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This paper relies on a decision-tree approach to aid a buying firm in determining the optimal size of its supply base in the presence of risks. The risk under consideration refers to any unpredictable operations interruptions caused by all suppliers being unavailable to satisfy the buying firm's demand. The relationship between the levels of risk and associated trade-offs is captured by a decision-tree model, from which the expected cost function is formulated. The exact or approximate optimal solutions for various scenarios, as well as their sensitivity, are obtained and examined.
Berger et al. (2005) studied this question.