A robust optimization approach to dispatching technicians under stochastic service times

We consider the problem of dispatching technicians to service/repair geographically distributed equipment. This problem can be cast as a vehicle routing problem with time windows, where customers expect fast response and small delays. Estimates of the service time, however, can be subject to a significant amount of uncertainty due to misdiagnosis of the reason for failure or surprises during repair. It is therefore crucial to develop routes for the technicians that would be less sensitive to substantial deviations from estimated service times. In this paper we propose a robust optimization model for the vehicle routing problem with soft time windows and service time uncertainty and solve real-world instances with a branch and price method. We evaluate the efficiency of the approach through computational experiments on real industry routing data.     

New mixed integer-programming model for the pickup-and-delivery problem with transshipment

In recent years, many important real-world applications are studied as “rich” vehicle routing problems that are variants and generalizations of the well-known vehicle routing problem. In this paper we address the pickup-and-delivery version of this problem and consider further generalization by allowing transshipment in the network. Moreover, we allow heterogenous vehicles and flexible fleet size. We describe mixed integer-programming formulations for the problem with and without time windows for services. The number of constraints and variables in the models are bounded by polynomial size of the problem. We discuss several problem variants that are either captured by our models or can be easily captured through simple modifications. Computational work gave promising results and confirms that transshipment in network can indeed enhance optimization.     

Heuristics and memetic algorithm for the two-dimensional loading capacitated vehicle routing problem with time windows

This work deals with a new combinatorial optimization problem, the two-dimensional loading capacitated vehicle routing problem with time windows which is a realistic extension of the well known vehicle routing problem. The studied problem consists in determining vehicle trips to deliver rectangular objects to a set of customers with known time windows, using a homogeneous fleet of vehicles, while ensuring a feasible loading of each vehicle used. Since it includes NP-hard routing and packing sub-problems, six heuristics are firstly designed to quickly compute good solutions for realistic instances. They are obtained by combining algorithms for the vehicle routing problem with time windows with heuristics for packing rectangles. Then, a Memetic algorithm is developed to improve the heuristic solutions. The quality and the efficiency of the proposed heuristics and metaheuristic are evaluated by adding time windows to a set of 144 instances with 15–255 customers and 15–786 items, designed by Iori et al. (Transport Sci 41:253–264, 2007) for the case without time windows.     

Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation

This paper considers the routing of vehicles with limited capacity from a central depot to a set of geographically dispersed customers where actual demand is revealed only when the vehicle arrives at the customer. The solution to this vehicle routing problem with stochastic demand (VRPSD) involves the optimization of complete routing schedules with minimum travel distance, driver remuneration, and number of vehicles, subject to a number of constraints such as time windows and vehicle capacity. To solve such a multiobjective and multi-modal combinatorial optimization problem, this paper presents a multiobjective evolutionary algorithm that incorporates two VRPSD-specific heuristics for local exploitation and a route simulation method to evaluate the fitness of solutions. A new way of assessing the quality of solutions to the VRPSD on top of comparing their expected costs is also proposed. It is shown that the algorithm is capable of finding useful tradeoff solutions for the VRPSD and the solutions are robust to the stochastic nature of the problem. The developed algorithm is further validated on a few VRPSD instances adapted from Solomon’s vehicle routing problem with time windows (VRPTW) benchmark problems.     

遗传算法与蚂蚁算法的融合在带时间窗的车辆路径问题中的应用

对带时间窗的车辆路径问题(VRPTW)的求解分为两个过程,先由遗传算法求解出初步的可行解,由此生成信息素初始分布,而后采用蚂蚁算法找出问题的最优解或近似最优解.通过具体算例,从数值计算上探索了遗传算法和蚂蚁算法融合后的优化能力,获得了满意的效果.     

An optimization approach for communal home meal delivery service: A case study

This paper is the first to discuss the communal home meal delivery problem. The problem can be modelled as a multiple travelling salesman problem with time windows, that is closely related to the well-studied vehicle routing problem with time windows. Experimental results are reported for a real-life case study from Central Finland over several alternative scenarios using the SPIDER commercial solver. The comparison with current practice reveals that a significant savings potential can be obtained using off-the-shelf optimization tools. As such, the potential for supporting real-life communal routing problems can be considered to be important for VRP practitioners.     

A unified tabu search heuristic for vehicle routing problems with time windows

This paper presents a unified tabu search heuristic for the vehicle routing problem with time windows and for two important generalizations: the periodic and the multi-depot vehicle routing problems with time windows. The major benefits of the approach are its speed, simplicity and flexibility. The performance of the heuristic is assessed by comparing it to alternative methods on benchmark instances of the vehicle routing problem with time windows. Computational experiments are also reported on new randomly generated instances for each of the two generalizations.     

Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints

When vehicle routing problems with additional constraints, such as capacity or time windows, are solved via column generation and branch-and-price, it is common that the pricing subproblem requires the computation of a minimum cost constrained path on a graph with costs on the arcs and prizes on the vertices. A common solution technique for this problem is dynamic programming. In this paper we illustrate how the basic dynamic programming algorithm can be improved by bounded bi-directional search and we experimentally evaluate the effectiveness of the enhancement proposed. We consider as benchmark problems the elementary shortest path problems arising as pricing subproblems in branch-and-price algorithms for the capacitated vehicle routing problem, the vehicle routing problem with distribution and collection and the capacitated vehicle routing problem with time windows.     

求解硬时间窗约束下随机需求库存-路径问题的优化算法

随机需求库存-路径问题(Stochastic Demand Inventory Routing Problem, SDIRP)即考虑随机需求环境下供应链中库存与配送的协调优化问题,是实施供应商管理库存策略过程中的关键所在,也是典型的NP难题之一。文章以具有硬时间窗约束的随机需求库存-路径问题(Stochastic Demand Inventory Routing Problem with Hard Time Windows, SDIRPHTW)为研究对象,将SDIRPHTW分解为直接配送的随机库存-路径问题和具有硬时间窗约束的路径优化问题两个子问题,并以最小化系统运行成本和用车数量为目标,设计了一个基于(s,S)库存策略和修正C-W节约法的启发式算法。最后,通过相应的数值算例验证了算法的有效性。     

Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care

This paper addresses a vehicle scheduling problem encountered in home health care logistics. It concerns the delivery of drugs and medical devices from the home care company’s pharmacy to patients’ homes, delivery of special drugs from a hospital to patients, pickup of bio samples and unused drugs and medical devices from patients. The problem can be considered as a special vehicle routing problem with simultaneous delivery and pickup and time windows, with four types of demands: delivery from depot to patient, delivery from a hospital to patient, pickup from a patient to depot and pickup from a patient to a medical lab. Each patient is visited by one vehicle and each vehicle visits each node at most once. Patients are associated with time windows and vehicles with capacity. Two mixed-integer programming models are proposed. We then propose a Genetic Algorithm (GA) and a Tabu Search (TS) method. The GA is based on a permutation chromosome, a split procedure and local search. The TS is based on route assignment attributes of patients, an augmented cost function, route re-optimization, and attribute-based aspiration levels. These approaches are tested on test instances derived from existing VRPTW benchmarks.     

A branch-price-and-cut algorithm for the vehicle routing problem with time windows and multiple deliverymen

We address a variant of the vehicle routing problem with time windows that includes the decision of how many deliverymen should be assigned to each vehicle. In this variant, the service time at each customer depends on the size of the respective demand and on the number of deliverymen assigned to visit this customer. In addition, the objective function consists of minimizing a weighted sum of the total number of routes, number of deliverymen and traveled distance. These characteristics make this variant very challenging for exact methods. To date, only heuristic approaches have been proposed for this problem, and even the most efficient optimization solvers cannot find optimal solutions in a reasonable amount of time for instances of moderate size when using the available mathematical formulations. We propose a branch-price-and-cut method based on a new set partitioning formulation of the problem. To accelerate the convergence of the method, we rely on an interior-point column and cut generation process, a strong branching strategy and a mixed-integer programming-based primal heuristic. Additionally, a hierarchical branching strategy is used to take into account the different components of the objective function. The computational results indicate the benefits of using the proposed exact solution approach. We closed several instances of the problem and obtained upper bounds that were previously unknown in the literature.     

带时间窗分车运输同时收发车辆路径问题及其启发式算法

本文结合汽车零部件第三方物流的实际背景,提出了带时间窗的可分车运输同时收发车辆路径问题(简称SVRPSPDTW),并给出了问题的数学模型,同时提出两个求解该问题的启发式算法,最后进行了数值试验.由于没有可以利用的算例,本文在Solomn测试基准库的基础上构建了针对新问题的算例.计算结果表明,所有算例计算时间均不超过1秒,且算法1无论是从车辆的使用数还是从车辆行驶的路径总长度上都明显优于算法2,从而说明算法1是寻找SVRPSPDTW问题初始可行解的较为有效的算法.     

A hybrid multi-objective evolutionary algorithm for solving truck and trailer vehicle routing problems

This paper considers a transportation problem for moving empty or laden containers for a logistic company. Owing to the limited resource of its vehicles (trucks and trailers), the company often needs to sub-contract certain job orders to outsourced companies. A model for this truck and trailer vehicle routing problem (TTVRP) is first constructed in the paper. The solution to the TTVRP consists of finding a complete routing schedule for serving the jobs with minimum routing distance and number of trucks, subject to a number of constraints such as time windows and availability of trailers. To solve such a multi-objective and multi-modal combinatorial optimization problem, a hybrid multi-objective evolutionary algorithm (HMOEA) featured with specialized genetic operators, variable-length representation and local search heuristic is applied to find the Pareto optimal routing solutions for the TTVRP. Detailed analysis is performed to extract useful decision-making information from the multi-objective optimization results as well as to examine the correlations among different variables, such as the number of trucks and trailers, the trailer exchange points, and the utilization of trucks in the routing solutions. It has been shown that the HMOEA is effective in solving multi-objective combinatorial optimization problems, such as finding useful trade-off solutions for the TTVRP routing problem.     

