Remarkable progress has been made in the development of algorithmic procedures and the availability of software for stochastic programming problems. However, some fundamental questions have remained unexplored. This paper identifies the more challenging open questions in the field of stochastic programming. Some are purely technical in nature, but many also go to the foundations of designing models for decision making under uncertainty. Recent work in stochastic programming has mostly been

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... at the design of solution procedures and the development of accompanying software; an overly brief review of the present state-of-the-art is provided in $1. This effort should be continued and expanded, and should remain the central concern of the research in stochastic programming. However, to support the application of stochastic programming in a practical environment, there are a number of fundament a1 questions that still go begging for appropriate answers. This paper, based on my lecture at the International Conference on Stochastic Programming in Udine (Italy) in 1992, takes stock and goes through a list of the challenges that must be met if one is going to have the adequate technical tools to validate the stochastic programming model in the context of decision making under uncertainty, and to justify the approximations that must be accepted to render the problem solvable by existing or projected computational means.