Supply chain coordination with contracts
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Supply Chain Coordination with Contracts. A Typical Supply Chain. A Paradigm Shift. From optimization within an organization to optimization for a SC. Design incentive structures (contracts) to coordinate various parties of the SC to achieve system optimization. Why Coordination?.

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Presentation Transcript


A paradigm shift
A Paradigm Shift

  • From optimization within an organization to optimization for a SC.

  • Design incentive structures (contracts) to coordinate various parties of the SC to achieve system optimization.


Why coordination
Why Coordination?

  • Each player (company) in the SC has different, and often time, conflicting objectives.

  • These individual objectives are usually not in line with that of the SC.

  • An incentive structure (contract) is needed to align the optimization action of each individual player for the interest of the SC (Contract Design)

  • Make the pie bigger then divide!


Popular sc systems studied in literature
Popular SC Systems Studied in Literature:

  • Two levels: a supplier and a retailer (or multiple retailers).

  • Product: seasonal or stable (newsvendor v.s. EOQ)

  • Demand:

    • deterministic or stochastic

    • insensitive or sensitive to retail price

  • Objective Function: risk neutral or risk averse.

  • Other variations: information asymmetry, multiple replenishment opportunities, competing retailers, …


Contract design and evaluation
Contract Design and Evaluation

  • For a given SC structure, which contracts coordinate the SC?

  • How does the contract allocate profit among players of the SC?

  • Efficiency v.s. administrative cost for a given contract.


Newsvendor problem
Newsvendor Problem

  • News paper demand unknown but distribution known with cdf F.

  • Underage cost (Price-Cost): Cu

  • Overage cost (Cost - Salvage): Co

  • How much to order to maximize the expected profit?


Newsvendor solution
Newsvendor Solution

  • At the best order quantity,

    marginal underage = marginal overage

    => [1- F(Q)] ͯ Cu = F(Q) ͯ Co

    => F(Q) = Cu / (Cu+ Co) (1)

  • If F is a Normal distribution with mean μ and std σ ,

    => Q = μ + σ ͯ z,

    where z is the z-value based on (1).


Performance measures
Performance Measures

  • Expected lost sales (for Normal dist.):

    = σ ͯ [Normdist(z,0,1,0)-z ͯ (1-Normsdist(z,0,1,1)]

  • Expected sales:

    = Exp demand – Exp lost sales

  • Expected leftover inv:

    = Q – Exp sales

  • Expected profit:

    = (Price-Cost)*Exp sales

    – (Cost-Salvage)*Exp inv


A sunglass supply chain
A Sunglass Supply Chain

  • Sunglass designer and manufacturer (called supplier):

    • Manufacturing cost: $35

    • Whole sale price: $75

  • Sunglass retailer:

    • Retail price: $115

    • End-of-season price: $25

  • Estimated demand:

    Normal ( =250, =125)


Best decision for retailer
Best Decision for Retailer

  • Underage cost Cu : $115 - $75 = $40

  • Overage cost Co : $75 - $25 = $50

  • Cu / (Cu + Co) = 40 / (40 + 50) = 44.4%

  • z = -0.1397

  • Q = 250 + (-0.1397)*125 = 233

  • Expected sale = 191

  • Expected leftover Inventory = 42

  • Expected profit = $40*191-$50*42 =$5,540


Supplier and system profit
Supplierand System Profit

  • Supplier’s profit = 233*($75-$35) = $9,320

  • System profit = $5,540+$9,320 = $14,860.

  • Retailer takes all risk

  • Supplier assumes no risk

  • Can we do better for the supply chain (system)?


What s best for the system
What’s Best for the System?

  • Underage cost Cu : $115 - $35 = $80

  • Overage cost Co : $35 - $25 = $10

  • Cu / (Cu + Co) = 80 / (80 + 10) = 88.9%

  • z = 1.2206

  • Q = 250 + 1.2206 *125 = 403

  • Expected sale = 243

  • Expected leftover = 160

  • Expected system profit = $17,840

    =>19% profit increase!


How to improve system performance
How to Improve System Performance

  • Retailer needs to order more!

  • Option 1: Reduce whole sale price

  • What happened?

  • We need a win-win (not win-lose) mechanism

  • Option 2: How about buy back contract?

  • Specified by a whole sale price and a buy back price.


Option 1 reduce whole sale price
Option 1: Reduce whole sale price

What happened?

  • If the supplier reduce the whole sale price from $75 to $65, what happens?

  • Best Decision for Retailer

  • Underage cost Cu : $115 - $65 = $50

  • Overage cost Co : $65 - $25 = $40

  • Cu / (Cu + Co) = 50 / (50 + 40) = 55.55%


Option 1 reduce whole sale price1
Option 1: Reduce whole sale price

  • z = 0.1397

  • Q = 250 + (0.1397)*125 = 267

  • Expected sale = 208

  • Expected leftover Inventory = 59

  • Expected profit = $50*208-$40*59 =$8,040

  • Supplier’s profit = 267*($65-$35) = $8,010

  • System profit = $5,540+$9,320 = $16,050.


Option 1 reduce whole sale price2
Option 1: Reduce whole sale price

  • Conclusion: System total profit will increase but the supplier’s profit will decrease.

