The shortest I've seen is KGP-HIJ MEMU. When trains were being shifted to Hijli, SER ran a dedicated MEMU between the two stations for FOUR kms only. Needless to say, I have seen the memu go completely empty, mainly because people were either unaware of it and it ran at odd timings[when compared to the timings of the trains that had been shifted to HIJ from KGP].