Optimal Pricing Policy Research Articles

Bundling strategies for complementary products in a horizontal supply chain

PurposeThis paper aims to address the following problems: What are the firms’ optimal pricing and quality policies under three scenarios (no bundling, pure bundling and mixed bundling)? In what condition will one bundling strategy dominate the others? How does the degree of complementarity affect the firms’ decision?Design/methodology/approachUsing the game theory, this study first establishes three models of bundling strategies: no bundling, pure bundling and mixed bundling and then obtains the optimal prices and quality decisions. This study uses numerical analysis to explore the relationships between the prices (demands and profits) and some key parameters and to obtain some valuable management complications.FindingsSome interesting and valuable management implications are established: regardless of the degree of complementarity, adopting a pure bundling or mixed bundling strategy is better than separately selling an individual product; a high degree of complementarity leads to reduced profit in the no bundling and mixed bundling scenarios, whereas the condition in the pure bundling strategy is the opposite; and when the degree of complementarity is adequately large, choosing pure bundling strategy is more profitable.Research limitations/implicationsOn the one hand, this study does not calculate the profit sharing ratio, and hence, the equilibrium profit sharing ratio can be explored in future work. On the other hand, marketing efforts (e.g. advertising and promotion) can be included in the study.Practical implicationsThis study derives the necessary conditions for the most effective bundling strategy that maximizes firm’s profits, and these conclusions can provide a decision reference to the bundling decisions of firms.Originality/valueFirst, the optimal bundling strategies in a horizontal supply chain consisting of two firms is considered. Under the pure and mixed bundling strategies, the two firms sell the bundled product by building a cooperative program. Second, both the pricing policies and quality decisions of supply chain members under the different bundling strategies are studied.

Dynamic pricing, quality investment, and replenishment model for perishable items

AbstractThe deterioration of perishable items results not only in direct quantitative losses, but also in qualitative losses, which would reduce the customer acceptability. To maintain or improve the quality level, sellers usually invest in functionality, aesthetics, safety or any other attributes. In addition to quality, price also plays a critical role in influencing the purchase choice of consumers and the profit of a firm. Most inventory management models for perishables are restricted to physical quantity deterioration and do not address joint dynamic pricing and quality investment strategies. This paper studies an optimal replenishment model with dynamic pricing and quality investment for perishable products, where the quality and physical quantity deteriorate simultaneously. The demand rate is decreasing in sales price and increasing in quality level. A dynamic optimization model is proposed to maximize the total profit per unit time and solved on the basis of Pontryagin's maximum principle. The optimal joint dynamic pricing, quality investment, and replenishment policy is obtained. A numerical example and sensitivity analysis on the key system parameters are presented to illustrate the validity of the theoretical results. Some managerial implications for the pricing and quality investment for the perishables are provided.

Retailer’s Joint Ordering, Pricing, and Preservation Technology Investment Policies for a Deteriorating Item under Permissible Delay in Payments

This article develops an inventory model for deteriorating items with controllable deterioration rate (by using preservation technology) under trade credit policy. As in practical scenarios the demand of an item is directly associated with its selling price, keeping this in mind, it is assumed to be a price dependent demand. The main objective of the inventory model is to determine jointly the optimal ordering, pricing, and preservation technology investment policies for retailer so that the total profit is maximized. The effects of key parameters on optimal solution are studied through a sensitivity analysis with the aim of examining the behavior of the inventory model with controllable deterioration under the permissible delay in payments.

Deep Koopman Controller Synthesis for Cyber-Resilient Market-Based Frequency Regulation

Abstract This paper investigates a data-driven countermeasure for price spoofing in the context of cyber security and market-based frequency regulation. Market-based control of transmission power networks relies on cyber-physical infrastructure, which raises questions of system vulnerability in relation to cyber-security. In this paper, we consider the challenge of engineering a robust data-driven controller in the presence of price spoofing, i.e. where hacking mechanisms adjust price signals in an ex-post market. We extend a recently developed algorithm called deep dynamic mode decomposition to learn Koopman operators of nonlinear systems with affine inputs. Based on the learned input-Koopman operator model, a design algorithm for nonlinear controller synthesis is devised to compute optimal dynamic pricing policies that restore the nominal frequency and recover economic efficiency in the presence of price spoofing. The efficacy of the proposed data-driven Koopman controller synthesis approach is validated through tests on a IEEE 39-bus benchmark.

