Two-stage problem of quantile optimization of an investment project

Наумов, А. В.

doi:10.1134/s106423071002005x

Cited by 2 publications

(2 citation statements)

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“…This problem was formulated in [14] for the expectation criterion. In [15], this problem was stated with quantile criterion. In this work, a method to find an upper bound on the optimal value of the objective function was developed.…”

Section: Optimization Of a Hospital Budgetmentioning

confidence: 99%

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Variable neighborhood search for stochastic linear programming problem with quantile criterion

et al. 2019

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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.

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Section: Optimization Of a Hospital Budgetmentioning

confidence: 99%

“…In Table 4, results of solving the problem by the suggested algorithm are given for different values of α. Also, upper bounds obtained by the method from [15] and known lower bounds are presented in Table 4. The lower bounds were obtained by using the procedure described in Sect.…”

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confidence: 99%