In my production planning problem, I want to select around 1000 items from a set of 15000 items to process in a given day. There are multiple constraints to satisfy and new items come in every day. It’s very much like a multi-dimensional knapsack problem with some extra constraints.
Each item has its own identifier and they are truly unique items. But they can be grouped for practical purposes so that (let’s say) 10 items could be represented by a single value and set of multi-dimensional costs.
I’d like to know whether it’s generally better for a MIP solver to represent selection of items by ten 0/1 decision variables or one integer decision variable that must be < 11 for ten items in a group. I know if I use the ten variables I’d also need to do something to break symmetry of solutions – like maybe add a term to minimize items IDs in the objective function.
I’d appreciate any thoughts or pointers to good resources on this. Thanks.
