Introduction Complete Information Background Asymmetric Information Behavioral Analysis Dynamic Procurement Concluding Contract Complexity and Performance . . Feryal Erhun Department of Management Science & Engineering Stanford University . . . TutORials in Operations Research, INFORMS - November 15, 2011
Introduction Complete Information Background Asymmetric Information Behavioral Analysis Dynamic Procurement Concluding Outline Introduction 1 Optimal Contracts Under Complete Information 2 A Little Bit of Background 3 Optimal Contracts Under Asymmetric Cost Information 4 A Behavioral Analysis of the Efficiency of Simple Contracts 5 Under Asymmetric Demand Information Dynamic Procurement 6 Concluding Remarks 7
Introduction Complete Information Background Asymmetric Information Behavioral Analysis Dynamic Procurement Concluding Contract Complexity as a Design Factor Today, approximately half of the revenue generated in the U.S. manufacturing industry is spent on procurement (U.S. Department of Commerce 2006) Since products and their production processes have become more complex, firms are now buying more complex items and services. Hence it is critical for firms to streamline these intricate procurement processes to maintain a competitive edge in the market. Many factors influence the design of procurement contracts such as price, availability, cost, and delivery schedule. In this tutorial, we provide a brief overview of some of the commonly used procurement contracts and discuss contract complexity as a design factor.
Introduction Complete Information Background Asymmetric Information Behavioral Analysis Dynamic Procurement Concluding Two Commonly Used Procurement Contracts Wholesale Price Contracts: Common in the supply chain management literature motivated by the observation that “many supply-chain transactions are governed by simple [price-only] contracts, defined only by a per-unit wholesale price” (Lariviere and Porteus 2001). Employed for a wide variety of products and services, including paper, alarm systems, pharmaceuticals, software, components for airplanes, electronics design, assembly and components, and healthcare services. Simple: they require only the specification of a single parameter – the wholesale price. Quantity Discount Contracts: Praised by academic literature as they have been shown theoretically to increase sales, reduce costs, increase channel efficiency, allow for self-selected price discrimination, and eliminate inefficiencies due to information asymmetry Observed regularly in practice. However, there is evidence that they do not perform consistently in practice (Altintas, Erhun, and Tayur 2008).
Introduction Complete Information Background Asymmetric Information Behavioral Analysis Dynamic Procurement Concluding Outline Introduction 1 Optimal Contracts Under Complete Information 2 A Little Bit of Background 3 Optimal Contracts Under Asymmetric Cost Information 4 A Behavioral Analysis of the Efficiency of Simple Contracts 5 Under Asymmetric Demand Information Dynamic Procurement 6 Concluding Remarks 7
Introduction Complete Information Background Asymmetric Information Behavioral Analysis Dynamic Procurement Concluding Model Definition 1 Consider a simple stylized two-stage supply chain with one supplier and one buyer where the buyer (she) buys goods from the supplier (he) and sells them in an end consumer market. The supplier’s unit cost of production is c . The supplier quotes unit wholesale price w to the buyer. The buyer chooses order quantity q . The buyer faces a market where the price P is inversely related to the quantity sold. Let us assume a linear demand curve P = a − bq where a is the market potential and b is the price sensitivity. Assume that all of this information is common knowledge. 1 F. Erhun and P. Keskinocak, 2003. Game Theory in Business. Overview Article.
Introduction Complete Information Background Asymmetric Information Behavioral Analysis Dynamic Procurement Concluding Decentralized Supply Chain Both the supplier and the retailer maximize their own profits Supplier’s profit: Π S = ( w − c ) q Buyer’s profit: Π B = ( P − w ) q = ( a − bq − w ) q A dynamic game of complete information First, the supplier chooses the unit wholesale price w . After observing w , the buyer chooses the order quantity q . Solve this game using backwards induction: ∂ Π B = a − 2 bq − w = 0 ⇒ q ( w ) = a − w . ∂ q 2 b Given q ( w ) = ( a − w ) / (2 b ), the supplier maximizes Π S = ( w − c ) q = ( w − c )( a − w ) / (2 b ). ∂ Π S ∂ w = a − w − w + c = 0 ⇒ w = a + c . 2
Introduction Complete Information Background Asymmetric Information Behavioral Analysis Dynamic Procurement Concluding Centralized Supply Chain A single decision-maker who is concerned with maximizing the entire chain’s profits Π = ( a − bq − c ) q . ∂ Π ∂ q = a − 2 bq − c = 0 ⇒ q ( c ) = a − c 2 b .
