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Supply Contract Allocation

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Supply Contract Allocation

Gyana R. Parija

Bala Ramachandran

IBM T.J. Watson Research Center

INFORMS Miami 2001

- Risk management
- Uncertain customer demand
- Long supply lead time

- Fixed quantity supply contracts
- Newsvendor solution: Manufacturer covers the risk of uncertain demand

- Supply contracts with quantity flexibility
- Supplier and manufacturer share the risk
- Price premium required to cover supplier’s cost
- Profit sharing on upside demand potential

Business Issues in Managing Supply Contracts

- Buyer can manage a portfolio of supply contracts to hedge against
uncertainty and manage procurement costs

- Different kinds of supply sources:
- Contracts with different kinds of flexibility (quantity, time …)

- Contracts with different Terms & Conditions

- Spot Markets

- Trade-offs between flexibility to postpone purchase commitment due to demand variability, supplier quantity discounts etc.
- Possibility to mitigate inventory risk by optimizing contract quantities and
purchasing excess requirements from spot market

- Negotiation of competitive prices with component suppliers and
contract manufacturers

Drivers impacting Supply Contracts

- Demand Forecast and Volatility
- Supplier Price & Quantity Discounts
- Spot Market Price Volatility
- Inventory Carrying costs
- Price Decline costs & Salvage value
- Risk Tolerance
- Industry Supply Demand Balance
- Lead Times & Service levels
- Capacity Reservation for Multi-product contracts

- Research Issues
- Analyzing the costs and benefits associated with supplier flexibility
- Manufacturer/buyer: determining the amount of flexibility needed
- Supplier: determining the price premium to be charged
- Channel coordination

- Developing optimized procurement strategy
- utilize updated demand forecasts
- rolling horizon flexibility (e.g., buyer commits to purchase a certain quantity every period)

- Capacity reservation
- allocation among multiple suppliers
- utilizing spot market

- Analyzing the costs and benefits associated with supplier flexibility
- Current work
- Supplier-Manufacturer flexibility model
- Procurement / inventory optimization model with supply flexibility

Strategic Sourcing – Allocation between Suppliers and Marketplaces

- Determines quantities for strategic supplier contracts
- Mitigates inventory risk by optimizing the contract quantity and
purchasing excess requirements from spot market

Minimize

Q1,xi

Subject to: for i = 1,… I

for i = 1,… I

Solution Methodology

1. Analytical Formulation with Grid Search

- Normality assumptions for demand, spot market price
- Analytical expressions derived for expected cost, variance of cost, risk of exceeding budget
- Grid Search to identify optimum
- Reasonable approach for small number of contracts

2. Stochastic Programming with OSL Stochastic Extensions

- Discretized probability distributions for demand, spot market price
- Linear, Mixed-integer Stochastic Programming Problem

RISK OPTIMAL SOLUTION

Contract Quantity - 1200

Expected spot purchase - 17

Expected cost - $ 1163

Budget Risk – 3%

COST OPTIMAL SOLUTION

Contract Quantity – 900

Expected spot purchase - 140

Expected cost - $ 1154

Budget Risk – 27%

Strategic Sourcing – Allocation between Suppliers and Marketplaces

- Supply sources – strategic supplier, spot market
- Determine contract quantity with strategic supplier such that the
risk of the procurement cost exceeding budget is < 5%

Eg. One strategic supplier, spot market, Budget constraint

Contract Portfolio Management

- Determines quantities to be procured under different supply contracts,
given supplier price schedules

- Trade-off between contract flexibility, quantity discounts, and
spot market purchases

Minimize:

Qj,xij

Subject to:

for j = 1, …, J

for i = 1, …, I and j = 1, …, J

Contract

Q<600

600 <= Q < 900

900 <= Q < 1300

Q>= 1300

Long Term Contract

1.2

1.16

1.12

1.07

20% Quantity Flexibility Contract

1.3

1.26

1.21

1.15

RISK OPTIMAL SOLUTION

Fixed Quantity Contract – 920

20% Flexibility Contract - 160

Expected cost - $ 1253

Budget Risk – 14 %

COST OPTIMAL SOLUTION

Fixed Quantity Contract – 920

20% Flexibility Contract - 0

Expected cost - $ 1203

Budget Risk – 22 %

Contract Portfolio Management

- Determine contract quantities with strategic supplier such that the
risk of the procurement cost exceeding budget is < 20%

Supplier Price Schedule

Multi-product Contracts with Business Volume Discounts

- Aggregate Capacity Reservation for multiple products
- Supplier gives business volume discounts based on overall commitment
- Trade-off between business volume discounts, inventory liabilities

