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Monotonic bounds in multistage mixed-integer stochastic programming

Francesca Maggioni (), Elisabetta Allevi () and Marida Bertocchi
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Francesca Maggioni: Bergamo University
Elisabetta Allevi: Brescia University
Marida Bertocchi: Bergamo University

Computational Management Science, 2016, vol. 13, issue 3, 423-457

Abstract: Abstract Multistage stochastic programs bring computational complexity which may increase exponentially with the size of the scenario tree in real case problems. For this reason approximation techniques which replace the problem by a simpler one and provide lower and upper bounds to the optimal value are very useful. In this paper we provide monotonic lower and upper bounds for the optimal objective value of a multistage stochastic program. These results also apply to stochastic 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 solution. The computational complexity of the proposed lower and upper bounds is discussed and an algorithmic procedure to use them is provided. Numerical results on a real case transportation problem are presented.

Keywords: Multistage stochastic programming; Group subproblems; Mixed-integer programs; Value of stochastic solution; Computational complexity; Bounds (search for similar items in EconPapers)
Date: 2016
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