SCENARIOS format

This is the most frequently used format in practice, due to its flexibility, which permits modelling of a variety of dependencies, both within and across time periods. Every scenario is a path from the root of the event tree to one of the leaves. Each scenario branches from a parent scenario and inherits all of its values. Hence the stoch file needs to record only those values that differ from the parent scenario.

We illustrate the use of this format with an asset management problem taken from the text by Birge and Louveaux [1]. A decision maker has to determine the optimal investment levels in various investment opportunities subject to uncertain returns. At predetermined intervals the assets can be redistributed, based on the returns realized to date. The objective is to meet a certain investment goal at the end of the planning horizon; falling short of the financial goal carries a penalty.

The mathematical formulation of this problem is as follows.

where

b is the initial budget,

C is the capital target at the end of the planning horizon,

T is the number of stages considered,

I is the set of investment opportunities,

S_t is the scenario bundle indistinguishable at time t,

s_t+1(s_t) is the set of branches that occur in scenario bundle s_t after time t,

and p_s is the probability of scenario s.

Time file

Core file

Stoch file

MPL file

Reference

[1] J.R. Birge and F. Louveaux, Introduction to Stochastic Programming, Springer Series in Operations Research, Springer Verlag, New York, 1997.