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?



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