Unbounded parallel-batch scheduling with family jobs and delivery coordination

We study a scheduling problem that integrates parallel-batch production with family jobs and job delivery at the same time. The jobs are first processed on an unbounded parallel-batch machine and then delivered in batches to their specified customers by a transportation vehicle. We assume that jobs from different families (customers) cannot be processed together by the batch machine and also transported together by the vehicle. The objective is to minimize the time when the vehicle finishes delivering the last delivery batch to its customer and returns to the machine. We first show that the problem is NP-hard, and then propose for it a heuristic algorithm with a worst-case performance ratio of 3/2.     

Machine scheduling with job class setup and delivery considerations

We study machine scheduling problems in which the jobs belong to different job classes and they need to be delivered to customers after processing. A setup time is required for a job if it is the first job to be processed on a machine or its processing on a machine follows a job that belongs to another class. Processed jobs are delivered in batches to their respective customers. The batch size is limited by the capacity of the delivery vehicles and each shipment incurs a transport cost and takes a fixed amount of time. The objective is to minimize the weighted sum of the last arrival time of jobs to customers and the delivery (transportation) cost. For the problem of processing jobs on a single machine and delivering them to multiple customers, we develop a dynamic programming algorithm to solve the problem optimally. For the problem of processing jobs on parallel machines and delivering them to a single customer, we propose a heuristic and analyze its performance bound.     

Single machine scheduling with job delivery to multiple customers

We investigate a single machine scheduling problem with job delivery to multiple customers. In this problem, each job needs to be processed on the single machine, and then delivered by a single vehicle to its customer, where the job has a physical size representing the fraction of space it occupies on the vehicle. The vehicle delivers a shipment from the machine to a customer and has to return back to the machine for delivering the next shipment. It takes different constant time for the round trips between the machine and the different customers. The goal is to minimize the makespan, by that time all the jobs are processed and delivered to their respective customers, and the vehicle returns back to the machine. We propose a 2-approximation algorithm for the general case; when there are only two customers, we present an improved 5/3-approximation algorithm. The design and performance analysis of these two algorithms integrate several known results and techniques for the single machine scheduling problem, the bin-packing problem, and the knapsack problem.     

An ant colony-based algorithm for integrated scheduling on batch machines with non-identical capacities

In this paper, a production–distribution scheduling problem with non-identical batch machines and multiple vehicles is considered. In the production stage, n jobs are grouped into batches, which are processed on m parallel non-identical batch machines. In the distribution stage, there are multiple vehicles with identical capacities to deliver jobs to customers after the jobs are processed. The objective is to minimize the total weighted tardiness of the jobs. Considering the NP-hardness of the studied problem, an algorithm based on ant colony optimization is presented. A new local optimization strategy called LOC is proposed to improve the local exploitation ability of the algorithm and further search the neighborhood solution to improve the quality of the solution. Moreover, two interval candidate lists are proposed to reduce the search for the feasible solution space and improve the search speed. Furthermore, three objective-oriented heuristics are developed to accelerate the convergence of the algorithm. To verify the performance of the proposed algorithm, extensive experiments are carried out. The experimental results demonstrate that the proposed algorithm can provide better solutions than the state-of-the-art algorithms within a reasonable time.

     

Vehicle power train optimization using multi-objective bird swarm algorithm

In this paper, a multi-objective bird swarm algorithm (MOBSA) is proposed to cope with multi-objective optimization problems. The algorithm is explored based on BSA which is an evolutionary algorithm suitable for single objective optimization. In this paper, non-dominated sorting approach is used to distinguish optimal solutions and parallel coordinates is applied to evaluate the distribution density of non-dominated solution and further update the external archive when it is full to overflowing, which ensure faster convergence and more widespread of Pareto front. Then, the MOBSA is adopted to optimize benchmark problems. The results demonstrate that MOBSA gets better performance compared with NSGA-II and MOPSO. Since a vehicle power train problem could be treated as a typical multi-objective optimization problem with constraints, with integration of constrained non-dominated solution, MOBSA is adopted to acquire optimal gear ratios and optimize vehicle power train. The results compared with other popular algorithm prove the proposed algorithm is more suitable for constrained multi-objective optimization problem in engineering field.

