3,359 research outputs found
On the Value of Multistage Risk-Averse Stochastic Facility Location With or Without Prioritization
We consider a multiperiod stochastic capacitated facility location problem
under uncertain demand and budget in each period. Using a scenario tree
representation of the uncertainties, we formulate a multistage stochastic
integer program to dynamically locate facilities in each period and compare it
with a two-stage approach that determines the facility locations up front. In
the multistage model, in each stage, a decision maker optimizes facility
locations and recourse flows from open facilities to demand sites, to minimize
certain risk measures of the cost associated with current facility location and
shipment decisions. When the budget is also uncertain, a popular modeling
framework is to prioritize the candidate sites. In the two-stage model, the
priority list is decided in advance and fixed through all periods, while in the
multistage model, the priority list can change adaptively. In each period, the
decision maker follows the priority list to open facilities according to the
realized budget, and optimizes recourse flows given the realized demand. Using
expected conditional risk measures (ECRMs), we derive tight lower bounds for
the gaps between the optimal objective values of risk-averse multistage models
and their two-stage counterparts in both settings with and without
prioritization. Moreover, we propose two approximation algorithms to
efficiently solve risk-averse two-stage and multistage models without
prioritization, which are asymptotically optimal under an expanding market
assumption. We also design a set of super-valid inequalities for risk-averse
two-stage and multistage stochastic programs with prioritization to reduce the
computational time. We conduct numerical studies using both randomly generated
and real-world instances with diverse sizes, to demonstrate the tightness of
the analytical bounds and efficacy of the approximation algorithms and
prioritization cuts
Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition
In this paper, we study chance constrained mixed integer program with
consideration of recourse decisions and their incurred cost, developed on a
finite discrete scenario set. Through studying a non-traditional bilinear mixed
integer formulation, we derive its linear counterparts and show that they could
be stronger than existing linear formulations. We also develop a variant of
Jensen's inequality that extends the one for stochastic program. To solve this
challenging problem, we present a variant of Benders decomposition method in
bilinear form, which actually provides an easy-to-use algorithm framework for
further improvements, along with a few enhancement strategies based on
structural properties or Jensen's inequality. Computational study shows that
the presented Benders decomposition method, jointly with appropriate
enhancement techniques, outperforms a commercial solver by an order of
magnitude on solving chance constrained program or detecting its infeasibility
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