Time Window Constraints Research Articles

Optimization of Truck–Cargo Matching for the LTL Logistics Hub Based on Three-Dimensional Pallet Loading

This study investigates the truck–cargo matching problem in less-than-truckload (LTL) logistics hubs, focusing on optimizing the three-dimensional loading of goods onto standardized pallets and assigning these loaded pallets to a fleet of heterogeneous vehicles. A two-stage hybrid heuristic algorithm is proposed to solve this complex logistics challenge. In the first stage, a tree search algorithm based on residual space is developed to determine the optimal layout for the 3D loading of cargo onto pallets. In the second stage, a heuristic online truck–cargo matching algorithm is introduced to allocate loaded pallets to trucks while optimizing the number of trucks used and minimizing transportation costs. The algorithm operates within a rolling time horizon, allowing it to dynamically handle real-time order arrivals and time window constraints. Numerical experiments demonstrate that the proposed method achieves high pallet loading efficiency (close to 90%), near-optimal truck utilization (nearly 95%), and significant cost reductions, making it a practical solution for real-world LTL logistics operations.

Prize-collecting Electric Vehicle routing model for parcel delivery problem

Electric Vehicle (EV)-based parcel delivery is getting much more popular these days due to EVs being eco-friendly and sustainable. One well-known problem in the literature to study last-mile delivery via EVs is the Electric Vehicle Routing Problem (EVRP). One limitation of EVRP is that it assumes all customers must be visited directly by EVs. This forces companies to purchase or utilize additional EVs, increasing operational costs for EV utilization and routing. To overcome this limitation, the present work introduces the Prize-collecting EVRP with Time Windows (PC-EVRP-TW), utilizing multiple EVs for the home-delivery service of high-priority customers (customers with high loyalty or premium memberships), leaving the rest for the next day or outsourcing to a third-party shipper. It also ensures a minimum number of served demands to maintain service quality. PC-EVRP-TW is modeled by mixed-integer linear programming and solved by a problem-specific hybrid metaheuristic aiming to minimize EVs’ route and usage cost and maximize collected profits (prizes) while satisfying EVs’ load and battery capacity, task completion, and time window constraints. Analyses were performed on the optimal solution of PC-EVRP-TW. The results show that the company could achieve significant route cost savings, up to 22% compared to EVRP-TW. Additionally, remarkable reductions in EV usage costs, 6%, 16%, and 18%, were observed for various-size instances of PC-EVRP-TW. These findings highlight the potential for practitioners and managers to realize substantial cost savings and optimize EV usage by selectively serving a prioritized subset of customers daily, particularly when facing high utilization costs and the inability to serve all customers directly.

Revolutionizing RPAS logistics and reducing CO2 emissions with advanced RPAS technology for delivery systems

To manage remotely piloted aircraft system (RPAS) networks effectively, this research presents a multi-objective location-routing optimization model. This model integrates time window constraints, concurrent pick-up and delivery demands, and rechargeable battery functionality, and also introduces a standardized framework to clarify the RPAS CO2 emission model. These integrations significantly decrease battery consumption in Remotely Piloted Aircraft Systems (RPAS) and lower transportation costs, while also optimizing delivery times, reducing operational risks, and minimizing CO2 emissions. The model’s enhancement for optimizing delivery schedules takes into account uncertain traffic conditions, thus improving accuracy in dynamic environments and further contributing to environmental sustainability. Risk assessment employs the Specific Operations Risk Assessment (SORA) standard, adding a third objective function. This combination of the model, further enhance the efficiency and sustainability of RPAS operations, by optimizing delivery schedules, reducing CO2 emissions and battery consumption, and improving accuracy under dynamic conditions. Also, it make RPAS logistics more practical and effective in real-world applications. As result, the NSGA-II algorithm achieves significant reductions across all objectives: 33.3 % in cost, 6.48 % in time, 33.3 % in risk, and 35.7 % in battery usage within 250 generations. The use of the NSGA-II meta-heuristic method for validation enhances the credibility and practicality of the model. The optimization model’s performance over 250 generations shows rapid initial improvements in cost, time, risk, and battery usage, followed by stabilization, indicating efficient convergence and effective evolutionary computation. Also the findings show that with a CO2 emission rate of 3.773 × 104 kg of CO2 per Wh, highlighting the model’s efficiency and effectiveness.

