Distribution contracts to support optimal inventory holdings under demand uncertainty

When suppliers produce products for which demand is uncertain, they face a problem of inducing downstream distributors to stock inventory levels that the suppliers prefer. This paper considers a wide array of alternative supply contracts, each of which consists of a mixture of constant per-unit wholesale prices, buy-back arrangements, and post sale payments contingent on sales made, such as revenue sharing or buybacks. We show that linear supply contracts specifying any combination of two of these three instruments can implement the vertical integrated outcome for a monopoly, thereby generating the supplier's preferred inventory configuration and price distribution. We extend our results to differentiated product oligopoly, demonstrating that each supplier obtains its preferred inventory configuration and price distribution, given the choices of its rival. Distributors choose optimal inventories from the suppliers' standpoint, even if suppliers do not know the distribution of demand uncertainty, and, given the perfect competition among distributors, all profits in the supply chain are captured by suppliers. Thus, suppliers are able to deal with demand uncertainty with remarkably little information about demand, and without the need to control dealer actions in detail. In particular, suppliers need not specify either dealer inventories or resale prices, but instead encourage distributors to order based on information in their possession and to set prices that generate desirable resale price dispersion.     

Structuring and contracting in competing supply chains

This paper considers two competing supply chains, each with multiple upstream suppliers producing complementary products and selling to a single buyer (e.g., assembler or retailer), who then sells the finished assembled product to a market that involves both demand uncertainty and competition. Our main research questions focus on what supply chain structure (integration vs. decentralization) and which contracting strategy a business should choose. We find that supply chains that decentralize perform better under strong market competition (i.e., high degree of product substitution between supply chains). However, when a large number of suppliers exist, supply chains that integrate perform better. When decentralized structures are used for both supply chains, a consignment with revenue sharing contract generally outperforms a wholesale price contract from the downstream retailer's point of view. Interestingly, for a supplier, a wholesale price contract, which pushes all demand risks to the downstream retailer, might not be preferred. For the entire supply chain, one contract strategy can outperform another depending on the degree of competition, the cost share of the buyer, and the number of suppliers.     

Vertical Exclusion with Downstream Risk Aversion or Limited Liability

An upstream firm with full commitment bilaterally contracts with two ex ante identical downstream firms. Each observes its own cost shock, and faces uncertainty from its competitor’s shock. When they are risk neutral and can absorb losses, the upstream firm contracts symmetric outputs for production efficiency. However, when they are risk averse, competition requires the payment of a risk premium due to revenue uncertainty. Moreover, when they enjoy limited liability, competition requires the upstream firm to share additional surplus. To resolve these trade‐offs, the upstream firm offers exclusive contracts in many cases.     

Using Revenue Sharing to Implement Flexible Prices: Evidence from Movie Exhibition Contracts

Movie exhibition contracts entail revenue‐sharing terms that go down with weeks since release. We develop a simple model to show how the form of these contracts can be explained by the distributors’ desire to set flexible prices. We then use detailed data on theater‐movie contracts in Spain, where we exploit the information available at the time of contracting for movies previously released in the U.S., and other movie and theater characteristics, to show how the implications of our flexible pricing argument are supported in the data, and differentiate our explanation from prior, more standard risk‐sharing and moral‐hazard explanations.     

Revenue Sharing and Competitive Balance When Teams are not Wage Takers

Recent papers have enriched the conventional modeling of teams’ behavior through a game theoretic background at the competition level (introducing a contest success function). We take a step forward and consider contest on the talent market as well. Each team takes into account the fact that the price to be paid recruiting talent is a function that depends on both its own demand and the demands from the rival teams. For the two-team model, we show that the removal of the assumption that teams are price takers implies that the invariance proposition only survives if the price-function for talent is linear increasing. The extension to the n-team model shows that this result no longer holds; in fact, revenue sharing improves the competitive balance. More generally, an improvement in competitive balance is the most likely if one rules out the possibility of a very convex price-function. In addition revenue sharing can reduce the economic inefficiency of teams’ behavior, and so profits may increase.     

Coordination of a supply chain with one manufacturer and multiple competing retailers under simultaneous demand and cost disruptions

This paper develops a coordination mechanism for a supply chain consisting of one manufacturer and n Cournot competing retailers when the production cost and demands are simultaneously disrupted. This differs from traditional supply chain coordination models under a static case and the case with only demand or cost disruption. The coordination mechanism with revenue sharing is considered, and the effects of production cost and demand disruptions on revenue sharing contract are discussed to investigate the optimal strategies of players with disruptions. The penalty cost is introduced explicitly to obtain the production deviation cost caused by the disruptions. In this study, it is obtained that the coordination contract considering the production deviation cost differs from that without disruption. Besides that, the disruptions may affect the order quantities, wholesale prices as well as revenue sharing contract. Then, the optimal strategies for different disruption levels under the centralized decision-making mode are proposed. Concerning the decentralized mode, the improved revenue sharing contract can be used to coordinate the decentralized decision-making supply chain effectively. Finally, the theoretical results are illustrated by conducting some numerical examples.     

