JuMP implementation of "Real-Time Order Fulfillment Decisions"

I was wondering if anyone knew of a JuMP (or any other, really) implementation of this paper:
“Benefits of Reevaluating Real-Time Order Fulfillment Decisions”.

This reformulated version presents the problem of minimizing the number of shipments from multiple warehouses to fulfill an online order as a network flow problem, whereas the original thesis paper had multiple formulations. I’d be interested in any one of them.

This seems to be common problem in eCommerce but my Google searches have so far failed me.

I’m new to optimization and Julia/JuMP, but have a particular project at work that is similar to this set up and JuMP seems to be best way to implement something like that (I normally program in Python).

Thanks for your help!