     

应急物资运输路径多目标优化模型及求解算法

针对应急前期运输商自有车辆不足的实际背景,采用自有车辆和第三方租用车辆共同配送的运输模式,对混合车辆路径的组合优化问题进行研究。首先,考虑需求点和运输商的不同利益诉求,以系统满意度最大、系统配送时间和总成本最小为优化目标,建立带软时间窗的多目标混合车辆路径优化模型。其次,考虑NSGA-Ⅱ算法在求解该类问题时收敛性差和Pareto前沿分布不均匀的缺点,将蚁群算法的启发式策略和信息素正反馈机制用于生成子代种群,非支配排序策略模型用于指导算法的多目标择优过程,并引入变邻域下降搜索以扩大搜索空间,提出求解多目标的非支配排序蚁群算法以突破原有算法瓶颈。算例表明：构建的模型可对决策者在不同的情境下依据不同的优化目标选择合理的路径提供参考,提出的算法在求解不同规模的问题和不同分布类型的问题中均表现出较好的性能。     

零等待约束下多产品间歇过程的多目标调度

针对零等待约束下多产品间歇过程的总流程时间和完工时间最小化问题,提出一种多目标离散组搜索算法求解.在采用启发式规则产生初始解的基础上,通过发现者、追随者和巡逻者的操作设计,算法不断更新Pareto前沿,同时,混合了基于插入邻域的多目标局部搜索方法.大量计算实验表明,所提出的算法获得的非支配解集在IGD和Set Coverage指标上优于非支配排序遗传算法和模拟退火算法,可为多目标决策者提供更好的决策依据,利于间歇生产过程的优化运行.     

改进AHP-GA算法的多目标配送路径优化

为准确优化快递配送路径,建立了基于时间窗的快递配送路径优化的数学模型.提出改进AHP-GA算法对多目标配送车辆路径进行优化,利用中位数层次分析算法对多个子目标进行权重系数配比,避免了极端值的影响,从而将多目标优化问题转化为单目标优化问题.通过简单的自然数对车辆路径进行编码,避免了路径重复.考虑了客户对车辆到达时间窗要求,包括车辆在约定时间之前到达获得的机会成本、在约定时间之后到达的罚金成本.最后,本文以1个配送中心,20个服务客户为例,对构建的数学模型通过分别使用传统的GA算法和使用改进AHP-GA算法进行优化,仿真结果表明,利用改进AHP-GA算法进行多目标配送路径优化,可以更加高效地求得问题的最优解.     

Complexity results for an integrated single machine scheduling and outbound delivery problem with fixed sequence

In this paper, we consider an integrated production and outbound delivery scheduling problem. In particular, we address the situation in which the scheduling sequence and the delivery sequence are the same and predefined. A set of jobs are processed on a single machine, and finished jobs are delivered to the customers by a single capacitated vehicle. Each job has a processing time, and transportation times between customers are taken into account. Because the sequence is given, the problem consists in forming batches of jobs and our objective is to minimize the sum of the delivery times or general functions of the delivery times. The NP-hardness of the general problem is established, and a pseudopolynomial time dynamic programming algorithm is given. Some particular cases are treated, for which NP-hardness proofs and polynomial time algorithms are given. Finally, a fixed-parameter tractability result is given.     

考虑订单发货区域的物流配送调度问题研究

研究了一种考虑订单发货区域的物流配送问题,针对问题建立了两阶段多目标整数规划模型：订单车辆指派模型和车辆配送调度模型。基于对模型及问题特点的分析,构造了一种两阶段优化算法：第一阶段,基于聚类-约束满足优化算法为待发货订单指派最佳车辆;第二阶段,基于单亲遗传算法为车辆指定最佳的物流配送方案。通过数据仿真验证,模型和算法是可行且有效的。     

采用双档案协同进化离散多目标烟花算法的低碳疫苗冷链优化配送

建立低碳疫苗冷链配送问题的约束多目标优化模型,在满足可用车数量、车辆容量约束和时间窗约束的条件下,考虑最小化碳排放的企业运输成本和客户不满意度。提出一种双档案协同进化的离散多目标烟花算法,采用消除车辆数量和容量约束的解码方式,设计了部分映射爆炸算子,设置可行解档案和不可行解档案协同进化,并对不可行解档案实施可行性搜索。实验结果表明,与已有算法相比,所提算法在低碳疫苗冷链配送问题上能高效地搜索到一组收敛精度和分布性能更优的Pareto非支配解。     

