Time Window Constraints Research Articles

Vehicle Routing Problem for the Simultaneous Pickup and Delivery of Lithium Batteries of Small Power Vehicles under Charging and Swapping Mode

Due to the national policy of encouraging the development of power exchange modes, the reasonable planning of vehicle distribution paths to meet the demand of lithium battery power exchange points has become a topic of considerable research interest. In this study, we propose the “centralized charging + unified distribution” power exchange mode for optimizing the charging and transporting of lithium batteries. Considering lithium batteries are dangerous goods, the vehicle path problem of simultaneous pickup and delivery of lithium batteries with vehicle load and soft time window constraints is studied. The model objective is to minimize the transportation risk and total cost of delivery. By performing crossover and mutation operations on the initial solutions generated by the ant colony algorithm, a hybrid ant colony genetic algorithm (ACO-GA) is designed to solve the model. The results of ACO-GA are compared with the GA, ACO, and SAA methods using the Solomon dataset; the results show that the optimized ant colony algorithm can achieve a smaller total cost in solving the model. Finally, taking a lithium battery leasing business in Company A, we determine the optimal path under different preferences by setting different weights for distribution cost and transportation risk in the model transformation, which provides a reference for the company to select the distribution route. Thus, the model provides a reference for companies that intend to develop power exchange businesses.

Route planning of truck and multi-drone rendezvous with available time window constraints of drones

Route planning of truck and multi-drone rendezvous with available time window constraints of drones

A Lagrangian relaxation approach based on a time-space-state network for railway crew scheduling

The Crew Scheduling Problem (CSP) is an important and difficult problem in railway crew management. In this paper, we focus on the railway crew scheduling problem with time window constraints caused by meal break rules. To address these complex crew scheduling rules, we construct a Time-Space-State Network (TSSN), formulate the studied problem as an initial network flow model and a strengthened network flow model. By exploring the characteristics of the TSSN and the improved model, we develop an efficient algorithm based on Lagrangian relaxation to get a valid lower bound. The latter algorithm is combined with solving a set covering model to get a good quality upper bound solution for the studied CSP problem. We compare the performance of our Lagrangian relaxation approach with a commercial solver (CPLEX) and Column Generation (CG) on several real-world instances based of Chinese high-speed railways. The computational experiments show that our method can solve the railway CSP in a very short computation time compared to both CPLEX and CG, while obtaining (near-)optimal solutions for all instances. We thus propose an innovative efficient and effective approach to improve the railway CSP with meal break constraints.

Feeder delivery vehicle scheduling optimization of high-speed railway express based on trunk and branch intermodal transportation

In view of the traditional branch line end express delivery centralized mode cannot adapt to the growing demand of high-speed rail (HSR) express, resulting in poor connection between trunk and branch line, high cost and poor timeliness. In this paper, the problem of scheduling optimization of branch-line flexible distribution vehicles relying on intermodal transportation of trunk and branch lines is proposed. Considering the number of vehicles, vehicle capacity, customer service time window and other constraints, an integer linear programming mathematical model with the minimum total cost of vehicle transportation cost, usage cost and time window penalty cost as the optimization objective is established. A two-level nested heuristic algorithm with two-level coding structure is proposed to solve the problem. Finally, a simulation example is given to verify the effectiveness of the model and the algorithm. The results show that the vehicle scheduling optimization problem studied in this paper can effectively improve the timeliness and accuracy of HSR express delivery, and can significantly reduce the total vehicle delivery cost.

Branch-Cut-and-Price for the Time-Dependent Green Vehicle Routing Problem with Time Windows

