Lifts in tall buildings tend to be very energy efficient. This is because the design involves installing massive counterweights which move downwards when a lift compartment is moving upwards.
Today’s invention involves replacing the counterweight with another lift. Joined by a cable, the itinerary of one lift would therefore be the complement of the other ie in a 100 floor building, lift 1: 1->2->4->60 lift 2: 99->98->96->40.
These rolling itineraries would be displayed near each lift door so that people would have an extra choice of waiting for the next one moving in their preferred direction or grabbing the additional lift.
An even smarter system would allow travellers to enter their destination floor at the keypad and then calculate what their best option was (possibly also taking into account the widespread psychological preference for moving, anywhere, rather than waiting -and also the possibility of approximation: taking the lift to within a stair-walkable distance of their target floor).