Soft Time Window Constraints Research Articles

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.

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.

考虑碳排放成本的多车型农资配送路径优化研究

Agriculture is the foundation of the national economy, and agricultural materials are the basis of agricultural development. As the three rural issues (agriculture, countryside, and farmers) become increasingly important, the distribution of agricultural materials attracts extensive attention. Given the slow development of rural logistics, the traditional agricultural material distribution process encounters many problems, such as cumbersome distribution links, high distribution costs, and low profit for enterprises, which in turn cause high production costs and low income for farmers. In consideration of battery energy consumption and soft time window constraints, this study adopted the agricultural material distribution route as the study object and established an optimization model of the agricultural material distribution route with fixed , transportation, energy consumption, time window penalty, and carbon emission costs as the objective functions. With regard to the algorithm, the operation of differential update and chaotic disturbance was innovatively enhanced and applied to the improved ant colony algorithm to simulate the model and obtain the optimal distribution route optimization model. Results show that the traditional ant colony algorithm improved by differential updating and chaotic disturbance has the advantages of low distribution cost, reasonable route, small number of activated vehicles, and short convergence time. Compared with the traditional ant colony algorithm, the improved ant colony algorithm can converge to the global optimum faster. This study provides guidance and suggestions on route selection and vehicle configuration to reduce costs and increase efficiency and offers certain theoretical support to alleviate urban traffic pollution and implement carbon trading policies in the future.

Cooperative aerial and ground vehicle trajectory planning for post-disaster communications: An attention-based learning approach

The ground infrastructures are highly susceptible to disruption after disasters, which causes the paralysis of communication. In this case, solutions besides original architecture are needed to meet the requirements of communication. Since unmanned aerial vehicle (UAV) can be quickly sent to disaster events to provide temporary connection due to its agility and mobility, it is suitable for performing disaster relief. Nevertheless, the limited onboard energy restricts the UAVs from fulfilling such persistent tasks. To this end, we introduce a ground vehicle carrying backup batteries to handle the energy issue of the UAV. Considering a time-constrained disaster-affected area, we propose a cooperative trajectory planning scheme to provide emergency communications swiftly and timely. The goal of our optimization task is to minimize the total cost of the mission, which consists of the operation cost for mission completion and the penalty cost for latency. We show that the task can be regarded as an extension of traveling salesman problem with soft time window constraints, which is NP-hard in general, and we propose a novel attention-based deep reinforcement learning with a sequential model strategy to learn the policy for the UAV's visiting order, based on which the trajectories of the UAV and ground vehicle are jointly designed. Numerical results show that our proposed attention-based trajectory planning scheme is effective and efficient, providing a guideline for the system design of post-disaster communications.

Casualty rescue path optimization in cities in early post-earthquake period

After an earthquake, decision makers are required to make a rapid response. In order to minimize the damage caused after an earthquake disaster and improve the efficiency of casualty rescue, scientific and effective casualty transportation dispatching is required. Especially for small and medium-sized cities where materials are scarce and transportation is inconvenient, effective optimization of casualty dispatching can minimize the amount of casualties and improve rescue efficiency. Therefore, this paper analyzes and researches the post-earthquake casualty rescue problem against the background of the initial rescue stage after the earthquake disaster in small and medium-sized cities, so as to provide the government and other relevant post-earthquake emergency logistics management departments with decision-making references. By establishing a casualty rescue planning model for small and medium-sized cities pursuing the minimization of total rescue time, and applying genetic algorithm to solve the path optimization model with soft time window constraints. The empirical analysis substitutes the street city simulation data of Wuxi County, Chongqing, and generates the stochastic solution and the optimal solution by MATLAB software, and the study finds that the optimal solution has significantly better travel time than the stochastic solution.

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.

A Hybrid Solution Approach for Electric Vehicle Routing Problem with Soft Time-Windows

An electric vehicle routing problem (EVRP) with time windows is carried out using a hybrid algorithm. Through the modeling of problem, not only the energy consumptions and the charging durations of the EDVs, but also the conventional vehicle flow formulations and the soft time window constraints are taken into account. A hybrid solution method is proposed to solve EVRP. The proposed method combines genetic algorithm and simulated annealing algorithm to complement each other. In order to demonstrate the effectiveness of the proposed approach, simulations are carried out on a case study with 25 customers, 2 charging stations, a depot and 3 identical EDVs. The performance of the proposed method has been compared with the standalone genetic algorithm. It is resulted that the hybrid algorithm outperforms the genetic algorithm in terms of both solution accuracy and computational time.