Motivated by rising concerns regarding global warming and traffic congestion effects, we study the time-dependent green vehicle routing problem with time windows (TDGVRPTW), aiming to minimize carbon emissions. The TDGVRPTW is a variant of the time-dependent vehicle routing problem (TDVRP) in which, in addition to the time window constraints, the minimization of carbon emissions requires determination of the optimal departure times for vehicles, from both the depot and customer location(s). Accordingly, the first exact method based on a branch-cut-and-price (BCP) algorithm is proposed for solving the TDGVRPTW. We introduce the notation of a time-dependent (TD) arc and describe how to identify the nondominated TD arcs in terms of arc departure times. In this way, we reduce infinitely many TD arcs to a finite set of nondominated TD arcs. We design a state-of-the-art BCP algorithm for the TDGVRPTW with labeling and limited memory subset row cuts, together with effective dominance rules for eliminating dominated TD arcs. The exact method is tested on a set of test instances derived from benchmark instances proposed in the literature. The results show the effectiveness of the proposed exact method in solving TDGVRPTW instances involving up to 100 customers. Summary of Contribution: Due to the environmental situation, green vehicle routing problems (GVRPs) aim to consider greenhouse gas emissions reduction, while routing the vehicles, and play a key role in transportation and logistics. Vehicle greenhouse gas emissions strongly depend on the vehicle speeds and traffic conditions which in real life vary continuously over time. To tackle these challenges, we address the time-dependent green vehicle routing problem with time windows (TDGVRPTW) aimed at reducing total carbon emissions under time-dependent travel times and time window constraints. We design an effective exact method for the TDGVRPTW based on a state-of-the-art branch-cut-and-price algorithm. The paper is both of methodological value for researchers and of interest for practitioners. For researchers, the presented algorithm is amenable for various routing constraints and provides a ground for further studies and research. For practitioners, the paper suggests insights on how the carbon emissions change based on different vehicle speed profiles. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This research is supported by the National Natural Science Foundation of China [Grants 71831003, 71831006, 72171043, and 71901180] and the Fundamental Research Funds for the Central Universities [Grants N170405005 and N180704015]. Supplemental Material: The electronic companion is available at https://doi.org/10.1287/ijoc.2022.1195 .

Hybrid multiobjective evolutionary algorithm considering combination timing for multi-type vehicle routing problem with time windows

Vehicle routing problem (VRP) has been a classical combinatorial optimization challenge, which has been extensively investigated in recent decades. As a VRP typical variant, multi-type vehicle routing problem with time windows (MT-VRPTW) has been concerned with multiple types of heterogeneous fleets of vehicles, within the delivery time window and limited capacity constraints. For such complicated multiobjective optimization problems, hybrid multiobjective evolutionary algorithm (HMOEA) has become an effective method, however, the research on hybrid algorithms and combination timing is still challenging. This study proposes a hybrid multiobjective evolutionary algorithm based on combination timing (HMOEA-CT) to solve MT-VRPTW with the criteria of minimizing the number of vehicles and wasting time simultaneously. The HMOEA-CT combines a fast convergence in multiple directions (FCMDs)-based global search and a problem-specific difference (PSD)-based local search in different evolutionary stages. The FCMD is assumed to be the global exploration search strategy, which converges faster at the center and edge regions of the Pareto front. The PSD is used to improve the local exploitation search ability by directing poor-performing individuals closer to better-performing individuals. Furthermore, the PSD cooperates with FCMD at the right time according to the different evolutionary stages to improve efficiency. Experimental results on Solomon benchmark problems demonstrate the competitive performance comparison of the HMOEA-CT with traditional multiobjective evolutionary algorithms.

Hybrid Heuristic for Vehicle Routing Problem with Time Windows and Compatibility Constraints in Home Healthcare System

This work involves a heuristic for solving vehicle routing problems with time windows (VRPTW) with general compatibility-matching between customer/patient and server/caretaker constraints to capture the nature of systems such as caretakers’ home visiting systems or home healthcare (HHC) systems. Since any variation of VRPTW is more complicated than regular VRP, a specific, custom-made heuristic is needed to solve the problem. The heuristic proposed in this work is an efficient hybrid of a novice Local Search (LS), Ruin and Recreate procedure (R&R) and Particle Swarm Optimization (PSO). The proposed LS acts as the initial solution finder as well as the engine for finding a feasible/local optimum. While PSO helps in moving from current best solution to the next best solution, the R&R part allows the solution to be over-optimized and LS moves the solution back on the feasible side. To test our heuristic, we solved 56 benchmark instances of 25, 50, and 100 customers and found that our heuristics can find 52, 21, and 18 optimal cases, respectively. To further investigate the proficiency of our heuristic, we modified the benchmark instances to include compatibility constraints. The results show that our heuristic can reach the optimal solutions in 5 out of 56 instances.

Green Fuzzy Tourist Trip Design Problem

The shift from mass tourism to more personalized travel denotes great importance in the construction of tourist itineraries. Given the negative impacts of transport and tourism on the environment, sustainability criteria play an important role. The Tourist Trip Design Problem is related to the design of itineraries for tourists. Planning is complex in tourist regions of developing countries where the information associated with tourist activities is difficult to access, vague, and incomplete. With this information, tourists must plan their trip, and the conditions and limitations they establish for it are flexible and imprecise. Fuzzy optimization can address problems with this type of information and constraints. Therefore, in this paper, an analysis of the tourism supply chain is carried out, taking as a case study the Department of Sucre on Colombia's Caribbean coast. A Multiconstraint Multimodal Team Orienteering Problem with Time Windows and fuzzy constraints is developed to model the tourism trip design problem that maximizes profit and minimizes CO2 emissions. The model is tested using datasets from the literature and the real world. The results demonstrate consistency with the fuzzy approach and generate a set of low-emission solutions.