Flexible yard crane scheduling for mixed railway and road container operations in sea-rail intermodal ports with the sharing storage yard

The sea-rail intermodal port, serving as the “cornerstone” supporting the seamless connection of landside and quayside transportation, plays a crucial role in determining the service level of the container multimodal transport through port’s operational organization efficiency. With on-dock rails, the physical integration between railways and water transport is smoothly achieved. However, within the port, the diversity in container flows adds complexity to operational organization and decision-making. In this paper, we formulate a flexible crane scheduling model to reduce the mutual interference during the mixed operations of railway containers and road containers in the sharing yard. The model addresses the time window constraints of railway containers required by train schedule, and the uncertain scenarios of external truck arrivals. To solve this problem, we design a two-stage approach that encompasses a task reassignment phase and a sequential decision-making phase. Furthermore, we test the model and algorithm performance through various experiments of different scales. Our results show that the designed algorithm designed solves instances of 20 tasks in 18.7 s, compared to 3600 s for the model solver. It efficiently handles real-world instances with over 200 tasks and 100 scenarios. Finally, sensitivity analysis is carried out to capture the influence of railway container ratio, truck arrival patterns, and train time windows on yard operations. Under intensive operation, we find that road containers, following a uniform arrival pattern, are least affected by railway container operations when the proportion of railway containers in the sharing block ranges from 70% to 80%. We also observe that the flexibility of crane service increases as the time window for railway container operations becomes more lenient.

A Heuristic Routing Algorithm for Heterogeneous UAVs in Time-Constrained MEC Systems

The rapid proliferation of Internet of Things (IoT) ground devices (GDs) has created an unprecedented demand for computing resources and real-time data-processing capabilities. Integrating unmanned aerial vehicles (UAVs) into Mobile Edge Computing (MEC) emerges as a promising solution to bring computation and storage closer to the data sources. However, UAV heterogeneity and the time window constraints for task execution pose a significant challenge. This paper addresses the multiple heterogeneity UAV routing problem in MEC environments, modeling it as a multi-traveling salesman problem (MTSP) with soft time constraints. We propose a two-stage heuristic algorithm, heterogeneous multiple UAV routing (HMUR). The approach first identifies task areas (TAs) and optimal hovering positions for the UAVs and defines an effective fitness measurement to handle UAV heterogeneity. A novel scoring function further refines the path determination, prioritizing real-time task compliance to enhance Quality of Service (QoS). The simulation results demonstrate that our proposed HMUR method surpasses the existing baseline algorithms on multiple metrics, validating its effectiveness in optimizing resource scheduling in MEC environments.

Improved PSO-Based Two-Phase Logistics UAV Path Planning under Dynamic Demand and Wind Conditions

Unmanned aerial vehicles (UAVs) have increasingly become integral to logistics and distribution due to their flexibility and mobility. However, the existing studies often overlook the dynamic nature of customer demands and wind conditions, limiting the practical applicability of their proposed strategies. To tackle this challenge, we firstly construct a time-slicing-based UAV path planning model that incorporates dynamic customer demands and wind impacts. Based on this model, a two-stage logistics UAV path planning framework is developed according to the analysis of the customer pool updates and dynamic attitudes. Secondly, a dynamic demand and wind-aware logistics UAV path planning problem is formulated to minimize the weighted average of the energy consumption and the customer satisfaction penalty cost, which comprehensively takes the energy consumption constraints, load weight constraints, and hybrid time window constraints into consideration. To solve this problem, an improved particle swarm optimization (PSO)-based multiple logistics UAV path planning algorithm is developed, which has good performance with fast convergence and better solutions. Finally, extensive simulation results verify that the proposed algorithm can not only adhere to the UAV’s maximum load and battery power constraints but also significantly enhance the loading efficiency and battery utilization rate. Particularly, compared to the genetic algorithm (GA), simulated annealing (SA), and traditional PSO strategies, our proposed algorithm achieves satisfactory solutions within a reasonable time frame and reduces the distribution costs by up to 9.82%.

