Optimal Pricing Policy Research Articles

Simultaneous Optimization of Capacity Decision and Pricing Policy of a Hotel in Stochastic Demand Environment

In the context of the hotel industry, one of the biggest and capital-intensive challenges a decision maker has is to decide on the capacity of the hotel. While taking this decision, the decision maker needs to take seasonality of demand into consideration. Also, the interplay between price and demand also play a major role on this decision. In this study, an effort is made to simultaneously identify the optimal capacity and pricing policy of a hotel in the presence of a stochastic demand environment. Differential calculus is used to identify the solution. Both capacity and price are considered as decision variables for the decision maker. To comply with reality, the seasonality in demand is incorporated in the form of bi-level demand. Numerical illustrations are also shown to explain the decision-making process. This study offers a starting point for an entrepreneur to decide both capacity and pricing for their upcoming hotel.

Optimal pricing and trade-in policies in a dual-channel supply chain when considering market segmentation

Many companies are implementing trade-in programmes through multiple channels. This may ultimately lead to fiercer channel conflict and competition. Few studies have explored firms’ optimal trade-in policies in such an environment. To fill the gap, we build a theoretical model that captures the features of a dual-channel situation in which a manufacturer implements a trade-in programme through retail and direct channels simultaneously. Compared with the case in which there is no trade-in rebate, the results show that a trade-in programme can intensify or mitigate the double marginalisation effect if the retailer can initially decide the trade-in rebate in the retail channel. This significantly relies on market segmentation. However, when the retailer cannot decide the trade-in rebate in the retail channel, the trade-in programme aggravates the double marginalisation effect. Second, the trade-in rebate offered by the retailer may be higher than the subsidy offered by the manufacturer, as long as the retailer can autonomously decide the trade-in rebate in the retail channel. Furthermore, we find that both the manufacturer and retailer prefer to obtain the right to autonomously decide the trade-in rebate in the retail channel, but the supply chain prefers that the manufacturer do it. Some numerical examples are provided to further explain these outcomes.

The optimization of pricing strategy for the wind power equipment aftermarket service

PurposeAlthough the wind power industry has been booming in China during the last decade, the development of wind turbine aftermarket service is still lagging behind, which seriously affects the operational efficiency of wind farms. If wind turbine manufacturers get involved in the aftermarket, the service pricing policy will impact the profits of both the manufacturer and the wind farm. Therefore, it is necessary to discuss an optimal service pricing strategy in the wind turbine aftermarket and design a method to improve electricity generation efficiency through service contract design. The paper aims to discuss these issues.Design/methodology/approachIn order to decide the maintenance quantity and channel effort level, the authors design a normal Stackelberg game and an efficiency value-added revenue-sharing contract and discuss two kinds of revenue increment sharing models under situations, in which the supply chain’s leaders are the wind farm and the wind turbine manufacturer, respectively.FindingsThe results show that in either case, there exist optimal power generation revenue-sharing ratios that can maximize profit. At the same time, the authors outline an optimal service pricing policy, maintenance demand policy and channel service effort-level policy. The results summarize the influences of wind aftermarket services on wind farms’ and wind turbine manufacturers’ profit, which provides managerial insights into the process of manufacturing servitization.Practical implicationsThe manufacturer’s channel effort level will influence the power generation increments very much, so the authors have developed a mechanism to stimulate the manufacturer improving the efficiency of aftermarket services.Originality/valueTaking the power generation increment revenue as the profit increment function, the authors discuss the influence of service price on the profit increment of the wind farm and the wind turbine manufacturer and also consider the influence of service price on the wind farms maintenance quantity and wind turbine manufacturers channel effort level.

Dynamic pricing for inventories with reference price effects

Abstract This article presents a dynamic pricing model of a retailer selling an inventory, accounting for consumer behavior. The authors propose an optimal control model, maximizing the intertemporal profit with consumers sensitive to the selling price and to a reference price. The optimal dynamic pricing policy is solved with Pontryagin’s maximum principle with a structural (general) demand function. The authors obtain an original pricing rule, which explicitly accounts for the impact of price and inventory on future profits. The dynamics of price do not have to imitate the dynamics of the reference price. Instead, the dynamics of price are tied to opposing effects linked to this reference price. The authors also discuss managerial implications with regards to behavioral pricing policies.