Multi-Objective Simulation Optimization Integrated With Analytic Hierarchy Process and Technique for Order Preference by Similarity to Ideal Solution for Pollution Routing Problem

Routing is one of the most important components of logistics and has a vital role in economic growth. Inefficient routing has also contributed to troubling pollutants that have adverse environmental effects worldwide. Over the years, operations research practitioners have therefore drawn considerable attention to the routing problem. In this paper, a pollution routing problem (PRP) with time window constraints and capacitated vehicles is considered to integrate environmental issues in routing for pollution reduction. This work introduces a simulation optimization methodology that includes the realization of important parameters in real-world applications to minimize the total lateness cost and fuel consumption. The proposed method was developed with Simio simulation software and non-dominated sorting genetic algorithm-II (NSGA-II). It evaluates the dynamic system operations over time and performs a comprehensive analysis. In addition, a two-step hierarchical multi-criteria decision-making (MCDM) method is employed to choose the best strategy for PRP. Results of the two-step hierarchical MCDM method demonstrated that the strategy considering the total cost of supply chain is the best alternative for the proposed system. The use of MCDM methods after simulation can be a more robust and effective way to find solutions to such complex problems.

Urban consolidation centers and city toll schemes–Investigating the impact of city tolls on transshipment decisions

Around the world, many cities are struggling with the negative effects of urban freight transport, such as congestion and emissions. To mitigate these negative effects, both innovative solutions, such as urban consolidation centers, and regulations, such as city toll schemes and delivery time windows, can be adopted. In this paper, we investigate the impact of city toll regulations on the vehicle routing and transshipment decisions of logistics service providers. We present a mixed-integer linear programming formulation and an adaptive large neighborhood search heuristic that address the interdependent decisions of vehicle routing and the use of urban consolidation centers, taking into account city toll schemes and time window constraints. In this context, we consider heterogeneous fleets, multiple trips per vehicle, and use a multigraph to address the trade-off between fastest and cheapest paths. We validate the adaptive large neighborhood search by comparing it with the mixed-integer linear programming model on test instances with up to 20 customers. To analyze how city toll schemes affect the cost attractiveness of urban consolidation centers and the fleet composition of logistics service providers, we conduct an extensive computational study featuring real-world instances that provide managerial insights for both local administrations and logistics service providers. Our results show that both per-day and per-entrance tolls can be used by local administrations to support the use of urban consolidation centers and that the number of truck entries into urban areas can be reduced. However, our results also indicate that due to the transshipment fee per unit load, the cost attractiveness of using urban consolidation centers is considerably lower for logistics service providers with larger delivery quantities per stop.

Secured Multi-Dimensional Robust Optimization Model for Remotely Piloted Aircraft System (RPAS) Delivery Network Based on the SORA Standard

The range of applications of RPAs in various industries indicates that their increased usage could reduce operational costs and time. Remotely piloted aircraft systems (RPASs) can be deployed quickly and effectively in numerous distribution systems and even during a crisis by eliminating existing problems in ground transport due to their structure and flexibility. Moreover, they can also be useful in data collection in damaged areas by correctly defining the condition of flight trajectories. Hence, defining a framework and model for better regulation and management of RPAS-based systems appears necessary; a model that could accurately predict what will happen in practice through the real simulation of the circumstances of distribution systems. Therefore, this study attempts to propose a multi-objective location-routing optimization model by specifying time window constraints, simultaneous pick-up and delivery demands, and the possibility of recharging the used batteries to reduce, firstly, transport costs, secondly, delivery times, and thirdly, estimated risks. Furthermore, the delivery time of the model has been optimized to increase its accuracy based on the uncertain conditions of possible traffic scenarios. It is also imperative to note that the assessment of risk indicators was conducted based on the Specific Operations Risk Assessment (SORA) standard to define the third objective function, which was conducted in a few previous studies. Finally, it shows how the developed NSGA-II algorithm in this study performed successfully and reduced the objective function by 31%. Comparing the obtained results using an NSGA-II meta-heuristic approach, through the rigorous method GAMS, indicates that the results are valid and reliable.

