Monopoly Pricing in a Vertical Market with Demand Uncertainty

We study a vertical market with an upsteam supplier and multiple downstream retailers. Demand uncertainty falls to the supplier who acts first and sets a uniform wholesale price before the retailers observe the realized demand and engage in retail competition. Our focus is on the supplier's optimal pricing decision. We express the price elasticity of expected demand in terms of the mean residual demand (MRD) function of the demand distribution. This allows for a closed form characterization of the points of unitary elasticity that maximize the supplier's profits and the derivation of a mild unimodality condition for the supplier's objective function that generalizes the widely used increasing generalized failure rate (IGFR) condition. A direct implication is that optimal prices between different markets can be ordered if the markets can be stochastically ordered according to their MRD functions or equivalently to their elasticities. Based on this, we apply the theory of stochastic orders to study the response of the supplier's optimal price to various features of the demand distribution. Our findings challenge previously established economic insights about the effects of market size, demand transformations and demand variability on wholesale prices and indicate that the conclusions largely depend on the exact notion that will be employed. We then turn to measure market performance and derive a distribution free and tight bound on the probability of no trade between the supplier and the retailers. If trade takes place, our findings indicate that ovarall performance depends on the interplay between demand uncertainty and level of retail competition

Large Newsvendor Games

We consider a game, called newsvendor game, where several retailers, who face a random demand, can pool their resources and build a centralized inventory that stocks a single item on their behalf. Profits have to be allocated in a way that is advantageous to all the retailers. A game in characteristic form is obtained by assigning to each coalition its optimal expected profit. A similar game (modeled in terms of costs) was considered by Muller et al. (2002), who proved that this game is balanced for every possible joint distribution of the random demands. In this paper we consider newsvendor games with possibly an infinite number of newsvendors. We prove in great generality results about balancedness of the game, and we show that in a game with a continuum of players, under a nonatomic condition on the demand, the core is a singleton. For a particular class of demands we show how the core shrinks to a singleton when the number of players increases.newsvendor games, nonatomic games, core, balanced games.

A Supply Chain Equilibrium Model with General Price-Dependent Demand

The concept of supply chain equilibrium has been widely employed to solve real-life cases. Under this concept, decisions makers move simultaneously and compete in a noncooperative manner to achieve a supply chain network equilibrium. This paper proposes a supply chain network equilibrium model consisting of multiple raw material suppliers, manufacturers and retailers. Unlike previous studies, we assume that the demand for the product at each retail outlet is modeled as general stochastic functions of price that encompass additive-multiplicative demand models used in previous studies. Under general price-dependent demand functions, we derive the optimality conditions of suppliers, manufacturers and retailers, and establish that the governing equilibrium conditions can be formulated as a finite-dimensional variational inequality problem. The existence and uniqueness of the solution to the variational inequality are examined. A sensitivity analysis and a series of numerical tests are conducted to illustrate the analytical effects of demand distribution, model parameters, demand level and variability on quantity shipments, prices, and expected profits. Managerial insights are reported to show the impact of different types of demand functions and model parameters on the equilibrium solutions

The newsvendor problem with advertising: an overview with extensions

The effect of advertising on sales has been the subject of recent studies as an important aspect in many demand-based problems. Herein, we deal with the newsvendor problem, due to its simple structure, as a suitable tool for illustrating how facets of marketing may affect decision-making concerning operational problems. In the setting presented, the newsvendor is faced with advertising-sensitive stochastic demand, where a demand-related random element comprises an advertising decision of the multiplicative or additive form. We assume that a suitable advertising strategy results in increased sales. Two advertising response functions are considered, these being concave downward and S-shaped. We review and extend the existing results relating to the newsvendor problem with marketing effects, which mostly pertain to the concave function. These are generalized by defining the S-shaped function, and some original insights into the effect of advertising are given. We establish that the optimal advertising expenditure for the multiplicative case is always less than or equal to the optimal amount in the equivalent deterministic model while it is always equal in the additive case. We finally illustrate the results that are obtained by providing numerical examples involving various advertising response functions, as well as management-related interpretations. © 2016, Springer-Verlag Berlin Heidelberg.European Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]; specific research project entitled "Modern Methods of Applied Mathematics for the Use in Technical Sciences'' [FSI-S-14-2290, 25053]; Ministry of Education, Youth and Sports under National Sustainability Programme I [LO1202]; Norway Grants via the EEA Scholarship Programme: Bilateral Scholarship Programme; Institutional cooperation projects [NF-CZ07-ICP-4-345-2016

An Elasticity Approach to the Newsvendor with Price Sensitive Demand

Cataloged from PDF version of article.We introduce a measure of elasticity of stochastic demand, called the elasticity of the lost-sales rate, which offers a unifying perspective on the well-known newsvendor with pricing problem. This new concept provides a framework to characterize structural results for coordinated and uncoordinated pricing and inventory strategies. Concavity and submodularity of the profit function, as well as sensitivity properties of the optimal inventory and price policies, are characterized by monotonicity conditions, or bounds, on the elasticity of the lost-sales rate. These elasticity conditions are satisfied by most relevant demand models in the marketing and operations literature. Our results unify and complement previous work on price-setting newsvendor models and provide a new tool for researchers modeling stochastic price-sensitive demand in other contexts

Approximating the Nonlinear Newsvendor and Single-Item Stochastic Lot-Sizing Problems When Data Is Given by an Oracle

