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Stochastic Programming


Prof. Ntaimo

Data e luogo


6/02/12 ore 11:00-13:00  e 15:00 - 17:00 Aula T024

9/02/12 ore 11:30-13:30 e 15:00 - 17:00 Aula T024

13/02/12 ore 11:00-13:00 e 15:00 - 17:00 Sala Seminari

17/02/12 ore 11:00-13:00  e 15:00 - 17:00 Aula T024

29/02/12 ore 11:00-13:00 e 15:00 - 17:00 Aula T024

05/03/12 ore 11:00-13:00 e 15:00 - 17:00  Aula T024

Motivazioni e obiettivi



Course Description and Objectives

This is an introductory course to stochastic programming (SP). The field of SP is currently developing rapidly with contributions from many disciplines such as operations research, mathematics, and probability. SP has a wide range of applications especially in science and engineering such as manufacturing, transportation, telecommunications, facility location, electricity power generation, health care, etc. The aim of the course is to introduce students to optimal decision-making problems with data uncertainty. The course will cover basic theory and decomposition methods, and will give an overview of selected applications. Emphasis will be placed on both theory and algorithm implementation.This is a first course in SP and is suitable for students with knowledge of linear programming (LP), elementary analysis, probability, and computer programming. This course has a research level orientation and as such, students will be required to review literature on SP.





Topics Covered:



1. Introduction            to SP                                                                          

2. SP Models and Applications                                                                     

3. Deterministic Large-Scale Decomposition Methods                                 

4. Stochastic Linear Programming Methods                                      

5. Computational Experimentation                                                   




Detailed Topical Outline:



1. Introduction

1.1 Decision-making in an uncertain world

      1.1.1 Applications

      1.1.2 Decision stagesand decision trees

      1.1.3 Decision models

1.2 Probability spaces and random variables

1.3 Numerical example: From LP to SP

Class-notes, Chapters1-2 in Birge and Louveaux, 1997.


2. SP Models and Applications

2.1 Recourse models and chance-constrained models

2.2 Applications

                 2.2.1 Facility location under uncertainty

  • Facility location in an aging society
  • Nursing home location

                 2.2.2 Transportation problems under uncertainty

  • Bus/shuttle scheduling for the elderly

Class notes; Chapter 3in Birge and Louveaux, 1997; Chapter 1 in Ruszczynski and Shapiro, 2003.


3. Deterministic Large-Scale Decomposition Methods

3.1 Basic theory - convexity, separation, convergence

3.2 Benders decomposition

3.3 Regularized Benders

3.4 Dantzig-Wolfe decomposition

            Class-notes, Chapters10-11 in Martin, 1999


4. Stochastic Linear Programming Methods

4.1 The L-shaped method

4.2 Multi-cut L-shaped method

4.3 Regularized L-shaped method

Class-notes, Chapter 5 in Birge and Louveaux, 1997; Chapter 3 in Ruszczynski and Shapiro, 2003.


5. Computational Experimentation

5.1 Empirical testing

5.2 SMPS format, sparse matrix representation, etc.

5.3 Introduction to the CPLEX Callable Library


Modalità di svolgimento
Modalità d'esame
Materiale didattico



No course textbook is required. Course notes will be provided by the instructor.



Birge, J.R. and F. Louveaux, Introduction to Stochastic Programming, 1st Edition, DuxburyPress, Belmont, CA, 2003. ISBN 0 534 35964 7.

Martin,R.K. Large Scale Linear and Integer Optimization: A Unified Approach, Kluwer, 1999.

Ruszczynski, A. and A. Shapiro (Eds.), Stochastic Programming.Handbooks in OperationsResearch and Management Science Volume 10. New York, NY, 2003. ISBN 0 444 50854 6

ILOG CPLEX 11.0, User’s Manual and Reference Manual, ILOG, S.A., 2005,

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20126 Milano - Edificio U14 - ultimo aggiornamento di questa pagina 02/05/2012