  • Supplier will not reduce selling price to retailer. NO COORDINATION.

  • In fact, at whole sale price of $85.5, the supplier’s profit maximized.


Option 2 how about buy back contract
Option 2: How about buy back contract?

  • Assume that the supplier offers to buy back unsold items back at the price of $40 each, what happens?

    Retailer:

  • Underage cost Cu : $115 - $75 = $40

  • Overage cost Co : $75 - $30 = $45

  • Cu / (Cu + Co) = 40 / (40 + 45) =0.4707

  • z = -0.0738


Option 2 how about buy back contract1
Option 2: How about buy back contract?

  • Q = 250 + (-0.0738)*125 = 241

  • Expected sale = 195

  • Expected leftover = 45

  • Expected profit = $5,775

    Supplier:

  • Suppliers profit

    = 241*($75-$35) - 45*($30-$25)=$9,415

  • System profit = $5,775+$9,415=$15,190

    All better off.


Retailer s profit with bb price at 65
Retailer’s Profit with BB Price at $65

  • Underage cost Cu : $115 - $75 = $40

  • Overage cost Co : $75 - $65 = $10

  • Cu / (Cu + Co) = 40 / (40 + 10) = 80%

  • z = 0.8416

  • Q = 250 + 0.8416*125 = 355

  • Expected sale = 236

  • Expected leftover = 119

  • Expected profit = $8,250


Supplier s and system profit with bb price at 65
Supplier’s and System Profit with BB Price at $65

  • Suppliers profit

    = 355*($75-$35) - 119*($65-$25)=$9,440

  • System profit = $8,250 + $9,440=$17,690

  • System profit is higher

  • Both supplier and retailer are also better off (Win-Win).

  • How to improve system profit further?


Optimal whole sale and bb price
Optimal Whole Sale and BB Price

  • Need to make sure retailer’s Q is optimal for the system.

  • System Q is determined by

    (Price-Cost)/(Price-Cost + Cost-Salvage)

  • Retailer’s Q is determined by

    (Price-Whole)/(Price-Whole + Whole-BuyBack)

  • Two ratios should equal to each other


Optimal whole sale and bb price1
Optimal Whole Sale and BB Price

  • Optimal Buy Back Price =

    Price – (Price-Whole Sale Price)*

    (Price-Salvage)/(Price-Cost)

  • Profit calculations


Optimal whole sale and bb price2
Optimal Whole Sale and BB Price

  • If the whole sale price is $75, the optimal BB price must be $70.

    Retailer

  • Underage cost Cu : $115 - $75 = $40

  • Overage cost Co : $75 - $70 = $5

  • Cu / (Cu + Co) = 40 / (40 + 5) = 0.8889

  • z = 1.2206

  • Q = 250 + 1.2206*125 = 403

  • Expected profit =$8,920


Optimal whole sale and bb price3
Optimal Whole Sale and BB Price

Supplier

  • Expected Profit =$8,920

  • Total Expected Profit = $17,840

  • Are they happy?

  • Not for supplier


Observation
Observation

  • To keep the Cu / (Cu + Co) = 0.8889, when whole sale price (as well as BB price) increases, the supplier’s profit increases

  • When whole sale price is $85.5 and BB price is $81.81,

  • Retailer’s expected profit is $6,565.5

  • Supplier’s profit is $11,261.50

  • Both are better off


Observation1
Observation

  • When whole sale price is $90.13 and the BB price is $87.02,

  • The retailer’s profit is $5,540 (same as before)

  • Therefore the whole sale price cannot be over $90.13!


Observations on optimal buy back contract
Observations on Optimal Buy Back Contract

  • Optimal whole sale and buy back price pairs are not unique. All lead to optimal system profit.

  • All profit allocations are possible.

    => Buy Back contract is flexible!

  • Zero sum game, but based on the largest pie possible.

    => Achieve supply chain coordination.


Other advantages of buy back contract
Other Advantages of Buy Back Contract

  • Preserve brand name

  • Prevent strategic shoppers

  • Re-distribute inventories

  • Alleviate fears from product upgrade

  • Encourage supplier to promote its products


Disadvantages of buy back contract
Disadvantages of Buy Back Contract

  • Cost of return and salvage

  • Irrational retailer

  • Dampen retailer’s incentive to sell


Quantity discount contract
Quantity Discount Contract

  • Supplier offers lower price for larger orders

  • Increase underage cost and decrease overage cost

    => larger Q


Options contract
Options Contract

  • Retailer buy capacity option form supplier pre-season

  • Retailer exercise the option as season starts

  • Encourages supplier to build up capacity pre-season for uncertain market


Revenue sharing
Revenue Sharing

  • Retailer pays lower whole sale price

  • Supplier shares revenue generated by retailer

    => both share risk of demand uncertainty

    => Q increases

  • Successfully used by Blockbuster


Quantity flexibility contract
Quantity Flexibility Contract

  • Retailer order pre-season.

  • Retailer is obligated to buy at least a % and has an option of buying up to b% of pre-season order when season starts.

  • Risk sharing to courage supplier build sufficient capacity pre-season.


Price protection
Price Protection

  • Retailer will be compensated by the price differences as product price drops.

  • Encourage retailer to order sufficient (hopefully close to system optimal) quantity.


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