INDEP format

The INDEP format is used to build an event tree implicitly from one-dimensional marginal information. We illustrate the format using two versions of a power generation model first employed by Louveaux and Smeers[2]. A decision maker has to decide on the capacities x_i of a number of technologies for the generation of power and has to operate the resulting facility so as to satisfy uncertain demand. Mathematically this can be formulated as follows:

where x_i represents the installed capacity using technology i,

y_ijs is the demand satisfied from power station i at node j under scenario s,

z_is is the production shortfall at power station i under scenario s,

c_i is the unit expansion cost at station i,

t_ij is the unit allocation cost from power station i to demand node j,

M is a penalty cost for production shortfall,

p_s is the probability of scenario s,

h is the minimum total production capacity of the system,

B is the budget available for expansion,

d_js is the demand at demand node j under scenario s.

We use data that have been slightly modified from the original source and were taken from Higle and Sen[1].

BLOCKS format

Multidimensional marginals can be handled similarly to model distributions with intrastage dependencies, but independence between stages. The time file and core file are the same, only the stoch file needs to be adjusted.

Time file

Core file

Stoch file (Discrete distributions)

Stoch file (Continuous distributions)

Stoch file (BLOCKS format)

References

1. J.L. Higle and S. Sen, Stochastic Decomposition: A Statistical Method for Large Scale Stochastic Linear Programming, Kluwer Academic Publishers, Dordrecht–Boston–London, 1996.

2. F.V. Louveaux and Y. Smeers, “Optimal investments for electricity generation: A stochastic model and a test problem”, in: Yu. Ermoliev and R.J-B Wets (eds.), Numerical Techniques for Stochastic Optimization, Springer Verlag, Berlin–New York–London, 1988.