Dynamic Pricing of Inventory/Capacity With Infrequent Price Changes

We consider a problem of dynamically pricing a single product sold by a monopolist over a short time period. If demand characteristics change throughout the period, it becomes attractive for the company to adjust price continuously to respond to such changes (i.e., price-discriminate intertemporally). However, in practice there is typically a limit on the number of times the price can be adjusted due to the high costs associated with frequent price changes. If that is the case, instead of a continuous pricing rule the company might want to establish a piece-wise constant pricing policy in order to limit the number of price adjustments. Such a pricing policy, which involves optimal choice of prices and timing of price changes, is the focus of this paper. We analyze the pricing problem with a limited number of price changes in a dynamic, deterministic environment in which demand depends on the current price and time, and there is a capacity/inventory constraint that may be set optimally ahead of the selling season. The arrival rate can evolve in time arbitrarily, allowing us to model situations in which prices decrease, increase, or neither. We consider several plausible scenarios where pricing and/or timing of price changes are endogenized. Various notions of complementarity (single-crossing property, supermodularity and total positivity) are explored to derive structural results: conditions sufficient for the uniqueness of the solution and the monotonicity of prices throughout the sales period. Furthermore, we characterize the impact of the capacity constraint on the optimal prices and the timing of price changes and provide several other comparative statics results. Additional insights are obtained directly from the solutions of various special cases

Identifying Cartels that Use the Illinois Brick Ruling as a Shield

“Identifying Cartels that Use the Illinois Brick Ruling as a Shield” looks at a landmark Supreme Court ruling, known as the Illinois Brick (IB) decision, which bars “indirect purchasers” from bringing antitrust suits against upstream product manufacturers. The research suggests the IB ruling not only reduced the costs associated with antitrust enforcement but has the potential to enable firms upstream in the supply chain to engage in collusion through the use of the wholesale price plus fixed fee structure (WPFF). WPFF allows manufacturers to pay a fixed fee to retailers, compensating them for stocking fewer, higher cost items than they would under perfect competition. The fee acts as a disincentive for retailers to level antitrust suits against manufacturers. And consumers, whose welfare is reduced by the collusion, are forbidden from bringing antitrust action by the IB ruling. The incentive to collude is greater when demand uncertainty for a product is higher, the number of retailers in the market is higher, and the number of manufacturers is lower. Public enforcers of antitrust law can use this knowledge to focus their monitoring efforts on firms embedded in the type of supply chain structures described here while using WPFF contracts.https://repository.upenn.edu/pennwhartonppi/1064/thumbnail.jp

Why Taxing Carbon May Not Make the World More Green

Although taxing carbon is an idea that enjoys significant support among policymakers and business leaders, new research indicates that carbon taxation can actually cause energy investments to gravitate away from the cleanest energy technologies. This counterintuitive finding reflects two key characteristics of energy markets: the worldwide increase in renewable energy sources whose output is intermittent and variable; and greater market liberalization, which has made the spot driving of electricity more volatile. The intermittency of renewable energy sources requires backup generation, typically from generators using fossil fuels. The dynamics of market liberalization amplify this negative effect of intermittency. Policymakers need to take steps to reduce intermittency by supporting storage technologies or setting monetary incentives to increase renewable generation capacity investment.https://repository.upenn.edu/pennwhartonppi/1052/thumbnail.jp

Revenue Management Games: Horizontal and Vertical Competition

A well-studied problem in the literature on airline revenue (or yield) management is the optimal allocation of seat inventory among fare classes, given a demand distribution for each class. In practice, the seat allocation decisions of one airline affect the passenger demands for seats on other airlines. In this paper, we examine the seat inventory control problem under both horizontal competition (two airlines compete for passengers on the same flight leg) and vertical competition (different airlines fly different legs on a multileg itinerary). Such vertical competition can be the outcome of a code-sharing agreement between airlines, because each airline sells seats on the partner airlines’ flights but the airlines are unwilling, or unable, to coordinate yield management decisions. We provide a general sufficient condition under which a pure-strategy Nash equilibrium exists in these revenue management games, and we also compare the total number of seats available in each fare class with, and without, competition. Analytical results as well as numerical examples demonstrate that more seats are protected for higher-fare passengers under horizontal competition than when a single airline acts as a monopoly. Under vertical competition the booking limit may be higher or lower, however, than the monopoly level, depending on the demand for connecting flights in each fare class. Finally, we discuss revenue-sharing contracts that coordinate the actions of both airlines

IS TOM CRUISE THREATENED? AN EMPIRICAL STUDY OF THE IMPACT OF PRODUCT VARIETY ON DEMAND CONCENTRATION

Multiple studies suggested that expanding product variety due to adoption of the Internet will satisfy consumer\u27s increasingly heterogeneous tastes, thus causing the so-called Long Tail effect (i.e., increasing demand for niche products). In this paper we empirically examine the impact of product variety on demand concentration. We use two large data sets from the movie rental industry and analyze the data at both movie-level and consumer-level. We employ multiple measures to understand the changing demand concentration and incorporate the potential endogeneity of product variety. Multiple models analyzed in our study consistently suggest that larger product variety is likely to increase the demand for hits and decrease the demand for niche products. We propose that new products appear much faster than consumers discover them. Finally, we find no evidence that niche titles satisfy consumer tastes any better than popular titles and that a small number of heavy users are more likely to venture into niches than light users