Procurement planning in a multi-period supply chain: An epiphany

Pricing and inventory distribution strategy in a multi-period supply chain environment has not yet been comprehensively explored. We derive closed-form solutions for both two-and three-echelon supply chains under a manufacturer-stackelberg game framework where the supply chain members execute integrated procurement planning by taking account upto four consecutive selling periods. Optimal pricing and inventory distribution policy is identified in the perspective of each member among three pragmatic procurement scenarios. Our results demonstrate that both integrated procurement strategies outperform conventional single-period decision and reduce double-marginalization effect. But, the retailer can prefer bulk procurement to earn maximum profit. The distributor acts as a catalyst, prevents the retailer from executing integrated multi-period procurement planning and creates conflict among supply chain members. Procurement decisions in presence of strategic inventory may lead to suboptimal profits compared to bulk procurement and supply chain members can face some implementation issues. Supply chain members always receive higher profits if the retailer distributes inventory strategically in a multi-period supply chain.

Retailer's optimal pricing and replenishment policy for new product and optimal take-back quantity of used product

In the world of limited resources, recovery of used products for reselling or recycling is a critical issue from the economic and environmental point of view. In this paper, we have assumed that a retailer sells the new product to customers as well as collects and sells the used products. We adopt a price dependent quadratic demand function, and the return of used product as a price and time-dependent linear function. The proposed problem is formulated as a profit maximization problem for the retailer. The objective is to find the optimal selling price, the optimal ordering quantity for the new product, and the optimal quantity of used product simultaneously such that the retailers total profit is maximized. The model is validated by a numerical example and sensitivity analysis is performed for the key parameters.

On the effect of price policies in the design of formulated products

In this work an extended pooling problem is formulated to select the optimal price policy for the ingredients of a formulated product such as a detergent. Various contracts for obtaining discounts as a function of the amount purchased are considered including fixed discount, linear, logit, a discount beyond a certain amount purchased and constant elasticity. The feature is that while certain ingredients are used in large amounts, others represent only a small fraction of the product. The problem becomes an MINLP that it is solved for the optimal product formulation selecting the contract on a year and on a multiperiod basis. Various mathematical reformulations are proposed. The results show the selection of the contract is ingredient dependent but it is quite robust with the environmental burden. However, this decision can change when actual contract conditions on the limiting amounts for the discount are provided to the model.

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.

When Prospect Theory Meets Consumer Choice Models: Assortment and Pricing Management with Reference Prices

Problem Definition: Reference prices arise as price expectations against which consumers evaluate products in their purchase scenarios. We investigate what will happen when prospect theory (e.g., reference prices) meets consumer choice models from the perspectives of both the consumers and the firm. Academic/Practical Relevance: Consumers see multiple relevant products on a particular purchase occasion, and often compare their prices to form the willingness to pay when considering whether to purchase a particular product. Reference prices, which are not included in many choice models, may impact consumer choice behavior, so we incorporate reference prices into consumer choice models and investigate the operations management problems. Methodology: We take the widely used multi-nomial logit model as a showcase to examine the effects of reference prices through analytical and empirical study. We consider the optimization problems on assortment planning and pricing under consumer choice models with a variety of reference prices, including the lowest price and the assortment variety. Results: Our empirical study on a real data set demonstrates that incorporating reference prices into choice models can significantly improve goodness-of-fit and prediction accuracy of consumer choice behavior. Furthermore, we characterize the optimal policies for the assortment planning and pricing problems under the consumer choice models with various reference prices. In particular for the pricing problems under the reference prices defined by either the lowest price or assortment variety, we show that the optimal pricing policy has the following structure: products can be grouped into several categories based on their costs; the products in the same category charge either the same profit markup or the same price. Managerial Implications: In practice, reference prices should be taken into account in model estimation and operations management. Ignoring reference prices may lead to substantial losses.

