Chance-Constrained Programming with 0-1 or Bounded Continuous Decision Variables

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Abstract
This paper considers the chance-constrained programming problem where the decision variables can be either bounded and continuous or restricted to be either zero or one, and where some or all of the parameters are random variables that may be statistically dependent. Both exact and approximate solution procedures are presented, where most of these are based on several linear inequalities that permit this problem to be approximated by a number of ordinary (integer or noninteger) linear programming problems. Either zero-order or linear decision rules are allowed for the continuous variables, and a general method of making “second-stage decisions” with either continuous or 0-1 variables is developed.

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