The movable unit equipped with a set of lockers has been recently developed as a new mode to improve the efficiency of the last mile delivery. Locating a set of movable parcel locker units appropriately is a fundamental factor to promote the merits of movable parcel lockers. However, the difficulty in determining where to locate movable parcel locker units arises from the stochastic characteristics of demands. Therefore, we propose a robust optimization approach to determine the number of movable parcel locker units and their locations simultaneously with the aim to minimize the operating cost under stochastic demands and mobility restrictions. To reduce the complexity of the optimization model, the non-linear constraints have been transformed into the linear counterparts, resulting in an integer linear programming (ILP) model that can be solved by commercially available mathematical programming solvers. The results from the numerical examples indicate the proposed approach can obtain high robustness with a small extra cost within reasonable time. In addition, it is found that if each unit is equipped with more lockers, fewer movable parcel locker units are required to accommodate the demands with less operating cost, as the demand points can be clustered into a few intensive self-pickup sites.

In the form of unattended Collection-and-Delivery Points (CDP), the fixed parcel lockers can save courier miles and improve the delivery efficiency. However, due to the fixed location and combination, the fixed parcel locker cannot accommodate the change of demands effectively. In this paper, an approach to supplementing fixed lockers by mobile parcel lockers to meet the demands of the last mile delivery has been proposed. With the goal of minimizing the operating cost, the location and route optimization problems of mobile parcel lockers are integrated into a non-linear integer programming model. An embedded GA has been developed to optimally determine the locations of distribution points, the number of mobile parcel lockers needed by each distribution point and the schedules and routes of mobile parcel lockers, simultaneously. Finally, a numerical example is given to compare the optimization results of the schemes with and without the aggregation problem. The results show that the scheme with the aggregation problem can greatly save the delivery time. However, for the scheme without the aggregation problem, time windows are more continuous, so it saves the number of vehicles.

Parcel lockers have continuously growing in popularity as an alternative mode for last-mile delivery services due to their capability of effectively alleviating the risk of a delivery failure, increasing the possibility of delivery consolidation, and reducing the number of drop-off sites. However, poorly located of parcel lockers be less efficient. When determining the parcel locker location, inadequate consideration of uncertain demands can potentially increase the risk of unsatisfied demands. To remedy this issue, a robust optimization model is proposed in this paper with consideration of the demand uncertainties, including the large and small parcels to be received and sent. Not only can the collection locations be optimally determined, but so can the number of large and small parcel lockers for each location at the same time under various robust levels. Meanwhile, the sites whose demands are covered by one of the collection locations are also determined by the constraints of acceptable walking distance. A series of numerical experiments has been performed to evaluate the proposed model, with the main focus being on the solution robustness. Since the set of non-linear constraints are transformed into the linear counterparts, the robust solution can be obtained by the existing solvers within a reasonable time with moderate computing power. The experimental results also provide useful guidance for the practical application of the method, as slightly more conservative decision making can secure the solution robustness with only a marginal increase in costs.

Urban subway, because of its speed and punctuality, receives considerable popularity and injects great vitality into the city's economic development. However, overcrowding frequently observed in subway carriages during peak hours potentially leads to an increase in accident risk, while there are still some spaces available in buses in some situations. Such imbalance between the two public transits, which was examined based on the load ratios reported for Beijing public transits in a map App, motives us to develop a periodic stop-skipping strategy to shift the excessive demand from subway to bus to alleviate the overloaded situations while to reduce the unwanted influence on the passengers. To achieve such bi-objectives, we propose a non-linear model with consideration of the passengers' choice under the stop-skipping operation. To avoid to exhaustively examine all stop patterns, the stop patterns required to evaluate are identified theoretically. We develop a genetic algorithm to generate the optimal plan, with the triggering mechanism devised to give the priority to the safety objective. With the calibrated choice model, four sets of numerical experiments were performed to evaluate the proposed approach. The results indicate that our approach can effectively alleviate the overcrowding while the efficiency can be increased in some circumstances as the remaining bus capacity is utilized. The optimality and the efficiency of the algorithm and the effectiveness of the triggering mechanism were also verified. The proposed approach can be applied as an effective and economical way to rebalance the peak demand when the bus capacity is surplus.