Martin A. Lariviere

Supply Chain Coordination with Revenue-Sharing Contracts: Strengths and Limitations

Under a revenue-sharing contract, a retailer pays a supplier a wholesale price for each unit purchased, plus a percentage of the revenue the retailer generates. Such contracts have become more prevalent in the videocassette rental industry relative to the more conventional wholesale price contract. This paper studies revenue-sharing contracts in a general supply chain model with revenues determined by each retailers purchase quantity and price. Demand can be deterministic or stochastic and revenue is generated either from rentals or outright sales. Our model includes the case of a supplier selling to a classical fixed-price newsvendor or a price-setting newsvendor. We demonstrate that revenue sharing coordinates a supply chain with a single retailer (i.e., the retailer chooses optimal price and quantity) and arbitrarily allocates the supply chains profit. We compare revenue sharing to a number of other supply chain contracts (e.g., buy-back contracts, price-discount contracts, quantity-flexibility contracts, sales-rebate contracts, franchise contracts, and quantity discounts). We find that revenue sharing is equivalent to buybacks in the newsvendor case and equivalent to price discounts in the price-setting newsvendor case. Revenue sharing also coordinates a supply chain with retailers competing in quantities, e.g., Cournot competitors or competing newsvendors with fixed prices. Despite its numerous merits, we identify several limitations of revenue sharing to (at least partially) explain why it is not prevalent in all industries. In particular, we characterize cases in which revenue sharing provides only a small improvement over the administratively cheaper wholesale price contract. Additionally, revenue sharing does not coordinate a supply chain with demand that depends on costly retail effort. We develop a variation on revenue sharing for this setting.

Contracting to Assure Supply: How to Share Demand Forecasts in a Supply Chain

Forecast sharing is studied in a supply chain with a manufacturer that faces stochastic demand for a single product and a supplier that is the sole source for a critical component. The following sequence of events occurs: the manufacturer provides her initial forecast to the supplier along with a contract, the supplier constructs capacity (if he accepts the contract), the manufacturer receives an updated forecast and submits a final order. Two contract compliance regimes are considered. If the supplier accepts the contract under forced compliance then he has little flexibility with respect to his capacity choice; under voluntary compliance, however, he maintains substantial flexibility. Optimal supply chain performance requires the manufacturer to share her initial forecast truthfully, but she has an incentive to inflate her forecast to induce the supplier to build more capacity. The supplier is aware of this bias, and so may not trust the manufacturers forecast, harming supply chain performance. We study contracts that allow the supply chain to share demand forecasts credibly under either compliance regime.

Selling to the Newsvendor: An Analysis of Price-Only Contracts

We consider a simple supply-chain contract in which a manufacturer sells to a retailer facing a newsvendor problem and the lone contract parameter is a wholesale price. We develop a mild restriction satisfied by many common distributions that assures that the manufacturers problem is readily amenable to analysis. The manufacturers profit and sales quantity increase with market size, but the resulting wholesale price depends on how the market grows. For the cases we consider, we identify relative variability (i.e., the coefficient of variation) as key: As relative variability decreases, the retailers price sensitivity decreases, the wholesale price increases, the decentralized system becomes more efficient (i.e., captures a greater share of potential profit), and the manufacturers share of realized profit increases. Decreasing relative variability, however, may leave the retailer severely disadvantaged as the higher wholesale price reduces his profitability. We explore factors that may lead the manufacturer to set a wholesale price below that which would maximize her profit, concentrating on retailer participation in forecasting and retailer power. As these and other considerations can result in a wholesale price below what we initially suggest, our base model represents a worst-case analysis of supply-chain performance.

Supply Chain Contracting and Coordination with Stochastic Demand

Recent years have seen a growing interest among both academics and practitioners in the field of supply chain management. With that has come a growing body of work on supply chain contracts. Few firms are so large and few products so simple that one organization can manage the entire provision of the good. Rather, most supply chains require the coordination of independently managed entities who seek to maximize their own profits. Issues of who controls what decisions and how parties will be compensated become critical. An understanding of contractual forms and their economic implications is therefore an important part of evaluating supply chain performance.

A Note on Probability Distributions with Increasing Generalized Failure Rates

Distributions with an increasing generalized failure rate (IGFR) have useful applications in pricing and supply chain contracting problems. We provide alternative characterizations of the IGFR property that lead to simplify verifying whether the IGFR condition holds. We also relate the limit of the generalized failure rate and the moments of a distribution.