Opportunistic Returns and Dynamic Pricing: Empirical Evidence from Online Retailing in Emerging Markets

We investigate how dynamic pricing can lead to more product returns in the online retail industry. Using detailed sales data of more than two million transactions from the Indian online retail market, where price promotions are very common, we document two types of strategic customer behavior that have not been considered in previous research. First, customers who monitor product prices after purchase may initiate opportunistic returns because of price drops. Second, customers who anticipate a future return may strategically choose a payment method that facilitates product returns. Our logistic regression models indicate that (1) realized post-purchase price drops lead to a higher probability of return, and (2) anticipated price drops after purchase lead to a higher probability of using cash on delivery, a payment method with a lower return cost for consumers. Our findings are robust to alternative model specifications and sample selection procedures. We demonstrate that an optimal pricing policy should take into consideration the potential costs of two types of strategic customer behavior: opportunistic returns and strategic choice of payment method.

Intertemporal Price Discrimination Via Randomized Pricing

The undesirable but inevitable consequence of running promotions is that consumers can be trained to time their purchases strategically. In this paper, we study randomized promotions, where the firm randomly offers discounts over time, as an alternative strategy of intertemporal price discrimination. Specifically, we consider a base model where a monopolist sells a single product to a market with a constant stream of two market segments. The segments are heterogeneous in both their product valuations and patience levels. The firm pre-commits to a price distribution, and in each period, a price is randomly drawn from the chosen distribution. We characterize the optimal price distribution as a randomized promotion policy and show that it serves as an intertemporal price discrimination mechanism such that high-valuation customers would purchase immediately at a regular price upon arrival and low-valuation customers would wait for a random promotion. Compared against the optimal cyclic pricing policy, which is optimal within the strategy space of all deterministic pricing policies, the optimal randomized pricing policy beats the optimal cyclic pricing policy if low-valuation customers are sufficiently patient and the absolute discrepancy between high and low customer valuations is large enough. We extend the model in two directions. We first consider Markovian pricing policies where prices are allowed to be intertemporally correlated in a Markovian fashion. This additional maneuver allows the firm to reap an even higher profit when low-valuation customers are sufficiently patient, by avoiding consecutive promotions but on average running the promotion more frequently with a smaller discount size. We then consider a model with multiple customer segments, and show that a two-point price distribution remains optimal and our conclusion from the two-segment base model still holds under certain conditions that are adopted in the literature. Our results imply that the firm may want to deliberately randomize promotions in the presence of forward-looking customers.

A dynamic macroscopic parking pricing and decision model

A dynamic macroscopic parking pricing model is developed to maximize the revenue for a city, while simultaneously minimizing the total cruising time on the network. The proposed responsive pricing scheme takes the parking search phenomenon into consideration. This means that the parking fee also changes in response to the number of searching vehicles, in addition to changes in response to the parking occupancy. Compared to most literature, this macroscopic pricing model is embedded into a dynamic macroscopic urban traffic and parking model and has rather low data requirements, mostly related to average values and probability distributions at the network level. The case study of an area within the city of Zurich, Switzerland shows that the model provides a preliminary idea for city councils regarding an optimal parking pricing policy resulting in financial revenues that can be obtained without having a significant negative effect on short-term traffic performance and environmental conditions.

Dynamic Pricing with Service Unbundling

In this study, we investigate unbundling when a firm dynamically prices a basic service, while separating the sale of a fixed‐price add‐on. We characterize the optimal dynamic unbundling pricing policy and investigate its structural properties. We find that the value function with unbundling increases in the degree of dependence between consumers’ reservation prices for basic service and add‐on. However, there are no similar monotonicity properties for the optimal price of the basic service. For several families of commonly used joint distributions, we show that the influence of the dependence parameter on the optimal price of the basic service depends on a threshold, which is a function of the dependence parameter. Moreover, the price of the bundled service is higher under unbundling when the add‐on price is high, and vice versa. Our model is then compared with the bundling model through a numerical experiment. Among most cases where unbundling outperforms, the degree of dependence is non‐negative. It is further revealed that given the non‐negativity of dependence, unbundling is worth practicing under the following situations: (i) the variance of the reservation price for the basic service (add‐on) is low (high); (ii) the mean of the reservation price for the basic service (add‐on) is high (low); (iii) the demand intensity is low; (iv) the capacity of the basic service is high; and (v) the incremental cost of the basic service (add‐on) is low (high). Finally, unbundling can improve the firm's expected profit and the consumers’ surplus at the same time.