Bi-Objective Mixed Integer Nonlinear Programming Model for Low Carbon Location-Inventory-Routing Problem with Time Windows and Customer Satisfaction

In order to support a low-carbon economy and manage market competition, location–inventory–routing logistics management must play a crucial role to minimize carbon emissions while maximizing customer satisfaction. This paper proposes a bi-objective mixed-integer nonlinear programming model with time window constraints that satisfies the normal distribution of stochastic customer demand. The proposed model aims to find Pareto optimal solutions for total cost minimization and customer satisfaction maximization. An improved non-dominated sorting genetic algorithm II (IMNSGA-II) with an elite strategy is developed to solve the model. The model considers cost factors, ensuring that out-of-stock inventory is not allowed. Factors such as a carbon trading mechanism and random variables to address customer needs are also included. An entropy weight method is used to derive the total cost, which is comprised of fixed costs, transportation costs, inventory costs, punishment costs, and the weight of carbon emissions costs. The IMNSGA-II produces the Pareto optimal solution set, and an entropy–TOPSIS method is used to generate an objective ranking of the solution set for decision-makers. Additionally, a sensitivity analysis is performed to evaluate the influence of carbon pricing on carbon emissions and customer satisfaction.

Cold chain distribution network design with heterogeneous fleet under carbon reduction policy application effect

ABSTRACT To integrate cold chain distribution network design problem with heterogeneous fleet, a multi-objective optimisation model is proposed to simultaneously optimise distribution routes, the quantity of internal combustion and electric refrigerated trucks (ERTs), and the number and location of distribution centres and charging stations with time window constraints, where the cold chain distribution operating cost and the customer dissatisfaction cost are minimised. A hybrid solution methodology, combining a multi-objective artificial fish swarm algorithm with a label-based optimisation algorithm, is presented to address this model. Extensive computational experiments verify the effectiveness of the proposed method. Moreover, a sensitivity analysis, focusing on the range of ERTs, the purchase subsidy for ERTs, the carbon tax and the carbon emission quota, informs the development of diverse carbon reduction policies. A comparative analysis of the implementation effect of carbon reduction policies can provide optimisation decision support for promoting sustainability in the electrification of cold chain distribution.

A Constraint Programming Approach for Discrete Time–Cost Tradeoff Problems in a Time-Constrained Activity Network

The discrete time-cost tradeoff problem (DTCTP) is a well-researched topic in the field of operations research. The majority of existing DTCTP models are based on traditional activity networks, which permit the execution of an activity as soon as all its predecessors have been completed. This assumption is reasonable, but it is important to note that there are always exceptions. The main work of this study was threefold. Firstly, we expanded the analysis of the DTCTP to encompass time-constrained activity networks (DTCTPTC), which encompassed three different types of time constraints. The first constraint was the time-window constraint, which limited the time interval during which an activity could be executed. The second constraint was the time-schedule constraint, which specified the times at which an activity could begin execution. The third constraint was the time-switch constraint, which required project activities to start at specific times and remain inactive during designated time periods. Secondly, a constraint programming (CP) model was developed for the purpose of solving the DTCTPTC. The model employed interval variables to define the activity and its potential time constraints, while CP expressions were utilized to ensure the feasibility of the solution. The objective was to identify the optimal execution mode for each activity, the optimal start times for time-scheduled activities, and the optimal work/rest patterns for time-switch activities, with the aim of minimizing the total cost of the project. Finally, the efficacy of the proposed CP model was validated through two case studies based on two illustrative projects of varying sizes. The outcomes were then compared against existing algorithms. The results demonstrated that time constraints were important factors affecting schedule optimization, and the proposed CP model had the ability to solve large-scale DTCTPTC.

Optimizing delivery routes for sustainable food delivery for multiple food items per order

The diversity of consumer demand for take-out food has led to the characteristic structure of one order with multiple items, where the different food items in a single order are provided by two or more merchants. In the context of multi-item delivery for take-out orders with time windows, this study investigates vehicle routing for order delivery. This research aims to improve the service level of merchants and the efficiency of delivery vehicles. Food vendors receive orders from consumers through online platforms, then package the food items according to the orders. This method is a preliminary exploration of the issue of fulfilment of takeout orders on online platforms, and can provide preliminary theoretical support for decision-making on the delivery process of takeout orders on online platforms. In the context of online catering sales platforms and offline food sales merchants, this paper studies the delivery problem of takeaway orders with a time window and the characteristics of one order and multiple items, and constructs a method that takes the order delivery time requirements into account and minimizes the total order fulfilment cost. Taking into account the time window constraints of both physical restaurants and consumers, genetic algorithms are utilized to solve the order delivery problem. Finally, through case studies and experiments, the effectiveness and feasibility of the mathematical model are validated. Practical recommendations and insights are provided from the perspective of management and route planning.

