1. 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. Evaluating procurement strategiesAnssi Käki and Ahti Salo 2 Manufacturers problem n 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. Products Components Suppliers Market Material flow Common Product specific n To minimize costs and hedge supply risks, the manufacturer can use normal orders or capacity reservation options*.

3. Evaluating procurement strategiesAnssi Käki and Ahti Salo 3 Research perspective n Typical risk mitigation strategies include –Supplier diversification (supply uncertainty)* –Common components (demand risk pooling)**. Products Components Suppliers 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 n 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).

4. Evaluating procurement strategiesAnssi Käki and Ahti Salo 4 Research questions and approach n 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). n 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.

5. Evaluating procurement strategiesAnssi Käki and Ahti Salo 5 Stochastic optimization model n Unit costs include i) fixed order, ii) capacity reservation, iii) capacity execution, iv) inventory holding and scrap and v) shortage. Initial, first and second stage costs

6. Evaluating procurement strategiesAnssi Käki and Ahti Salo 6 Decision steps: Initial fixed orders

7. Evaluating procurement strategiesAnssi Käki and Ahti Salo 7 Decision steps: Capacity reservations

8. Evaluating procurement strategiesAnssi Käki and Ahti Salo 8 Decision steps: Capacity execution

9. Evaluating procurement strategiesAnssi Käki and Ahti Salo 9 Costs

10. Evaluating procurement strategiesAnssi Käki and Ahti Salo 10 Example of one product, component and perfectly reliable supplier Initial stage: Order & Reservation First stage: Execution & holding Second stage: Scrap

11. Evaluating procurement strategiesAnssi Käki and Ahti Salo 11 n Without option, the optimal policy is q 0,1 =50, q 0,2 =100 and With optionWithout option Example contd Order Holding & scrap n Supplier perspective: Supplier benefit depends on how expected extra capacity can be used with options

12. Evaluating procurement strategiesAnssi Käki and Ahti Salo 12 Scenario trees are built with moment matching method* n Demand: »Expected product sales »Variance and skewness »Correlation between sales n Supply capability: »Expected capability (0…100%) »Variance and skewness »Correlation between suppliers n Correlation between aggregated demand and supply 1st stage targets: E[D]=500 Var[D]=10 000 Skew[D]=2 2nd stage targets: E[D] i,2 = 5 x D i,1 Var[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 = S i,1 Var[S] = Var[S] Skew[S]=-0.5 * Hoyland and Wallace (2001).

13. Evaluating procurement strategiesAnssi Käki and Ahti Salo 13 Heuristic for multivariate scenario generation n To maintain other statistical properties (marginal distributions) while varying correlation (joint distribution), we use a scenario enumeration heuristic. Enumeration heuristic

14. Evaluating procurement strategiesAnssi Käki and Ahti Salo 14 Demand scenarios of two products Scenario enumeration: demand of product one (y-axis value) remains unchanged n Plotted data contains 2nd stage values of 10 x 10 trees with equal probabilities. n Red lines are OLS regression lines; they are statistically significant in positive and negative case (p<0.01).

15. Evaluating procurement strategiesAnssi Käki and Ahti Salo 15 Demand vs. supply scenarios n Plotted data contains 2nd stage values of 10 x 10 trees with equal probabilities. n Negative-case OLS regression line is statistically significant (p<0.01).

16. Evaluating procurement strategiesAnssi Käki and Ahti Salo 16 Sample of four multivariate scenario trees n Some properties are in common for all scenarios, for example: n Scenarios represent different business environments, for example: DemandSupply D1D2S1S2 E 2453259095.6 %95.7 % Std 212222443.3 Skew 1.241.28-0.27-0.33 ScenarioCorrelation Between demandsDemand 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 -0.020.01

17. Evaluating procurement strategiesAnssi Käki and Ahti Salo 17 Worst case risks grow, if inter-dependencies occur No inter-dependeciesComplementary products E15933 CVaR (5%)34800E16056+1 % CVaR (5%)44700+28 % >

18. Evaluating procurement strategiesAnssi Käki and Ahti Salo 18 Use of common component can aggregate worst case risk No inter-dependenciesComplementary products E11941.00 CVaR (5%)28900.00E13781.00+15 % CVaR (5%)44300.00+53 % > >

19. Evaluating procurement strategiesAnssi Käki and Ahti Salo 19 High demand drives costs more compared to low supply capability No inter-dependenciesComplementary products

20. Evaluating procurement strategiesAnssi Käki and Ahti Salo 20 Preliminary results n Our approach allows systematic analysis of the performance of procurements policies n 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. Evaluating procurement strategiesAnssi Käki and Ahti Salo 21 Next steps n Improve uncertainty modeling: –Detailed assessment of supplier capability –Analysis and improvement of scenario enumeration heuristic. n Supplement the optimization model with risk constraints*. n Investigate model expansion with respect to time stages and other variables, such as components, products and suppliers. n Evaluate new strategies, such as forecast-sharing based procurement. * E.g. Sodhi (2005) considers Demand-at-Risk and Inventory-at-Risk.

22. Evaluating procurement strategiesAnssi Käki and Ahti Salo 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. Evaluating procurement strategiesAnssi Käki and Ahti Salo 23 Appendix – Computational aspects n 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* n 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.