1 Evaluating procurement strategies Evaluating procurement strategies under uncertain demand and risk of under uncertain demand and risk of component unavailability component unavailability Anssi Käki and Ahti Salo Systems Analysis Laboratory Aalto University School of Science and Technology P.O.Box 11100, 00076 Aalto FINLAND
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1 Evaluating procurement strategies under uncertain demand and risk of component unavailability Anssi Käki and Ahti Salo Systems Analysis Laboratory Aalto.
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1
Evaluating procurement strategies under uncertain Evaluating procurement strategies under uncertain
demand and risk of component unavailabilitydemand and risk of component unavailability
Anssi Käki and Ahti SaloSystems Analysis Laboratory
Aalto University School of Science and TechnologyP.O.Box 11100, 00076 Aalto
FINLAND
Evaluating procurement strategies Anssi Käki and Ahti Salo 2
Manufacturer’s problemManufacturer’s problem
What procurement policies are best when there are– Uncertainties in end product demand and supplier capability
– Inter-dependencies between uncertainties.
* E.g. Martínez-de-Albéniz and Simchi-Levi (2003) consider similar options.
ProductsComponentsSuppliers Market
Material flow
Common
Product specific
To minimize costs and hedge supply risks, the manufacturer
can use normal orders or capacity reservation options*.
Evaluating procurement strategies Anssi Käki and Ahti Salo 3
Research perspectiveResearch perspective Typical risk mitigation strategies include
– Supplier diversification (supply uncertainty)*– Common components (demand risk pooling)**.
ProductsComponentsSuppliers Market
* See Tang (2006) for literature review, Kleindorfer&Wu (2003) and Federgruen&Yang (2008) for models. ** E.g. Groenevelt &Rudi (2000), Van Mieghem (2004).
Material flow
Correlated uncertainty
Common
Product specific
Our approach is novel, for it combines following aspects:– Non-stationary and inter-dependent (correlated) uncertainties– Uncertainty modeling without probability distributions– Risk mitigation with options instead of supplier diversification– Stochastic demand and supply (costs are deterministic).
Evaluating procurement strategies Anssi Käki and Ahti Salo 4
Research questions and approachResearch questions and approach
Our initial research questions include:
1. When does capacity reservation option reduce the expected and worst case
procurement cost?
2. What is the impact of common component on costs?
3. Does negative correlation between demand and supply capability increase
costs?
* Adopted from Hochreiter and Pflug (2007).
To answer these questions, we propose a framework with following
steps*:
1. Data preprocessing / ”realistic” initial assumptions
2. Multivariate scenario generation and
3. Building and solving of a stochastic cost-minimization model.
Evaluating procurement strategies Anssi Käki and Ahti Salo 5
Stochastic optimization modelStochastic optimization model
Unit costs include i) fixed order, ii) capacity reservation,
iii) capacity execution, iv) inventory holding and scrap and
v) shortage.
]]))[(min[(min212,102,02,01,0 ,,
cce
crqq
fEfEf
Initial, first and second stage costs
Evaluating procurement strategies Anssi Käki and Ahti Salo 6
Evaluating procurement strategies Anssi Käki and Ahti Salo 13
Heuristic for multivariate scenario generationHeuristic for multivariate scenario generation To maintain other statistical properties (marginal distributions) while varying correlation
(joint distribution), we use a ”scenario enumeration heuristic”.
Enumeration heuristic
Evaluating procurement strategies Anssi Käki and Ahti Salo 14
0 2000 4000 6000 8000 10000 0
2000
4000
6000
8000
10000
12000Negatively correlated products
0 2000 4000 6000 8000 10000 0
2000
4000
6000
8000
10000
12000Uncorrelated products
0 2000 4000 6000 8000 10000 0
2000
4000
6000
8000
10000
12000Positively correlated products
Demand scenarios of two productsDemand scenarios of two products
Scenario enumeration: demand of product one (y-axis value) remains unchanged
Plotted data contains 2nd stage values of 10 x 10 trees with equal probabilities. Red lines are OLS regression lines; they are statistically significant in positive and
negative case (p<0.01).
Evaluating procurement strategies Anssi Käki and Ahti Salo 15
Demand vs. supply scenariosDemand vs. supply scenarios
0 1000 2000 3000 4000 5000 6000 7000 8000 86
88
90
92
94
96
98
100
Average of aggregated demand
Su
pp
ly c
ap
ab
ility
ave
rag
e
Uncorrelated
0 1000 2000 3000 4000 5000 6000 7000 86
88
90
92
94
96
98
100
Average of aggregated demand
Su
pp
ly c
ap
ab
ility
ave
rag
e
Negatively correlated
Plotted data contains 2nd stage values of 10 x 10 trees with equal probabilities. Negative-case OLS regression line is statistically significant (p<0.01).
Evaluating procurement strategies Anssi Käki and Ahti Salo 16
Sample of four multivariate scenario treesSample of four multivariate scenario trees
Some properties are in common for
all scenarios, for example: Scenarios represent different
business environments, for example:
Demand SupplyD1 D2 S1 S2
E 2453 2590 95.6 % 95.7 %
Std 2122 2244 3.3 3.3
Skew 1.24 1.28 -0.27 -0.33
Scenario Correlation
Between demands Demand vs. supply capability
Complementary products- E.g. same products for different sales areas
0.38 -0.40
Substitute products- E.g. similar products for same sales area
-0.36 -0.35
Only demand-supply dependency- E.g., products independent, but market demand drives supply capability
0.02 -0.41
No inter-dependencies- E.g., differentiated products and supply capability not demand-driven
-0.02 0.01
Evaluating procurement strategies Anssi Käki and Ahti Salo 17
Scenario trees by moment matching is hard:– Non-linear, non-convex optimization problem
– With constant probabilities, amount of variables is N1+N1xN2+N1xN2xN3+…,
where Nn = amount of nodes of stage n
– If probabilities are decision variables, problem is even harder
– There are more efficient heuristics available*
Test runs show that the stochastic optimization model is
solvable with e.g. 100 x 100 = 10 000 scenarios (solving time
less than one minute with Lenovo SL500 laptop and CPLEX
12.0).
* See: Hochreiter, R. (2009). Algorithmic aspects of scenario-based multi-stage decision process optimization. In: Rossi, F., Tsoukias, A. (eds.) Algorithmic Decision Theory 2009. LNCS, vol. 5783, pp. 365–376. Springer, Heidelberg.