3.1 Coordination by Contracts

Question 1

Definition of Supply Chain Coordination

Answer 1

▪ All stages of the supply chain take actions that are aligned and increase supply chain profits.
▪ Create incentives such that locally optimal decisions correspond to globally optimal decisions for the complete supply chain

Question 2

Obstacles to Coordination

Answer 2

▪ Local optimization of decisions regarding pricing and ordering at every stage of the supply chain (double marginalization).
▪ Information is distorted or delayed as it moves between different stages of the supply chain (information asymmetry).

Question 3

Impacts of Obstacles to Coordination

Answer 3

▪ Lower order quantities and lower product availability due to double marginalization.
▪ Global supply chain optimum cannot be achieved.
▪ Bullwhip effect: Increasing variability of orders and inventory along the value chain.

Question 4

Contract Theory

Answer 4

Contracts set incentives for the different stages of the supply chain to behave in an overall optimal way, despite their different objectives.
→ Align local plans with goals of the full supply chain.
→ One party proposes a contract (e.g., the manufacturer), the other party (e.g., the retailer) reacts (Stackelberg situation).

Question 5

Contract Procedure

Answer 5

• Classification of the Decision Situation
• Designing a Contract
• Evaluating the Efficiency
• Parametrization and Implementation

Question 6

Classification of the Decision Situation

Answer 6

▪ Demand situation:
− Deterministic
− Deterministic & price sensitive
− Uncertain (stochastic)
▪ Information (a)symmetry:
Different knowledge of supply chain actors regarding important parameters, especially regarding PoS data and self-inflicted fluctuations in demand (e.g., due to promotions)

Question 7

Fig. Models

Answer 7

Question 8

Designing a Contract - Overview

Answer 8

1. Defining decision competencies
2. Setting the contract parameters
   ▪ Pricing/discounts
   ▪ Order quantities
   ▪ Other requirements (e.g., supply lead time or quality

Question 9

1. Defining Decision Competencies

Answer 9

▪ Target:
Controlling downstream stages of the supply chain by shifting decision making competencies, e.g. manufacturer wants to (partly) control retail processes
▪ Examples for practical implementations:
− Resale Price Maintenance:
Manufacturer dictates retailer’s selling price
− Quantity Fixing:
Manufacturer controls delivery quantity
− Vendor Managed Inventory:
Manufacturer manages the retailer’s inventory (e.g., Procter & Gamble at Walmart)

Question 10

2. Setting the Contract Parameters – Pricing / Discounts - Overview

Answer 10

▪ Lot-size based discounts
− All-Unit Quantity Discounts
− Marginal-Unit Quantity Discounts
▪ Order-size based discounts
− Volume-Based Quantity Discount
− Two-Part Tariffs
▪ Revenue sharing agreements
→ Target: Improve coordination to increase total supply chain profits and extract surplus from retailer through price discrimination

Question 11

Lot-Size based discounts – All-Unit Quantity Discount

Answer 11

If a certain break-point for order quantity is reached, the discount applies to the complete order quantity (if the selected lot size is between qi ≤ Q < qi+1 , every unit causes costs of Ci).
→ Unit costs decrease with increasing lot size (C0 ≥ C1 ≥ … ≥ Cr).

Question 12

Lot-size based discounts – Marginal-Unit Quantity Discount

Answer 12

If the lot size exceeds a certain break point (q1,…, qr), a discount is granted for quantity of Qi – qi units (given a lot size between q1 ≤ Q < q2, the costs are C0* q1 + C1* (Q – q1)).
→ Marginal unit costs decrease at specified break points.

Question 13

Order-quantity based discounts – Volume-Based Quantity Discount

Answer 13

▪ If the total order quantity exceeds a certain threshold within a fixed time horizon, a discount is granted (orders are aggregated).
▪ Be Careful: There is an incentive to place high orders towards the end of the time horizon to reach the discount level (→ Hockey Stick Phenomena).
→ Use of rolling horizon planning to cope with hockey stick phenomena.

