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

Motivation Growing mismatches between demand and supply expose companies to serious operational risks. (Hendricks & Singhal 2005) Strategies for mitigating procurement risks can be evaluated with stochastic models. Yet, these models are not used in practice. (Kouvelis et al. 2006, Tang 2006) We show that the models results of can be very sensitive to assumptions about uncertainties. Thus, the uncertainties must be well understood when deploying models.

Motivation How many components are needed, if demand planners state that our demand forecast is , with a variation of items?

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.

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. Manufacturer orders m and reserves o. Suppliers total capacity is set to K=m+o. Demand d, characterized by F(x), is realized. Manufacturer exercises e=min[d-m,o] + options.

Capacity reservation option Expected sales for capacity K Manufacturers profit for revenue r and prices w m, w o, w e We set w m = $1.0, w o = $0.2, w e = $0.9 and r = $2.0. Optimal strategy can be derived via maximization of (m,o)

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

Example with bimodal demand Optimal strategies can be determined with numeric integration. Even if the optimal profits are identical, strategies differ significantly. Demandm*o*m*+o* * Product one $8 250 Product two $8 250 Difference+33%-33%-14%0%

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

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. Product typem*o*m*+o* * Substitute $ Differentiated $ Complementary $16 940

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

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

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.

Thank you! 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): Hendricks, K. B. and Singhal, V. R. (2005). Association between supply chain glitches and operating performance. Management Science, 51(5): 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): 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: Tang, C. S. (2006). Review: Perspectives in supply chain risk management. International Journal of Production Economics, 103: References