  This paper investigates a specific instance of the static repositioning
problem within station-based bike-sharing systems. Our study incorporates
operational and damaged bikes, a heterogeneous fleet, and multiple visits
between stations and the depot. The objective is to minimize the weighted sum
of the deviation from the target number of bikes for each station, the number
of damaged bikes not removed, and the total time used by vehicles. To solve
this problem, we propose a matheuristic approach based on a randomized
multi-start algorithm integrated with an integer programming model for
optimizing the number of operatives and damaged bikes that will be moved
between stations and/or the depot (loading instructions). The algorithm's
effectiveness was assessed using instances derived from real-world data,
yielding encouraging results. Furthermore, we adapted our algorithm to a
simpler problem studied in the literature, achieving competitive outcomes
compared to other existing methods. The experimental results in both scenarios
demonstrate that this algorithm can generate high-quality solutions within a
short computational time.