The single-item stochastic lot-sizing problem is to find an inventory replenishment policy in the presence of discrete stochastic demands under periodic review and finite time horizon. A closely related problem is the single-period newsvendor model. It is well known that the newsvendor problem admits a closed formula for the optimal order quantity whenever the revenue and salvage values are linear increasing functions and the procurement (ordering) cost is fixed plus linear. The optimal policy for the single-item lot-sizing model is also well known under similar assumptions. In this paper we show that the classical (single-period) newsvendor model with fixed plus linear ordering cost cannot be approximated to any degree of accuracy when either the demand distribution or the cost functions are given by an oracle. We provide a fully polynomial time approximation scheme for the nonlinear single-item stochastic lot-sizing problem, when demand distribution is given by an oracle, procurement costs are provided as nondecreasing oracles, holding/backlogging/disposal costs are linear, and lead time is positive. Similar results exist for the nonlinear newsvendor problem. These approximation schemes are designed by extending the technique of K-approximation sets and functions.National Science Foundation (U.S.) (Contract CMMI-0758069)United States. Office of Naval Research (Grant N000141110056

The effects of subsidies on increasing consumption through for-profit and not-for-profit newsvendors

Subsidy programs are widely offered in both developing and developed countries to encourage consumption of products that generate positive social, health, and environmental externalities. We study the effect of subsidies on product consumption under uncertain market demand. To reach a target consumer population, the program sponsor may subsidize a for-profit or a not-for-profit firm on each unit of the product purchased by the firm or on each unit of the sale generated by the firm. We show that subsidy programs provide stronger incentives to a not-for-profit firm than to its for-profit counterpart in inducing a large consumption whenever the sponsor is having a very limited budget or a very generous budget. When subsidizing a not-for-profit firm, the sponsor should always choose the purchase subsidy over the sales subsidy because the former can induce a larger consumption than the latter with the same subsidy spending. However, this is not always true when the subsidy program is administered through a for-profit firm, unless the firm is a price taker in the market or the sponsor has a limited budget. Our analysis leads to new theoretical development of price-setting newsvendor problem for both the for-profit and not-for-profit operations under subsidy.National Natural Science Foundation of China. Grant Numbers: 71471107, 7143100

Data-driven revenue management

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007.Includes bibliographical references (p. 125-127).In this thesis, we consider the classical newsvendor model and various important extensions. We do not assume that the demand distribution is known, rather the only information available is a set of independent samples drawn from the demand distribution. In particular, the variants of the model we consider are: the classical profit-maximization newsvendor model, the risk-averse newsvendor model and the price-setting newsvendor model. If the explicit demand distribution is known, then the exact solutions to these models can be found either analytically or numerically via simulation methods. However, in most real-life settings, the demand distribution is not available, and usually there is only historical demand data from past periods. Thus, data-driven approaches are appealing in solving these problems. In this thesis, we evaluate the theoretical and empirical performance of nonparametric and parametric approaches for solving the variants of the newsvendor model assuming partial information on the distribution. For the classical profit-maximization newsvendor model and the risk-averse newsvendor model we describe general non-parametric approaches that do not make any prior assumption on the true demand distribution. We extend and significantly improve previous theoretical bounds on the number of samples required to guarantee with high probability that the data-driven approach provides a near-optimal solution. By near-optimal we mean that the approximate solution performs arbitrarily close to the optimal solution that is computed with respect to the true demand distributions.(cont.) For the price-setting newsvendor problem, we analyze a previously proposed simulation-based approach for a linear-additive demand model, and again derive bounds on the number of samples required to ensure that the simulation-based approach provides a near-optimal solution. We also perform computational experiments to analyze the empirical performance of these data-driven approaches.by Joline Ann Villaranda Uichanco.S.M

Contractual Pricing Problems for Retail Distribution under Different Channel Structures

In many industries, including the retail industry, the profits of a supply chain primarily come from the revenue determined by pricing decisions, while the costs of a supply chain are mainly determined by production and inventory decisions. Lack of coordination between the involved parties concerning pricing and inventory decisions may cost all parties in the supply chain system. Historically, contracts have been viewed and served as effective mechanisms to achieve supply chain coordination. In particular, a coordination contract is such that the total profit of the entities under the contract is equal to the optimal supply chain profit (a.k.a., system profit) under centralized control. Hence, profit potential of each entity is in fact maximized under a coordination contract. Also, a coordination contract is said to achieve the so-called channel coordination objective. In this context, we consider supplier-buyer (e.g., manufacturer-retailer) systems and take into account a recent trend shifting the leadership in contract design from the supplier to the buyer. In particular, we are interested in powerful entities (e.g., mass retailers or government) leading contractual efforts in various practical settings. We consider two classes of problems related to such powerful entities. We first study coordination efforts through contracts in single- and multi-product settings from the supplier- and buyer-driven perspectives by considering supplier- and buyer-driven contracts. Previous literature on the leadership shift focuses on the single-product setting while overlooking general buyer-driven contracts under full information. We propose more general buyer-driven contracts and provide a comparison of supplier- and buyer-driven settings in terms of the realized profit and prices while taking into account for not only the supplier's and buyer's but also the consumers' perspectives. Our results lead to a new buyer-driven contract called the generic contract: a simple, general, effective, and practical coordination contract which is amenable to generalization for handling multi-product, multi-supplier, and multi-buyer settings. Also, the generic contract offers room for negotiation between the buyer and supplier because even when the supplier is the more powerful entity. Last but not least, the generic contract is advantageous not only for the buyer and the supplier but also for the consumers. We next study a newsvendor problem for a private retailer where government interventions are implemented to induce the retailer to make socially optimal decisions. Very limited literature has studied the social welfare issue for public interest goods with random price-dependent demand, especially in the multiplicative form. We develop a model and methodology for designing government intervention mechanisms that improve/maximize the expected social welfare and analyze the impact of demand uncertainty on coordination performance. We consider two new government regulatory mechanisms, and a new market intervention along with two existing market interventions. Our results demonstrate that government regularity mechanisms are effective in improving the expected social welfare and using any combination of two market interventions achieves the optimal expected social welfare