Just-in-time scheduling of unrelated parallel machines with family setups and soft time window constraints

ABSTRACT This study addresses an unrelated parallel machine scheduling problem with family setups and soft time windows, which includes considerations for machine eligibility. The objective is to minimize the total weighted tardiness and earliness, and to maximize the number of Just-in-Time jobs. Four different metaheuristic algorithms are compared to determine which type – single-point (simulated annealing), population-based evolutionary (artificial immune system, genetic algorithm), or swarm intelligence algorithms (ant colony optimization) – is more effective in solving this problem. Two strategies, namely penalty and repair, are proposed to handle precedence constraints. Experimental results demonstrate that ant colony optimization with local search which employs the repair strategy, as a swarm intelligence-based algorithm outperforms its rivals in terms of objective function values and robustness. The performance of this algorithm has shown an improvement in objective function values ranging from 2.12% to 8.52% on average, with a relative percentage deviation of 10.35.

Navigation Resource Allocation Algorithm for LEO Constellations Based on Dynamic Programming

Navigation resource allocation for low-earth-orbit (LEO) constellations refers to the optimal allocation of navigational assets when the number and allocation of satellites in the LEO constellation have been determined. LEO constellations can not only transmit navigation enhancement signals but also enable space-based monitoring (SBM) for real-time assessment of GNSS signal quality. However, proximity in the frequencies of LEO navigation signals and SBM can lead to significant interference, necessitating isolated transmission and reception. This separation requires that SBM and navigation signal transmission be carried out by different satellites within the constellation, thus demanding a strategic allocation of satellite resources. Given the vast number of satellites and their rapid movement, the visibility among LEO, medium-earth-orbit (MEO), and geostationary orbit (GEO) satellites is highly dynamic, presenting substantial challenges in resource allocation due to the computational intensity involved. Therefore, this paper proposes an optimal allocation algorithm for LEO constellation navigation resources based on dynamic programming. In this algorithm, a network model for the allocation of navigation resources in LEO constellations is initially established. Under the constraints of visibility time windows and onboard transmission and reception isolation, the objective is set to minimize the number of LEO satellites used while achieving effective navigation signal transmission and SBM. The constraints of resource allocation and the mathematical expression of the optimization objective are derived. A dynamic programming approach is then employed to determine the optimal resource allocation scheme. Analytical results demonstrate that compared to Greedy and Divide-and-Conquer algorithms, this algorithm achieves the highest resource utilization rate and the lowest computational complexity, making it highly valuable for future resource allocation in LEO constellations.

Research on a multiobjective cooperative operation scheduling method for agricultural machinery across regions with time windows

This article aims to solve the problems of high cost, low efficiency, and task delay caused by the lack of scientific scheduling strategies during the agricultural harvest season. Considering the constraints of operation time windows, a multimachine multiobjective cross-regional collaborative operation scheduling model is constructed with the goal of minimizing the transfer distance of agricultural machinery and nonoperational scheduling costs. A multiobjective genetic algorithm (HTSMOGA) based on a hybrid time window priority rule and a tabu search strategy is designed. The initial population is generated by utilizing time window priority rules, genes with earlier operation start times are preferentially retained, and a mixed search strategy is introduced to avoid local optimal solutions. Experiments were conducted among 24 farms in a region of Hebei Province, and the results showed that, compared with other algorithms, the HTSMOGA achieved an average reduction of 17.18 % in the transfer distance of agricultural machine operations and 19.36 % in the nonoperational waiting time. Therefore, this study provides a rational and feasible solution for the cross-regional operation scheduling of agricultural machinery cooperatives and provides theoretical support for ensuring the timely completion of harvesting tasks and the cost savings and efficiency of agricultural machinery operations.

