An Improved Proximity Bound for Bike-Dock Reallocation Problem in Bike Sharing System

We consider a class of nonlinear integer programming problems arising from re-allocation of dock-capacity in a bike sharing system. The main aim of this note is to derive an improved proximity bound for the problem and its scaled variant. This makes it possible to refine the time bound for the polynomial-time proximity-scaling algorithm by Freund et al. (2022).