Sunday

SB13
4 - Lower-bound Analyses of the Lift-and-Project Ranks of
Graph-based Polytopes
Yu Hin Au, PhD Candidate, University of Waterloo, 200 University
Ave., W., Waterloo, ON, N2L3G1, Canada, yau@uwaterloo.ca
We’ll discuss some ongoing work on obtaining inapproximability results for
Bienstock-Zuckerberg and Lasserre lift-and-project algorithms on graph-based
optimization problems. This is joint work with Levent Tuncel.
■ SB13
13- West 106 B- CC
Computational Issues on Solving Mixed Integer
Second Order Cone Optimization Problems
Sponsor: Optimization/Linear Programming and Complementarity
Sponsored Session
Chair: Julio Cesar Goez, PhD Candidate, Lehigh University, 18015,
United States of America, jgoez1@gmail.com
1 - Computational Effectiveness of Split Cuts for Second-order
Conic Programming
Sina Modaresi, University of Pittsburgh, 3700 O’Hara Street,
Pittsburgh, United States of America, sim23@pitt.edu,
Mustafa Kilinc, Juan Pablo Vielma
Split cuts are one of the most effective cuts for linear MIPs and they are
equivalent to MIR cuts. We show that this equivalency does not hold for secondorder
conic MIPs by giving examples where split cuts strictly dominate conic MIR
cuts proposed by Atamturk et al.. However, split cuts have to be added as
nonlinear inequalities, while conic MIR cuts can be added as linear inequalities to
the extended formulation. We compare the trade-off between the speed and the
strength of these cuts.
2 - Branch and Bound for Mixed Integer Second Order Cone
Optimization: Impact of Disjunctive Conic Cuts
Julio Cesar Goez, PhD. Candidate, Lehigh University, 18015,
United States of America, jgoez1@gmail.com, Pietro Belotti,
Ted Ralphs, Tamás Terlaky, Imre Polik
We investigate the use of Disjunctive Conic Cuts (DCC) in a Branch and Cut
framework when solving MISOCO problems. Various criteria are explored to
select the disjunctions to build DCCs at different nodes of the tree. Additionally,
we explore different criteria for node selection and branching rules. These
experiments will help us to understand the impact that DCCs have in decreasing
the size of the search tree and the solution time.
3 - Restrict-and-Relax Search for 0-1 Integer Programs
Menal Guzelsoy, SAS, 100 SAS Campus Drive, Cary, NC, 7513,
United States of America, menal.guzelsoy@sas.com,
George Nemhauser, Martin Savelsbergh
We introduce restrict-and-relax search, an algorithm for 0-1 integer programs
that explores a dynamic search tree by not only fixing variables (restricting), but
by also unfixing previously fixed variables (relaxing). Starting by solving a
restricted integer program, we may at any tree node selectively relax/restrict
variables using dual/structural information. A proof-of-concept computational
study demonstrates the effectiveness of the algorithm.
4 - A Regularized Interior-Point Method for
Semidefinite Programming
Ahad Dehghani, McGill University, Montreal, Canada,
ahad.dehghani@mcgill.ca, Jean-Louis Goffin, Dominique Orban
Interior-point methods in semi-definite programming (SDP) require the solution
of a sequence of linear systems which are used to derive the search directions.
Safeguards are typically required in order to handle rank-deficient Jacobians and
free variables. We propose a primal-dual regularization to the original SDP and
show that it is possible to recover an optimal solution of the original SDP via
inaccurate solves of a sequence of regularized SDPs for both the NT and dual
HKM directions.
INFORMS Phoenix – 2012
84
■ SB14
14- West 106 C- CC
Uncertainty in Project Management
Contributed Session
Chair: Bajis Dodin, Professor, University of California, School of
Business Administration, Riverside, CA, 92521, United States of
America, bajis.dodin@ucr.edu
1 - Enumerating Feasible Task Sets with Ordered, Unmeasured
Material Constraints
Jordan Srour, Assistant Professor, Lebanese American University,
P.O. Box 13-5053, Beirut, Lebanon, fjsrour@gmail.com,
Walid Nasrallah
We investigate the solution space for selecting a subset of project tasks under a
resource shortage. The amount of resource required by each task is not known,
but the tasks are fully ordered accordingly. We enumerate the ways to select a
subset of tasks without exceeding the resource constraint. We highlight the
relationship of this enumeration to published number sequences arising from
regular Boolean functions. We provide both an enumeration algorithm and
enumerations up to n=10.
2 - Stochastic Approach for Project Scheduling Based on
Fund Availability
Yuvraj Gajpal, Assistant Professor, King Fahd University of
Petroleum and Minerals, KFUPM Box 634, Dhahran,
Saudi Arabia, gajpaly@gmail.com, Ashraf Elazouni
The paper considers a finance based project where the contractors finance projects
mainly through the owners’ progress payments supplemented by fund procured
through establishing credit-line accounts. In this situation the best proactive
approach for contractor is to schedule construction activities based on the
available finance. A stochastic heuristic approach is proposed to device financebased
schedules of multiple projects.
3 - A Nonlinear Programming Model for Stochastic Project
Crashing
Ronald Davis, Associate Professor, San Jose State University,
College of Business, One Washington Square, San Jose, CA,
95192, United States of America, ronald.davis@sjsu.edu
When beta distributions are used for every activity early start and finish time
distribution in a project network, moment preserving beta approximations for the
sum and product of beta cdfs can be coded in VBA to allow an analytic stochastic
forward pass to be carried out, without simulation. Introduction of crashing
variables and costs yields a nonlinear programming formulation to minimize
crash cost subject to a constraint on mean project duration. Realistic example
SOLVER results are shown.
4 - Portfolio Management in a Highly Uncertain Environment: The
Role of Interdependencies
Olga Kokshagina, PhD Student, Centre for Scientific Management
(CGS), CGS Mines ParisTech, 60 Boulevard Saint-Michel, Paris,
75272, France, olga.kokshagina@mines-paristech.fr, Patrick Cogez,
Pascal Le Masson, Benoit Weil
This work deals with portfolio management strategies in high uncertainty. There
exist strategies that consider projects separately or dependently. Literature shows
first, the dependencies have a tendency to increase complexity and cost of the
system. Second, there is a possibility to share risks in between projects, to
highlight the effect of learning. Our paper investigates the contradictory role of
interdependencies and the relevant management strategies in particular industrial
situations.
5 - Scheduling & Financial Planning in Probabilistic Projects
Bajis Dodin, Professor, University of California, School of Business
Administration, Riverside, CA, 92521, United States of America,
bajis.dodin@ucr.edu, Abdelghani Elimam
In probabilistic projects (PP) required duration and resources for some or all
activities are given as random variables characterized by their own probability
distribution functions (PDFs). Managing a PP requires dealing with several
important issues. In this paper, we analyze the impact of the various stochastic
variations on the duration, and cost of the project. Procedures for determining the
PDFs of project cost and duration, and project schedule are developed.