I am implementing a solution for packages consolidation (basing on Nurse Problem solution) with OR-Tools CP Solver.
There is a factory that manufactures some small Packages that need to be transported by post to the customers. It would be optimal to consolidate some mini_Packages into bigger Packages (for example if we respect total weight limit, we can merge 3 light mini_Packages into one Package and pay transport costs once not 3 times).
Mini_Packages have some important attributes in data source (fixed destination, weight, acceptable delivery date range).
My main 0-1 integer variable looks like:
x[mini_package_number, optimal_shipment_date, package_number]
It == 1 if mini_Package should be send on a certain day, consolidated to a certain Package_number.
A mini_Package represents a single product item. Name of the product is an attribute of mini_Package, given in a certain list (position on the list = mini_Package_number).
products = [34, 12, 12, 456 ...]
mini_Package 0 contains product 34
mini_Package 1 contains product 12
mini_Package 2 also contains product 12
There are some products that cannot be merged together. If a mini_Packages represent a certain product it cannot be merged (to the same Package) with another mini_Package that represents conflicting product.
The format of conflict matrix can be adjusted for the model.
At the moment I plan following format:
conflict_list = [(1,3), (3,6), (5,19)]
product 1 and 3 cannot go together
product 3 and 6 cannot go together
product 5 and 19 cannot go together
Conflict list represents mutually exclusive pairs, however it is important that final Package may merge more products (for example four mini_Packages with non-conflicting products 1, 1, 2, 6).
Do you have any ideas how such a logic could be implemented?