Optimal pricing and replenishment policy for deteriorating inventory under stock-level-dependent, time-varying and price-dependent demand

Technological advance and changing customer preferences lead to falling demand with the passage of time for some products, often referred to as short life cycle. In this paper, we examine the inventory management of a short life cycle product that also deteriorates as time elapses. We consider a finite horizon multi-period setting where demand is deterministic, stock-level-dependent, time varying, and price-dependent. We seek to maximize the average profit per period by choosing an appropriate replenishment and pricing policy. Leveraging properties of the objective function, we develop an algorithm that determines the optimal value of several system decision variables that maximize profitability. We provide a numerical example that illustrates our solution approach after which we perform a sensitivity analysis.

Pricing policies for selling indivisible storable goods to strategic consumers

We study the dynamic pricing problem faced by a monopolistic retailer who sells a storable product to forward-looking consumers. In this framework, the two major pricing policies (or mechanisms) studied in the literature are the preannounced (commitment) pricing policy and the contingent (threat or history dependent) pricing policy. We analyse and compare these pricing policies in the setting where the good can be purchased along a finite time horizon in indivisible atomic quantities. First, we show that, given linear storage costs, the retailer can compute an optimal preannounced pricing policy in polynomial time by solving a dynamic program. Moreover, under such a policy, we show that consumers do not need to store units in order to anticipate price rises. Second, under the contingent pricing policy rather than the preannounced pricing mechanism, (i) prices could be lower, (ii) retailer revenues could be higher, and (iii) consumer surplus could be higher. This result is surprising, in that these three facts are in complete contrast to the case of a retailer selling divisible storable goods Dudine et al. (2006). Third, we quantify exactly how much more profitable a contingent policy could be with respect to a preannounced policy. Specifically, for a market with $N$ consumers, a contingent policy can produce a multiplicative factor of $\Omega(\log N)$ more revenues than a preannounced policy, and this bound is tight.

Optimal Pricing, Quality Investment and Replenishment Policies for Perishable Items

Optimal Pricing, Quality Investment and Replenishment Policies for Perishable Items

Managing a retailer’s dual-channel supply chain under price- and delivery time-sensitive demand

PurposeThis paper aims to explore optimal pricing policies and characteristics of a two-level dual-channel supply chain under price- and delivery time-sensitive demand. Besides price of the product, the delivery lead time is also a crucial factor in customers’ purchase decisions. A longer delivery lead time would diminish customers’ acceptance and faithfulness on the online channel, while a shorter delivery lead time would lead to incorporation of a substantial amount of logistics costs. In formulation of mathematical model, the effects of delivery lead time on the manufacturer and the retailer’s pricing strategies and profits in cooperative and non-cooperative dual-channel supply chain are explained analytically.Design/methodology/approachThe analytical models are formed for both non-cooperative and cooperative scenarios under inconsistent and consistent pricing. The authors examine whether revenue sharing (RS) contract or delivery cost sharing contract can solely coordinate the dual-channel supply chain. If a single contract fails, then the combination of RS contract with delivery cost sharing to achieve channel coordination is discussed.FindingsIt is found that the RS or delivery cost sharing contract cannot coordinate the channel individually but revenue and delivery cost sharing contract jointly coordinate the channel. All analytical results are illustrated numerically, along with sensitivity analysis.Research limitations/implicationsThere are many correlated issues that need to be further investigated. First, one good extension to this research may include the consideration of the channel structure with competitive retailers. It will be interesting to analyze the performance of coordination mechanisms by considering the retailer as a Stackelberg leader in retailing.Originality/valueThe findings and subsequent methodological discussions aim to provide practical guidance to retailers who are allowing customers to choose how, when and where they interact and purchase by offering a combination of websites (fully functional and mobile-enabled), catalogs and stores with increasing convergence of channels.

