Raviv, Tal, Michal Tzur, and Iris A. Forma
EURO Journal on Transportation and Logistics (2013) Vol 2, Issue 3, pp- 187-229
Used by the Quanticol project
Static repositioning refers to repositioning bikes among stations during night time in order to suit the demand of the next day. In the paper, the authors use a convex penalty function for each station f(Si) to represent the expected number of shortage events for the next day, where Si is the number of bikes in the ith station after reposition. The goal is to minimise w1*(f(S0)+f(S1),…+f(Sn)) + w2*OC, where w1 and w2 and two scale factor, OC refers to the total operation cost.
In their first model of an arc-indexed formulation, the vehicle’s route consists of indexed-arcs between stations, and each station can only be visited once. The vehicle loads on and off some bikes when visiting each station. In their second model of a time-indexed formulation, the time available for repositioning of bikes is discrete into slots of short period. In each time slot, some stations can be visited and repositioning operation can be undertaken in these stations. By doing this, a station can be visited multiple times. Both of the models can be converted to a Mixed Integer Linear Programming problem and solved.