Monotonic bounds in multistage mixed-integer stochastic programming

Multistage stochastic programs bring computational complexity which may increase exponentially in real case problems. For this reason approx- imation techniques which replace the problem by a simpler one and provide lower and upper bounds to the optimal solution are very useful. In this pa- per we provide monotonic lower and upper bounds for the optimal objective value of a multistage stochastic program. These results also apply to stochas- tic multistage mixed integer linear programs. Chains of inequalities among the new quantities are provided in relation to the optimal objective value, the wait-and-see solution and the expected result of using the expected value so- lution. Numerical results on a supply real case transportation problem have been provided.

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