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| 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],
Rainer-Harbach 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 |
|
| Alvarez-Valdes 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 upper-level model minimizes the total penalty cost; the lower-level model minimizes the travel cost | Yes |
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