# Scenario Tree Construction in Multi-Stage Stochastic Programming

I gonna use the approach used in this document. Suppose there are $$T$$ stages and uncertain parameter is $$\xi_{t}, \quad t \in \{1,2,\dots,T\}$$. In this algorithm, it is required to calculate the distance between two scenarios $$\xi^s$$ and $$\xi^{s^{\prime}}$$ which is $$C_t = \sum_{\tau=1}^{t}|\xi_{\tau}^s-\xi_{\tau}^{s^{\prime}}|$$ and two scenarios are joined if this distance is small. In this model, I think it is assumed that $$\xi_t \in R$$. I am wondering what I should do if $$\xi$$ is multi-dimensional? For example, $$\xi_{ijt}$$ represents the demand of customer $$i$$ for product $$j$$ at time $$t$$. In this case, the distance between two scenarios will be $$C_t = \sum_{\tau=1}^{t} \sum_{i=1}^{I} \sum_{j=1}^{J} |\xi_{ij\tau}^s-\xi_{ij\tau}^{s^{\prime}}|$$

It is obvious that if the dimension of uncertain parameter increases, $$C_t$$ increases and it is less likely to be able to merge two scenarios. It issue will be more problematic if the dimension of uncertain parameter increases. I would be thankful if you can let me know, how I should handle it.

There is a package for this purpose in GAMS. Can I know if there is any code in other software or programming languages?

In general, is there any package for scenario tree construction?