A branch-and-bound algorithm for single-machine scheduling with batch delivery and job release times

This paper addresses scheduling a set of jobs with specified release times on a single machine for delivery in batches to customers or to other machines for further processing. This problem is a natural extension of minimizing the sum of flow times in the presence of release time by considering the possibility of delivering jobs in batches and introducing batch delivery costs. The scheduling objective adopted is that of minimizing the sum of flow times and delivery costs. The extended problem arises in the context of coordination between machine scheduling and a distribution system in a supply chain network. Structural properties of the problem are investigated and used to devise a branch-and-bound solution scheme. Computational experiments show significant improvement over an existing dynamic programming algorithm.     

不同支配关系的NSGA-III算法在机器人制造单元调度问题中的应用

随着经济的发展,机器人制造单元对制造行业的生产效率和生产质量有很大提高.相对于传统的柔性制造单元,带机器人搬运的车间的调度问题还考虑了加工物料的搬运环节.因此,生产调度所面临的问题越来越复杂.针对Pareto支配关系在高维多目标优化中的支配能力不足,本文将Lorenz支配和CDAS支配分别与NSGA-III算法相结合,并首次应用到带机器人制造单元的高维多目标车间调度问题上来.考虑到现代生产过程的复杂化,本文提出对最大完工时间、加工总能耗、交货期提前量、延迟量、生产总成本等多个目标同时进行优化,用于确定机器人工作时操作状态和搬运顺序,提高生产效率.通过实验发现基于Lorenz支配和CDAS支配的NSGA-III算法在该生产调度问题上比传统的NSGA-III在解的收敛性和均匀性上表现更优.     

Using genetic algorithm for lot sizing and scheduling problem with arbitrary job volumes and distinct job due date considerations

This paper considers an integrated lot sizing and scheduling problem for a production–distribution environment with arbitrary job volumes and distinct due dates considerations. In the problem, jobs are firstly batch processed on a batching machine at production stage and then delivered to a pre-specified customer at the subsequent delivery stage by a capacitated vehicle. Each job is associated with a distinct due date and a distinct volume, and has to be delivered to the customer before its due date, i.e. delay is not allowed. The processing time of a batch is a constant independent of the jobs it contains. In production, a constant set-up time as well as a constant set-up cost is required before the first job of this batch is processed. In delivery, a constant delivery time as well as a constant delivery cost is needed for each round-trip delivery between the factory and the customer. Moreover, it is supposed that a job that arrives at the customer before its due date will incur a customer inventory cost. The objective is to find a coordinated lot sizing and scheduling scheme such that the total cost is minimised while guaranteeing a certain customer service level. A mixed integer formulation is proposed for this problem, and then a genetic algorithm is developed to solve it. To evaluate the performance of the proposed genetic algorithm, a lower bound on the objective value is established. Computational experiments show that the proposed genetic algorithm performs well on randomly generated problem instances.     

Agile optimization of a two‐echelon vehicle routing problem with pickup and delivery

In this paper, we consider a vehicle routing problem in which a fleet of homogeneous vehicles, initially located at a depot, has to satisfy customers' demands in a two‐echelon network: first, the vehicles have to visit intermediate nodes (e.g., a retail center or a consolidation center), where they deliver raw materials or bulk products and collect a number of processed items requested by the customers in their route; then, the vehicles proceed to complete their assigned routes, thus delivering the processed items to the final customers before returning to the depot. During this stage, vehicles might visit other intermediate nodes for reloading new items. In some real‐life scenarios, this problem needs to be solved in just a few seconds or even milliseconds, which leads to the concept of “agile optimization.” This might be the case in some rescue operations using drones in humanitarian logistics, where every second can be decisive to save lives. In order to deal with this real‐time two‐echelon vehicle routing problem with pickup and delivery, an original constructive heuristic is proposed. This heuristic is able to provide a feasible and reasonably good solution in just a few milliseconds. The constructive heuristic is extended into a biased‐randomized algorithm using a skewed probability distribution to modify its greedy behavior. This way, parallel runs of the algorithm are able to generate even better results without violating the real‐time constraint. Results show that the proposed methodology generates competitive results in milliseconds, being able to outperform other heuristics from the literature.     