Dynamic supply chain coordination under consignment and vendor-managed inventory in retailer-centric B2B electronic markets

This study examines the dynamic performance of vertically decentralized two-echelon channel coordination for deteriorating goods under consignment and vendor-managed inventory (VMI) contracts with revenue sharing from retailer-centric business-to-business transactions in both traditional markets and electronic markets (EMs). The research presents the profit-maximization problem and devises a method for making cross-enterprise dynamic joint decisions by combining calculus with dynamic programming for a retailer-led Stackelberg supply chain under cooperative and non-cooperative game settings over a multi-period planning horizon. The applicability of the proposed model is assessed using a case study involving a highly perishable product, sliced raw fish, in a supply chain comprising a regional seafood supplier and a local store belonging to a large national retail chain. The analytical results show that, in a cooperative setting, the EM with a consigned revenue-sharing VMI contract tends to achieve lower retail prices, larger stock quantity, improved channel efficiency, and increases in both retailer and supplier profits through an additional one-part tariff. Additionally, consumers benefit from lower retail prices and society benefits from increased overall channel profits in the cooperative channel and EM.     

Theory of the Perfect Game: Competitive Balance in Monopoly Sports Leagues

Based on the limiting assumption that sports owners are profit maximizers the invariance proposition holds that revenue sharing has no impact on competitive balance in sports leagues. If owners are win-maximizing sportsmen instead, then revenue sharing can lead to increased competitive balance and higher payrolls. Evidence of the sportsman effect is provided by erosion of monopsonistic exploitation in the four major American sports leagues where players now share about 60% of revenues. Monopsony power erosion forces sports-league cartels to exploit statutory monopoly power in monster deals for media rights fees and public venue subsidies. New evidence on competitive balance suggests that revenue sharing leads to increased balance with or without team salary caps. Optimum competitive balance is an empirical question, and the answer lies between random competition of the NFL and deterministic dynasties of the NBA.      

Competition under capacitated dynamic lot-sizing with capacity acquisition

Lot-sizing and capacity planning are important supply chain decisions, and competition and cooperation affect the performance of these decisions. In this paper, we look into the dynamic lot-sizing and resource competition problem of an industry consisting of multiple firms. A capacity competition model combining the complexity of time-varying demand with cost functions and economies of scale arising from dynamic lot-sizing costs is developed. Each firm can replenish inventory at the beginning of each period in a finite planning horizon. Fixed as well as variable production costs incur for each production setup, along with inventory carrying costs. The individual production lots of each firm are limited by a constant capacity restriction, which is purchased up front for the planning horizon. The capacity can be purchased from a spot market, and the capacity acquisition cost fluctuates with the total capacity demand of all the competing firms. We solve the competition model and establish the existence of a capacity equilibrium over the firms and the associated optimal dynamic lot-sizing plan for each firm under mild conditions.     

Competing buyers,rent extraction and inefficient exclusion

The article illustrates how a seller profitably can prevent entry of a potential competitor, even when entry would increase industry profit. Entry is prevented by offering exclusive contracts to the buyers. The buyers are assumed to be differentiated firms, competing in a downstream market. Exclusion occurs in equilibrium as long as there is some degree of competition among the downstream firms, and even when there are no economies of scale in upstream production.     

An inventory reservation problem with nesting and fill rate-based performance measures

In many inventory settings companies wish to provide customer-differentiated service levels. These may, for example, be motivated by differences in the perceived customer lifetime value or by specific contractual agreements. One approach to provide differentiated service levels is to reserve some portion of the available inventory exclusively for specific customer classes. Existing approaches to inventory reservation are typically based on the assumption that a company can assign a customer specific revenue or penalty cost to any order or unit of demand filled or unfulfilled. In practice, however, it is usually extremely difficult to accurately estimate (especially long term) monetary implications of meeting or not meeting customer demand and corresponding service level requirements. The research presented in this paper addresses the problem of setting appropriate inventory reservations for different customer classes based on fill rate-based performance measures. We model a single period inventory reservation problem with two customer classes and nesting. We develop exact expressions for two conflicting performance measures: (1) the expected fill rate of high priority customers and (2) the expected loss in the system fill rate induced by inventory reservation. With these expressions a decision maker can analyze the tradeoff between the loss in overall system performance and the higher expected fill rates for prioritized customers. We provide analytical insights into the effects of nesting and the impact of relevant problem parameters on these two performance measures. The analytical insights are illustrated and highlighted through a set of numerical examples. Although we limit our analysis to a single period inventory reservation problem, we expect that our results can be utilized in a wide range of problem settings in which a decision maker has to ration a perishable resource among different classes of customers.     

