Search

This paper presents a sequence of models for optimal overnight charging and rebalancing of shared electric scooters (e-scooters) by allowing e-scooters to be charged while being transported on rebalancing vehicles. This problem is first modeled as a mixed-integer program for the multi-commodity inventory routing problem, where commodities represent e-scooters with different states of charge. To avoid prohibitive computation burden, continuous approximation techniques are proposed to estimate costs associated with the pickup and drop-off operations in small local neighborhoods, and the formulation turns into a discrete-continuous hybrid model for the integrated operations at both local and line-haul levels. A series of numerical experiments are conducted to demonstrate that, as compared to direct application of the discrete formulation, the proposed hybrid approach can produce good quality solutions for large-scale instances in a much shorter computation time.

In this paper, we analyze the route efficiency trade-offs that emerge from combining first-mile pickup and last-mile delivery operations in an urban distribution system. We build on the extant literature on continuum approximation of optimal route distances and propose adjustment factors that account for the effects of integrated pickup and delivery operations. By means of comprehensive numerical experiments and regression analysis, we further propose a set of closed-form adjustment factors that improve existing continuum approximation-based route length estimations. These adjustment factors incorporate some non-trivial route efficiency trade-offs emerging from first-mile and last-mile integration that cannot easily be captured through continuum approximation. The proposed extensions are particularly relevant for the optimal strategic design and operational planning of large-scale, high-density last-mile distribution systems that are gaining in importance in light of e-commerce and omni-channel retailing. Our analyses suggest that the efficiency gains emerging from integrating first-mile pickup and last-mile delivery operations can be as high as 30%. However, the effective efficiency gains are sensitive to vehicle capacity constraints and other factors complicating the optimal stop sequence in integrated routes. We apply our proposed method to a real-world case study informed by operational data from one of India’s largest e-commerce platforms for the city of Bengaluru. We find that by properly integrating its first-mile and last-mile operations, the company could reduce its urban traffic and emissions impact by up to 16%, while increasing the asset utilization and reducing the cost of operations of its vehicle fleet.

Cooperation is a powerful strategy to achieve the objective of the green pickup and delivery problem (GPDP) that minimizes carbon emissions of pickup and delivery service. However, the cooperative GPDP may not be accepted by all the partners, as the cost of cooperative GPDP may be higher than that of the non-cooperative minimum cost PDP. Therefore, a reasonable compensation mechanism is desired to form an acceptable cooperative GPDP, and a fair method of profit distribution, based on the mechanism, is needed to stabilize the cooperation. In this paper, we analyze the situations in which a compensation is needed and develop the lower bound of the compensation. Further, we propose an exact method to calculate the actual compensation and the profit distribution based on cooperative game theory. The proposed exact method can efficiently solve the largest scale instance in Li & Lim benchmarks, i.e., pdptw1000-LR1_10_1 with 1,054 customers and 19,306 products. The proposed compensation and profit distribution mechanism based on cooperative game theory is also applied to a real-world GPDP and achieve satisfactory performance. Some interesting and important managerial insights are found and discussed.

The one-commodity pickup and delivery problem (1-PDP) has a wide range of applications in the real world, e.g., for repositioning bikes in large cities to guarantee the sustainable operations of bike-sharing systems. It remains a challenge, however, to solve the problem for large-scale instances. This paper proposes a hybrid modeling framework for 1-PDP, where a continuum approximation (CA) approach is used to model internal pickup and delivery routing within each of multiple subregions, while matching of net surplus or deficit of the commodity out of these subregions is addressed in a discrete model with a reduced problem size. The interdependent local routing and system-level matching decisions are made simultaneously, and a Lagrangian relaxation based algorithm is developed to solve the hybrid model. A series of numerical experiments are conducted to show that the hybrid model is able to produce a good solution for large-scale instances in a short computation time.

The dynamic Pickup and Delivery Problem with Time Windows (PDPTW) is faced by courier companies serving same-day pickup and delivery requests for the transport of letters and small parcels. This article focuses on the dynamic PDPTW for which future requests are not stochastically modelled or predicted. The standard solution methodology for the dynamic PDPTW is the use of a rolling time horizon as proposed by Psaraftis. When assigning a new request to a vehicle it may be preferable to consider the impact of a decision both on a short-term and on a long-term horizon. In particular, better managing slack time in the distant future may help reduce routing cost. This paper describes double-horizon based heuristics for the dynamic PDPTW. Computational results show the advantage of using a double-horizon in conjunction with insertion and improvement heuristics.

The dynamic pickup and delivery problem with time windows arises in courier companies making same-day pickup and delivery of letters and small parcels. In this problem solution quality is affected by the way waiting time is distributed along vehicle routes. This article defines and compares four waiting strategies. An extensive empirical study is carried out on instances generated using real-life data.

This paper describes a solution method for a multiple traveling salesman problem with time window constraints (m-TSPTW). The method was developed for local truckload pickup and delivery problems such as those supporting rail or maritime intermodal operations but is suitable for application in other problems in which the number of tasks assigned to each server at any time is relatively small. We present a model and describe an iterative solution technique in which explicit time constraints are replaced by binary flow variables. At each iteration two versions of the problem, one over-constrained and the other under-constrained are solved. The solution to the over-constrained problem provides a feasible solution, while the optimality gap provided by the two solutions informs the decision of whether to continue searching or to implement the best solution found so far. A specific time window partitioning scheme is used to ensure that the cost of solutions found are monotonically non-increasing. The method developed is suitable for real-time or quasi real-time implementation.

The pickup and delivery problem with time windows requires that a group of vehicles satisfy a collection of customer requests. Each customer request requires the use of a single vehicle both to load a specified amount of goods at one location and to deliver them to another location. All requests must be performed without violating either the vehicle capacity or the customer time window stipulated at each location. In this paper, we present a reactive tabu search approach to solve the pickup and delivery problem with time windows using three distinct move neighborhoods that capitalize on the dominance of the precedence and coupling constraints. A hierarchical search methodology is used to dynamically alternate between neighborhoods in order to negotiate different regions of the solution space and adjust search trajectories. In order to validate our technique's effectiveness, we have constructed a new set of benchmark problems for the pickup and delivery problem with time windows based on Solomon's benchmark vehicle routing problem with time windows data sets. Computational results substantiate the solution quality and efficiency of our reactive tabu search approach.