Dynamic Pricing for Reusable Resources in Competitive Market With Stochastic Demand

The market for selling reusable products (e.g., car rental, cloud services and network access resources) is growing rapidly over the last few years, where service providers maximize their revenues through setting optimal prices. While there has been lots of research on pricing optimization, existing works often ignore dynamic property of demand and the competition among providers. Thus, existing pricing solutions might be far from optimal in realistic markets. This paper provides the first study of service providers' dynamic pricing in consideration of market competition and makes three key contributions along this line. First, we propose a comprehensive model that takes into account the dynamic demand and interaction among providers, and formulate the optimal pricing policy in the competitive market as an equilibrium. Second, we propose an approximate Nash equilibrium to describe providers' behaviors, and design an efficient algorithm to compute the equilibrium which is guaranteed to converge. Third, we derive many properties of the model without any further constraints on demand functions, which can reduce the search space of policies in the algorithm. Finally, we conduct extensive experiments with different parameter settings, showing that the approximate equilibrium is very close to the Nash equilibrium and our proposed pricing policy outperforms existing strategies.

Dynamic Pricing and Replenishment with Customer Upgrades

We study a joint implementation of price‐ and availability‐based product substitution to better match demand and constrained supply across vertically differentiated products. Our study is motivated by firms that utilize dynamic pricing as well as customer upgrades, as ex ante and ex post mechanisms, respectively, to mitigate inventory mismatches. To gain insight into how offering product upgrades impacts optimal price selection, we formulate a multiple period, nested two‐stage model where the firm first sets prices and replenishment levels for each product while the demand is still uncertain, and after observing the demand, decides how many (if any) of the customers to upgrade to a higher quality product. We characterize the structure of the optimal upgrade, pricing and replenishment policies and find that firms having greater flexibility to offer product upgrades can restrain their reliance on dynamic pricing, enabling them to better protect the price differentiation between the products. We also show how the quality differential between the products or changes in the replenishment cost structures influence the optimal policy. Using insights gained from the optimal policy structure, we construct a heuristic policy and find that it performs well across various parameter values. Finally, we consider an extension in which the firm dynamically sets upgrade fees in each period. Our results overall help further our understanding of the intricate relationship among a firm's decisions on pricing, replenishment, and product upgrades in an effort to better match demand and constrained supply.

Optimal pricing and lot-sizing policy for supply chain system with deteriorating items under limited storage capacity

This research work considers a two-echelon supply chain model for deteriorating items in which the retailer's warehouse capacity of display area is limited. Therefore, the retailer stores remaining units in the back room which has unlimited capacity. The demand rate is assumed to be dependent on the retailer's selling price and displayed stock level. The proposed approach explicitly models the interdependence among price of a product, demand for the product and the integration among the retailer and the supplier under four different policies: non-integrated, integrated, supplier-led Stackelberg policy and retailer-led Stackelberg policy. Furthermore, this paper also establishes several theoretical results to show that the solution provides the maximum total relevant profit. By using differential calculus method, it is proved that the optimal solution not only exists but also is unique. In this study, the impact of price, inventory level and the integration among retailer and the supplier is explicitly analyzed in the emerging retail scenario with limited shelf space.

Pricing policies for a dual-channel retailer with cross-channel returns

Abstract Many retailers are adopting a dual-channel retailing strategy (DCRS) in which products are offered through two channels: physical stores and online stores. Due to regulations or competitive measures, such a strategy allows customers who find a purchase unsatisfactory to obtain a full refund through a same-channel return or a cross-channel return. No papers have collectively studied the aforementioned types of customer returns in a dual-channel context. This paper studies optimal pricing policies for a centralized and decentralized dual-channel retailer (DCR) with same- and cross-channel returns. How dual-channel pricing behavior is impacted by customer preference and rates of customer returns is discussed. It is found, through sensitivity analysis, that when a channel with significant customer preference faces a high rate of returns, decentralized channels generate a greater system profit for retailers than coordinated channels that have a unified pricing strategy. A DCR with a Stackelberg scheme has the proclivity to be more profitable when under the leadership of a channel with a high rate of returns and significant customer preference.

