Transcript PSG Procurement

Supply Contract Allocation
Gyana R. Parija
Bala Ramachandran
IBM T.J. Watson Research Center
INFORMS Miami 2001
A Simple Supply Chain
S up p liers
•
Uncertain customer demand
Long supply lead time
Fixed quantity supply contracts
•
•
C usto m e rs
Risk management
•
•
•
M an u factu re r
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
•
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
I
Minimize
E ((  c x ) Q  c ( D  Q )  r ( Q  D ) )
i 1
Q1,xi

i1
i
1
2
1

1
I
Subject to:  x i  1
for i = 1,… I
i 1
bx Qx b x
i
i
1

 (B)  
x  { 0 ,1}
i
i
i 1
for i = 1,… I
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
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%
RISK OPTIMAL SOLUTION
COST OPTIMAL SOLUTION
Contract Quantity - 1200
Contract Quantity – 900
Expected
spotconstraint
purchase - 17
Budget
Expected spot purchase - 140 Eg. One strategic supplier, spot market,
Expected cost - $ 1163
Expected cost - $ 1154
Budget
Risk – 3%
Expected Total Procurem ent cost
Probability of exceeding budget
Budget Risk – 27%
1300.00
0.500
1280.00
0.400
Probability
E(cost)
1260.00
1240.00
1220.00
1200.00
0.300
0.200
0.100
1180.00
1160.00
0.000
1140.00
0
500
1000
Contract purchase quantity
1500
0
500
1000
Contract Procurement Quantity
1500
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
J
I
J
I
j 1
j 1
i 1
j 1
i 1
r 1
E ((   c ij x ij ) Q j (1   j )   (  c i 1 x i 1 ) Min ( 2 j Q j , ( D   Q r (1   r )  Q j (1   j )) ) 
J
J
c sp ( D   Q r (1   j ))  r (  Q j (1   j )  D ) )

j 1
Subject to:


j 1
I
 x 1
for j = 1, …, J
b ij x ij  Q j x j  b ( i  1 ) j x ij
for i = 1, …, I and j = 1, …, J
i 1
ij

 (B)  
x ij  { 0 ,1}
Contract Portfolio Management
 Determine contract quantities with strategic supplier such that the
risk of the procurement cost exceeding budget is < 20%
Supplier Price Schedule
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
COST OPTIMAL SOLUTION
1.3
1.26
0
1600-1800
20% Flexibility
Contract
420
Fixed Quantity Contract
1800-2000
1280
1280
1400-1600
1120
1200-1400
2200-2400
960
Fixed Quantity Contract
1000-1200
2000-2200
800
640
480
400
320
160
800
0
1000
960
1200
1120
1400
640
1600
800
Prob(cost >
Budget)
480
1800
E(cost)
160
2000
320
2200
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
Fixed Quantity Contract – 920
20% Flexibility Contract - 0 Expected Procurement cost
Expected cost - $ 1203
Budget Risk – 22
%
2400
1.21
1.15
RISK OPTIMAL SOLUTION
Fixed Quantity Contract – 920
20% Flexibility Contract - 160
Expected costRisk
- $ of
1253
Exceeding Budget
Budget Risk – 14 %
0
20% Flexibility
Contract
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
N
N
i 1
i1
i

i2
i 1

i
i
i 1
J
Subject to:
N
J
E ((  c Q )  (  c ( D  Q ) )  r ( Q  D ) )  (  c Q )(  d x )
 x 1
for j = 1, …, J
j
j 1
N
b x  ( c Q ) x  b x
j
j
i 1

 (B)  
x  { 0 ,1}
j
i
i
j
j 1
j
for j = 1, …, J
i
i
j 1
j
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
c  ( r  c  )  ( Q )  c
1*
2
1
2
Eg. One strategic supplier, spot market, Budget constraint = 1300
Contract Quantity = 900  Risk Tolerance = 25%
Reservation Price = 1.04
Expected Total cost
Probability of Exceeding B udget
1600.00
0.600
1400.00
0.500
1200.00
0.400
1000.00
800.00
0.300
600.00
0.200
400.00
0.100
200.00
0.000
0.00
0
0.2
0.4
0.6
0.8
Contract Price
1
1.2
1.4
0
0.5
1
Contract Price
1.5
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  0
where P = (D-Q)+ and S = (Q-D)+
Stochastic Programming Formulation- Single Sourcing
 Single sourcing - Allocation between strategic supplier and spot market
 Quantity discounts from strategic supplier
J
E ((  c Q  c P  rS )
Minimize
j 1
Qj,xj
1j
j
sp
J
Subject to:  x  1
j
j 1
b x Q b x
j
j
j
x  { 0 ,1}
j
Q , P, S  0
j
j 1
j
for j = 1,… J
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
1015
1015
1016
1017
1018
1019
1019
1020
1021
1022
1023
1023
1024
c
1.44
1.45
1.45
1.45
1.45
1.45
1.46
1.46
1.46
1.46
1.46
1.47
1.47
Probability of Pair
0.001
0.000577778
0.002111111
0.001866667
0.001777778
0.000644444
0.001155556
0.002022222
0.002
0.002266667
0.000355556
0.0018
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 akmaxxjk
jkQjk + P – S = D
Qjk, P, S, xjk  0 , xjk is binary
akmin ,akmax 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
0.003
Probability
0.0025
0.002
0.0015
0.001
0.0005
0
0
500
1000
Scenario Number
1500
2000
Stochastic Programming Formulation – Multiple Sourcing
 Multiple sourcing - Allocation between suppliers and spot market
 Quantity discounts from suppliers
I
J
i 1
j 1
E ((   c Q  c P  rS )
Minimize
Qij,xij
ij
ij
sp
J
Subject to:  x ij  1
for i = 1,… I
j 1
b x Q
ij
ij
ij
b x
x  { 0 ,1}
ij
Q , P, S  0
ij
ij  1
ij
for i = 1,… I & j = 1, … J