Authors: Ivanov, Sergey
Kibzun, Andrey
Mladenović, Nenad 
Urošević, Dragan 
Title: Variable neighborhood search for stochastic linear programming problem with quantile criterion
Journal: Journal of Global Optimization
Volume: 74
Issue: 3
First page: 549
Last page: 564
Issue Date: 15-Jul-2019
Rank: M21
ISSN: 0925-5001
DOI: 10.1007/s10898-019-00773-2
Abstract: 
We consider the stochastic linear programming problem with quantile criterion and continuous distribution of random parameters. Using the sample approximation, we obtain a stochastic programming problem with discrete distribution of random parameters. It is known that the solution to this problem provides an approximate solution to the problem with continuous random parameters if the size of the sample is large enough. Applying the confidence method, we reduce the problem to a mixed integer programming problem, which is linear with respect to continuous variables. Integer variables determine confidence sets, and we describe the structure of the optimal confidence set. This property allows us to take into account only confidence sets that may be optimal. To find an approximate solution to the problem, we suggest a modification of the variable neighborhood search and determine structures of neighborhoods used in the search. Also, we discuss a method to find a good initial solution and give results of numerical experiments. We apply the developed algorithm to solve a problem of optimization of a hospital budget.
Keywords: Quantile criterion | Sample average approximation | Stochastic programming | Variable neighborhood search
Publisher: Springer Link

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