Optimal economic ordering policy with deteriorating items under different supplier trade credits for finite horizon case

This paper develops and solves a general finite horizon trade credit economic ordering policy for an inventory model with deteriorating items under inflation and time value of money when shortages are not allowed. The time horizon is divided into different cycles each of which has its own demand rate and its own trade credit period offered from the supplier to his retailer so that the retailer should pay his supplier before or after the end of the permissible trade credit of that cycle. Up to the end of the trade credit of a cycle, the retailer is free of charge, but he is charged on an interest for those items not being sold before this end. The retailer can also earn the interest of the money from the generated sales revenue in any cycle by depositing such revenue into an interest bearing account. The objective of the retailer is then to minimize his net total relevant costs. A closed form of this net total cost is derived and the resulting model is solved. Then rigorous mathematical methods are used to show that, under some seemingly possible conditions, there exist a unique vector of the relevant decision variables that solve the underlying inventory system. A numerical example which shows the applicability of the theoretical results is given.     

Oligopoly intermediation,relative rivalry and market conduct

We consider two firms that compete against each other jointly in upstream and downstream markets under two pricing games: Purchasing to stock (PTS), in which firms select input prices prior to setting consumer prices; and purchasing to order (PTO), in which firms sell forward contracts to consumers prior to selecting input prices. The antitrust implications of the model depend on the relative degree of oligopoly rivalry in the upstream and downstream markets. Firms strategically precommit to setting prices in the less rivalrous market, which serves to soften competition in the more rivalrous market, resulting in anticompetitive effects. Bertrand prices emerge in equilibrium when the markets are equally rivalrous, while Cournot outcomes arise with upstream monopsony or downstream monopoly markets. The slope of firm reaction functions depends on relative rivalry, a feature we use to derive testable hypotheses for antitrust analysis of a wide variety of industry practices.     

Revenue Sharing with Heterogeneous Investments in Sports Leagues: Share Media,Not Stadiums

This study examines revenue sharing in sports leagues where franchises engage in multiple types of investments. Previous literature typically treats revenues and investments as homogeneous, but we add to the literature by differentiating between investment types and revenue sources. This is important because investment in talent leads to winning, which is a zero-sum game for the league and therefore owners have an incentive to limit talent investment. However, other investments, such as stadiums, are not a zero-sum game, and therefore the implications of revenue sharing are different for the league. We provide sufficient conditions under which it is more efficient to share media revenue compared to stadium revenue. We conclude by providing applications of this model.     

Channel coordination with the newsvendor model using asymmetric information

In this paper, after surveying short-term two-echelon supply channel coordination methods, we present an extended version of the newsvendor model in which the supplier has to fulfil all demand of the customer, even if this calls for an additional setup of production. Given uncertain demand forecast, the solution is an optimal production quantity that minimises the expected total cost including setup, inventory holding and obsolete inventory costs. Then, the model is studied in a decentralised setting where the customer has private information about the demand forecast, while the supplier knows the various cost factors. We suggest such a coordination protocol and payment scheme that provides both partners the right incentive for minimising the total cost: the customer is interested in sharing her unbiased demand forecast and uncertainty, while the supplier's rational decision concurs with the overall optimum. Hence, local decisions based on asymmetric information coordinate the channel in the global sense. The results are also demonstrated by taking some real-life test cases from an industrial study that motivated our work.     

A discounted cash flow approach to the base stock inventory model

A widespread approach to inventory modelling is to associate costs with measures of system performance and determine the control policy which minimises the long run average cost per unit time. This type of approach ignores the impact of a control policy on the timing of the cash flows associated with payments to suppliers and revenue streams from customers. The approach in this paper is to concentrate on cash flows and determine the control policy which maximises the expected net present value of the cash flows associated with a demand, valued at the time when that demand occurs. There is a Poisson demand process, a fixed lead time, unsatisfied demand is backordered and the system is controlled using a base stock policy. A solution procedure is given and a comparison is made with an equivalent simple interest model and with the standard cost model with linear holding and shortage costs.     

