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Chance-Constrained Programming with Decision-Dependent Uncertainty

Miguel Lejeune (mlejeune***at***gwu.edu)
Francois Margot (fmargot11***at***gmail.com)
Alan Delgado de Oliveira (alandelgado***at***email.gwu.edu)

Abstract: We study a class of joint chance-constrained stochastic problems with decision-dependent uncertainty CC-DD. A coupling function models the dependency between decision and endogenous random variables. We propose deterministic reformulations equivalent to the general chance-constrained problem with decision-dependent uncertainty CC-DD and applicable to any coupling function. We define the properties of coupling functions and explain the importance of properly modeling decision-dependent uncertainty. We then provide the explicit formulation of problem CCDD in the decision-dependent service uncertainty context and derive exact mixed-integer nonlinear reformulations. We design an algorithmic framework which includes the derivation of convex MINLP relaxation problems, the use of new multiterm convexification methods for bilinear terms, the derivation of tight lower and upper bounds, and the design of a nonlinear branch-and-bound algorithm featuring a conification-relaxation method and the new smallest domain branching rule. Experiments based on real-life data show the scalability and computational efficiency of the method.

Keywords: Chance Constraint, Decision-Dependent Uncertainty, Multiterm Polynomial Relaxation, Mixed-Integer Nonlinear Programming, Nonlinear Branch-and-Bound Algorithm, Coupling Function

Category 1: Stochastic Programming

Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 3: Applications -- OR and Management Sciences


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Entry Submitted: 09/19/2018
Entry Accepted: 09/19/2018
Entry Last Modified: 03/08/2019

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