Logistics vehicle routing optimisation with synchronised transfer

This paper presents a synchronized transfer strategy in which operators can schedule logistics vehicles among employees and arrange the transfer of commodities. The transfer time consists of the vehicle waiting time and commodity transition time. By adopting the strategy, logistics vehicles can visit fewer communities, resulting in savings in transportation cost under ensuring punctual delivery. An integer programming model based on a space-time-state network is proposed to describe the complex transfer process. To simplify the model, time window and vehicle capacity constraints are embedded into the network. The alternating direction method of multipliers (ADMM) is designed to solve the model. In the ADMM-based solution framework, the original model can be converted into a series of shortest-path searching subproblems and iteratively solved using a dynamic programming (DP) algorithm. Our computational results show that the proposed model and algorithm are efficient and competitive.

An enhanced exact algorithm for the multi-trip vehicle routing problem with time windows and capacitated unloading station

This paper introduces a vehicle routing problem that simultaneously considers multiple trips, time windows, and a capacitated unloading station. This problem is a generalization of the multi-trip vehicle routing problem with time windows, which determines a set of least-cost vehicle routes to fulfill all customer demands while respecting the constraints of vehicle capacity and time windows. Due to restricted resources (e.g., equipment and labor force) at the depot, vehicles may need to wait in a queue for being unloaded when they arrive. This unloading capacity constraint significantly complicates the problem, as it causes a trip to involve three stages—traveling, waiting, and unloading. We formulate this problem as an arc flow model and a trip-based set partitioning model, where the latter is solved by a branch-price-and-cut (BPC) algorithm. To improve the computational aspect of the BPC framework, a two-phase column generation (CG) algorithm is designed. First, a bidirectional labeling algorithm is tailored to solve the pricing problem, where two accelerating strategies are employed to speed up the resolution process. Meanwhile, k-path inequalities and limited-memory subset row inequalities are utilized to tighten the linear relaxation of the master problem. Computational results based on the instances adapted from the well-known Solomon’s benchmark show that the developed BPC algorithm can solve most instances within 50 customers to optimality in a short time frame and some instances of 100 customers to optimality within a 3-hour time limit. Moreover, our BPC algorithm performs better than exact algorithms in the literature for similar problem variants in both solution quality and computing time.

Path Optimization of Container Multimodal Transportation Considering Differences in Cargo Time Sensitivity

To optimize the container multimodal transportation path selection problem with differences in cargo time sensitivity, this paper introduces the concept of mixed time windows and establishes an integer programming model from the perspective of carriers. The objective is to minimize the total transportation cost while meeting the customer’s on-time delivery requirements. The model imposes hard time window constraints on cargoes with on-time delivery requirements and soft time window constraints on general cargoes. A bi-level genetic algorithm is employed to solve the model. A case study is conducted to demonstrate the effectiveness of the proposed approach. Experimental results show that the bi-level genetic algorithm’s convergence ability, efficiency, stability, and global search capabilities are far superior to those of traditional single-level genetic algorithms. This indicates that the use of multi-stage solution approaches can mitigate the shortcomings of genetic algorithms in dealing with high-dimensional problems. In addition, when analyzing the effects of time penalty intensity and time window on decision-making results, it is found that the more time-sensitive cargoes are more likely to be affected by the time window setting, and will tend to sacrifice costs to ensure that the time demand is met. At the same time an increase in demand for time-sensitive services is accompanied by an increase in operating costs. Accurate assessment and classification of time sensitivity of cargoes can effectively prevent wasting resources in unnecessary areas, and ultimately maximize decision outcomes and ensure the most efficient use of resources.

Multi-Domain Collaborative Task Allocation and Conflict Resolution in Unmanned Systems under Complex Constraints

Under the background that multi-domain collaborative tasks with complex constraints executed by heterogeneous unmanned systems, based on a consensus-based bundle algorithm, a consensus-based synergy algorithm is proposed to solve the distributed multi-domain collaborative task planning problem. First, a multi-domain collaborative task allocation model and score evaluation system are established by considering task resource requirement constraints, task timing constraints, and path threat constraints. Second, the time sequence constraints of collaborative tasks are transformed into elastic time window constraints. The bidding method based on collaborative constraints is used for task allocation, and the improved consistency conflict resolution principle is adopted to realize distributed multi-domain collaborative task allocation conflict resolution. Finally, the path planning is coupled to the task allocation process by using the Bezier curve path, and the results of multi-domain collaborative task allocation and path planning are obtained synchronously. Simulation results show that the proposed algorithm can effectively solve the problem of multi-domain collaborative task planning for heterogeneous unmanned systems.