Hybrid and approximate algorithms for the dial-a-ride problem with adaptive ride times considering different service strategies

The dial-a-ride problem (DARP) is that of satisfying a number of pickup and drop-off customer requests, using a fleet of vehicles. In real life, traffic conditions can affect expected travel times, and hence the satisfaction of rigid pickup/drop-off time windows and scheduled ride times. This article considers the DARP with customer-adaptive ride times under different service conditions and strategies. The problem is formulated as a mixed integer linear programming model that minimizes service cost and customer inconvenience. A hybrid genetic–variable neighbourhood search algorithm (GAVNS) is proposed to solve the problem. Experiments are conducted to compare the performance of GAVNS with that of an approximate column generation algorithm, and to evaluate the application of different strategies on service efficiency and customer satisfaction. The results demonstrate the efficiency of GAVNS, and that limited violations of time-window and ride-time constraints can improve the service efficiency while preserving customer satisfaction levels.

Analyses on the Effects of Time Windows Choices on Sustainable Vehicle Allocation Problems

This study aims to analyze the effects of the time windows choices in Vehicle Allocation Problems with respect to economic, social, and environmental indicators. As far as we know, such an attempt does not exist in the related literature. For this purpose, we first present a Mixed Integer Programming model for a generic Vehicle Allocation Problem with profit maximization objective under time windows constraints. This model is used to conduct analyses for demonstrating the applicability of the model in practice and to reveal potential effects of the time windows choices on economic, social, and environmental outcomes of allocation decisions in Vehicle Allocation Problems. The numerical results show that loosened time windows have the potential to provide economic and environmental benefits in the addressed problem. We also propose a collaboration policy attractive to both the transportation company and its customers through price discounts, which improves economic and social performances of the addressed transportation logistics network.

The pickup and delivery problem with transshipments: Critical review of two existing models and a new formulation

The pickup and delivery problem with transshipments (PDP-T) is generalized from the classical pickup and delivery problem (PDP) by allowing the transfer of requests between vehicles. After considering the time window constraints, the PDP-T is further generalized to the pickup and delivery problem with time windows and transshipments (PDPTW-T). In this paper, we review two state-of-the-art models for the PDP-T and PDPTW-T. We point out the possible issues existing in the models and provide our revisions. In addition, we develop a new mixed-integer linear programming formulation to solve the PDP-T and PDPTW-T. The performance of the proposed model is evaluated by solving 340 generated PDP-T instances and 360 open-access PDPTW-T instances. Computational results show that the proposed model outperforms the existing models in terms of solution quality and computing time. PTP-T instances with up to 25 requests and 2 transfer stations are solved to optimality by using the proposed model. As a comparison, the best-known benchmarks in the literature are instances with 5 requests and 1 transfer station. In addition, the computing time is significantly reduced. In our experiments, the average computational time for solving PDP-T is reduced by 96%. For PDPTW-T instances, the solvable scale is increased from 3 requests and 4 transfer stations to 5 requests and 4 transfer stations. The average computing time is reduced by 40%.

A self-adaptive hyper-heuristic based multi-objective optimisation approach for integrated supply chain scheduling problems

Recent global changes have prompted manufacturers to shift their production systems to make-to-order (MTO) supply chain (SC), enabling them to adapt customised customer requirements with their rapidly changing behaviours, reduce inventory costs, and obtain competitive advantages in the market. However, traditional MTO-based scheduling approaches fail to consider all the SC stages required for optimal schedules. This study proposes an integrated SC scheduling problem (ISCSP), where supplier, manufacturer and batching decisions are simultaneously optimised in response to heterogeneous customer requirements with time window constraints. Both economic and environmental sustainability for the supply portfolio is considered while the manufacturer is modelled using the flexible job shop scheduling (FJS) problem. Since the proposed ISCSP is an extension of the FJS problem, this can also be considered an NP-hard problem, which cannot be solved by traditional optimisation techniques, particularly for larger instances. Thus, a self-adaptive multi-operator and multi-objective hyper-heuristic (SA(MO)2H) is designed, where the low-level heuristic utilises strengths of four solution updating heuristics and is intelligently guided by the reinforcement learning, to address the problem. The proposed SA(MO)2H integrates environmental sustainability into the evolutionary process to achieve the best possible supply portfolio, adopting the VIKORSORT approach. Finally, a rigorous experimental study on solving a wide range of instances is conducted to evaluate the performance of SA(MO)2H against its non-intelligent versions and five existing algorithms. Overall, the most beneficial facet of the developed ISCSP and SA(MO)2H is the visibility and meaningful managerial insights provided by the multi-portfolio solutions fostering the responsive relationship among SC stages.

