Pickup and Multi-delivery Problem with Time Windows

The pickup and delivery problem with time windows (PDPTW) is an NP-hard discrete optimization problem of serving transportation requests using a fleet of homogeneous trucks. Its main objective is to minimize the number of vehicles, and the secondary objective is to minimize the distance traveled during the service. In this paper, we propose the longest common subsequence based selective route exchange crossover (LCS-SREX), and apply this operator in the memetic algorithm (MA) for the PDPTW. Also, we suggest the new solution representation which helps handle the crossover efficiently. Extensive experimental study performed on the benchmark set showed that using LCS-SREX leads to very high-quality feasible solutions. The analysis is backed with the statistical tests to verify the importance of the elaborated results. Finally, we report one new world’s best routing schedule found using a parallel version of the MA exploiting LCS-SREX.

This study investigates a new variant of the pickup and delivery problem with time windows (PDPTW) applied in cold chain transportation, which quantifies the effect of time on the quality of perishable products. Multiple commodities with incompatibility constraints are considered, where some types of products cannot be transported in a vehicle simultaneously because of their different properties and requirements for storage temperatures. The aim is to determine vehicles’ pickup and delivery routes as well as their departure times from the depot such that the travel cost and refrigeration cost of vehicles and the quality decay cost of products are minimized. We formulate this problem as a set partitioning model, which is solved exactly by a tailored branch-and-price (B&P) algorithm. To tackle the asymmetry issue arising from the pricing problem of the B&P framework, we develop a novel asymmetric bidirectional labeling algorithm. Benchmark instance sets based on real-world statistical data and classic PDPTW instance sets are first generated for this problem. Numerical results show that our B&P algorithm can solve most instances to optimality in an acceptable time frame. Moreover, our results demonstrate that integrating the refrigeration and quality decay costs into the objective function can significantly lower the total cost of cold chain transportation activities, compared with the widely adopted objective function minimizing only the travel cost. Funding: This work was supported by the National Key R&D Program of China [Grant 2018YFB1700600] and the National Natural Science Foundation of China [Grants 72101049, 71971090, 71821001]. Supplemental Material: The online supplement is available at https://doi.org/10.1287/trsc.2022.1167 .

This paper presents a generic two-stage optimization model and a simulation framework for on-demand grocery delivery. The proposed simulation framework can be used to reproduce any historical day's behaviour or evaluating various what-if scenarios. The two-stage optimization model's objective is to minimize the Cost Per Delivery (CPD) and maximize Customer Experience (CX). In the first stage, Last-Mile (LM) delivery optimization is modelled as a Pickup and Delivery Problem with Time Windows (PDPTW). Both static and dynamic variants of the PDPTW model are tried out and compared to their performances. A Just-In-Time (JIT) heuristic is integrated with PDPTW to minimize waiting time. The second stage solves the First-Mile (FM) delivery optimization using a multi-objective assignment model for trading off between the CPD and CX. The proposed framework is simulated with actual order data and it was found that the the dynamic PDPTW model results in significant savings in CPD while maintaining a good CX.

In this paper we present a parallel solver for the vehicle routing problem with time windows (VRPTW) and the pickup and delivery problem with time windows (PDPTW). The solver is based on parallel competition of particular solvers solving the given problem instance. The particular solvers are based on negotiation between a fleet of agents representing individual vehicles using a cost structure corresponding to the wellknown travel time savings insertion heuristic. The performance of the solver is assessed on the Homberger-Gehring and Li-Lim benchmark sets for the VRPTW and PDPTW case respectively. While both sets are widely used across the routing community, they were not addressed by previous agent-based studies. Thus the achieved average solution quality of 95% and 87% for the VRPTW and PDPTW cases represents a new best known result for these benchmark sets for agent-based approaches. An analysis of the solver's convergence, runtime and parameter sensitivity is provided within the experimental evaluation section, that has also not been provided by previous agent-based studies.

In this paper problems of planning in transportation systems based on Pickup and Delivery Problem with Time Windows (PDPTW) are discussed. The results of two variants of evolutionary algorithms illustrate the pros and cons of using different approaches, and their cooperation in hybrid island model indicates how they can help each other in achieving better solutions. This leads to the general idea of an agent-based cooperative system, in which many different techniques may be used simultaneously, exchanging the obtained solutions. Experimental study of such a system that uses evolutionary algorithms and tabu search concludes the work.Keywordstransport planning and schedulingPickup and Delivery Problem with Time Windowsevolutionary algorithmsmulti-agent systems

Over the last decade, platforms have emerged in numerous industries and often transformed them, posing new challenges for transportation research. Platform providers such as Uber, Uber Freight, Blackbuck, or Lyft mostly do not have immediate control over the physical resources needed to move people or goods. They often operate in a multi-sided market setting, where it is crucial to design clear incentives to motivate a third party to engage in collaboration. As a consequence, collaboration incentives become an integral part of decision support models for platform providers and they need to be developed at the operational level and applied dynamically. Naturally, this involves a trade-off between the interests of platform providers, shippers, and carriers. In this work, we investigate the real-world case of a platform provider operating as an intermediary between shippers and carriers in a less-than-truckload (LTL) business. We propose a new mixed-integer programming (MIP) formulation for the underlying collaborative pickup and delivery problem with time windows (PDPTW) that minimizes the price the platform pays to the carriers and enforces collaboration incentives for carriers through individual rationality constraints. This is facilitated by a dynamic pricing approach which ensures that carriers are better off collaborating than working on their own. The pricing is bounded by the costs and market conditions to keep the price range reasonable. We explore possible policies to be implemented by the platform and find that their business remains profitable when individual rationality is enforced and the platform could even guarantee increased profit margins to the carriers as incentives.

