Supply Contract Allocation Gyana R. Parija Bala Ramachandran IBM T.J. Watson Research Center INFORMS...
-
Upload
roland-anthony -
Category
Documents
-
view
219 -
download
0
Transcript of Supply Contract Allocation Gyana R. Parija Bala Ramachandran IBM T.J. Watson Research Center INFORMS...
Supply Contract Allocation
Gyana R. Parija
Bala Ramachandran
IBM T.J. Watson Research Center
INFORMS Miami 2001
A Simple Supply Chain
Suppliers Manufacturer Customers
• 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 againstuncertainty 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
• 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
))()()((1121
11
DQrQDcQxcE
i
I
ii
11
I
ii
x
iiiiixbxQxb
11
}1,0{i
x
)(B
Solution Methodology
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
1. Analytical Formulation with Grid Search
2. Stochastic Programming with OSL Stochastic Extensions
Discretized probability distributions for demand, spot market price
Linear, Mixed-integer Stochastic Programming Problem
Strategic Sourcing – Allocation between Suppliers and Marketplaces
Eg. One strategic supplier, spot market, Budget constraint
Expected Total Procurement cost
1140.00
1160.00
1180.00
1200.00
1220.00
1240.00
1260.00
1280.00
1300.00
0 500 1000 1500
Contract purchase quantity
E(c
ost
)
Probability of exceeding budget
0.000
0.100
0.200
0.300
0.400
0.500
0 500 1000 1500
Contract Procurement Quantity
Prob
abili
ty
Supply sources – strategic supplier, spot market
Determine contract quantity with strategic supplier such that the risk of the procurement cost exceeding budget is < 5%
COST OPTIMAL SOLUTIONContract Quantity – 900
Expected spot purchase - 140Expected cost - $ 1154
Budget Risk – 27%
RISK OPTIMAL SOLUTIONContract Quantity - 1200
Expected spot purchase - 17Expected cost - $ 1163
Budget Risk – 3%
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
J
jjj
J
jjrsp
j
rjjrrjji
I
ii
J
jjjij
I
iij
J
j
DQrQDc
QQDQMinxcQxcE
11
1
11
11
111
)))1(())1((
)))1()1((,2()()1()((
Minimize:Qj,xij
11
I
iij
x
ijjijjijijxbxQxb
)1(
}1,0{ij
x
Subject to:
)(B
for j = 1, …, J
for i = 1, …, I and j = 1, …, J
Contract Portfolio Management
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
Supplier Price Schedule
Determine contract quantities with strategic supplier such that the risk of the procurement cost exceeding budget is < 20%
0
160
320
480
640
800
960
1120
1280
0
400
8001000
1200
1400
1600
1800
2000
2200
2400
E(cost)
Fixed Quantity Contract
20% Flexibility Contract
Expected Procurement cost
1000-1200 1200-1400 1400-1600 1600-1800 1800-2000
2000-2200 2200-2400
0
160
320
480
640
800
960
1120
1280
0
42000.10.20.30.40.50.60.70.80.9
1
Prob(cost > Budget)
Fixed Quantity Contract
20% Flexibility Contract
Risk of Exceeding Budget
COST OPTIMAL SOLUTIONFixed Quantity Contract – 920
20% Flexibility Contract - 0Expected cost - $ 1203
Budget Risk – 22 %
RISK OPTIMAL SOLUTIONFixed Quantity Contract – 92020% Flexibility Contract - 160
Expected cost - $ 1253Budget Risk – 14 %
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
}1,0{j
x
Subject to:
)(B
for j = 1, …, J
for j = 1, …, J
N
i
J
jjjiiiii
N
ii
N
ii
xdQcDQrQDcQcE1 1
211
1))(())())(()((
11
J
jj
x
jjji
N
iijj
xbxQcxb1
1
)(
Strategic Sourcing – Determining Contract Reservation Prices
Eg. One strategic supplier, spot market, Budget constraint = 1300Contract Quantity = 900 Risk Tolerance = 25%
Reservation Price = 1.04
Supply risk may be specified by a choice of contract quantity – Q1
Determine contract price for which Q1 is optimal
212*1)()( cQcrc
Expected Total cost
0.00
200.00
400.00
600.00
800.00
1000.00
1200.00
1400.00
1600.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Contract Price
Probability of Exceeding B udget
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0 0.5 1 1.5
Contract Price
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
• 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 0where P = (D-Q)+ and S = (Q-D)+
Stochastic Programming Formulation- Single Sourcing
Minimize Qj,xj
Subject to:
for j = 1,… J
)((1
1rSPcQcE
spj
J
jj
11
J
jj
x
jjjjjxbQxb
1
}1,0{j
x
0,, SPQj
Single sourcing - Allocation between strategic supplier and spot market
Quantity discounts from strategic supplier
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)
Sample Input
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
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);
Output
• Optimal Quantity: 1087• Expected Cost: $ 1229
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 ak
maxxjk
jkQjk + P – S = D
Qjk, P, S, xjk 0 , xjk is binary
akmin ,ak
max discount range constants
Input Data
• 10 suppliers• 5 discount types
– (800,899), (900,999), …, (1200, 1299)
• 50 price combinations
Output
• Order Quantity = 1271
• Supplier : 2
• Discount Range : 5 ($0.89/unit)
• Surplus of 944 units (scenario 10)
• Optimal (Expected) Cost = $ 910.34
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
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
Acknowledgements
• Steve Buckley – IBM Research• Kendra Taylor – Georgia Tech• Markus Ettl – IBM Research• Gelonia Dent - IBM Research
Thank You !
Distribution of Pairs
Distribution of Pairs
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0 500 1000 1500 2000
Scenario Number
Pro
bab
ilit
y
Stochastic Programming Formulation – Multiple Sourcing
Minimize Qij,xij
Subject to: for i = 1,… I
for i = 1,… I & j = 1, … J
)((1 1
rSPcQcEspij
I
iij
J
j
11
J
jij
x
ijijijijijxbQxb
1
}1,0{ij
x
0,, SPQij
Multiple sourcing - Allocation between suppliers and spot market
Quantity discounts from suppliers