I'm a software dev that's pretty new to OR and want to solve a specific problem I came across at my job. From what I've researched it is a variation of resource-constrained assignment problem, but with variety of those problems it's quite hard for me to confirm.
I have n jobs that need to be assigned to m production facilities:
- only some of those facilities are viable locations for producing
- some (but not all) products are stock constrained
- cost of producing those is variable and depends on number of jobs assigned to that location (edit: for 1-10 items unit cost would \$10, for 10-100 \$9 etc. and it would differ between production houses)
- number of jobs assigned should be between min-max for that location (but might be exceeded either way if no feasible solution found).
There are multiple objectives depending on other factors, but I should be able to get it down to a single number by using weights.
I've found different papers that deal with RCAP, but what I struggle to understand is how to incorporate constraint 3 into any LP model or any other of those solutions. Additionally in "Model Building in Mathematical Programming" I've read that LP is not that good for those kinds of problems as it multiplies variables very fast and specialized algorithms work better, but I struggle to find one that fits my needs.
Is local search options a better solution for real-world application? I've looked into OptaPlanner, but it seems like a too-good-to-be-true solution and I'd rather explore all different options before committing to one. What approaches/problems/tools would you suggest I read up on?
In my case, I'd need to deal with up to 100 production houses and up to 10000 orders.