Question 14

Order-quantity based discounts – Two-Part Tariffs

Answer 14

▪ Manufacturer charges an up-front fixed payment from the retailer.
▪ In turn, the manufacturer offers the retailer a lower unit price (can even be as low as the manufacturer’s production costs).
▪ The manufacturer realizes all its profit over the fixed payment (Franchise Fee).
▪ The retailer selects an order quantity considering the given fixed/variable costs.
▪ Owing to the franchise fee, this type of “discount” is only realized once the order quantity exceeds a certain threshold.

Question 15

Revenue Sharing Agreement

Answer 15

▪ The retailer pays a share of the revenue of every sold unit to the manufacturer.
▪ The manufacturer charges the retailer a lower price per unit.
→ Overstocking costs decrease → retailer increases product availability → increase in total supply chain profits.
▪ Requirement: Manufacturer has to implement control mechanisms for retailer sales (e.g., using IT).

Question 16

Setting the Contract Parameters – Order Quantities Overview

Answer 16

▪ Setting minimum order quantities
▪ Quantity flexibility agreement
▪ Buyback and return agreements
▪ Rationing schemes

Question 17

Minimum Order Quantity

Answer 17

▪ Retailer is forced to purchase a minimum quantity per order or period from the manufacturer.
▪ For smaller orders, higher prices or penalties could be part of negotiations.
→Target: Reducing variability for the manufacturer (bullwhip effect).

Question 18

Quantity flexibility

Answer 18

▪ Manufacturer allows a certain deviation from order forecasts (quantity flexibility).
▪ The retailer’s orders must adhere to the negotiated flexibility range.
▪ Beneficial in combination with postponement or multiple retailers / regions with independent demand.
→ Target: Better capacity planning, risk distribution, and avoiding of exaggerated forecasts.

Question 19

Buyback and Return Agreements

Answer 19

▪ Manufacturer buys back unsold inventory at an agreed upon buyback price from the retailer.
→ Overstocking costs decrease → product availability increases → total profits increase
▪ Be Careful: Reverse transportation might hurt profit and could have a negative environmental impact.
→ Target: Risk sharing to protect against overly cautious ordering by retailer due to demand variability

Question 20

Rationing schemes

Answer 20

▪ A manufacturer commits its scarce inventory or capacities to multiple retailers.
▪ Classifying the retailers into customer categories.
▪ Use of queuing systems.
→ Target: Avoiding competition and exaggerated forecasts in the distribution of scarce inventory / capacities.

Question 21

Supply Lead Time Requirements

Answer 21

▪ Manufacturer offers different (guaranteed) supply lead times at different prices.
▪ Retailer offers a bonus payment if order is on time.
→ Target: Reducing safety inventory.

Question 22

Quality Requirements

Answer 22

▪ Manufacturer offers warranty and assures a certain quality.
▪ Manufacturer offers several production processes or levels of quality at different prices.
→ Target: Reducing ordering costs.

Question 23

Evaluation of Efficiency

Answer 23

▪ Impact of contract on total supply chain profits
▪ Impact of contract on individual profits of manufacturer and retailer

Question 24

Parametrization and Implementation

Answer 24

▪ Negotiating the contractual terms, formulation and execution of the contract

Question 25

Analyzing the Mechanisms of Contract Design

Answer 25

Analysis based on a supply chain with a manufacturer (M) and a retailer (R), and highly aggregated models for a single time period.
▪ Analysis of decentralized decisions of players (individual point of view)
→ Uncoordinated supply chain
▪ Analysis of centralized decision (supply chain view, complete information)
→ Global optimum for supply chain
▪ Design and implementation of contract coordination mechanisms to incentivize both actors to achieve the total optimum solution despite individual decisions.
→ Contract → “Coordinated” supply chain

Question 26

Deterministic Demand - Decision Situation

Answer 26

▪ Deterministic demand 𝐷
▪ Retailer makes decision about lot size Q depending on their fixed ordering costs 𝑆𝑅, their holdings costs ℎ𝑅
and the wholesale price 𝑐R

Question 27

Deterministic Demand - Individual Costs

Answer 27

𝒄𝑴 Production costs per unit
𝑺𝑴 Fixed ordering costs
𝒉 Holding costs
𝒄𝑹 Wholesale price per unit
𝑺𝑹 Fixed costs of retailer
𝒉 Holding costs
𝑫 Deterministic demand

