I’ve diacussed this with a buddy of mine a few years ago. For validation: he is a senior manager at FedEx in Ohio region, dealing with standard delivery (non-rush, overnight, or freight).
The issue with deliveries is more complex as there are several systems with different incentives involves (and managers who bonus is determined by different factors then simply efficient delivery).
1. Deliveries arrive via large container and are organized by postal code but not in any specific order.
Why? Because the plane/truck is packed for maximum haul not maximum efficiency of delivery.
2. When packages are sorted for their destination and packaged onto trucks, the incentive is to maximize haul, not maximize delivery efficiency.
Why? The worker is incentivized to clear the backlog not to organize for delivery method. There are size constraints. As someone commented further down, it’s like a game of Tetris.
3. The delivery person just has to deal with what’s given and has to complete three rounds (usually).
In a normal situation, my buddy used some “fun math” and an excel sheet to attempt to maximize deliveries. Theoretically, his system would save an average of $0.02 on each package (his calculation, have no clue how he came up with this number or can verify). He was given recognition and bonus as, supposedly, this was a huge feat. However, his system totally broke down during holidays/peak season; There was no way to organize packages in step one accuretly enought that translates to step 2 and 3.
I, as a novice, suggested something like: “why don’t they use robots to sort, scan, and organize packages?” He patiently explained that the cost to retrofit all delivery stations would be enormous. The delivery margin on standard packages are razor thin and would require too much time to recoup and that any advancements went to the “big boys” (freight and overnight) as they generate the most profit).
As such, any suggestion that this is an easy problem that can be solved by some math is obtuse. The system itself would have to be redesigned at a large scale and proven to work prior to testing as any error would cut profits that investors do not like.