The Low Carbon Pickup and Delivery Problem with Time Windows and its Optimization Approach

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

Adaptive large neighborhood search for the pickup and delivery problem with time windows, profits, and reserved requests

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.

Strong cutting planes for the capacitated multi-pickup and 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 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 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 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 .

A scenario-based planning for the pickup and delivery problem with time windows, scheduled lines and stochastic demands

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.

The pickup and delivery problem with time windows and last-in-first-out (LIFO) loading (PDPTWL) is a combinational optimization problem extended from the well-known vehicle routing problem (VRP), in which the type of customer point is no longer single and the loading order of the requests must meet the LIFO constraint. Due to its NP-hard nature, it is difficult for exact algorithms and heuristics with a linear structure to solve a large-scale problem in a reasonable time. In this paper, we propose a fast decomposition and reconstruction framework (D&R) to solve the PDPTWL with high quality in a relatively short time. An angle-based sweep method is used to decompose a complete solution into multiple sub-solutions, each of which is assigned to a tabu search for optimization. To speed up the whole process, the optimization procedure of sub-solutions is performed by different processors of multi-core CPU in parallel. Three neighborhood operators and three strategies to reduce the number of vehicles are designed to cope with the tabu search for further improvement. Moreover, the adaptive memory mechanism is added to provide a better start when the optimization procedure falls into the local optima. We compare our framework against the best known solutions on 119 instances with up to 300 requests, the results show that our framework is able to improve over 85% (107 out of 119) of the best known solutions. More specifically, the number of vehicles is optimized by about 60% (74 out of 119) and the driving distance by about 50% (59 out of 119). In addition on instances with the largest size of requests, the computational time of our framework can be 1/50 of the comparative results, confirming its efficiency.

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 pickup and delivery problem with time windows and occasional drivers

This paper studies an evolutionary algorithm to solve a new multiobjective optimization problem, the Pickup and Delivery Problem with Time Windows and Demands (PDP-TW-D), which is applicable to ope...

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.