Facility location optimod

[sjk1209]

Why this Mod?

The facility location problem is important in various industries and sectors. It involves determining the optimal locations for facilities such as warehouses, distribution centres, and manufacturing plants. By strategically placing facilities, companies can minimize transportation costs, reduce inventory holding costs, and optimize supply chain operations.

What will the API be?

The input data will be
- facilities: list of facilities
- customers: list of customers
- opening_cost: fixed opening cost of a facility (dictionary)
- capacity: capacity of each facility (dictionary)
- demand: customer demands (dictionary)
- service_cost: cost to serve each customer from each facility (dictionary)

The API will look something like
open_facilities, service_schedule, objective = solve_facility_loc(facilities, customers, opening_cost, capacity, demand, service_cost)

[simonbowly]

Sounds great! Would be good to also discuss with @stevedwards: while the network design model in #36 is quite a different problem, it would be good to make sure the terminology used in documentation is consistent between the two if there is overlap there.

[stevedwards]

I think the network design model is too abstract and having mods be more concrete like this facility location mod could actually be more user-friendly.

[rluce]

Robert Freund (MIT) walked me through an MBA-level class exercise touching facility location. In the example the locations were potential new landfills, connecting homes of the region to them. Two twists we could have generalized in this mod are:

• Fixed number of facilities to be build vs. variable number with fixed-charge costs for each in the objective
• Fairness constraint: Use auxiliary data on the sites to ensure a fairness constraint. In the concrete example it was used to prevent concentration of new landfills in low-income regions.

Moreover we should have examples where different metrics give raise to the cost connecting sites and nodes (e.g., l2 norm on larger geographic distances, l1 norm in urban US areas)