Research on Coordination and Optimization of Order Allocation and Delivery Route Planning in Take-Out System

This paper studies the take-out route delivery problem (TRDP) with order allocation and unilateral soft time window constraints. The TRDP considers the order allocation and delivery route optimization in the delivery service process. The TRDP is a challenging version of vehicle routing problem. In order to solve this problem, this paper aims to minimize the total cost of delivery, builds an optimization model of this problem by using cumulative time, and adds time dimension in order allocation and path optimization dimensions. It can not only track the real-time location of delivery personnel but also record the delivery personnel to perform a certain task. The main algorithm is the dynamic allocation algorithm designed from the perspective of dispatch efficiency, and the subalgorithm is the improved genetic algorithm. Finally, some experiments are designed to verify the effectiveness of the established model and the designed algorithm, the order allocation and route optimization are calculated with/without the consideration of traffic jam, and the results show that the algorithm can generate better solution in each scene.

A memetic algorithm for a home health care routing and scheduling problem

This work addresses a home health care routing and scheduling problem with time window and synchronization constraints. Each patient is associated with a period of availability according to their preferences while some visits may require the presence of two staff members simultaneously, which requires the synchronization of two visits. In this paper, the problem is studied with hard and soft patients time window and synchronization constraints. We developed a mixed integer programming model and a memetic algorithm featuring two original crossover operators. Experiments are conducted on benchmark instances from the literature as well as new instances based on real life data from a home health care provider in France. The results highlight the efficiency of the memetic algorithm since it provides great results while being flexible to the instance type. Indeed, the memetic algorithm is efficient whether the problem is studied with hard or soft time window and synchronization constraints, various caregivers qualification or several home health care offices.

Joint optimization of green vehicle scheduling and routing problem with time-varying speeds.

Based on an analysis of the congestion effect and changes in the speed of vehicle flow during morning and evening peaks in a large- or medium-sized city, the piecewise function is used to capture the rules of the time-varying speed of vehicles, which are very important in modelling their fuel consumption and CO2 emission. A joint optimization model of the green vehicle scheduling and routing problem with time-varying speeds is presented in this study. Extra wages during nonworking periods and soft time-window constraints are considered. A heuristic algorithm based on the adaptive large neighborhood search algorithm is also presented. Finally, a numerical simulation example is provided to illustrate the optimization model and its algorithm. Results show that, (1) the shortest route is not necessarily the route that consumes the least energy, (2) the departure time influences the vehicle fuel consumption and CO2 emissions and the optimal departure time saves on fuel consumption and reduces CO2 emissions by up to 5.4%, and (3) extra driver wages have significant effects on routing and departure time slot decisions.

Impact of the workload definition on the multi-objective home health care problem

Home health care services provide nursing and general hygiene cares in patient homes. Recently, structures providing home health care tend to optimize their activities leading to an increased interest in this problem. An important aspect of the problem is the balancing of the workload between the caregivers. The workload can be defined as the aggregation of several times: the travel time, the time spent on providing cures and the idle time. Because of its multi-objective nature, it is important to find a good compromise between the minimization of working time, the non-satisfaction of patients’ soft time window and synchronization constraints, and the workload balancing. In order to analyze the trade-off between the various objectives, we propose to model the home health care routing and scheduling problem as a multi-objective problem. Different definitions of the workload are studied in order to analyze their impacts on the trade-off between the objectives. A metaheuristic from the literature is used for the experiments. The results highlight the importance of workload definition on the trade-off between the different objectives and the ease of optimizing one objective over the others.

Energy-Efficient Location-Routing Problem with Time Windows with Dynamic Demand

Sustainability and energy savings have attracted considerable attention in recent years. However, in the traditional location-routing problem (LRP), the objective function has yet to minimize the distance traveled regardless of the amount of energy consumed. Although, distance is one of the major factors determining the energy consumption of a distribution network, it is not the only factor. Therefore, this paper explains the development of a novel formulation of the LRP that considers energy minimization, which is called the energy-efficient location-routing problem (EELRP). The energy consumed by a vehicle to travel between two nodes in a system depends on many forces. Among those, rolling resistance (RR) and aerodynamic drag are considered in this paper to be the major contributing forces. The presented mixed-integer non-linear program (MINLP) finds the best location-allocation routing plan with the objective function of minimizing total costs, including energy, emissions, and depot establishment. The proposed model can also handle the vehicle-selection problem with respect to a vehicles’ capacity, source of energy, and aerodynamic characteristics. The formulation proposed can also solve the problems with hard and soft time window constraints. Also, the model is enhanced to handle the EELRP with dynamic customers’ demands. Some examples are presented to illustrate the formulations presented in this paper.

The Optimization of Transportation Costs in Logistics Enterprises with Time-Window Constraints

This paper presents a model for solving a multiobjective vehicle routing problem with soft time-window constraints that specify the earliest and latest arrival times of customers. If a customer is serviced before the earliest specified arrival time, extra inventory costs are incurred. If the customer is serviced after the latest arrival time, penalty costs must be paid. Both the total transportation cost and the required fleet size are minimized in this model, which also accounts for the given capacity limitations of each vehicle. The total transportation cost consists of direct transportation costs, extra inventory costs, and penalty costs. This multiobjective optimization is solved by using a modified genetic algorithm approach. The output of the algorithm is a set of optimal solutions that represent the trade-off between total transportation cost and the fleet size required to service customers. The influential impact of these two factors is analyzed through the use of a case study.

