Table 1: Summary of the static BRP in the literature.

ReferencesNumber of trucksObjectivesPickup and dropoff quantities as decision variables

Benchimol et al. [3]1Minimize total travel costNo

Cruz et al. [4]1Minimize route costNo

Lin and Chou [5]≥1Minimize total transportation time or distanceNo

Di Gaspero et al. [6, 7], Raidl et al.[8], 
Rainer-Harbach et al. [9, 10]
≥1Minimize the weighted sum of the total absolute deviation from the target number of bikes, the total number of loading/unloading quantities, and the overall time required for all routesYes

Di Gaspero et al. [11]≥1Minimize the weighted sum of the total absolute deviation from the target number of bikes, and the travel timesYes

Angeloudis et al. [12]≥1Minimize total travel timeYes

Dell’Amico et al. [13, 14]≥1Minimize total route costNo

Forma et al. [15]≥1Minimize the weighted sum of the penalty cost and total travel timeYes

Alvarez-Valdes et al. [16]≥1Minimize the weighted sum of the total service time and the coefficient of variations of the duration of all routesYes

Ho and Szeto [17]≥1Minimize the weighted sum of the penalty cost and total travel timeYes

Schuijbroek et al. [18]≥1Minimize maximum tour lengthYes

Pal and Zhang [19]≥1Minimize the makespan of the rebalancing fleet (maximum tour length)No

Bulhões et al. [20]≥1Minimize total route costNo

Szeto and Shui [21]≥1Minimize first the positive deviation from the tolerance of total demand dissatisfaction and then service time in the form of the total service time or maximum service time of all vehiclesYes

Liu et al. [22]≥1Minimize the weighted sum of the total number of unsatisfied customers, the inconvenience of getting a bike and total operational timeYes

Chemla et al. [23]1Minimize route costNo

Nair et al. [24]1Minimize total redistribution costYes

Erdoğan et al. [25]1Minimize total route and handling costYes

Ho and Szeto [26]1Minimize total penalty costYes

Erdoğan et al. [27]1Minimize route costNo

Kadri et al. [28]1Minimize the total waiting time of the imbalanced stationsNo

Li et al. [29]1Minimize the sum of travel, imbalance, substitution, and occupancy costsYes

Szeto et al. [30]1Minimize the weighted sum of the total number of unsatisfied customers and the vehicle’s total operational timeYes

This paper1The upper-level model minimizes the total penalty cost; the lower-level model minimizes the travel costYes