Evaluating Procurement Strategies Under Uncertain Demand and Risk of Component Unavailability

1. Evaluating procurement strategies under uncertain demand and risk of component unavailability Anssi Käki and Ahti Salo Systems Analysis Laboratory Aalto University School of Science and Technology P.O.Box 11100, 00076 Aalto FINLAND

2. Manufacturer’s problem Suppliers Products Components Market Materialflow Common Product specific • To minimize costs and hedge supply risks, the manufacturer can use normal orders or capacity reservation options*. 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.

3. Research perspective • Ourapproach is novel, for itcombinesfollowingaspects: • Non-stationary and inter-dependent (correlated) uncertainties • Uncertaintymodelingwithoutprobabilitydistributions • Riskmitigationwithoptionsinstead of supplierdiversification • Stochasticdemand and supply (costsaredeterministic). Materialflow Correlateduncertainty Suppliers Products Components Market Common Product specific Typicalriskmitigationstrategiesinclude • Supplierdiversification (supplyuncertainty)* • Common components (demandriskpooling)**. * See Tang (2006) for literature review, Kleindorfer&Wu (2003) and Federgruen&Yang (2008) for models. ** E.g. Groenevelt &Rudi (2000), Van Mieghem (2004).

4. Research questions and approach • To answer these questions, we propose a framework with following steps*: • Data preprocessing / ”realistic” initial assumptions • Multivariate scenario generation and • Building and solving of a stochastic cost-minimization model. Our initial research questions include: • When does capacity reservation option reduce the expected and worst case procurement cost? • What is the impact of common component on costs? • Does negative correlation between demand and supply capability increase costs? • * Adopted from Hochreiter and Pflug (2007).

5. Stochasticoptimizationmodel Initial, first and second stage costs Unit costs include i) fixed order, ii) capacity reservation, iii) capacity execution, iv) inventory holding and scrap and v) shortage.

6. Decision steps: Initial fixed orders

7. Decision steps: Capacity reservations

8. Decision steps: Capacity execution

9. Costs

10. Example of oneproduct, component and perfectlyreliablesupplier Initial stage: Order & Reservation First stage: Execution & holding Second stage: Scrap

11. Examplecont’d Order Holding & scrap • Supplierperspective: •  Supplierbenefitdepends on howexpectedextracapacitycanbeusedwithoptions Without option, the optimal policy is q0,1=50, q0,2=100 and

12. Scenario trees are built withmoment matching method* • 1st stage targets: • E[D]=500Var[D]=10 000Skew[D]=2 • 2nd stage targets: • E[D] i,2= 5 x Di,1Var[D]= 5 x Var[D] • Skew[D]=2 • 1st stage targets: • E[S]=97%Var[S]=10% • Skew[S] = -0.5 • 2nd stage targets: • E[S] i,2= Si,1Var[S] =Var[S] • Skew[S]=-0.5 Demand: Expected product sales Variance and skewness Correlation between sales Supply capability: Expected capability (0…100%) Variance and skewness Correlation between suppliers Correlation between aggregated demand and supply • * Hoyland and Wallace (2001).

13. Heuristic for multivariate scenario generation Enumeration heuristic To maintain other statistical properties (marginal distributions) while varying correlation (joint distribution), we use a ”scenario enumeration heuristic”.

14. Demand scenarios of two products • 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). Scenario enumeration: demand of product one (y-axis value) remains unchanged

15. Demand vs. supply scenarios • 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).

16. Sample of four multivariate scenario trees Some properties are in common for all scenarios, for example: Scenarios represent different business environments, for example:

17. Worst case risksgrow, ifinter-dependenciesoccur No inter-dependecies Complementary products >

18. Use of common componentcanaggregateworst case risk No inter-dependencies Complementary products > >

19. Highdemanddrivescostsmorecomparedto lowsupplycapability No inter-dependencies Complementary products

20. Preliminaryresults Our approach allows systematic analysis of the performance of procurements policies Initial observations: • Capacity reservation option seems to reduce costs (minimum reduction 5%, depending on scenario and setup). • Use of common components has an impact on expected costs, which is highest with complementary products > non-correlated > substitute products. • Maximum costs can be significantly higher in case of complementary products and a common component. • There is some evidence that negative correlation between demand and supply capability would increase especially worst case costs.

21. Nextsteps Improve uncertainty modeling: • Detailed assessment of supplier capability • Analysis and improvement of scenario enumeration heuristic. Supplement the optimization model with risk constraints*. Investigate model expansion with respect to time stages and other variables, such as components, products and suppliers. Evaluate new strategies, such as forecast-sharing based procurement. * E.g. Sodhi (2005) considers ”Demand-at-Risk” and ”Inventory-at-Risk”.

22. References Federgruen, A. and Yang, N. (2008). Selecting a portfolio of suppliers under demand and supply risks. Operations Research, 56(4):916-936. Groenevelt, H. and Rudi N. (2000). Product design for component commonality and the effect of demand correlation. Working paper, University of Rochester, Rochester, NY Hochreiter, R. and Pflug, G. C. (2007). Financial scenario generation for stochastic multi-stage decision processes as facility location problems. Annals of Operations Research, 152(1):257-272. Hoyland, K. and Wallace, S. W. (2001). Generating scenario trees for multi-stage decision problems. Management Science, 47(2):295-307. Kleindorfer, P. R. and Wu, D. J. (2003). Integrating long- and short-term contracting via business-to-business exchanges for capital intensive industries. Management Science, 49(11):1597-1615. Martínez-de-Albéniz, V. and Simchi-Levi, D. (2003). A portfolio approach to procurement contracts. MIT Sloan School of Management Paper 188, Available at http://ebusiness.mit.edu/research/papers/188DSleviPortfolioApproach.pdf. Sodhi, M. S. (2005). Managing demand risk in tactical supply chain planning for a global consumer electronics company. Production and Operations Management, 14(1):69-79. Tang, C. S. (2006). Review: Perspectives in supply chain risk management. International Journal of Production Economics, 103:451–488. Van Mieghem, J. A. (2004). Commonality strategies: Value drivers and equivalence with flexible capacity and inventory substitution. Management Science, 50(3):419-424.

23. Appendix – Computationalaspects • * 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. 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).