Product Line Design and Production Technology

In this paper we characterize the impact of production technology on the optimal product line design. We analyze a problem in which a manufacturer segments the market on quality attributes and offers products that are partial substitutes. Because consumers self-select from the product line, product cannibalization is an issue. In addition, the manufacturer sets a production schedule in order to balance production setups with accumulation of inventories in the presence of economies of scale. We show that simultaneous optimization of the product line design and production schedule leads to insights that differ significantly from the common intuition and assertions in the literature, which omits either the demand side or the supply side of the equation. In particular, we demonstrate that more expensive production technology always leads to lower product prices and may at the same time lead to higher quality products. Further, a less efficient production technology does not necessarily increase total production costs or reduce consumer welfare. We also demonstrate that in the presence of production technology, the demand cannibalization problem may distort product quality upward or the number of products upward, which is contrary to the standard result

Procurement in Supply Chains When the End-Product Exhibits the \u27Weakest Link\u27 Property

We consider a supply chain with one manufacturer who assembles an end-product using multiple outsourced parts. The end-product exhibits the “weakest-link” property, such that if any of its component parts fails, the end-product fails. The supplier of each component part can improve the (uncertain) quality of her parts by exerting costly effort that is unobservable to the manufacturer and is non-contractible. We analyze three possible contractual agreements between the manufacturer and suppliers: Acceptable Quality Level (AQL), Quality–Based Incentive Pricing (Q–Pricing) and Group Warranty. Under AQL, the manufacturer inspects all incoming parts, but establishes different quality thresholds and pays the suppliers different amounts for achieving the different thresholds. Under Q-Pricing, the manufacturer also inspects all incoming parts but pays each supplier a constant amount for each good part. Under Group Warranty there is no testing of the individual parts; instead all suppliers are responsible for any failed end-product. We compare the efficiency of these three contractual arrangements as a function of the exogenous variables

TECHNICAL NOTE—Robust Newsvendor Competition Under Asymmetric Information

We generalize analysis of competition among newsvendors to a setting in which competitors possess asymmetric information about future demand realizations, and this information is limited to knowledge of the support of demand distribution. In such a setting, traditional expectation-based optimization criteria are not adequate, and therefore we focus on the alternative criterion used in the robust optimization literature: the absolute regret minimization. We show existence and derive closed-form expressions for the robust optimization Nash equilibrium solution for a game with an arbitrary number of players. This solution allows us to gain insight into the nature of robust asymmetric newsvendor competition. We show that the competitive solution in the presence of information asymmetry is an intuitive extension of the robust solution for the monopolistic newsvendor problem, which allows us to distill the impact of both competition and information asymmetry. In addition, we show that, contrary to the intuition, a competing newsvendor does not necessarily benefit from having better information about its own demand distribution than its competitor has

Inventory Competition and Incentives to Back-Order

In this paper we consider the issue of inventory control in a multi-period environment with competition on product availability. Specifically, when a product is out of stock, the customer often must choose between placing a back-order or turning to a competitor selling a similar product. We consider a competition in which customers may switch between two retailers (substitute) in the case of a stock-out at the retailer of their first choice. In a multi-period setting, the following four situations may arise if the product is out of stock: (i) sales may be lost; (ii) customers may back-order the product with their first-choice retailer; (iii) customers may back-order the product with their second-choice retailer; or (iv) customers may attempt to acquire the product according to some other more complex rule. The question we address is: how do the equilibrium stocking quantities and profits of the retailers depend on the customers\u27 back-ordering behaviors? In this work we consider the four alternative back-ordering scenarios and formulate each problem as a stochastic multi-period game. Under appropriate conditions, we show that a stationary base-stock inventory policy is a Nash equilibrium of the game that can be found by considering an appropriate static game. We derive conditions for the existence and uniqueness of such a policy and conduct a comparative statics analysis. Analytical expressions for the optimality conditions facilitate managerial insights into the effects of various back-ordering mechanisms. Furthermore, we recognize that often a retailer is willing to offer a monetary incentive to induce a customer to back-order instead of going to the competitor. Therefore, it is necessary to coordinate incentive decisions with operational decisions about inventory control. We analyze the impact of incentives to back-order the product on the optimal stocking policies under competition and determine the conditions that guarantee monotonicity of the equilibrium inventory in the amount of the incentive offered. Our analysis also suggests that, counterintuitively, companies might benefit from making their inventories “visible” to competitors\u27 customers, since doing so reduces the level of competition, decreases optimal inventories and simultaneously increases profits for both players

Revenue Management Through Dynamic Cross Selling in E-Commerce Retailing

We consider the problem of dynamically cross-selling products (e.g., books) or services (e.g., travel reservations) in the e-commerce setting. In particular, we look at a company that faces a stream of stochastic customer arrivals and may offer each customer a choice between the requested product and a package containing the requested product as well as another product, what we call a “packaging complement.” Given consumer preferences and product inventories, we analyze two issues: (1) how to select packaging complements, and (2) how to price product packages to maximize profits. We formulate the cross-selling problem as a stochastic dynamic program blended with combinatorial optimization. We demonstrate the state-dependent and dynamic nature of the optimal package selection problem and derive the structural properties of the dynamic pricing problem. In particular, we focus on two practical business settings: with (the Emergency Replenishment Model) and without (the Lost-Sales Model) the possibility of inventory replenishment in the case of a product stockout. For the Emergency Replenishment Model, we establish that the problem is separable in the initial inventory of all products, and hence the dimensionality of the dynamic program can be significantly reduced. For both models, we suggest several packaging/pricing heuristics and test their effectiveness numerically