Minimize:

Qi

Subject to:

for j = 1, …, J

for j = 1, …, J

Strategic Sourcing – Determining Contract Reservation Prices

- Supply risk may be specified by a choice of contract quantity – Q1
- Determine contract price for which Q1 is optimal

Eg. One strategic supplier, spot market, Budget constraint = 1300

Contract Quantity = 900 Risk Tolerance = 25%

Reservation Price = 1.04

- OSL Stochastic Extensions is a set of tools and functions used to obtain an optimal allocation decision
- To apply here, we linearize the function
- Generate a list of representative scenarios along with their probabilities
- Create input SMPS files readable by OSL Stochastic Extensions

- Solve using OSL Stochastic Extensions (C++ interface)
- Special structured linear MIP amenable to fast preprocessing techniques in OSLSE

- MinQ E[Cost] = E[c.Q + ĉ.(D-Q)+ – v.(Q-D)+ ]
Q 0

A nonlinear stochastic program in current state becomes:

- MinQ E[Cost] = E[c.Q + ĉ.P – v.S]
Q + P – S = D

Q, P, S 0

where P = (D-Q)+ and S = (Q-D)+

Minimize

Qj,xj

Subject to:

for j = 1,… J

Stochastic Programming Formulation- Single Sourcing

- Single sourcing - Allocation between strategic supplier and spot market
- Quantity discounts from strategic supplier

- Purchase price: $ 1.10/unit
- Surplus selling price $ 0.55/unit
- 1576 scenarios (demand, spot price)
- Demand ~ normal (1000,200)
- Spot price ~ normal (1.5,0.3)

D c Probability of Pair

10151.440.001

10151.450.000577778

10161.450.002111111

10171.450.001866667

10181.450.001777778

10191.450.000644444

10191.460.001155556

10201.460.002022222

10211.460.002

10221.460.002266667

10231.460.000355556

10231.470.0018

10241.470.002

- EKKContext *env=ekks_initializeContext();
- EKKStoch *stoch=ekks_newStoch(env,"MyStoch",50000);
- int type=ekks_readSMPSData(stoch,"supp.core","supp.time","supp.stoch");
- ekks_describeFullModel(stoch,1);
- ekks_bendersLSolve(stoch,0);
- int numints=ekks_markIntegers(stoch);
- EKKModel *model=ekkse_getCurrentModel(stoch);
- EKKIntegerPresolve *info=(EKKIntegerPresolve *) malloc(sizeof(EKKIntegerPresolve));
- ekk_integerPresolve(model,info,0,0);
- ekk_branchAndCut(model,NULL,NULL,info,NULL,5,1);
- ekks_printNodeSolution(stoch,1,1,COLUMNS);
- ekks_printNodeSolution(stoch,1,2,COLUMNS);
- ekks_printObjectiveDistribution(stoch);
- ekks_deleteStoch(stoch);
- ekks_endContext(env);

- Optimal Quantity: 1087
- Expected Cost: $ 1229

- MinQ E[Cost] = E[j k cjkQjk + ĉ.P–v.S]
subject to k xjk = 1, all j

akminxjk Qjkakmaxxjk

jkQjk + P – S =D

Qjk, P, S, xjk 0 , xjk is binary

akmin ,akmax discount range constants

- 10 suppliers
- 5 discount types
- (800,899), (900,999), …, (1200, 1299)

- 50 price combinations

- Order Quantity = 1271
- Supplier : 2
- Discount Range : 5 ($0.89/unit)
- Surplus of 944 units (scenario 10)
- Optimal (Expected) Cost = $ 910.34

- OSLSE Technology
- Provides the right modeling environment for contract portfolio management problems
- Optimization problem resolution in reasonable times

- Deployment – solution based on this industrial strength solver technology can be easily deployed in any commercially available e-commerce suite

- Adding other realistic factors to the model such as
- Budget constraints with allowable Risks
- Knapsack constraint in 0-1 variables in the SP formulation – increase in computational work

- Contract terms and service levels and their effects on the allocation decision

- Budget constraints with allowable Risks

- Steve Buckley – IBM Research
- Kendra Taylor – Georgia Tech
- Markus Ettl – IBM Research
- Gelonia Dent - IBM Research

Thank You !

Stochastic Programming Formulation – Multiple Sourcing

- Multiple sourcing - Allocation between suppliers and spot market
- Quantity discounts from suppliers

Minimize

Qij,xij

Subject to: for i = 1,… I

for i = 1,… I & j = 1, … J