Spring School on
Stochastic Optimization

March 2 - May 26, 2001

Department of Mathematics,
University of Coimbra, Coimbra, Portugal,
sponsored by
Centro de Matemática da Universidade de Coimbra (CMUC)
Porto Editora, Lda.

Speaker:
Dennis Bricker
University of Iowa

Web page of the course with more information.
APL Software for Stochastic Optimization.


The school will consist of a series of two-day (and five-hour) lectures every other week, namely, on friday afternoons and saturday mornings. Professor Bricker plans to lecture an innovative course on stochastic programming of potential interest to mathematicians, economists and engineers, especially to doctoral students and post-docs. The school will introduce research topics in stochastic programming and will propose research problems at a variety of levels to be worked out between classes.

More precisely, the school will introduce the student to various models, applications and computational algorithms for optimal decision-making when the available information is incomplete or when actions must be selected before the occurrence of random events. Models include optimization with multistage linear programming with recourse, stochastic dynamic programming, and Markov decision processes. Discussion of successful applications in various areas, such as production scheduling, financial planning and portfolio management, agriculture, forest and fishery harvest management, hydropower and water resources, and transportation.

The school will be held at room Pedro Nunes every scheduled Friday from 4pm to 7pm, and every scheduled Saturday from 10am to 12pm. The school will meet in the following days:

March 2-3     16-17     30-31
April 20-21
May 18-19     25-26

The school will award a diploma by the last lecture.


References:

Ross, S. M. (1983). Introduction to Stochastic Dynamic Programming. New York: Academic Press.

Tijms, H. C. (1994). Stochastic Models: An Algorithmic Approach. Chichester: John Wiley & Sons.

Birge, R. and F. Louveaux (1997). Introduction to Stochastic Programming. New York: Springer-Verlag.

Various materials available in journals and on the WWW.

Accommodation:
For the accommodation on Friday nights at reduced prices, a list of some nearby hotels may be found in http://www.mat.uc.pt/~cita2001/accommodation.html. Participants are advised to choose Residencial Botânico (Phone: 239 714 824, Fax: 239 405 124) for its location. Hotel reservations should be made directly to the hotels.


Registration:
Participants should preregister to the school (deadline is March 1st, 2001). School enrollment is very limited. There is a symbolic registration fee of 15000 PTE that includes coffee breaks and six dinners. Payment is due at the first day of classes. To preregister, participants should send name, institution, position, phone number and email to rute@mat.uc.pt mentioning 'preregistration in spring school' in the subject. For further information please contact


Rute Andrade rute@mat.uc.pt
Mathematics Department Phone: 239 791144
University of Coimbra              Fax: 239 832568
3001-454 Coimbra - Portugal


Organizing Committee:
João L. Soares (chair), Ernesto Martins, and Luís N. Vicente


Outline:

  1. Preliminaries: Stochastic Processes; Discrete-time Markov Chains; Decision analysis & decision trees

  2. Finite-stage Dynamic Programming (DP): Deterministic DP; Stochastic DP; Applications

  3. Markov Decision Problems (Infinite-stage DP)

    1. Models: Minimization of average cost/stage in steady state; Minimization of discounted (present value) future costs
    2. Algorithms: LP algorithm; Policy iteration method; Value iteration method
    3. Applications

  4. Two-stage Stochastic linear programming (SLP) with recourse

    1. Decomposition methods

      1. Benders' decomposition ("L-shaped") method
      2. Lagrangian relaxation & duality
      3. Cross-decomposition method

    2. Approximation and random sampling of scenarios
    3. Applications

  5. Extensions of two-stage stochastic LP

    1. Stochastic integer LP (discrete first-stage decisions)
    2. N-stage stochastic LP