Introduction Complete Information Background Asymmetric Information Behavioral Analysis Dynamic Procurement Concluding Centralized vs. Decentralized Supply Chains Decentralized supply chain Centralized supply chain Wholesale price ( w ) w = ( a + c ) / 2 w q ∗ = ( a − c ) / (2 b ) Quantity ( q ) q = ( a − c ) / (4 b ) P ∗ = ( a + c ) / 2 Market price ( P ) P = (3 a + c ) / 4 Π S = ( a − c ) 2 / (8 b ) Π ∗ Supplier’s profit (Π S ) S = ( w − c ) q Π B = ( a − c ) 2 / (16 b ) Π ∗ B = ( P ∗ − w ) q Buyer’s profit (Π B ) Π ∗ = ( a − c ) 2 / (4 b ) Π = 3( a − c ) 2 / (16 b ) Total profits (Π) In the decentralized supply chain Sales quantity is lower Market price is higher Total profit is lower compared to the centralized supply chain. This inefficiency is due to double marginalization (Spengler 1950).
Introduction Complete Information Background Asymmetric Information Behavioral Analysis Dynamic Procurement Concluding Supply Chain Coordination Coordination Strategic Virtual Decentralized I nformation supply chain with contracts sharing partnership integration Higher connectivity, trust, and efficiency Global optimization: Identify what is best for the entire system in terms of system-wide costs/profits Who will optimize? (Conflicting goals) How will the savings be shared among the participants? Dynamic system: Customer demand, supplier capabilities, supply chain roles and relationships and relative market power of the channel members
Introduction Complete Information Background Asymmetric Information Behavioral Analysis Dynamic Procurement Concluding Quantity Discount Contracts Assume the supplier charges w ( q ) where w is a decreasing function of q . Let R ( q ) be the buyer’s (expected) revenue when she stocks q units of the final product. R ( q ) is a finite, concave function of q with R (0) = 0. Assume R ′ (0) > c (otherwise, production is never profitable). Buyer’s (expected) profit: Π B = R ( q ) − w ( q ) q . DSC has the same optimal quantity as CSC if Π B is an affine transformation of Π. Hence, we need R ( q ∗ ) − w ( q ∗ ) q ∗ = α ( R ( q ∗ ) − cq ∗ ) Π B = ⇒ � R ( q ∗ ) � w ( q ∗ ) = (1 − α ) + α c . q ∗ Note that Π S = (1 − α ) R ( q ∗ ) − (1 − α ) cq ∗ = (1 − α )Π.
Introduction Complete Information Background Asymmetric Information Behavioral Analysis Dynamic Procurement Concluding Supply Chain Coordination Revisited Quantity discount contracts eliminate double marginalization and coordinate the supply chain. There are other contract structures that achieve coordination in such simple settings; Buyback contracts (Pasternack 1985): the buyer can return leftover units to the supplier at the end of the selling season for b per unit where b < w . Revenue-sharing contracts (Cachon and Lariviere 2005): the buyer shares a fraction α < 1 of her revenues with the supplier. Further reading materials: Supply contracts: Tsay, Nahmias, and Agrawal (1998) and Cachon (2003) Contract theory: Laffont and Martimort (2002) and Salani´ e (1997)
Introduction Complete Information Background Asymmetric Information Behavioral Analysis Dynamic Procurement Concluding Outline Introduction 1 Optimal Contracts Under Complete Information 2 A Little Bit of Background 3 Optimal Contracts Under Asymmetric Cost Information 4 A Behavioral Analysis of the Efficiency of Simple Contracts 5 Under Asymmetric Demand Information Dynamic Procurement 6 Concluding Remarks 7
Introduction Complete Information Background Asymmetric Information Behavioral Analysis Dynamic Procurement Concluding The Revelation Principle The revelation principle is an important concept for designing games when the players have private information. Consider a seller who wishes to design an auction to maximize his expected revenue. Specifying the many different auctions the seller should consider could be an enormous task: The first-price sealed-bid auction. The bidders may have to pay an entry fee. Some of the losing bidders might have to pay money, perhaps in amounts that depend on their own and others’ bids. The seller might set a reservation price, etc. The revelation principle shows how to create an incentive compatible game from any game with a Bayesian Nash equilibrium.
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