
References  Number of trucks  Objectives  Pickup and dropoff quantities as decision variables 

Benchimol et al. [3]  1  Minimize total travel cost  No 

Cruz et al. [4]  1  Minimize route cost  No 

Lin and Chou [5]  ≥1  Minimize total transportation time or distance  No 

Di Gaspero et al. [6, 7], Raidl et al.[8], RainerHarbach et al. [9, 10]  ≥1  Minimize 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 routes  Yes 

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

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

Dell’Amico et al. [13, 14]  ≥1  Minimize total route cost  No 

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

AlvarezValdes et al. [16]  ≥1  Minimize the weighted sum of the total service time and the coefficient of variations of the duration of all routes  Yes 

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

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

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

Bulhões et al. [20]  ≥1  Minimize total route cost  No 

Szeto and Shui [21]  ≥1  Minimize 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 vehicles  Yes 

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

Chemla et al. [23]  1  Minimize route cost  No 

Nair et al. [24]  1  Minimize total redistribution cost  Yes 

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

Ho and Szeto [26]  1  Minimize total penalty cost  Yes 

Erdoğan et al. [27]  1  Minimize route cost  No 

Kadri et al. [28]  1  Minimize the total waiting time of the imbalanced stations  No 

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

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

This paper  1  The upperlevel model minimizes the total penalty cost; the lowerlevel model minimizes the travel cost  Yes 
