Articles in a boeing topic on fuel conservation showing the different in operating costs of running APU or GPU Table reproduced below
COSTS PER KWH (33 KW DEMAND LOAD)
TYPE POWER GALS $/GAL. S/KWH
GPU (Diesel) 0.085 0.36 0.03
GPU (Gasoline) 0.197 0.50 0.10
APU. 1.63 0.40 0.65
The APU cost is 6 times more expensive. Note that the operating cost were derived when the fuel price was $0.50/US gal. Today the average price is $2.50/gal
Draw your own conclusions but here the APU is only run when the aircraft is ready for departure and 5 minutes before arrival at the gate