When Prospect Theory Meets Consumer Choice Models: Assortment and Pricing Management with Reference Prices

Problem definition: Reference prices arise as price expectations against which consumers evaluate products in their purchase scenarios. We investigate what will happen when prospect theory (e.g., reference prices) meets consumer choice models from the perspectives of both the consumers and the firm. Academic/practical relevance: Consumers see multiple relevant products on a particular purchase occasion and often compare their prices to form the willingness to pay when considering whether to purchase a particular product. Reference prices, which are not included in many choice models, may impact consumer choice behavior, so we incorporate reference prices into consumer choice models and investigate the operations management problems. Methodology: We take the widely used multinomial logit model as a showcase to examine the effects of reference prices through analytical and empirical study. We consider the optimization problems on assortment planning and pricing under consumer choice models with a variety of reference prices, including the lowest price and the assortment variety. Results: Our empirical study on a real data set demonstrates that incorporating reference prices into choice models can significantly improve goodness of fit and prediction accuracy of consumer choice behavior. Moreover, we characterize the optimal policies for the assortment planning and pricing problems under the consumer choice models with various reference prices. In particular, for the pricing problems under the reference prices defined by either the lowest price or assortment variety, we show that the optimal pricing policy has the following structure: products can be divided into several groups based on their costs; the products in the same group charge either the same markup or the same price. Managerial implications: In practice, reference prices should be taken into account in model estimation and operations management. Ignoring reference prices may lead to substantial losses. The online appendix is available at https://doi.org/10.1287/msom.2017.0688 .

Inventory control and pricing for regret-averse newsvendor

The decision maker’s perception of regret affects a company’s inventory control and pricing decisions. In this paper, we investigate how regret aversion behaviors affect the inventory control and pricing decisions under a newsvendor setting. To capture the regret aversion behaviors of the newsvendor, we provide a regret aversion utility function. Based on the built regret aversion utility function and the classic inventory control and pricing model, we construct utility function by integrating the profit utility and the regret aversion utility, and then analyze the conditions of optimal solution on the inventory and pricing policy under additive and multiplicative demand in details. Further, by the analysis of properties and numerical study, we show that the optimal policy for regret-averse newsvendor deviates from the one for regret-neutral newsvendor and changes with the regret aversion parameters to varying degree. We also show the impact tendency of newsvendor’s regret aversion behaviors on the optimal inventory and pricing policy under the additive and multiplicative demand.

Joint optimal inventory, dynamic pricing and advertisement policies for non-instantaneous deteriorating items

In this paper, a novel model for dynamic pricing and inventory control of non-instantaneously deteriorating items is proposed. To reflect the dynamic nature of the problem, the selling price is modeled as a time-dependent function of the initial selling price and the discount rate. To this end, the product is sold at the initial price value for a time period; then its price is exponentially discounted to boost customer demands. The demand rate is a function of dynamic price, advertisement and changes in price over time. The model seeks to maximize total profit of the system by determining the optimal replenishment cycle, initial price, discount rate, and frequency of advertisement. In order to characterize the optimal solution, some useful theoretical results are derived upon which an iterative solution algorithm is developed. To demonstrate validity of the proposed model and applicability of the developed algorithm, numerical results are provided that are accompanied by an efficient sensitivity analysis on the important parameters of the model.

Piracy on the Internet: Accommodate it or fight it? A dynamic approach

This paper uses a dynamic stochastic model to solve for the optimal pricing policy of music recordings in the presence of P2P file-sharing networks eroding their sales. We employ a policy iteration algorithm on a discretized state space to numerically compute the optimal pricing policy. The realistically calibrated model reflects the real-world figures we observe and provides estimates of the optimal pricing policy as well as comparative statics figures. The pricing policy is such that, for a given P2P network size, prices are increasing in the number of buyers of the product and, for a given number of buyers of the product, prices are non-monotonic in the P2P network size. Surprisingly, in the presence of P2P networks, increases in production costs and decreases in the valuation of the product increase the consumer and total surplus. A higher valuation of the product leads to a lower steady state price. Increased switching costs have a negative effect on prices and profits, so the long term incentive to attract new consumers dominates the short term incentive to harvest loyal consumers. The full enforcement of intellectual property rights has adverse effect on both consumer surplus and total welfare.

Does Loss Aversion Preclude Price Variation?

