Technical Sessions – Monday July 11

HC-10 IFORS 2011 - Melbourne
� HC-10
Thursday, 13:30-15:00
Meeting Room 111
Computational Developments in Stochastic
Programming
Stream: Stochastic Programming
Invited session
Chair: Miguel Lejeune, Decision Sciences, George Washington
University, 2201 G Street, NW, 20052, Washington, DC, United
States, mlejeune@gwu.edu
1 - Computations with Fenchel Decomposition for
Stochastic Integer Programming
Lewis Ntaimo, Industrial & Systems Engineering, Texas A&M
University, 3131 TAMU, 77843, College Station, TX, United
States, ntaimo@tamu.edu
We present the computational performance of the Fenchel decomposition (FD)
method for two-stage stochastic integer programs. FD is a cutting plane method
based on Fenchel cutting planes. In this talk, we report on two implementations
of the FD method: one based on cuts derived using both first- and second-stage
variables, and the other based only on the second-stage variables. Computational
results with instances from the literature demonstrating the comparative
performance of the FD method to disjunctive decomposition (D2) and a direct
solver will be presented.
2 - Stochastic Network Design for Disaster Preparedness
Xing Hong, Engineering Management & Systems Engineering,
The George Washington University, United States,
xhong@gwmail.gwu.edu, Miguel Lejeune, Nilay Noyan
We propose a method enabling to prepare commodities for disasters affected areas.
The problem is formulated as a probabilistically constrained model which
determines the inventory levels of commodities and the transportation capacities.
A pre-processing method is used to simplify the probabilistic constraint,
and then the obtained problem is solved with a pattern-based method, which
permits to characterize the demand uncertainty finely and solve the problem
efficiently. Our model is applied to the risk of hurricanes in the Southeastern
US region and the risk of earthquakes in the Seattle area.
3 - Dynamic Probabilistic Lot-Sizing with Service Level
Constraints
Simge Kucukyavuz, Ohio State University, 43210, Columbus,
OH, United States, kucukyavuz.2@osu.edu, Saumya Goel
We consider a dynamic probabilistic lot-sizing problem with a type-I service
level constraint. We assume that the distribution of the random demand over
the planning horizon is non-stationary and has finite support. We formulate this
problem as a multi-stage chance-constrained program and develop a branchand-cut
method for its solution. We present computational results to show the
effectiveness of the proposed method.
4 - Game Theoretical Approach for Reliable Enhanced Indexation
Miguel Lejeune, Decision Sciences, George Washington
University, 2201 G Street, NW, 20052, Washington, DC, United
States, mlejeune@gwu.edu
We propose a game theoretical model to construct an enhanced indexation
model. The goal is to maximize the excess return that can be attained with
high probability, while ensuring that the relative risk does not exceed a given
threshold. The asset returns are characterized by a joint discrete probability
distribution. To hedge against the estimation risk, we consider that only limited
information about the probability distribution of the index return is available.
We show that the game theoretical model can be recast as a convex programming
problem, and present numerical results.
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� HC-11
Thursday, 13:30-15:00
Meeting Room 112
Knapsack, Assignment Problems
Stream: Integer Programming
Invited session
Chair: Takuro Hidaka, Department of Information and System
Engineering, Chuo University, Kasuga, Bunkyo-ku, 112-8551,
Tokyo, Japan, taku_hidaka@yahoo.co.jp
1 - A Branch-and-bound Procedure for the Precedenceconstrained
Knapsack Problem
Byungjun You, Computer Science, National Defense Academy
of Japan, 1-10-20 Hasirimizu, 239-8686, Yokosuka, Kanagawa,
Japan, g48095@nda.ac.jp, Takeo Yamada
The knapsack problem (KP) is generalized to the case where items are partially
ordered through a set of precedence relations. Each item can be accepted only
when all the preceding items have been included in the knapsack. The knapsack
problem with these additional constraints is referred to as the precedenceconstrained
knapsack problem (PCKP). To solve PCKP exactly, we present a
branch-and-bound procedure based on the "tree KP relaxation’. Computational
experiments on a series of instances demonstrate advantage of our method over
commercial MIP solvers.
2 - Two Pegging Tests for the Assignment Problem with
Multiple Constraints
Takeo Yamada, Computer Science, National Defense Academy,
1-10-20 Hashirimizu, 239 8686, Yokosuka, Kanagawa, Japan,
yamada@nda.ac.jp
We present soft and hard pegging tests to reduce the size of the assignment
problem with multiple constraints (MCAP). To apply the pegging test
to MCAP, we need to have the simplex tableau in optimality, and for large instances
this is often beyond the computer capacity. We avoid this difficulty by
introducing the Lagrangian relaxation, before applying the pegging test. Moreover,
we present a ‘hard’ pegging approach to the resulting assignment problem,
as opposed to the standard ‘soft’ pegging where the thresholds are only
approximately computed.
3 - Metaheuristic Approach for Task Assignment with Dynamic
Durations
Markus Günther, Department of Business Administration and
Economics, Bielefeld University, Universitaetsstr. 25, 33615,
Bielefeld, Germany, markus.guenther@univie.ac.at, Verena
Schmid
We consider a problem typically faced by companies operating in a multinational
environment. Given different project characteristics and hand-over efforts
we investigate the assignment of tasks to geographically dispersed employees.
Geographic and cognitive distance among employees determines
hand-over times between tasks. Their duration depends on the skill levels
in various domains of the assigned employee. Depending on previously performed
tasks their skill levels may change over time. We propose a mixed integer
problem formulation which will be solved using Variable Neighborhood
Search.
4 - Inverse Assignment Model for Class Scheduling Problem
in Tutoring School
Takuro Hidaka, Department of Information and System
Engineering, Chuo University, Kasuga, Bunkyo-ku, 112-8551,
Tokyo, Japan, taku_hidaka@yahoo.co.jp, Tomomi Matsui
We consider a problem for constructing a class schedule of a tutoring school.
Given sets of students and teachers, we need to assign each student to a teacher.
The problem finds an assignment which maximizes the sum of fitness of selected
student-teacher pairs. When we use the assignment model, we need to
determine a value of fitness for each student-teacher pair. We propose an inverse
optimization model for finding fitness values which accommodate to real
schedule data used in a tutoring school. We show that our inverse optimization
problem becomes to a linear programming problem.