op ad literature which limits their studies for cases that profit function is concave with respect to variables, optimal prices and advertising strategies are obtained for all the solution space. Surprisingly for the very high values of the advertising effect coefficient, a finite optimal advertising expenditure is achieved.     

Pricing and market segmentation using opaque selling mechanisms

In opaque selling certain characteristics of the product or service are hidden from the consumer until after purchase, transforming a differentiated good into somewhat of a commodity. Opaque selling has become popular in service pricing as it allows firms to sell their differentiated products at higher prices to regular brand loyal customers while simultaneously selling to non-loyal customers at discounted prices. We develop a stylized model of consumer choice that illustrates the role of opaque selling in market segmentation. We model a firm selling a product via three selling channels: a regular full information channel, an opaque posted price channel and an opaque bidding channel where consumers specify the price they are willing to pay. We illustrate the segmentation created by opaque selling as well as compare optimal revenues and prices for sellers using regular full information channels with those using opaque selling mechanisms in conjunction with regular channels. We also study the segmentation and policy changes induced by capacity constraints.     

Dynamic pricing and strategic retailers in the energy sector: A multi-leader-follower approach

We consider strategic retail pricing in markets, where retail companies buy commodities at fluctuating wholesale prices and resell them to final consumers by applying dynamic retail tariffs. This is of especially large relevance in the context of energy markets where substantial wholesale price fluctuations are observed. Policy makers currently foster the introduction of such dynamic tariff schemes. From a modelling point of view, we propose a multi-leader-follower problem to investigate the implications of strategic retail pricing and we compare the impacts of implementing dynamic tariffs on retailers and final consumers. Our analysis tackles different aspects: first, we formulate the model and provide theoretical results. Second, we develop algorithms, which solve the multi-leader-follower problem and allow us to characterize the resulting market equilibria. Third, we calibrate and solve our framework based on data of the German retail electricity market for the years 2020 and 2021. This allows us to quantitatively assess the impact of introducing real time prices on retailers’ profits and customers’ benefits. As our results show, dynamic real-time pricing on the one hand typically increases market efficiency, which confirms previous results obtained without the explicit consideration of strategic behavior. On the other hand, however, as a novel aspect, dynamic real-time pricing turns out to significantly reduce equilibrium profits in case of strategic firms. This effect is especially large in environments with strongly fluctuating wholesale prices.     

Inventory control by different service levels

This paper examines the multiple period inventory control problem of a single product with multiple (two) prices, depending on service level, in which optimal pricing and ordering decisions are made in each period. Traditional inventory and pricing models consider only single products, single prices, and single service levels. However, this research paper finds that a seller can improve inventory control and revenue by offering multiple prices depending on service level. This research considers a single product with multiple (two) pricing policies corresponding to service level as follows: if the customer is willing to delay the shipment, he/she will be offered a lower regular price. Otherwise, the customer will pay the regular price plus extra charges for express service. In this paper, I show the following: (1) there is an optimal pricing and replenishment policy that can control inventory and (2) there exists a finite threshold for inventory levels such that if the inventory level at the beginning of each period is higher than the threshold, the customer will be offered the express service at the regular price, without any extra charge.     

A dynamic pricing approach for returned products in integrated forward/reverse logistics network design

During the last decade, the stringent pressures from environmental and social requirements have spurred an interest in designing a reverse logistics network. In this paper, we address the problem of designing and planning a multi-echelon, multi-period, multi-commodity and capacitated integrated forward/reverse logistics network. Returned products are categorized with respect to their quality levels, and a different acquisition price is offered for each return type. Furthermore, the reservation incentive of customers, the expected price of customers for one unit of used product described by uniform distribution, is applied to model the customers’ return willingness. Due to the fact that the remaining worthwhile value in the used products is the corporation’s key motivation for buying them from customers, a dynamic pricing approach is developed to determine the acquisition price for these products and based on it determine the percentage of returned products collected from customer zones. The used products’ acquisition prices at each time period are determined based on the customers’ return willingness by each collection center.     

Dynamic pricing,product and process innovation

The question of simultaneous dynamic pricing, product and process investment policies is crucial for manufacturing and high-tech industries. This paper models these policies in an optimal control setting. On the supply side, the firm sets prices, product and process investment levels over time. On the demand side, current demand depends on price and quality. Under an additive separable demand function, dynamic pricing increases with quality and cost. Therefore, both product innovation and process innovation impact the pricing policy. Under a multiplicative separable demand function, dynamic pricing policy follows the dynamic of production cost and is independent of the evolution of product quality. Thus, process innovation is the main determinant of a firm’s pricing policy over time and product innovation has no impact.     

