Two-stage stochastic mixed-integer linear programming: The conditional scenario approach

In this paper we consider the two-stage stochastic mixed-integer linear programming problem with recourse, which we call the RP problem. A common way to approximate the RP problem, which is usually formulated in terms of scenarios, is to formulate the so-called Expected Value (EV) problem, which onl...

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Bibliographic Details
Published in:Omega (Oxford) Vol. 70; pp. 31 - 42
Main Author: Beltran-Royo, C.
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.07.2017
Subjects:
Conditional expectation
Conditional Scenario
Scenario
Stochastic mixed-integer linear programming
Conditional expectation
Stochastic mixed-integer linear programming
Conditional Scenario
Scenario
ISSN:0305-0483, 1873-5274
Online Access:Get full text
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Summary:In this paper we consider the two-stage stochastic mixed-integer linear programming problem with recourse, which we call the RP problem. A common way to approximate the RP problem, which is usually formulated in terms of scenarios, is to formulate the so-called Expected Value (EV) problem, which only considers the expectation of the random parameters of the RP problem. In this paper we introduce the Conditional Scenario (CS) problem which represents a midpoint between the RP and the EV problems regarding computational tractability and ability to deal with uncertainty. In the theoretical section we have analyzed some useful bounds related to the RP, EV and CS problems. In the numerical example here presented, the CS problem has outperformed both the EV problem in terms of solution quality, and the RP problem with the same number of scenarios as in the CS problem, in terms of solution time. •Context: Two-stage stochastic mixed-integer linear programming.•We introduce the Conditional Scenario Optimization (CSO) approach.•CSO is a midpoint between Scenario Optimization and Deterministic Optimization.•CSO has outperformed Deterministic Optimization in terms of solution quality.•CSO has outperformed Scenario Optimization in terms of solution time.
ISSN:0305-0483
1873-5274
DOI:10.1016/j.omega.2016.08.010