2016 INFORMS Annual Meeting Program

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INFORMS Nashville – 2016
47
SB13
104C-MCC
Advances in Structured Nonconvex Optimization
Sponsored: Optimization, Global Optimization
Sponsored Session
Chair: Fatma Kilinc Karzan, Assistant Professor, Carnegie Mellon
University, 5000 Forbes Ave, Pittsburgh, PA, 15213, United States,
1 - Solving Standard Quadratic Programming By Cutting Planes
Andrea T. Lodi, École Polytechnique de Montréal,
Standard quadratic programs are non-convex quadratic programs with the only
constraint that variables must belong to a simplex. By a famous result of Motzkin
and Straus, those problems are connected to the clique number of a graph. We
propose cutting planes to obtain strong bounds: our cuts are derived in the
context of Spatial Branch & Bound, where linearization variables represent
products. Their validity is based on Motzkin-Straus result. We study the relation
between these cuts and the ones obtained by the first RLT level. We present
extensive computational results using the cuts in the context of the Spatial
Branch & Bound implemented by the commercial solver CPLEX.
2 - Some Cut-generating Functions For Second-order Conic Sets
Asteroide Santana, Georgia Institute of Technology, Atlanta, GA,
30308, United States,
Santanu Subhas Dey
In this paper, we study cut generating functions for conic sets. Our first main
result shows that if the conic set is bounded, then cut generating functions for
integer linear programs can easily be adapted to give the integer hull of the conic
integer program. Then we introduce a new class of cut generating functions
which are non-decreasing with respect to second-order cone. We show that,
under some minor technical conditions, these functions together with integer
linear programming-based functions are sufficient to yield the integer hull of
intersections of conic sections in R2.
3 - Polynomial Dc Decompositions And Applications
Georgina Hall, Princeton University, Princeton, NJ, United States,
, Amir Ali Ahmadi
Difference of Convex (DC) programming is a class of optimization problems
where the objective and constraints are given as the difference of convex
functions. Although several important problems (e.g., in machine learning)
already appear in DC form, such a decomposition is not always available. We
consider this decomposition question for polynomial optimization and present
some new applications, primarily to distance geometry problems.
4 - A Second-order Cone Based Approach For Solving The Trust
Region Subproblem And Its Variants
Nam Ho-Nguyen, Carnegie Mellon University, Pittsburgh, PA,
United States, Fatma Kilinc-Karzan
We study the trust region subproblem (TRS) of minimizing a nonconvex
quadratic function over the unit ball with additional conic constraints. We follow
a second-order cone based approach to derive an exact convex formulation of the
TRS, and under slightly stronger conditions, give a low-complexity
characterization of the convex hull of its epigraph without any additional
variables. Our study highlights an explicit connection between the nonconvex
TRS and smooth convex quadratic minimization, which allows for the application
of cheap iterative methods to the TRS.
SB14
104D-MCC
OR In Agriculture
Invited: Agricultural Analytics
Invited Session
Chair: Margarit Khachatryan, Monsanto, United States,
1 - Government Interventions In Promoting Sustainable Practices
In Agriculture
Duygu Akkaya, Stanford Graduate School of Business, Stanford,
CA, United States, , Hau Lee,
Kostas Bimpikis
Sustainable practices in agriculture such as organic farming have attracted
immense attention lately due to the increase in environmental and health
concerns. Government support is often used to incentivize producers to convert
to sustainable practices. We investigate the effectiveness of government
interventions including tax, subsidy and hybrid policies in terms of their impact
on sustainable practice adoption, producers’ profits, consumer welfare, and return
on government spending using a setting in which producers with traditional and
sustainable production options serve consumers that have a high valuation for
sustainable production.
2 - Accelerating Digital Agriculture Through Automated R&D Trial
Placement Into Field Zones
Qinglin Duan, Monsanto, St. Louis, MO, United States,
, David Ciemnoczolowski
The trend towards Digital Agriculture requires increasing information on
conditions within fields and corresponding decisions about product selection and
management. To provide placement and management prescriptions, products
must be tested across differing conditions within fields. We formulate the zone
mapping problem as a 2D bin-packing model with trials of known dimensions
and operational constraints. The model is integrated into Monsanto’s geospatial
field platform with analytics relating climate, soils, and topography to crop
performance. Optimized placement has enabled representative testing across
environments and set the foundation for advancements in digital agriculture.
3 - Combining Expert Estimates With Data To Obtain Hybrid
Yield Distributions
Saurabh Bansal, Penn State University, ,
Genaro J Gutierrez
We discuss a Copula based approach to combine expert judgments for yield
distributions with data, and illustrate its application for the seed corn business.
4 - A Mathematical Model For Farm Scale Land Management
Considering Uncertainty
Qi Li, Iowa State University, Guiping Hu
Farmers make decisions on types of crops to plant and irrigation frequency and
pattern on an annual basis. This is often done under various uncertainties, such as
precipitation amount, crop prices, and soil profile. In the study, a farm level
precision farmland management model based on stochastic programming is
proposed. The model focuses on the uncertainties in weather, yield and market
prices. Advanced statistical methods such as time series analysis and spatial
analysis are also investigated to generate representative realizations for the
uncertainties.
SB15
104E-MCC
Building Better Models: Innovations in
Predictive Analytics
Invited: Modeling and Methodologies in Big Data
Invited Session
Chair: CP Teo, NUS, 1 Business Link, Singapore, 598727, Singapore,
1 - Multi-product Pricing Problem Using Experiments
Zhenzhen Yan`, National University of Singapore, Singapore,
Singapore, , Cong Cheng, Karthik Natarajan,
Chung-Piaw Teo
We study the multi-product pricing problem using pricing experiments. In
particular, we develop a data driven approach to this problem using the theory of
marginal distribution. We show that the pricing problem is convex for a large class
of discrete choice models, including the classical logit and nested logit model. Our
model remains convex as long as the marginal distribution is log-concave. More
importantly, by fitting data to optimize the selection of choice model, we develop
an LP based approach to the semi-parametric version of the pricing problem.
Preliminary tests using a set of automobile data show that this approach provides
near optimal solution, even with random coefficient logit model.
2 - Disruption Risk Mitigation In Supply Chains –
The Risk Exposure Index Revisited
Sarah Yini Gao, NUS, 1, Singapore, Singapore,
, Chung-Piaw Teo, David Simchi-Levi
We proposed a new method to integrate probabilistic assessment of disruption
risks into the REI approach, and measure supply chain resiliency by analyzing the
Worst-case CVaR of total lost sales under disruptions. We show that the optimal
emergency inventory positioning strategy in this model can be fully characterized
by a conic program. Moreover, the optimal primal and dual solutions to the conic
program can be used to shed light on comparative statics in the supply chain risk
mitigation problem.
3 - Provably Data-Driven Approximation Schemes For Joint Pricing
And Inventory Control Models
Hanzhang Qin, Massachusetts Institute of Technology, Cambridge,
MA, United States, Davis Simchi-Levi, Li Wang
We propose a data-driven algorithm to solve the joint inventory and pricing
problem for a single-product, multi-period model under independent demand.
Our algorithm provides a near-optimal solution under any degree of accuracy and
pre-specified confidence probability and requires polynomial number of sample
data and is polynomial in the number of time periods. This algorithm differs from
other online data-driven counterparts in the sense that we make all decisions
based on past data only.
SB15