Problem definition: In modern retailing, frequent discounts are seemingly at odds with the idea that price variation antagonizes loss-averse consumers and hence, diminishes their demand for products and services. Our research question then is whether (or not) loss aversion rules out price variation—and in particular, cyclic pricing. Academic/practical relevance: Pricing and revenue management subject to behavioral considerations are key research areas in operations management. Our approach contributes to this research by highlighting the importance of incorporating heterogeneity in consumers’ behavioral responses in pricing models. Methodology: We model a monopolist selling a product over time to loss-averse consumers who differ in their sensitivity to gains/losses. Although the market is thus segmented, the firm cannot price discriminate among consumers based on that sensitivity. We then characterize the structural properties of the firm’s optimal pricing policy. Results: We show that charging a long-run constant price may be suboptimal and then derive conditions under which the optimal policy is cyclic. These findings establish that loss aversion does not preclude price variation and thereby, underscore the importance of incorporating consumer heterogeneity into pricing policies. Managerial implications: For operations management scholars, our model highlights the importance of heterogeneity in consumers’ behavioral responses to firms’ policies and shows that structurally different insights are obtained from pricing models if this heterogeneity is appropriately accounted for. This approach offers new avenues in pricing and revenue management research. For managers, our model suggests that they could vary prices, under certain conditions, without worrying that price variation will antagonize consumers. Our model offers insights on what these conditions are, which managers may incorporate in devising the pricing policies.

Optimal Policies for Selling New and Remanufactured Products

Because of environmental and economic reasons, an increasing number of original equipment manufacturers (OEMs) nowadays sell both new and remanufactured products. When both products are available, customers will buy the one that gives them a higher (and non‐negative) utility. Thus, if the firm does not price the products properly, then product cannibalization may arise and its revenue may be adversely impacted. In this paper, we study the pricing problem of a firm that sells both new and remanufactured products over a finite planning horizon. Customer demand processes for both new and remanufactured products are random and price‐sensitive, and product returns (also called cores) are random and remanufactured upon receipt. We characterize the optimal pricing and manufacturing policies that maximize the expected total discounted profit. If new products are made‐to‐order (MTO), we show that when the inventory level of remanufactured product increases, the optimal price of remanufactured product decreases while the price difference between new and remanufactured products increases; however, the optimal selling price of new product may increase or decrease. If new products are made to stock (MTS), then the optimal manufacturing policy is of a base‐stock policy with the base‐stock level decreasing in the remanufactured product inventory level. To understand the potential benefit in implementing an MTO system, we study the difference between the value functions of the MTO and MTS systems, and develop lower and upper bounds for it. Finally, we study several extensions of the base model and show that most of our results extend to those more general settings.

Video Delivery Architecture for Hierarchical HetNet: HH-D2D Caching

ABSTRACTOver the last few years, smart devices and mobile devices drive the wide growth in mobile data communications. This increase is a major challenge for mobile network operators (MNOs). The MNOs are forced to operate with their maximum capacity limits and this growth needs mobile data offloading to accomplish the capacity demands. The mobile data offloading through device-to-device (D2D) communication can help to reduce the network congestion at low operational and capital expenses. The data offloading through D2D attracts the mobile users to participate, by paying them proper incentives in returns of their services. The offloading requires mutual agreement and benefits both the parties, MNOs and mobile users. In this paper, we categorize the smart devices (SDs) on the basis of their storage and methoding capabilities. Furthermore, we create the hierarchy of SDs to utilize the available resources efficiently with minimum cost and higher benefits. We present a main node–friend node (MNFN) selection and matching mechanism, which efficiently selects and utilizes available high-end SDs (HSDs) on the basis of available resources for offloading purpose. It also decides the optimal pricing policy for the selected SDs. The efficiency of MNFN has been realized in terms of bandwidth and storage demand. Subsequently, we implement caching in MNs, and FNs with the help of our novel hierarchical heterogeneous D2D (HH-D2D) caching-based video dissemination architecture to solve the bit rate issues in the mobile network. The particular focus of our work is on video data, due to high demands. Simulation results show that FN caching increases bit rate up to ∼26 times, while MNFN caching improves bit rate up to ∼40 times.