Plant-wide optimal scheduling of multi-grade PET production with time window constraints: A hybrid discrete/continuous-time optimization formulation

Plant-wide scheduling optimization of multi-grade PET production is of great significance for increasing the economic benefits and market competitiveness of PET plants. However, dealing with changeover operations between the production of products with different grades is challenging due to multiple timing limitations in the actual process. This study proposes a novel plant-wide scheduling optimization model for multi-grade PET production. The model focuses on three major categories of products, namely PET fibers, PET chips, and bottle-grade PET. Considering the impacts of nights and weekends on the production, a hybrid discrete/continuous-time representation method is developed to handle changeover operations with time window constraints. Afterward, a multi-objective optimization framework for multi-grade PET production is formulated to balance economic benefits and production stability. Case studies on a real-world PET plant are presented to verify the effectiveness and applicability of the proposed method.

Research on the assignment of elderly care service personnel with time window constraints

As the population continues to age, there is a growing need for elderly care services. In China, home care is widely embraced as a preferred method of caring for the elderly, and it has a promising commercial outlook. The strategic allocation of Elderly Care Service Personnel (ECSP) is a crucial component of the operational procedures for home care services. By strategically assigning elderly service personnel, it is possible to enhance the satisfaction and simultaneously minimize expenses. The issue of rationalizing the assignment of ECSP in the face of restricted resources is a genuine challenge that requires a solution, given the many types of elderly service demands and the skill requirements and time limits of certain projects. This study presents a strategy for assigning personnel on an hourly basis, taking into account time frame limits. This method involves several steps. Firstly, it involves assessing the specific service needs of the elderly, including the required door-to-door service time, service level, and gender preferences. Secondly, it calculates the service satisfaction and service operation cost of the Home Care Service Platform (HCSP) separately. Finally, it constructs a multi-objective elderly service personnel assignment method. This method aims to minimize the ECSP 's travel time and wasted time, maximize the satisfaction of the elderly by considering priority levels and ECSP scores, and minimize the operation cost of the HCSP. A model is developed to assign ECSP for elderly individuals, with the goal of minimizing travel time and wasted time, maximizing elderly satisfaction by considering priority and service personnel rating, and minimizing operating costs for the HCSP. Additionally, if there are unserved elderly individuals, an optimized path model is constructed using a cross-modified genetic algorithm to obtain the optimal matching result. Ultimately, an arithmetic example is employed to demonstrate the practicality and efficiency of the strategy put forth in this research. The findings demonstrate that the model presented in this research possesses distinct advantages in comparison to other conventional models.

生鲜农产品冷链集货车辆路径与货物配载联合优化研究

As a bridge connecting agricultural production and consumption, the circulation of agricultural products has the function of connecting supply and demand, guiding production and promoting consumption. However, the development of rural logistics in China is slow, and most logistics centers still rely on experience to plan the pick-up vehicle routings, resulting in long transport time and high cost. In order to improve the efficiency of pick-up and reduce transportation costs, a joint optimization model of cold-chain pick-up vehicle routing and cargo allocation for fresh agricultural products was proposed in this study. Soft time window constraint and three-dimensional loading constraints were considered, and the lowest pick-up cost was used as optimization goals in this model. In addition, adaptive large neighborhood search algorithm (ALNS) and heuristic depth-first search algorithm (HDFS) were combined to solve the model. A case study of Kunming International Flower Auction Center was conducted to compare the schemes of pick-up vehicle routing before and after optimization. Results demonstrate that the pick-up cost after optimization decreases by 9.6 %, the number of vehicles decreases by one, the total volume utilization rate of vehicles increases by 23 %, and the total load utilization rate of vehicles increases by 15 %. This study provides a model reference and solution method for enterprise operators to formulate schemes of pick-up vehicle routing quickly and reasonably.