Optimal Pricing and Replenishment Policies for Instantaneous Deteriorating Items with Backlogging and Permissible Delay in Payment under Inflation

SYNOPTIC ABSTRACTIn this article, we develop an economic order quantity model to investigate the optimal replenishment policies for instantaneous deteriorating items under inflation. Demand is assumed to be a linear function of the selling price and decreases negatively exponentially with time over a finite planning horizon under delay in payment. Shortages are allowed and partially backlogged. Under these conditions, we model the retailer’s inventory system as a profit maximization problem to determine the optimal selling price, optimal order quantity, and optimal replenishment time. An easy-to-use algorithm is developed to determine the optimal replenishment policies for the retailer. We also provide optimal present value of profit when shortages are completely backlogged as a special case. Numerical examples are presented to illustrate the algorithm provided to obtain optimal profit. We also obtain managerial implications from numerical examples to substantiate our model.

Mobile Network Operator and Mobile User Cooperation for Customized D2D Data Services

The explosive growth of smart devices has led to the evolution of multimedia data (mainly video) services in mobile networks. It attracted many mobile network operators (MNO) to deploy novel network architectures and develop effective economic policies. Mobile data offloading through smart devices (SDs) by exploring device-to-device (D2D) communications can significantly reduce network congestion and enhance quality of service at a lower cost, which is the key requirement of upcoming 5G networks. This reasonable cost solution is useful for attracting mobile users to participate in the offloading process by paying them proper incentives. It is beneficial for MNOs as well as mobile users. Moreover, D2D communications promise to be one of the prominent services for 5G networks. In this paper, we present a combinatorial optimal reverse auction (CORA) mechanism, which efficiently selects and utilizes available high-end SDs on the basis of available resources for offloading purposes. It also decides the optimal pricing policy for the selected SDs. The efficiency of CORA has been realized in terms of bandwidth and storage demand. Subsequently, we implement caching in SDs, eNodeB (eNB), and evolved packet core (EPC) with the help of our novel video dissemination cache update algorithm to solve the latency or delay issues in the offloading process. Due to high popularity, we specifically focus on video data. Simulation results show that the proposed SD caching scenario curtails the delay up to 75% and the combined cache (CC) scenario slashes the delay varying from 15 to 57%. We also scruitinize the video downloading time performance of various cache scenarios (i.e., CC, EPC cache, eNB cache, and SD cache scenarios).

Pricing a Matching Marketplace

This paper addresses the pricing problem of an online service marketplace under asymmetric information. An example is an online learning platform such as Coursera that provides courses from suppliers (in this case, universities) to learners. We focus on the matching function of the marketplace whereby it engages in sequential search on behalf of a consumer using partially-observable consumer and supplier attributes. We develop the optimal pricing policies for a general distribution of the unobservable valuations. When these distributions are exponential, it is optimal to charge the same total fee for each match rather than engage in price discrimination, and this entire fee should be levied on the less elastic side of the marketplace.

False failure returns: Optimal pricing and return policies in a dual-channel supply chain

This paper aim is to examine the optimal pricing and return policies for false failure returns in a dual-channel supply chain. Four prevailing return policies in which a manufacturer both operates an E-shop and sells its product through a brick-and-mortar retailer are analyzed, i.e. (I) the manufacturer handlings E-shop’s returns, while the retailer addresses brick-and-mortar store’s returns (NR); (II) the retailer tackles the whole (both E-shop’s and brick-and-mortar store’s) returns (ORR); (III) the manufacturer tackles the whole returns (ORM); and (IV) the manufacturer and the retailer are jointly responsible for the whole returns (RRM). Firstly, the optimal pricing and return policies comparing these four scenarios under uniform-pricing strategy are presented. Our conclusions show that the ORR is an optimal return policy. Compared with the NR, consumers will get a lower product pricing under the ORR and a higher product pricing under the ORM. With regard to the RRM, the product pricing is depended on consumer preference, return-rates of the E-shop and the brick-and-mortar store. Then, the optimal pricing and return policies are analyzed under differential-pricing strategy by conducting two-stage sequential games between the manufacturer and the retailer. The findings show that if consumers in the market prefer to purchase via the E-shop, the ORR is an optimal return policy. Otherwise, the NR is the optimal return policy. Compared with the NR, the ORR retailer’s product pricing will rely on the retailer’s and the manufacturer’s return-costs; the RRM retailer’s product pricing will depend on the return-costs of the retailer and the manufacturer, the return-rates of the E-shop and the brick-and-mortar store and so on. Finally, the influences of the manufacturer and the retailer establishing a Buy-back contract are discussed. Our results illustrated that the Buy-back contract doesn’t affect optimal pricing and return policies under both the uniform and the differential pricing strategies.