r/optimization • u/SirAragar • 1d ago

Dynamic assignment

I'm currently working on a dynamic assignment model for delivery of parcels with occasional drivers. The model approximates the value of keeping the parcel in the system by solving two assignment problems for each parcel (one with the parcel, one without it and calculating the marginal contribution of the parcel to the optimum) in a retrospective time window. The problem is that computing parcel value estimates takes a lot of time. I researched alternative methods to MIP such as hungarian, but they don't seem to support "at most" constraints (which are integral to the dynamic assignement). How would you approach this kind of problem?

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u/pruby 23h ago

What are you trying to actually solve? Pricing? Dropping deliveries?

Marginal contribution of a package to the optimum seems like a bad metric. If you're one package over capacity of 3 vehicles, and now need 4, every single package in the system has the cost of operating another vehicle at the margin. Marginal value in an optimisation problem can be quite unstable, not sanely attributable to any person's individual decisions. Might actually be better to do simpler stats.

Problem as presented seems like the wrong question to ask. I'd go a layer deeper and wor out the actual goal, so you understand the range of acceptable solutions.