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。     

The impact of dynamic pricing on the economic order decision

This paper analyzes the impact of dynamic pricing on the single product economic order decision of a monopolist retailer. Items are procured from an external supplier according to the economic order quantity (EOQ) model and are sold to customers on a single market without competition following the simple monopolist pricing problem. Coordinated decision making of optimal pricing and ordering is influenced by operating costs – including ordering and inventory holding costs – and the demand rate obtained from a price response function. The retailer is allowed to vary the selling price, either in a fixed number of discrete points in time or continuously. While constant and continuous pricing have received much attention in the literature, problems with a limited number of price changes are rather rare. This paper illustrates the benefit of dynamically changing prices to achieve operational efficiency in the EOQ model, that is to trigger high demand rates when inventories are high. We provide structural properties of the optimal time instants when the price should be changed. Taking into account costs for changes in price, it provides numerical guidance on number, timing, and size of price changes during an order cycle. Numerical examples show that the benefits of dynamic pricing in an EOQ framework can be achieved with only a few price changes and that products being unprofitable under static pricing may become profitable under dynamic pricing.     

Using revenue management to improve pricing and capacity management in programme management

This paper presents revenue management models for pricing, capacity planning, and capacity reallocation and demonstrates their applicability for programme (project) management. In programme management, the allocation of capacity (resource time) to schedule activities requires the resolution of time versus revenue trade-offs. Thus, capacity planning and scheduling present a hierarchical problem for programme managers. Furthermore, current programme management methods do not consider the issue of price sensitivity exhibited in many programme management situations. Because of this omission, critical linkages between capacity management and scheduling of activities among programmes have not been addressed. Specifically, the issue of the reservation of capacity specifically for higher revenue generating activities has been omitted from programme management research. This paper asserts that, through capacity planning and scheduling, specific capacity should be reserved for customers willing to pay higher prices to have critical activities, for example, change orders, expedited. This capacity has scheduling effects that impact the programme NPV. This paper proposes potential solutions to capacity and programme scheduling problems using revenue management techniques.     

Integrating inventory control and a price change in the presence of reference price effects: a two-period model

Demand and procurement planning for consumer electronics products must cope with short life cycles, limited replenishment opportunities and a willingness to pay that is influenced by past prices and decreases over time. We therefore propose the use of an integrated pricing and inventory control model with a two-period linear demand model, in which demand also depends on the difference between a price-history-based reference price and the current price. For this model we prove that the optimal joint pricing/inventory policy for the replenishment opportunity after the first period is a base-stock list-price policy. That is, stock is either replenished up to a base-stock level and a list-price is charged, or it is not replenished and a discount is given that increases with the stock-level. Furthermore, we use real-world cell phone data to study the differences between an integrated policy and traditional sequential optimization, where prices are initially optimized based on the expected demand and ordering cost, and the resulting demand distribution is used to determine an optimal inventory policy. Finally, we discuss possible extensions of the model.     

Integration of pricing and capacity allocation for perishable products

For years pricing and capacity allocation decisions in most revenue management models have been carried out independently. This article presents a comprehensive model to integrate these two decisions for perishable products. We assume that the supplier sells the same products to different micro-markets at distinct prices. Throughout the sales season, the supplier faces decisions as to which micro-markets or customer classes should be served and at what prices. We show that (i) at any time, a customer class is active (being served) if and only if the price offered is over a threshold level, but the optimal price may not be the highest one of the supplier’s choice; (ii) when the price decision is made in conjunction with inventory, it is similar to the procedure shown in pure pricing models, i.e., the optimal price comes from a subset of prices that forms a maximum increasing concave envelope; (iii) because of dynamic changes in the optimal prices, the nested-price structure does not necessarily hold in general and needs to be redefined; and (iv) the optimal pricing and capacity control policy is based on a sequence of threshold points that incorporate inventory, price and demand intensity. Numerical examples are provided.     

