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Monotonic bounds in multistage mixed-integer linear stochastic programming: theoretical and numerical results

Francesca Maggioni (francesca.maggioni***at***unibg.it)
Elisabetta Allevi (elisabetta.allevi***at***unibs.it)
Marida Bertocchi (marida.bertocchi***at***unibg.it)

Abstract: Multistage stochastic programs bring computational complexity which may increase exponentially 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 solution 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. Numerical results on a supply real case transportation problem have been provided.

Keywords: Multistage stochastic programming; Group subproblems; Mixed-integer programs; Value of stochastic solution

Category 1: Stochastic Programming

Citation: The paper is published in Computational Management Science (2016): F. Maggioni, E. Allevi, M. Bertocchi, (2016) Monotonic bounds in multistage mixed-integer stochastic programming, Computational Management Science, DOI: 10.1007/s10287-016-0254-5, First online: 06 April 2016.

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Entry Submitted: 02/02/2015
Entry Accepted: 02/02/2015
Entry Last Modified: 04/07/2016

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