Question 28

Deterministic Demand – SC-Optimum

Answer 28

▪ The selected lot size selected by the retailer (R) is based on local decisions by the manufacturer and retailer
➢ Double marginalization
▪ Considering the structure of costs of the entire SC, the (globally) optimal lot size of the SC is:

Question 29

Deterministic Demand - SC-Optimum – Results

Answer 29

▪ Joint optimization of lot size reduces the costs of supply chain.
▪ However: Retailer (R) has no incentive to select a higher lot size.
▪ Such an incentive can be offered by a contract with a specific price structure:
− All-Unit Quantity Discount

Question 30

Coordination – All-Unit Quantity Discount (All-Unit Discount on Lotsizes)

Answer 30

▪ Deterministic demand 𝐷
▪ Retailer selects the lot size Q (order to manufacturer) based on their fixed ordering costs 𝑆𝑅 , holding costs ℎ𝑅 and wholesale price 𝑐𝑅.
All-unit discount: Manufacturer offers discount if the lot size exceeds a certain threshold

Question 31

Coordination – All-Unit Quantity Discount (All-Unit Discount on Lotsizes) - Individual Costs

Answer 31

ĉ𝑹 (< 𝒄𝑹) Reduced wholesale
price per unit

Question 32

Price Sensitive Demand - Decision Situation

Answer 32

▪ Retailer distributes product with price sensitive demand 𝐷 𝑝 = 𝐴 − 𝐵𝑝.
▪ Manufacturer decides about wholesale price 𝑐𝑅.
▪ Based on wholesale price 𝑐𝑅 the retailer choses selling price 𝑝.
▪ Customer demand and order quantity of retailer are based on selling price 𝑝.

Question 33

Price Sensitive Demand - Individual Profit

Answer 33

𝒄𝑴 Unit production costs
𝑫(𝒑) Price-sensitive demand
𝑫(𝒑) Price-sensitive demand

Question 34

Price Sensitive Demand – SC-Optimum

Answer 34

▪ The wholesale price selected by the manufacturer
(M) as well as the selling price selected by the
retailer (R) are based on local decisions.
▪ Globally optimal supply chain profit:
𝐺𝑆𝐶(𝑝) = 𝐷(𝑝) * (𝑝 − 𝑐𝑀) = (𝐴 − 𝐵𝑝) * (𝑝 − 𝑐𝑀)
▪ Optimal selling price:
𝑝∗ = (𝐴+𝐵𝑐𝑀) / 2𝐵 (with 𝑐𝑅∗= 𝑐𝑀)

Question 35

Price Sensitive Demand – SC-Optimum - Conclusion

Answer 35

▪ Setting the optimal price increases the total profit of the supply chain.
▪ However: There is no incentive for the manufacturer to sell goods to the retailer at production cost, as the manufacturer would make no profit.
▪ Such an incentive could be created using a pricing / discount contract:
− Two-part tariffs
− Volume-based quantity discount

Question 36

Coordination – Two-Part Tariffs

Answer 36

▪ The manufacturer achieves his profit through a fixed payment 𝐹 (franchise fee).
▪ In return the price per unit is reduced 𝑐𝑅 = 𝑐𝑀.
▪ This price per unit results in the total optimum selling price 𝑝∗ for the retailer.

Question 37

Coordination – Two-Part Tariffs - Individual Profit

Answer 37

Question 38

Coordination – Volume-Based Quantity Discount

Answer 38

▪ The manufacturer offers a volume-based quantity discount if the order quantity reaches a threshold ( >= optimal demand).
▪ The retailer decides about selling price 𝑝∗.

Question 39

Coordination – Volume-Based Quantity Discount - Individual Profit

Answer 39

ĉ𝑹 (< 𝒄𝑹) Reduced wholesale
price

Question 40

Lot-Size Based Quantity Discounts Conclusion

Answer 40

▪ Lead to coordination of the supply chain in case of mass production.
▪ However, there is an increase in lot size and cycle inventory.
▪ If fixed ordering costs are very high, lot-size based discounts achieve better results than volume-based discounts.

