Impacts of the Shape of the Demand Distribution on Procurement Risk Mitigation

1. Impacts of the Shape of the Demand Distribution on Procurement Risk Mitigation April 29, 2011 POMS 22nd Annual Conference Anssi Käki and Ahti Salo School of Science, Aalto University, Finland

2. Motivation Growingmismatchesbetweendemand and supplyexposecompanies to seriousoperationalrisks. (Hendricks & Singhal 2005) Strategies for mitigatingprocurementriskscanbeevaluatedwithstochasticmodels. Yet, thesemodelsarenotused in practice. (Kouvelis et al. 2006, Tang 2006) We show that the models’ results of canbeverysensitive to assumptionsaboutuncertainties. Thus, the uncertaintiesmustbewellunderstoodwhendeployingmodels.

3. Motivation How many components are needed, if demand planners state that ”our demand forecast is 10 000, with a variation of  5 000 items”?

4. Contents We study the capacity reservation option model of Cachon & Larivere (2003). We illustrate how the optimal procurement strategy depends on the shape of demand distribution. Our results suggest that inaccurate assumptions about uncertainties may lead to non-optimal behaviour.

5. Capacity reservation option A component is procured from a single supplier. The demand for the component is uncertain. In the one-period model, at t=0 the manufacturer can: • Make firm commitments m • Reserve capacity o. The component demand d is realized; the manufacturer then decides how much to execute e, restricted by the reserved capacity o. Thus, the total order is m+e ≤ m+o.

6. Capacity reservation option • Manufacturer’s profit for revenue r and prices wm, wo, we • Optimal strategy can be derived via maximization of (m,o) • We set wm = $1.0, wo = $0.2, we = $0.9 and r = $2.0. Expected sales for capacity K

7. Example with bimodal demand Product two: one monopolistic customer accounts for approximately 2/3 of sales. The remaining sales comes from small customers. Expected sales is, again, 10 000. Product one: the expected sales is 10 000 and sales from 8 000 to 13 000 cover around 50% of probability mass.

8. Example with bimodal demand Optimal strategies can be determined with numeric integration. Even if the optimal profits are identical, strategies differ significantly.

9. Two products and a common component Example samples from joint distributions of two product demands ❸ ❶ ❷ A common component of two products with dependencies: ❶ Substitute products, such as comparable devices for the same market area.  Demands are likely to be negatively dependent. ❷ Differentiated products for different market segments.  There are no demand dependencies. ❸ Complementary products, such as a one device launched separately for two different market areas.  Demands are likely to be positively dependent.

10. Two products and a common component The optimal strategies and corresponding profits determined with a stochastic optimization model For complementary products, the distribution is wider and has heavier right-tail. The option is utilized more. Still, the demand fulfilled is on average 3% less  it is optimal to prepare for the ”fat-tail”, but the resulting expected profit is lower.

11. Practical implications How many components are needed, if demand planners state that the demand forecast is 10 000 5 000 items? If there is no flexibility (such as the capacity reservation option), the profit can be significantly less.

12. Practical implications • For example, setting arbitrarily m=8 000, o=4 000 would yield 23% less profits compared to the optimal. If there is a flexible alternative (the option in our case), the profit can still drop remarkably.

13. Conclusions When evaluating/implementing procurement approaches, careful analysis of uncertainties is essential. We have illustrated how the optimal procurement strategy is dependent on: • Demand distribution width and ”fat-tails” • Demand distribution modality • Demand-dependencies between two products that share a common component. Our future work will discuss how copula-based scenarios can be used to address more complex uncertainties, such as several products and uncertainty in supply.

14. Thank you! References Cachon, G. P. and Lariviere, M. A. (2001). Contracting to assure supply: How to share demand forecasts in a supply chain. Management Science, 47(5):629-646. Hendricks, K. B. and Singhal, V. R. (2005). Association between supply chain glitches and operating performance. Management Science, 51(5):695-711. Kouvelis, P., Chambers, C., and Wang, H. (2006). Supply chain management research and Production and Operations Management: Review, trends, and opportunities. Production and Operations Management, 15(3):449-469. Käki, A. and Salo, A. (2011). Impacts of the Shape of the Demand Distribution on Procurement Risk Mitigation. Proceedings of 22nd Annual POMS Conference. Available at: http://www.pomsmeetings.org/ConfPapers/020/020-0741.pdf Tang, C. S. (2006). Review: Perspectives in supply chain risk management. International Journal of Production Economics, 103:451-488.