Supply Chain Coordination & Contracts: Overcoming the Bullwhip Effect and Double Marginalization

The success of a supply chain (SC) depends on the actions of each member within the system and a single negative behavior can jeopardize results for the group as a whole. In most cases, a SC composed of independent agents acting in their own best interests is inefficient, as each firm prioritizes maximizing their own profits rather than optimizing system-wide profit. This is due to two reasons: first, different stages of the supply chain have conflicting objectives (vertically integrated vs. fragmented); second, information moving between different stages becomes distorted (bullwhip effect). These issues can be overcome by implementing supply chain coordinating contracts.

Vertically Integrated vs. Fragmented

Suppose we have a single-product supply chain with two stages: a manufacturer and a retailer. Let c denote our production cost, let p denote our selling price, where p ∈ [0,1], let d denote the demand. Assume both parts perfectly know the demand, which is linear and given by d=1-p.

We have present two cases:

1. Vertically integrated firm: manufacturing and retailing are performed by a single company with the objective of maximizing its profits
2. Fragmented supply chain: manufacturer and retailer are independent, so each party wants to maximize its own profits

The first case is represented by Figure 1 and the profit function is given by π=d·(p-c). Therefore, the optimal price is p*=(1+c)/2 and optimal profit is given by π*=(1-c)^2/4.

Now, let's take a look at the second case, represented by Figure 2. Here we introduce a new variable, w, to represent the retailer's acquisition cost (or manufacturer's sales price). Now we have different functions to each stage:

• The retailer's profit function is given by πr=d·(p-w), its optimal price is p*=(1+w)/2 and optimal profit is πr*=(1-w)^2/4
• The manufacturer's profit function is given by πm=((1-w)/2)(w-c), its optimal price is w*=(1+c)/2 and optimal profit is πm*=(1-c)^2/8

In the fragmented case, the final selling price will be p*=(3+c)/4 which is greater than (1+c)/2, the optimal price in the vertically integrated case. Moreover, in the fragmented case, the demand will be d=(1-c)/4, which is less than (1-c)/2, the demand in the vertically integrated case.

Therefore, we can say that in a fragmented supply chain, consumers end up paying more for less. This is caused by independent entities, such as suppliers and retailers, pursuing their own profit-maximizing goals, known as the double marginalization effect.

As a result, prices are inflated for consumers and profits are decreased for the entire supply chain. The presence of intermediaries in a supply chain can lead to distortion of incentives. In a disintegrated supply chain, each player focuses on maximizing their own profit and disregards the impact of their decisions on others and the consumer. This misalignment of incentives can result in high prices that reduce the consumer's surplus. It also decreases the profits of the firms in the supply chain, having negative effects for both companies and consumers.

There are two major types of solutions to the double marginalization problem:

1. Change the structure of the supply chain: this is the more obvious solution, on which firms resort to vertical integration, which is the case of single-brand stores such as Bulgary, Cartier, Adidas, Nike, etc.
2. Design the right incentives: align the interests using supply chain coordinating contracts such as two-part tariffs in franchising, quantity discounts, and resale price maintenance

The Bullwhip Effect

The bullwhip effect represents the increased fluctuation in orders as they move up the supply chain from retailers to wholesalers to manufacturers to suppliers, distorting demand information within the supply chain, as represented by Figure 3.

This undesired effect jeopardizes supply chain performance as it increases manufacturing costs, inventory costs, replenishment lead time, transportation cost, and labor cost for shipping and receiving. Furthermore, it also decreases the level of product availability (thus service) and erodes relationships across the supply chain.

Obstacles to Supply Chain Coordination

• Incentive obstacles

- Local optimization within functions or stages of a supply chain

- Sales force incentives

• Information processing obstacles

- Forecasting based on orders, not customer demand

- Lack of information sharing

• Operational obstacles

- Ordering in large lots

- Large replenishment lead times

- Rationing and shortage gaming

• Pricing obstacles

- Lot size-based quantity discounts

- Price fluctuations

• Behavioral obstacles

Five Ways to Achieve Supply Chain Coordination

1. Aligning goals and incentives

-Aligning incentives across functions

-Pricing for coordination

-Altering sales force incentives from sell-in to sell-through

2. Improving information accuracy

-Sharing point-of-sale data

-Implementing collaborative forecasting and planning

-Designing single stage control of replenishment

3. Improving operational performance

-Reducing replenishment lead time

-Reducing lot sizes

-Rationing based on past sales and sharing information to limit gaming

4. Designing pricing strategies to stabilize orders

-Moving from lot size-based volume to volume-based quantity discounts

-Stabilizing orders

5. Building partnerships and trust

Supply Chain Coordinating Contracts

Using the microeconomics' lenses of game theory, there is a whole field of study of coordinating contracts, including Oliver Hart and Bengt Holmstr?m who were awarded with the Nobel Memorial Prize in Economic Sciences in 2016 for their contributions to contract theory, particularly regarding how contracts can be designed to align incentives and manage risks.

The main types of supply chain coordinating contracts are:

• Buy back: Ensures incentives (critical-fractile) of integrated firm and independent retailer is the same, hence order quantity is the same. Can be used to prevent retailer from discounting left over items, rebalance inventory, and manipulate the competition between retailers
• Revenue sharing: Retailer pays wholesale price per unit purchased plus a percentage of the revenue the retailer generates. This type of contract was the foundation to Blockbuster's success (before streaming)
• Quantity flexibility: Retailer commits to purchase no less than a certain percentage below the forecast (minimum purchase agreement), manufacturer guarantees to deliver up to a certain percentage above, and single procurement price. Examples: Sun Microsystems, Toyota, IBM, HP
• Sales rebate: Supplier charges regular wholesale price per unit purchased but then giver the retailer a rebate per unit sold above a threshold, providing incentives for the retailer to make an effort to increase demand
• Quantity discount: Achieves coordination by manipulating the retailer's marginal cost curve, while leaving the retailer's marginal revenue curve untouched

Note that it is possible to render equivalent contracts. For example, for any buy back contract there exists a revenue sharing contract that generates the same cash flows for any realization of demand.

Suggested readings:

• Cachon and Netessine. Game theory in Supply Chain Analysis: In Supply Chain Analysis in the eBusiness Era. Link.
• Cachon and M.A. Lariviere. 2005. Supply Chain Coordination with Revenue-Sharing Contracts: Strengths and Limitations. Management Science. DOI.
• Tsay. 2001. Managing retail channel overstock: markdown money and return policies. Journal of Retailing. DOI.
• Tsay, A. 1999. The Quantity Flexibility Contract and Supplier-Customer Incentives. Management Science. DOI.
• Emmons, H. and S. Gilbert. 1998. Returns policies in pricing and inventory decisions for catalogue goods. Management Science. DOI.
• Pasternack, B. 1985. Optimal pricing and returns policies for perishable commodities. Marketing Science. DOI.