LCS-Based Selective Route Exchange Crossover for the Pickup and Delivery Problem with Time Windows

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.

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 .

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.

This paper addresses a new variant of Pickup and Delivery Problem with Time Windows (PDPTW) for enhancing customer satisfaction. In particular, a huge number of requests is served in the system, where each request includes a pickup node and several delivery nodes instead of a pair of pickup and delivery nodes. It is named Pickup and Multi-Delivery Problem with Time Windows (PMDPTW). A mixed-integer programming model is formulated with the objective of minimizing total travel costs. Computational experiments are conducted to test the correctness of the model with a newly generated benchmark based on the PDPTW benchmark instances. Results show that our proposed model is able to solve small-size instances. Alternative approaches for solving larger problems are proposed for future research.

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.

This paper presents an enhanced guided ejection search (GES) to minimize the number of vehicles in the NP-hard pickup and delivery problem with time windows. The proposed improvements decrease the convergence time of the GES, and boost the quality of results. Extensive experimental study on the benchmark set shows how the enhancements influence the GES capabilities. It is coupled with the statistical tests to verify the significance of the results. We give a guidance on how to select a proper algorithm variant based on test characteristics and objectives. We report one new world’s best result obtained using the enhanced GES.

This paper presents an adaptive memetic algorithm to solve the vehicle routing problem with time windows (VRPTW). It is a well-known NP-hard discrete optimization problem with two objectives--to minimize the number of vehicles serving a set of geographically dispersed customers, and to minimize the total distance traveled in the routing plan. Although memetic algorithms have been proven to be extremely efficient in solving the VRPTW, their main drawback is an unclear tuning of their numerous parameters. Here, we introduce the adaptive memetic algorithm (AMA-VRPTW) for minimizing the total travel distance. In AMA-VRPTW, a population of solutions evolves with time. The parameters of the algorithm, including the selection scheme, population size and the number of child solutions generated for each pair of parents, are adjusted dynamically during the search. We propose a new adaptive selection scheme to balance the exploration and exploitation of the solution space. Extensive experimental study performed on the well-known Solomon's and Gehring and Homberger's benchmark sets confirms the efficacy and convergence capabilities of the proposed AMA-VRPTW. We show that it is very competitive compared with other state-of-the-art techniques. Finally, the influence of the proposed adaptive schemes on the AMA-VRPTW behavior and performance is investigated in a thorough sensitivity analysis. This analysis is complemented with the two-tailed Wilcoxon test for verifying the statistical significance of the results.

This paper investigates the vehicle routing problem faced by a third‐party logistics (3PL) provider that performs the last‐mile delivery service in omni‐channel retailing for a number of companies engaged in household appliances and furniture. In the problem, each company is associated with a set of warehouses, physical stores, and customers that provide or require various commodities. The request of a company is to transport commodities from the selected warehouses and stores to the customers. In addition, the pickup or delivery service at each location should be started in a predefined time window. Since the loading and unloading follow the last‐in‐first‐out fashion, the handling time incurred by additional operation is considered. The studied problem is formulated as a multicommodity pickup and delivery problem with time windows and handling time (MPDPTWH). MPDPTWH aims to satisfy the requests on the 3PL platform with the minimum total duration of the routes. We present a mixed integer programming formulation of the problem and propose a multirestart randomized tabu thresholding algorithm (MRTTA) as well as a memetic algorithm (MA) to solve this problem heuristically. Then, the performance of the mathematical model and the two heuristics is assessed over three sets of MPDPTWH instances. After this, we compare the proposed MRTTA and MA with algorithms from the literature on a related problem. Furthermore, we perform the sensitivity analysis in a case study by discussing the impact of picking cost and handling time on the solution, and give the managerial insights.

The purpose of this paper is to present an exact solution method for an important planning problem faced by many shipping companies dealing with transportation of bulk cargoes. A bulk shipping company usually has a set of contract cargoes that it is committed to carry and will try to derive additional revenue from optional spot cargoes. Each cargo, either it is a contract or spot cargo, consists of a given quantity to be picked up in a given loading port and delivered in a given unloading port within specified time windows. The shipping company controls a fixed fleet for the purpose of transporting the cargoes. In most of the literature on ship routing and scheduling problems, a cargo cannot be transported by more than one ship. By introducing split loads, this restriction is removed and each cargo can be transported by several ships. The resulting planning problem can be denoted as a maritime pickup and delivery problem with time windows and split loads (PDPTWSL). We present an arc flow formulation of the PDPTWSL. We also suggest a solution method based on a priori generation of single ship schedules and two alternative path flow models that deal with the selection of ship schedules and assignment of cargo quantities to the schedules. Computational results show that the solution method can provide optimal solutions to small realistic planning instances. We also believe this paper provides an important starting point for research on other exact solution methods for the maritime PDPTWSL.

This paper introduces an adaptive large neighborhood search metaheuristic to solve the multi-trip multi-traffic pickup and delivery problem with time windows and synchronization (MTT-PDTWS). With adaptive destroy and repair operators, it learns over time which destroy and repair operators are the most effective and governs the operator selection biased toward highly effective one. The computational experiments display the impacts of these operators on the solution quality and the performance of the ALNS in comparison to the only existing tabu search methodology addressing the MTT-PDTWS.

This paper compares the performance of the classic genetic algorithm with the more recently proposed ant colony optimisation for solving real-world pickup and delivery problems with hard time windows. A real-world problem that is present worldwide - waste collection - is used to evaluate the algorithms. As in most real-world waste collection problems, many of the waste bins have time windows. The time windows stem from such things as safety regulations and customer agreements, and must be strictly adhered to. The optimisation showed that the genetic algorithm is better than the ant colony optimisation when utilising standard implementations of both algorithms. However, when the algorithms are enhanced with a local search procedure, the ant colony optimisation immediately becomes superior and achieves improved results. Local search seems to be a drawback for the genetic algorithm when hard time windows are involved. Various implementations of the local search procedure are evaluated in this paper using five different test sets. Recommendations for future implementations are given as well as additional enhancements which could improve the performance of the ant colony optimisation.

In this chapter, two kinds of intertwined decisions regarding the movement of vehicles in an in-plant milk-run delivery system are considered: routing decisions, which determine the set of sequences of stations visited by each tugger train, and scheduling decisions, which plan congestion free movement of the tugger trains. The problem under study, called the Multi Trip and Multi Cycle Pick-up and Delivery Problem with Time Windows and Congestion Free Traffic, can be viewed as an extension of the pick-up and delivery problem with time windows in which multiple tugger trains travel along closed-loop congestion-free routes in different cycles. A declarative model of the investigated milk-run delivery principle makes it possible to formulate a vehicle routing and scheduling problem the solution to which determines the route, the time schedule, and the type and number of parts that the different trucks must carry to fulfill orders from various customers/recipients. Due to the requirement of congestion-free milk-run traffic, a scheduling period slicing principle allowing to synchronize cyclic flows of different periods is applied. Its implementation, resulting in a cyclic schedule composed of quasi cyclic sub-schedules, implies a recursive formulation of a well-known constraint satisfaction problem. The goal is to find solutions that can minimize both vehicle downtime and the takt time of the production flow. Computer experiments illustrate the possibility of using the present approach in real-life systems.