Question 41

Volume-Based Quantity Discounts / Two-Part Tariffs - Conclusion

Answer 41

▪ Generally lead to a better coordination of the supply chain.
▪ However, may lead to an artificial increase in orders at the end of the period to take advantage of discounts.
▪ To cope with this, volume-based quantity discounts can be combined with rolling horizon planning.

Question 42

Uncertain Demand - Decision Situation

Answer 42

▪ The manufacturer offers a product with uncertain demand. After the sales season, the product expires and only has a salvage value
▪ The retailer orders the product before sales season / before customer demand is known.
▪ The manufacturer produces the exact quantity ordered by the retailer.

Question 43

Newsvendor Model – Assumptions

Answer 43

▪ Uncertain demand represented by normal distribution 𝑁(𝜇, 𝜎)
▪ Product “expires” after one season
▪ Ordering and delivery before beginning of season
▪ Manufacturer produces the exact order quantity
→ Retailer determines optimal order quantity when demand is uncertain by assessing costs of overstock and understock.
− Costs of overstock (𝐶𝑂 = 𝑐𝑅 − 𝑠)
− Costs of understock (𝐶𝑈 = 𝑝 − 𝑐𝑅)

Question 44

Newsvendor Model - ▪ Expected profit of retailer for order quantity 𝑸

Answer 44

Question 45

Newsvendor Model - Optimal Order Quantity 𝑸∗

Answer 45

Question 46

Newsvendor Model - Profit of retailer for order quantity 𝑸∗

Answer 46

Question 47

Newsvendor Model - Profit of manufacturer for order quantity 𝑸∗

Answer 47

Question 48

Uncertain Demand – SC Optimum

Answer 48

▪ The wholesale price selected by the manufacturer (M) and the CSL of the retailer (R), as well as the resulting order quantity are based on local decisions.
▪ The globally optimal CSL and the resulting order quantity is given by:

Question 49

Uncertain Demand - SC Optimum – Conclusions

Answer 49

▪ Optimal 𝐶𝑆𝐿𝑆𝐶∗ increases the total profit of the supply chain.
▪ However: The manufacturer has no incentive to sell the goods to the retailer for the production cost, as he would make no profit.
▪ In order to set such an incentive, a contract regulating pricing / discounts or order quantities can be used:
− Order quantity: Buyback
− Pricing and discounts: Revenue sharing

Question 50

Coordination –Buyback Contract

Answer 50

▪ Manufacturer offers retailer to buy back unsold units (buyback price 𝑏).
▪ Requirements: Buyback price 𝑏 is higher than salvage value 𝑠.
▪ Retailer: Costs for overstock decrease → Incentive to place larger order / increase in product availability
Principle:

Question 51

Coordination –Buyback Contract - Individual Profit

Answer 51

Question 52

Buyback Contract - Conclusion

Answer 52

▪ Buyback contracts improve product availability, leading to an increase of total supply chain profits.
▪ The higher the costs per unit, the higher the manufacturer can set the buyback price.
▪ However: Buyback contracts are not advisable when return costs are high. In this case, the return process should be adjusted

Question 53

Coordination – Revenue Sharing

Answer 53

▪ Retailer receives share 𝑢 0 ≤ 𝑢 ≤ 1 of the selling price of every sold unit. Manufacturer receives share (1 − 𝑢).
→ Revenue of retailer per unit sold: 𝑢 ⋅ 𝑝; Revenue of manufacturer: (1 − 𝑢) ⋅ 𝑝
▪ In turn, the manufacturer reduces the wholesale price.
▪ Retailer: Overstock costs decrease → Incentive to order place larger order / improve product availability

Question 53

Coordination – Revenue Sharing - Individual Profit

Answer 53

Question 54

Revenue Sharing - Conclusion

Answer 54

▪ Revenue sharing improves product availability and thus total supply chain profits.
▪ Depending on the design the retailer, manufacturer, or both benefit from revenue sharing.
▪ It is not necessary to return products (see buyback contracts).
▪ Information infrastructure is necessary, such that the manufacturer is able to record the retailer’s sales.
▪ Unit profit and overstock costs of the retailer are reduced by revenue sharing.
→ This could lead to a reduced effort of the retailer to sell products.