Should retailers hold a perishable product having different ages? The case of a homogeneous market and multiplicative demand model

This paper specializes in investigating the common practice of the coexistence of multiple competing perishables, each with different age and price, all of which are associated with the same product. The fundamental postulate investigated by our model is the replacement of the policy of selling a single product-age with a policy of selling multiple product-ages. Coexistence of multiple product-ages on the shelf is associated with shorter cycle lengths as well as with providing consumers with the option of choosing between a fresher product on average and a cheaper product on average. We use a utility corresponding to the factors of price and time. We axiomatically assume the coexistence of multiple product-ages while posing several propositions which present certain difficulties in preferring this policy. With the support of a multiplicative demand with respect to price and time, and by assuming that consumers are homogeneous in their preferences, we analyze a deterministic version of the problem and derive the optimal pricing policy given any cycle length and any duration for which both types coexist on the shelf. We prove that the optimal policy is not to sell multiple product-types at all. By means of a numerical example we show that the operational mode of the coexistence of multiple product-ages reduces the retailer's profit per unit time by at least 15%. Sensitivity analysis of some of the most influential parameters is introduced. The superiority of the single product-age operational mode over the competitor mode sharply decreases as the optimal cycle length is approached.

Optimal pricing and two-dimensional warranty policies for a new product

For commercial products, pricing and warranty are two crucial marketing strategies, which are used to promote the potential market share. The warranty policy adopted by most of the capital-intensive products, such as machines and automobiles, usually has two dimensions, i.e. warranty age and warranty usage. In this paper, we propose to investigate the profit-maximisation problem, in which the revenue and costs will be affected by the product price and the area of warranty region, for a new product sold under two-dimensional warranty. We assume that the product sales can be captured by a stochastic Bass model based on the nonhomogeneous Poisson process. The product follows a two-dimensional failure process and is covered by a non-renewable free minimal-repair warranty, with age and usage limits. We focus on three revenue/cost components, i.e. sales revenue, warranty cost and production cost, that will significantly affect a firm’s total profit. The profit is maximised by jointly optimising three decision variables, i.e. product price, warranty age limit and warranty usage limit. Numerical experiments are conducted to illustrate the effects of some key parameters, including product reliability, price elasticity, warranty elasticity and learning effect factor, on the optimal settings of the price and warranty region.

The effect of customer value and power structure on retail supply chain product choice and pricing decisions

Customer value in goods not only affect his purchase decision but also bring about a big challenge for retail supply chain management. A two-stage retail supply chain consisting of one manufacturer and one retailer is investigated in this paper. The manufacturer produces two substitute products which belong to two different generations while the retailer determines his product choice decisions and pricing policies with considering heterogeneous customer demand based on different customer value. The key issues faced by the retailer are which products to purchase, single or both? And how to make pricing policies in different power structures? From three different game theoretical perspectives, we found that the retailer's purchase decision criterions are based on two thresholds, and in each power structure the optimal pricing policies of manufacturer and retailer are obtained. In addition, the impact of power structure has been explored and it shows that different power structures have no effect on the retailer's product choice decision criterions and behaviors, however, they have a great influence on supply chain members’ pricing policies and performances. The revenue sharing contract achieves a Pareto improvement and makes a bigger pie, and the power structure determines the pie split between the supply chain members. Additionally, revenue sharing contract will not affect the retailer's purchase decision criterions and behaviors, either.

The reference effect in newsvendor model with strategic customers

PurposeThe purpose of this paper is to discuss the role of reference effect on newsvendor’s decision behavior in a market with strategic customers and work out the newsvendor’s optimal pricing policy and ordering quantity.Design/methodology/approachThis study utilizes the prospect theory and strategic customer framework to analyze the decision-making behavior on the newsvendor’s optimal pricing policy and ordering quantity. The paper further presents an extension of newsvendor model and provides the model’s properties. The paper finally analyzes the results with various parameters on the model and reports on the insights generated by the model.FindingsThe paper indicates that the ordering quantity is not altered with the changing proportion of strategic customers and myopic customers, but the ordering quantity and the pricing strategy are influenced in terms of newsvendor’s reference effect, loss aversion, product cost, and salvage price.Practical implicationsThe research findings have important implications for decision makers. Previous researches have studied the incomplete rationality newsvendor’s decision-making behavior mainly by analyzing the vendor’s risk preferences or loss aversion, but the effect of reference point also plays an important role in analyzing the decision-maker’s behavior. The paper provides the optimal pricing policy and ordering quantity with the reference effect considering the strategic customers behavior. This model is also a valid complementarity to behavioral operations management research area.Originality/valueThe paper examines the role of reference effect in newsvendor problem with the strategic customers and analyzes the impact of parameters such as loss aversion on the newsvendor’s decision behavior.