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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. Risk management Uncertain customer demand Long supply lead time Fixed quantity supply contracts

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Supply Contract Allocation

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  1. Supply Contract Allocation Gyana R. Parija Bala Ramachandran IBM T.J. Watson Research Center INFORMS Miami 2001

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 1 Supplier, 1 price class • 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)+

  15. 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

  16. Input Data • 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)

  17. D c Probability of Pair 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

  18. OSLSE Driver • 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);

  19. Output • Optimal Quantity: 1087 • Expected Cost: $ 1229

  20. j suppliers, k discount ranges • 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

  21. Input Data • 10 suppliers • 5 discount types • (800,899), (900,999), …, (1200, 1299) • 50 price combinations

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

  23. Conclusions • 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

  24. Further Work • 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

  25. Acknowledgements • Steve Buckley – IBM Research • Kendra Taylor – Georgia Tech • Markus Ettl – IBM Research • Gelonia Dent - IBM Research

  26. Thank You !

  27. Distribution of Pairs

  28. 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

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