An equilibrium analysis of linear, proportional and uniform allocation of scarce capacity

In many industries a suppliers total demand from the retailers she supplies frequently exceeds her capacity. In these situations, the supplier must allocate her capacity in some manner. We consider three allocation schemes: proportional, linear and uniform. With either proportional or linear allocation a retailer receives less than his order whenever capacity binds. Hence, each retailer has the incentive to order strategically; retailers order more than they desire in an attempt to ensure that their ultimate allocation is close to what they truly want. Of course, they will receive too much if capacity does not bind. In the capacity allocation game, each retailer must form expectations on how much other retailers actually desire (which is uncertain) and how much each will actually order, knowing that all retailers face the same problem. We present methods to find Nash equilibria in the capacity allocation game with either proportional or linear allocation. We find that behavior in this game with either of those allocation rules can be quite unpredictable, primarily because there may not exist a Nash equilibrium. In those situations any order above ones desired quantity can be justified, no matter how large. Consequently, a retailer with a high need may be allocated less than a retailer with a low need; clearly an ex post inefficient allocation. However, we demonstrate that with uniform allocation there always exists a unique Nash equilibrium. Further, in that equilibrium the retailers order their desired amounts, i.e., there is no order inflation. We compare supply chain profits across the three allocation schemes.

Strategically Seeking Service: How Competition Can Generate Poisson Arrivals

We consider a simple game in which strategic agents select arrival times to a service facility. Agents find congestion costly and, hence, try to arrive when the system is underutilized. Working in discrete time, we characterize pure-strategy Nash equilibria for the case of ample service capacity. In this case, agents try to spread themselves out as much as possible and their self-interested actions will lead to a socially optimal outcome if all agents have the same well-behaved delay cost function. For even modest sized problems, the set of possible pure-strategy Nash equilibria is quite large, making implementation potentially cumbersome. We consequently examine mixed-strategy Nash equilibria and show that there is a unique symmetric Nash equilibrium. Not only is this equilibrium independent of the number of agents and their individual delay cost functions, the arrival pattern it generates approaches a discrete-time Poisson process as the number of agents and arrival points gets large. Our results extend to the case of time varying preferences. With an appropriate initialization, the results also extend to a system with limited capacity. Our model lends support to the traditional literature on managing service systems. This work has generally ignored customers strategically choosing arrival times. Rather it is commonly assumed that customers seek service according to some well-behaved process (e.g., that interarrival times follow a renewal process). We show that assuming Poisson arrivals is an acceptable assumption even with strategic customers if the population is large and the horizon is long.

Are Reservations Recommended

We examine the role of reservations in capacity-constrained services with a focus on restaurants. Although customers value reservations, restaurants typically neither charge for them nor impose penalties for failing to keep them. However, reservations impose costs on firms offering them. We offer a novel motivation for offering reservations that emphasizes the way in which reservations can alter customer behavior. We focus on a market in which demand is uncertain and the firm has limited capacity. There is a positive chance that the firm will not have enough capacity to serve all potential customers. Customers are unable to observe how many potential diners are in the market before incurring a cost to request service. Hence, if reservations are not offered, some may choose to stay home rather than risk being denied service. This lowers the firms sales when realized demand is low. Reservations increase sales on a slow night by guaranteeing reservations holders service. However, some reservation holders may choose not to use their reservations resulting in no-shows. The firm must then trade off higher sales in a soft market with sales lost to no-shows on busy nights. We consequently evaluate various no-show mitigation strategies, all of which serve to make reservations more likely in equilibrium. Competition also makes reservations more attractive; when there are many small firms in the market, reservations are always offered.

Asymmetric Information and Economies of Scale in Service Contracting

We consider outsourcing in two important service settings: call center and order fulfillment operations. An important factor in both is the inherent economies of scale. Therefore, we advance a unifying model covering both applications and study the associated contracting problem under information asymmetry. At the time of contracting, the outsourcing firm, “the originator,” faces uncertainty regarding the demand volume but has private information about its probability distribution. The true demand is quickly observed once the service commences. The service provider invests in capacity before the start of the operation and offers a menu of contracts to screen different types of the originator. Adopting a mechanism design approach, we prove that a menu of two-part tariffs achieves the full-information solution. Hence, it is optimal among all possible contracts (in both settings) because of economies of scale and contractibility of realized demand.

Capacity Allocation over a Long Horizon: The Return on Turn-and-Earn

We consider a supply chain in which a supplier sells products to multiple retailers. When orders from the retailers exceed the suppliers capacity, she must employ an allocation mechanism to balance supply and demand. In particular, we consider a commonly used allocation scheme in the automobile industry: turn-and-earn, which uses past sales to allocate capacity. In essence, retailers “earn” an allotment of a vehicle after they sell one. In contrast to turn-and-earn, fixed allocation ignores past sales and gives each retailer an equal share of the capacity. Earlier work has demonstrated that turn-and-earn induces more sales in a two-period setting compared to fixed allocation. The question remains unanswered whether turn-and-earn induces similar behaviors over a long horizon when retailers possess private demand information. We construct a dynamic stochastic game of order competition over an infinite horizon to track the order dynamics of the supply chain. We obtain a richer set of equilibrium behaviors than existing models predict. Instead of a symmetric allocation outcome, we observe that sales leadership may arise in equilibrium and that retailers with different past sales adopt distinct ordering strategies to respond to demand uncertainty. Transient sales dynamics suggest that sales leadership may not be persistent and can be eliminated by the occurrence of extremely low demand. This provides a theoretical explanation for several behavioral observations of some U.S. automobile dealers. In addition to the sales-inducing effect, interestingly, turn-and-earn also causes the retailers to absorb local demand variability.