A Flexible Transport Service for Passengers

In recent decades, the rapid development of international economy has led to significant inter-regional trade imbalances. In marine transportation, the voluminous empty containers accumulated at ports in import dominated countries have to be re-circulated back to ports in export dominated countries for re-deployment. This repositioning of empty containers is crucial for shipping companies to provide effective transportation services. At present, empty container repositioning has proved to be highly expensive, contributing to 27% of the overall operation cost of shipping companies. Consequently, major stakeholders including the shipping companies have strived to reduce the repositioning cost. Unfortunately, few major improvements have been made over the years and there are still lingering research issues. The objective of this research, therefore, is to develop efficient and effective methodologies to obtain empty container repositioning plans that can significantly reduce transportation cost while fulfilling customer demands of empty and laden containers.
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\nIn this research, the empty container repositioning problem under two related real marine transportation scenarios has been studied. The first scenario considers multi-vessel transportation for both laden and empty containers with split vessel routing (denoted as ECRSVR). A mathematical model of ECRSVR is developed based on the formulation of the Pickup and Delivery Problem with Time Windows (PDPTW). However, a major research issue arises due to such integrated consideration of split vessel routing and transportation of empty and laden containers. The resulting model will encompass many more new decision variables and constraints. Thus, it cannot be readily solved by existing algorithms. To address this issue, a new Branch-and-Price (B&P) algorithm incorporating B&B and column generation is developed. Specifically, a new dynamic programming algorithm with new label structure and dominance rules is established to solve the pricing problem in B&P, and a new multi-layer branching scheme is developed for implementing the algorithm. The effectiveness and robustness of the proposed methodology are then tested on a set of randomly generated problems.
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\nThe second scenario extends the first by including transshipment activities in the ECRSVR (denoted as ECRSVRTS). Apparently, the inclusion of transshipment activities will significantly increase the size of the solution space of feasible routing and distribution schemes. Also, more constraints have to be included in the model to account for the interdependence between the distribution schemes of separate vessels. To tackle this problem, two mathematical models are developed. The first is a port-based model that explicitly characterizes the routing plans and distribution volumes for each vessel at each time interval as decision variables. The resulting integer program is non-linear and difficult to solve. Therefore, an equivalent event-driven node-based model inspired by the formulation of PDPTW is constructed. In this model, the pickup/delivery tasks and transshipment events are represented as nodes in a generated topology. The B&P scheme is then modified to solve the node-based model and a Hybrid Scatter Tabu Search (HSTS) is developed to solve the pricing problems. Results obtained from the numerical experiments using randomly generated test problems show that the proposed HSTS algorithm outperforms conventional scatter search and tabu search algorithms.

A genetic algorithm for the simultaneous delivery and pickup problems with time window

Granular tabu search for the pickup and delivery problem with time windows and electric vehicles

This study describes a pickup and delivery vehicle routing problem, considering time windows in reality. The problem of tractor truck routes is formulated by a mixed integer programming model. Besides this, three algorithms - a guided local search, a tabu search, and simulated annealing - are proposed as solutions. The aims of our study are to optimize the number of internal tractor trucks used, and create optimal routes in order to minimize total logistics costs, including the fixed and variable costs of an internal vehicle group and the renting cost of external vehicles. Besides, our study also evaluates both the quality of solutions and the time to find optimal solutions to select the best suitable algorithm for the real problem mentioned above. A novel mathematical model is formulated by OR tools for Python. Compared to the current solution, our results reduced total costs by 18%, increased the proportion of orders completed by internal vehicles (84%), and the proportion of orders delivered on time (100%). Our study provides a mathematical model with time constraints and large job volumes for a complex distribution network in reality. The proposed mathematical model provides effective solutions for making decisions at logistics companies. Furthermore, our study emphasizes that simulated annealing is a more suitable algorithm than the two others for this vehicle routing problem.

A cutting plane algorithm for the site layout planning problem with travel barriers

Aerial drone fleet deployment optimization with endogenous battery replacements for direct delivery of time-sensitive products

Pickup and delivery problem is commonly exist in logistics system, and its optimization considering time windows is essential in practical application. Meanwhile, with the increasing awareness of environmental protection, carbon emissions should also be considered during the routing design. In this paper, a low-carbon model is introduced for the pickup and delivery problem with time windows; a division method is proposed for the different delivery costs of logistics customers in different regions; a capacity constraint processing approach is proposed to solve the capacity of the vehicle during driving. Since the requirements for the logistic system are described by several objective formulations, the multi-objective approach is adopted to solve the optimization problem. The experiment selects two sets of Shanghai logistics data at different scales. Feasible solutions with advantages of different expectations can be obtained from the experiment result.

Strong cutting planes for the capacitated multi-pickup and delivery problem with time windows