Concrete Vehicle Scheduling Based on Immune Genetic Algorithm

At present, the demand for ready-mixed concrete (RMC) in construction industry is increasing day by day, and the supply mode of multiple delivery depots corresponding to multiple construction sites has been widely used. In order to further improve the joint distribution efficiency between various delivery depots, this research establishes a multiobjective optimal distribution model with time window constraints and demand postponement attributes for the problem that the subbatching plants need to work together. The model divides the reasons for demand postponement into two types: the constraint for timely unloading of trucks cannot be met on time and the constraint for timely pouring at the construction site cannot be met on time. This work improved the coding method of genetic algorithm based on the characteristics of the distribution model. Using hierarchical real-coding form, the coding operator of each layer can be evolved separately, which ensures the globality of the search, and, at the same time, an improved immune operator is added to ensure the local search performance. By comparison, the results obtained by improved GA are 7.05% higher than those of the standard GA, and the early convergence speed of improved GA is obviously better than that of the standard GA. The simulation experiments show that the total trucks’ waiting time during the process of providing delivery services from 5 concrete plants to 8 construction sites is 769 minutes, and the total waiting time of 8 construction sites is 507 minutes. Through practical case analysis, this work can enable RMC production enterprises and construction sites to effectively reduce the waiting time of corresponding operations, and the obtained results are close to the simulation results. The proposed method indeed improves the efficiency of RMC distribution.

The multi-product vehicle routing problem with cross-docking: a novel strategy hybrid bat algorithm for Industry 3.5 in Thailand's food industry

ABSTRACT This paper presents a multi-product vehicle routing problem with cross-docking operations for food industry to ensure products which can be delivered in time and with minimum transportation and hiring costs to perform for both supplier side and customer side. The problem was formulated as a special multi-product vehicle routing problem with cross-docking and time window constraints (MPVRPCDTW). A novel strategy hybrid based on the Bat algorithm (NSHBA) is presented to solve the MPVRPCDTW for the sustainable food industry by minimising the transportation cost and the number of vehicles, using the poultry industry as a case study. Additionally, a new disturbance algorithm (DA) was developed to find the best neighbourhood strategy to increase the efficiency and quality of solutions in the NSHBA. The computational results revealed that the NSHBA-DA outperformed the Bat algorithm, the differential evolution algorithm, and the particle swarm optimisation algorithm. The MATLAB App architecture based on all eight algorithms was designed and developed. The overall result of this study should prove to benefit the logistics staff in making the right decisions on cross-docking transportation by employing real-time data.

Research on comprehensive recovery of liner schedule and container flow with hard time windows constraints

COVID-19 has had a huge impact on the global container market. Many liner companies have adopted a blank sailing for some voyages to adjust capacity, and vessel schedule reliability continues to be sluggish. From the perspective of the container liner company, this paper studies the integrated recovery of liner schedule and container flow under the background of suspension of shipping service. With the goal of minimizing the total cost of the liner company, the hard time window constraints of the container flow on the suspended routes are set to construct the integrated recovery problem.The increased carbon emission cost during the restoration of the container flow is taken into account.A mixed integer nonlinear programming model is established, and the adaptive mutation particle swarm optimization (AMPSO) is used to solve the model. The results show that the total cost of the model is reduced by 10.66% compared with the total cost of the shipping schedule recovery model that did not consider the recovery of container flow.

Optimal allocation of shared parking spaces for hospital parkers considering parking choice behavior under bounded rationality

ABSTRACT Lack of parking spaces at downtown hospitals causes urban problems like patient access delays and additional carbon emissions. This paper proposes a cumulative prospect theory-based shared parking space allocation model (CPT-SPSA model) to alleviate the parking difficulties. The CPT-SPSA model aims to maximize the profit of the shared parking platform under time window constraints considering the parking choice behavior of hospital parkers. To determine the parking choice behavior, cumulative prospect theory (CPT) is utilized to model parkers’ evaluation of parking lots considering individual heterogeneity. Numerical experiments indicate that the profit of the platform and the utilization rate of the shared parking spaces are improved significantly and more successful matches of shared parking supply and demand are achieved under the CPT-SPSA model. Those with different parking purposes vary in acceptance of each parking lot. The platform can earn more profit by reasonably adjusting the parking fees of the shared parking spaces.

Optimization Model for Selective Harvest Planning Performed by Humans and Robots

This paper addresses the formulation of an individual fruit harvest decision as a nonlinear programming problem to maximize profit, while considering selective harvesting based on fruit maturity. A model for the operational level decision was developed and includes four features: time window constraints, resource limitations, yield perishability, and uncertainty. The model implementation was demonstrated through numerical studies that compared decisions for different types of worker and analyzed different robotic harvester capabilities for a case study of sweet pepper harvesting. The results show the influence of the maturity classification capabilities of the robot on its output, as well as the improvement in cycle times needed to reach the economic feasibility of a robotic harvester.