Recent progress of local search in handling the time window constraints of the vehicle routing problem

Vehicle routing and scheduling problems have a wide range of applications and have been intensively studied in the past half century. The condition that enforces each vehicle to start service at each customer in the period specified by the customer is called the time window constraint. This paper reviews recent results on how to handle hard and soft time window constraints, putting emphasis on its different definitions and algorithms. With these diverse time windows, the problem becomes applicable to a wide range of real-world problems.

Recent progress of local search in handling the time window constraints of the vehicle routing problem

Vehicle routing and scheduling problems have a wide range of applications and have been intensively studied in the past half century. The condition that enforces each vehicle to start service at each customer in the period specified by the customer is called the time window constraint. This paper reviews recent results on how to handle hard and soft time window constraints, putting emphasis on its different definitions and algorithms. With these diverse time windows, the problem becomes applicable to a wide range of real-world problems.

Vehicle routing with soft time windows and Erlang travel times

This paper investigates vehicle-routing problems in which the travel times are random variables, and deliveries are made subject to soft time-window constraints. In particular, we model the travel time using a shifted gamma distribution. Penalties are incurred for deviations from the customers' time windows—early or late—and are developed using a fixed cost, a linear cost penalty, and/or a quadratic loss penalty. Alternatively, specifying a given probability of meeting the time-window constraints is considered. A tabu-search metaheuristic is developed, and computational results on test problems from the literature are reported.

The vehicle routing problem with flexible time windows and traveling times

We generalize the standard vehicle routing problem by allowing soft time window and soft traveling time constraints, where both constraints are treated as cost functions. With the proposed generalization, the problem becomes very general. In our algorithm, we use local search to determine the routes of vehicles. After fixing the route of each vehicle, we must determine the optimal start times of services at visited customers. We show that this subproblem is NP-hard when cost functions are general, but can be efficiently solved with dynamic programming when traveling time cost functions are convex even if time window cost functions are non-convex. We deal with the latter situation in the developed iterated local search algorithm. Finally we report computational results on benchmark instances, and confirm the benefits of the proposed generalization.

Effective Local Search Algorithms for Routing and Scheduling Problems with General Time-Window Constraints

We propose local search algorithms for the vehicle routing problem with soft time-window constraints. The time-window constraint for each customer is treated as a penalty function, which is very general in the sense that it can be nonconvex and discontinuous as long as it is piecewise linear. In our algorithm, we use local search to assign customers to vehicles and to find orders of customers for vehicles to visit. Our algorithm employs an advanced neighborhood, called the cyclic-exchange neighborhood, in addition to standard neighborhoods for the vehicle routing problem. After fixing the order of customers for a vehicle to visit, we must determine the optimal start times of processing at customers so that the total penalty is minimized. We show that this problem can be efficiently solved by using dynamic programming, which is then incorporated in our algorithm. We report computational results for various benchmark instances of the vehicle routing problem. The generality of time-window constraints allows us to handle a wide variety of scheduling problems. As an example, we mention in this paper an application to a production scheduling problem with inventory cost, and report computational results for real-world instances.

A metaheuristic for the vehicle-routeing problem with soft time windows

This paper develops a metaheuristic for the vehicle-routeing and scheduling problem with soft time window constraints. A tabu search solution method is developed, which utilizes a mixed neighbourhood structure and an advanced recovery procedure to generate high-quality solutions. Computational results on test problems from the literature are reported. The metaheuristic achieves solutions that compare favourably with previously reported results.

A problem generator-solver heuristic for vehicle routing with soft time windows

In this paper we consider the vehicle routing problem with soft time window constraints (VRPSTW), in which vehicles are allowed to service customers before and after the earliest and latest time window bounds, respectively. This relaxation comes at the expense of appropriate penalties that reflect the effect that time window violations have on the customers’ satisfaction. The problem is of particular importance for fleet planning as it allows decision-makers from both the logistics and marketing-sales side to determine minimal fleet sizes by appropriate contract negotiations for order delivery times. To solve the problem, we couple the nearest-neighbour method with a problem generator that provides, in a structured manner, numerous instances that result from the manipulation of the level of time window violations and the population of customers that allow such violations. The proposed heuristic results in solutions that reduce the number of vehicles required for the hard case and provide minimal violations of time windows. Computational results on a set of benchmark problems show that our method outperforms previous approaches to the vehicle routing problem with soft time windows, and that it can serve as the basis for efficient and effective fleet planning.