I have an optimization model to fulfill the water requirements of a city’s distribution network. The model includes water sources from rainfall collection, river extraction, reservoir storage, and external supply. I need the model to prioritize the order of water sources to meet the demand: first from rainfall collection, then from river extraction, then from reservoir storage, and finally from external supply.

We have modelled it as such:
I am trying to solve a problem in which I have 4 variables: x1 (rainfall collection), x2 (river extraction), x3_t (reservoir storage drained), and x4_t (external supply). x_1 and x_2 can only be chosen once across all timestamps.

I need
x1+ x2 + x3_t + x4_t >= c_t, where t is the current timestamp

We also have x3_t < 100

I basically want to encode:

if x1 + x2 + x3_t >= c_t:
x4_t = 0

How can I enforce that I drain the reservoir storage as much as possible, and only once its drained, do I use the external supply if there’s any remaining demand?

We tried an attempt at big M, but we were quite confused how to make it work for this problem.