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Supply Contract Allocation. Gyana R. Parija Bala Ramachandran IBM T.J. Watson Research Center INFORMS Miami 2001. A Simple Supply Chain. Risk management Uncertain customer demand Long supply lead time Fixed quantity supply contracts

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Supply contract allocation

Supply Contract Allocation

Gyana R. Parija

Bala Ramachandran

IBM T.J. Watson Research Center

INFORMS Miami 2001


A simple supply chain
A Simple Supply Chain

  • 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


Related research activities
Related Research Activities

  • 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

  • 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 Marketplaces

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 Marketplaces

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 Marketplaces

  • 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 Marketplaces

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 Marketplaces

  • 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


Optimization solutions and library osl stochastic extensions
Optimization Solutions and Library(OSL) Stochastic Extensions

  • 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


1 supplier 1 price class
1 Supplier, 1 price class Extensions

  • 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 Extensions

  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


Input data
Input Data Extensions

  • 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)


Sample input

D c Probability of Pair Extensions

1015 1.44 0.001

1015 1.45 0.000577778

1016 1.45 0.002111111

1017 1.45 0.001866667

1018 1.45 0.001777778

1019 1.45 0.000644444

1019 1.46 0.001155556

1020 1.46 0.002022222

1021 1.46 0.002

1022 1.46 0.002266667

1023 1.46 0.000355556

1023 1.47 0.0018

1024 1.47 0.002

Sample Input


Oslse driver
OSLSE Driver Extensions

  • 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);


Output
Output Extensions

  • Optimal Quantity: 1087

  • Expected Cost: $ 1229


J suppliers k discount ranges
j suppliers, k discount ranges Extensions

  • MinQ E[Cost] = E[j k cjkQjk + ĉ.P–v.S]

    subject to k xjk = 1, all j

    akminxjk Qjkakmaxxjk

    jkQjk + P – S =D

    Qjk, P, S, xjk 0 , xjk is binary

    akmin ,akmax discount range constants


Input data1
Input Data Extensions

  • 10 suppliers

  • 5 discount types

    • (800,899), (900,999), …, (1200, 1299)

  • 50 price combinations


Output1
Output Extensions

  • Order Quantity = 1271

  • Supplier : 2

  • Discount Range : 5 ($0.89/unit)

  • Surplus of 944 units (scenario 10)

  • Optimal (Expected) Cost = $ 910.34


Conclusions
Conclusions Extensions

  • 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


Further work
Further Work Extensions

  • 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


Acknowledgements
Acknowledgements Extensions

  • Steve Buckley – IBM Research

  • Kendra Taylor – Georgia Tech

  • Markus Ettl – IBM Research

  • Gelonia Dent - IBM Research


Thank You ! Extensions



Stochastic Programming Formulation – Multiple Sourcing Extensions

  • 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


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