需求可拆分车辆路径问题的聚类求解算法

针对传统的车辆路径问题通常假设客户的需求不能拆分,即客户的需求由一辆车满足,而实际上通过需求的拆分可使需要的车辆数更少,从而降低配送成本的问题,分析了需求可拆分的车辆路径问题的解的特征,证明了客户需求不宜拆分应满足的条件,设计了符合解的特征的聚类算法,并对其求解.通过实验仿真,将所提出的聚类算法与蚁群算法和禁忌搜索算法进行比较,所得结果表明了所提出的算法可以更有效地求得需求可拆分车辆路径问题的优化解,是解决需求可拆分车辆路径问题的有效方法.     

An improved approximation algorithm for single machine scheduling with job delivery

In single machine scheduling with release times and job delivery, jobs are processed on a single machine and then delivered by a capacitated vehicle to a single customer. Only one vehicle is employed to deliver these jobs. The vehicle can deliver at most c jobs in a shipment. The delivery completion time of a job is defined as the time in which the delivery batch containing the job is delivered to the customer and the vehicle returns to the machine. The objective is to minimize the makespan, i.e., the maximum delivery completion time of the jobs. We provide an approximation algorithm for this problem which is better than that given in the literature, improving the performance ratio from 5/3 to 3/2.     

基于模糊物元模型的高维多目标FJSP研究*

为解决高维多目标柔性作业车间调度问题,提出了一种基于模糊物元模型与粒子群算法的模糊粒子群算法（Fuzzy Particle Swarm Optimization,FPSO）。该算法以模糊物元分析理论为依据,采用复合模糊物元与基准模糊物元之间的欧式贴近度作为适应度值引导粒子群算法的进化,并引入具有容量限制的外部存储器保留较优的Pareto非支配解以供决策者选择。此外,构建了优化目标为最大完工时间、设备总负荷、加工成本、最大设备负荷与加工质量的高维多目标优化模型,并以Kacem基准问题与实际生产数据为例进行仿真模拟与对比分析。结果表明,该算法具有良好的收敛性且搜索到的非支配解分布性较好,能够有效地应用于求解高维多目标柔性作业车间调度问题。     

An evolutionary approach for multi-objective vehicle routing problems with backhauls

The vehicle routing problem (VRP) is an important aspect of transportation logistics with many variants. This paper studies the VRP with backhauls (VRPB) in which the set of customers is partitioned into two subsets: linehaul customers requiring a quantity of product to be delivered, and backhaul customers with a quantity to be picked up. The basic VRPB involves finding a collection of routes with minimum cost, such that all linehaul and backhaul customers are serviced. A common variant is the VRP with selective backhauls (VRPSB), where the collection from backhaul customers is optional. For most real world applications, the number of vehicles, the total travel cost, and the uncollected backhauls are all important objectives to be minimized, so the VRPB needs to be tackled as a multi-objective problem. In this paper, a similarity-based selection evolutionary algorithm approach is proposed for finding improved multi-objective solutions for VRPB, VRPSB, and two further generalizations of them, with fully multi-objective performance evaluation.     

Solving a new bi-objective location-routing-inventory problem in a distribution network by meta-heuristics

This paper presents a novel bi-objective location-routing-inventory (LRI) model that considers a multi-period and multi-product system. The model considers the probabilistic travelling time among customers. This model also considers stochastic demands representing the customers’ requirement. Location and inventory-routing decisions are made in strategic and tactical levels, respectively. The customers’ uncertain demand follows a normal distribution. Each vehicle can carry all kind of products to meet the customer’s demand, and each distribution center holds a certain amount of safety stock. In addition, shortage is not allowed. The considered two objectives aim to minimize the total cost and the maximum mean time for delivering commodities to customers. Because of NP-hardness of the given problem, we apply four multi-objective meta-heuristic algorithms, namely multi-objective imperialist competitive algorithm (MOICA), multi-objective parallel simulated annealing (MOPSA), non-dominated sorting genetic algorithm II (NSGA-II) and Pareto archived evolution strategy (PAES). A comparative study of the forgoing algorithms demonstrates the effectiveness of the proposed MOICA with respect to four existing performance measures for numerous test problems.