不同价格水平下排队策略研究

在M/M/1排队中引入了不同的服务价格,基于"收益-成本"结构,以顾客和企业均追求利益最大化为出发点,在两种不可见情形下,研究了顾客均衡策略行为和企业最优服务定价决策,通过数值模拟,描述了休假期服务价格对顾客均衡策略的影响,以及几乎不可见情况下休假期服务价格对企业收益的作用和完全不可见情况下休假期服务价格随潜在到达率的变化情况,以及当企业获得最大收益时,正常工作期和休假期服务价格的关系.     

A Lagrangian decomposition approach for the pump scheduling problem in water networks

Dynamic pricing has become a common form of electricity tariff, where the price of electricity varies in real time based on the realized electricity supply and demand. Hence, optimizing industrial operations to benefit from periods with low electricity prices is vital to maximizing the benefits of dynamic pricing. In the case of water networks, energy consumed by pumping is a substantial cost for water utilities, and optimizing pump schedules to accommodate for the changing price of energy while ensuring a continuous supply of water is essential. In this paper, a Mixed-Integer Non-linear Programming (MINLP) formulation of the optimal pump scheduling problem is presented. Due to the non-linearities, the typical size of water networks, and the discretization of the planning horizon, the problem is not solvable within reasonable time using standard optimization software. We present a Lagrangian decomposition approach that exploits the structure of the problem leading to smaller problems that are solved independently. The Lagrangian decomposition is coupled with a simulation-based, improved limited discrepancy search algorithm that is capable of finding high quality feasible solutions. The proposed approach finds solutions with guaranteed upper and lower bounds. These solutions are compared to those found by a mixed-integer linear programming approach, which uses a piecewise-linearization of the non-linear constraints to find a global optimal solution of the relaxation. Numerical testing is conducted on two real water networks and the results illustrate the significant costs savings due to optimizing pump schedules.     

The value of information for price dependent demand

Predicting demand and determining optimal pricing are essential components of operations management. It is often useful to think in terms of the price elasticity of demand when reasoning about the demand curve. Firms wishing to invest in demand prediction and information gathering should reason about the relationship between the expected value of perfect information (EVPI) on demand and demand elasticity. Should firms pay more/less for information on demand if elasticity is high/low? Furthermore, when considering different product prices, correlation may exist between demand at different prices. Should firms pay more/less for information if the correlation between demand at different prices is high or low? This paper derives analytic and numeric results to answer these questions. We start with the assumption that demand is uncertain and follows a uniformly distributed band around a deterministic demand curve where the upper and lower bounds of the demand distribution vary with price. This formulation enables a closed form expression for EVPI that provides a useful benchmark. We find nuanced behavior of EVPI that depends on both the elasticity and the initial price preference. The EVPI approaches zero as elasticity increases (decreases) for a firm that initially prefers the low (high) price. Numerical results using the truncated normal and beta distributions relax assumptions about the uniform distribution and show EVPI is similar when the distribution variances are similar. Finally, we relax the assumption of perfect information and show the expected value of imperfect information (EVOI) follows similar patterns as EVPI with respect to demand elasticity.     

产品服务能力与定价联合优化策略机制研究——基于动态性和非线性视角

为了快速响应客户需求的动态变化和提高产品服务能力的管理效率,运用状态相关需求率函数和成本收益率函数,建立用以解决产品服务需求动态性和非线性难题的排队优化模型。通过考虑产品服务化过程中客户需求变化特征,从服务能力和价格两个维度将客户划分为实惠型、经济型、专业型和品质型四个不同类别。依据客户产品服务需求动态演变阶段,针对服务能力与价格的内在关联性,运用排队优化模型分别构建了成本领先策略、服务能力领先策略、价格领先策略和产品服务能力定价联合策略。最后,借助南阳泵业企业运营实例,验证了产品服务能力定价联合策略的优越性,并给出产品服务能力定价联合策略演化路径及其实施对策。     

基于多层博弈的智能电网住宅电力实时需求响应机制

通过建立多层博弈模型刻画智能电网系统中电力公司、家庭电力管理中心和家庭内各个电器设备间的电力实时需求响应过程。在此模型中,每个时段电力公司将电价通知各个家庭,每个家庭的电力管理中心接收到实时电价信息后为家庭内各个电器设备分配虚拟电价,各个设备则确定各自最优用电量并将其反馈给家庭电力管理中心,由其确定该家庭总用电量并发送至电力公司,电力公司再计算得到最优电价。证明了所建多层博弈模型的均衡存在唯一性,并得到均衡解。仿真结果验证了模型的有效性,并给出其实际应用价值。