Pricing in revenue management for multiple firms competing for customers

We consider the pricing strategies of multiple firms providing the same service in competition for a common pool of customers in a revenue management context. The firms have finite capacity and the demand at each firm depends on the selling prices charged by all firms, each of which satisfies demand up to a given capacity limit. We use game theory to analyze the systems when firms face either a deterministic demand or a general stochastic demand. The existence and uniqueness conditions of a Nash equilibrium are derived, and we calculate the explicit Nash equilibrium point when the demand at each firm is a linear function of price. We also conduct sensitivity analysis of the equilibrium prices with respect to cost and capacity parameters.     

Licensing Strategies in the Presence of Patent Thickets

Many key industries (e.g., biomedical, pharmaceuticals, telecommunications, and information technologies) are characterized by cumulative innovations, where the introduction of a new product or service often requires many complementary technologies. When these technologies are protected by intellectual property rights owned by many firms, patent thickets exist, which researchers have argued may hinder the development of cumulative innovations. Specifically, patent thickets may lead to excessive royalty burdens for potential licensees, which is called “royalty stacking,” and if such costs are passed on to consumers, prices of products based on cumulative technologies will be driven up, dubbed as “double marginalization.” The literature, however, does not address these issues under different forms of licensing contracts. This article develops a game‐theoretic model where a downstream firm seeks to license N patents that read on its product from upstream firms. It discusses a variety of licensing forms widely used in practice and attempts to discover whether royalty stacking and double marginalization occur under these forms of licenses. It also studies the impact of bargaining power between parties. It is found that when patent ownership becomes more fragmented, neither royalty stacking nor double marginalization occurs under profit‐based royalty, fixed fee, and hybrid licenses. Such problems occur only under pure quantity‐based or pure revenue‐based royalty licenses when the downstream firm's bargaining power is low. It is also shown that no matter how fragmented the ownership structure of patent is, hybrid licenses consisting of a fixed fee and a quantity‐ or revenue‐based royalty rate lead to the same market outcomes as a fully integrated firm that owns all the patents and the downstream market. This article has interesting implications for both research and practice. First, the results show that even under the same patent ownership structure, different forms of licenses lead to quite different market outcomes. Therefore, it is suggested that firms and policy makers pay more attention to contractual forms of licenses when trying to minimize the negative impact of patent thickets. Second, the extant literature has largely assumed that quantity‐based royalties are used, where double marginalization is the most severe. In practice, revenue‐based royalties are most common, under which double marginalization is much milder. Third, the results show that patent pools can be most effective in mitigating royalty stacking and double marginalization when quantity‐based or revenue‐based royalties are the sole or primary payment form, especially when downstream firms have low bargaining power.     

Economic viability of private commons: Framework and guidelines for profitability

Ongoing regulatory reforms have led to several novel spectrum sharing models under the general umbrella of dynamic spectrum sharing. The private commons model introduced by FCC in 2004 allows spectrum licensees to provide secondary access to spectrum on an opportunistic basis while retaining ownership. Since wireless communication systems are typically overprovisioned in order to deliver service-level guarantees to (primary) users under short-term load variations, this model bears significant potential by facilitating utilization of temporal and spatial surplus of capacity through serving secondary users at possibly different service levels. A potential barrier to adoption of the private commons model is the uncertainty about secondary price–demand relationship which is difficult to predict in an emerging market: A selected price for secondary access may be profitable for some values of secondary demand but not for others, leading to a profound uncertainty about ultimate benefit of spectrum sharing. This paper aims to eliminate such an uncertainty by devising concrete guidelines and methods for profitability. The paper establishes that the price of secondary spectrum access can be chosen to guarantee profitability for any value of secondary demand: It is shown that for both the coordinated and uncoordinated commons regimes a profitable price should exceed a threshold value, which can be calculated. Hence profitability of private commons is insensitive to the demand function. This observation has two complementary interpretations: From a business perspective it provides a constructive approach to profitability; and from a regulatory perspective it provides reassurance that private commons is a healthy model. The paper also leverages the insensitivity property and outlines a technique to further enhance revenue via iterative spectrum offerings.     

Anti-competitive effects of resale-below-cost laws

We show that resale-below-cost laws enable producers to impose industrywide price-floors to retailers. This mechanism suppresses downstream competition but also dampens upstream competition, leading to higher prices. Price-floor may be more profitable for producers than resale price maintenance contracts and, while resale price maintenance may have ambiguous effect on welfare, price-floors always harm welfare. Retailers' buyer power appears as a key element for a price-floor to work out.