In this paper, we study chance constrained mixed integer program withconsideration of recourse decisions and their incurred cost, developed on afinite discrete scenario set. Through studying a non-traditional bilinear mixedinteger formulation, we derive its linear counterparts and show that they couldbe stronger than existing linear formulations. We also develop a variant ofJensen's inequality that extends the one for stochastic program. To solve thischallenging problem, we present a variant of Benders decomposition method inbilinear form, which actually provides an easy-to-use algorithm framework forfurther improvements, along with a few enhancement strategies based onstructural properties or Jensen's inequality. Computational study shows thatthe presented Benders decomposition method, jointly with appropriateenhancement techniques, outperforms a commercial solver by an order ofmagnitude on solving chance constrained program or detecting its infeasibility.
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