The wafer probing scheduling problem (WPSP)

The wafer probing scheduling problem (WPSP) is a variation of the parallel-machine scheduling problem, which has many real-world applications, particularly, in the integrated circuit (IC) manufacturing industry. In the wafer probing factories, the jobs are clustered by their product types, which must be processed on groups of identical parallel machines and be completed before the due dates. Further, the job processing time depends on the product type, and the machine setup time is sequence dependent on the orders of jobs processed. Since the wafer probing scheduling problem involves constraints on job clusters, job-cluster dependent processing time, due dates, machine capacity, and sequence dependent setup time, it is more difficult to solve than the classical parallel-machine scheduling problem. In this paper, we formulate the WPSP as an integer programming problem. We also transform the WPSP into the vehicle routing problem with time windows (VRPTW), a well-known network routing problem which has been investigated extensively. An illustrative example is given to demonstrate the proposed transformation. Based on the provided transformation, we present three efficient algorithms to solve the WPSP near-optimally.     

一类新的车辆路径问题及其两阶段算法

本文结合汽车零部件第三方物流业的实际背景,提出了一类新的车辆路径问题,它是一种带时间窗约束的分车运输同时收发车辆路径问题(简称SVRPSPDTW).接着给出了问题的模型,并提出求解问题的启发式算法：两阶段算法. 最后在改进的Solomn的算例的基础上,进行了数值试验.     

有时间窗的车辆路径问题的局部下降搜索算法

介绍了一个求解有时间窗的车辆路径问题(vehicle routing problem with time windows,VRPTW)的启发式算法——基于λ-交换的局部下降搜索算法(Local search descent method based on λ-interchange).VRPTW是指合理安排车辆行驶路线,为一组预先设定有时间限制的客户运送货物,在不违反时间要求和车辆容量限制的条件下使得成本最小.它是一个典型的NP-难题,可以通过启发式算法获得近优解来解决.通过两个实验验证,显示了局部下降搜索算法的优良性能,取得了很好的效果,可以作为进一步研究复杂算法的基础.     

A note on the lifted Miller–Tucker–Zemlin subtour elimination constraints for routing problems with time windows

We propose lifted versions of the Miller–Tucker–Zemlin subtour elimination constraints for routing problems with time windows (TW). The constraints are valid for problems such as the travelling salesman problem with TW, the vehicle routing problem with TW, the generalized travelling salesman problem with TW, and the general vehicle routing problem with TW. They are corrected versions of the constraints proposed by Desrochers and Laporte (1991).     

An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles

The vehicle routing problem with multiple use of vehicles is a variant of the classical vehicle routing problem. It arises when each vehicle performs several routes during the workday due to strict time limits on route duration (e.g., when perishable goods are transported). The routes are defined over customers with a revenue, a demand and a time window. Given a fixed-size fleet of vehicles, it might not be possible to serve all customers. Thus, the customers must be chosen based on their associated revenue minus the traveling cost to reach them. We introduce a branch-and-price approach to address this problem where lower bounds are computed by solving the linear programming relaxation of a set packing formulation, using column generation. The pricing subproblems are elementary shortest path problems with resource constraints. Computational results are reported on euclidean problems derived from well-known benchmark instances for the vehicle routing problem with time windows.     

Vehicle routing problems with time windows and multiple service workers: a systematic comparison between ACO and GRASP

This paper systematically compares an ant colony optimization (ACO) and a greedy randomized adaptive search procedure (GRASP) metaheuristic. Both are used to solve the vehicle routing problem with time windows and multiple service workers. In order to keep the results comparable, the same route construction heuristic and local search procedures are used. It is shown that ACO clearly outperforms GRASP in the problem under study. Additionally, new globally best results for the used benchmark problems are presented.     

The rollon–rolloff waste collection vehicle routing problem with time windows

This study introduces a rollon–rolloff waste collection vehicle routing problem involving large containers that accumulate huge amounts of garbage at construction sites and shopping districts. In this problem, tractors move one container at a time between customer locations, a depot, disposal facilities, and container storage yards. The complicated constraints discussed in this study arise from having multiple disposal facilities, multiple container storage yards, seven service types of customer demands, different time windows for customer demands and facilities, various types and sizes of containers, and the lunch break of tractor drivers. In addition, real-world issues, such as changing service types, multiple demands at a customer’s location, and tractors with different work schedules, are dealt with. This study proposes a large neighborhood search based iterative heuristic approach consisting of several algorithms for the problem. The effectiveness of the proposed methods is demonstrated by computational experiments using benchmark data, some instances of which are derived from real-world problems.