第三方物流企业在JIT方式下的多商品分批调度问题

在有多个商品、小批量定货且交货期不同的情况下,如何将这种混合的离散定单任务分批次完成并确定每一批次的调运开始时间,是当前第三方物流企业提高运作效率迫切需要解决的实际问题.给出了一个不允许出现拖期且提前惩罚的分批次优化模型和优化规则及算法,算例的结果表明了方法的有效性.     

不确定条件下不同交货期窗口的Job Shop 调度

研究了具有不同交货期窗口的Job Shop 的提前/ 拖期调度问题,并考虑了处理时间的不确定 性,采用三角模糊数表示处理时间的不确定性,提出了基于遗传算法的求解算法. 仿真实验验证了 算法的有效性.     

带有交货期窗口的单机加权提前／拖期调度问题研究

提前/拖期调度在JIT生产中具有重要意义,带有交货期窗口的调度问题是一个更一般的问题,但目前尚缺乏有效的求解方法.本文提出一种求解带有交货期窗口的单机提前/拖期调度问题的遗传算法,是为克服简单遗传算法的早熟收敛现象而提出的一种新型的遗传算法,并用大量随机产生的实例进行了仿真研究,结果表明,本文提出的算法是有效的.     

基于改进差分进化算法的VRP-SDPTW研究

整合前向物流和逆向物流,提出带时间窗的同时送货和取货的车辆路径问题(VRP-SDPTW)的混合整数规划数学模型.首次提出改进的差分进化算法(IDE)求解该问题,算法对不可行解设计惩罚机制,当基因值超过规定的范围时,设计基于整数序规范的辅助算子解决变异问题,设计一种随进化代数自动更新的交叉率.数值实验表明,改进的差分进化算法能有效地求解VRP-SDPTW.     

考虑交货因素的热轧无缝钢管订单排程模型与算法

无缝钢管的市场需求具有多品种、小批量的特点，为了在满足客户需求的同时保证高效连续化生产，文章在满足生产工艺特征的基础上将配送地址和交货期等合同因素引入热轧无缝钢管订单排程问题中，建立了以适期交货、订单集中生产配送和最小化机器设备调整为优化目标的订单排程优化模型，并设计了两阶段求解算法：首先，以订单交货期与配送地址差异最小为目标，基于凝聚策略设计了订单聚类算法，将具有相同工艺约束、相似合同要求的订单进行聚类，并形成初始轧制计划；然后，以设备调整和提前/拖期最小为目标，设计混合变邻域搜索算法，对初始轧制批次进行排程优化。基于实际订单数据的实验结果表明，模型和算法对问题的描述和求解是可行有效的。     

基于资源流网络优化的Max-npv项目调度

活动拖期通过资源流网络的传递会严重影响项目的净现值收益。针对该问题，本文首先在确定性环境下采用模拟退火算法(SA)构建了Max-NPV(Maximize the Net Present Value)非鲁棒性基准调度计划，然后考虑到活动工期的不确定性，设计了MEPC(Minimize Expected Penalty Cost)资源流网络优化算法，通过鲁棒性资源分配实现净现值期望惩罚成本最小化。大规模仿真对比实验结果表明，在活动工期低、中、高三种不确定性程度下，相对于采用随机资源分配算法(SA+RRAS)构建的非鲁棒性调度计划，SA+MEPC算法构建的鲁棒性调度计划在项目净现值实际收益、调度计划的“解”鲁棒性和“质”鲁棒性三个方面都取得了更好的结果，并且应对活动拖期风险的能力也更强。     

资金和存储能力约束下基于改进差分进化算法的联合采购模型研究

针对贴近实际情况约束的联合采购问题研究之不足,分析了资金和存储能力约束条件下的联合采购决策模型,该模型属于NP-hard问题,目前缺乏稳定高效的求解算法.在对差分进化算法改进并测试性能的基础上,设计了一种稳定可靠的自适应混合差分进化求解算法.另外,目前联合采购模型研究中多假设需求、库存持有费用以及次要准备费用为确定的参数,现实中这些参数往往是变动的且很难准确确定,故基于改进的差分进化算法对这些参数进行敏感性分析,进而讨论了数据不准确性对联合采购策略的影响程度.     

武钢X70钢多目标质量管理建模应用研究

针对现有质量管理建模方法大多难以有效处理小样本、非线性复杂问题的缺陷,提出了一套基于差分进化算法(DE)与支持向量机的融合建模方法,并将其应用于武钢质量管理建模.与神经网络建模技术的拟合结果对比检验验证了该方法的有效性,表明该方法能够为多目标质量管理问题提供一种较为有效的解决方案.     

并行设备上的差异作业批调度问题及多项式算法

考虑了一类作业尺寸有差异的批调度问题,加工环境为并行批处理设备.以制造跨度为优化目标,建立了基于整数规划的数学模型;分析了制造跨度最小化问题的计算复杂性,给出问题可行解规模的上下界;然后设计了一种基于LPT规则和Batch First Fit规则的近似算法,证明了算法的时间性能为O(nlogn),算法在优化制造跨度时的最坏性能比为(8/3～2/3m).     

平行机作业环境下的订单分配与排序

针对一类平行机作业环境下的订单分配与排序问题,从整体的角度协同优化供应链中的订单分配、生产调度和分批运输调度。以完成所有订单的总订货提前期与生产运输总成本的加权和最小化为目标,构建了问题的数学模型。将基于向量组编码结构的禁忌搜索算法与基于动态规划方法的启发式算法相结合,设计了一种混合优化算法以求解问题。对不同策略和不同算法进行比较,数据实验结果显示了订单分配与排序策略的优越性及所提算法的有效性。     

MINIMIZING ABSOLUTE AND SQUARED DEVIATION OF COMPLETION TIMES FROM DUE DATES

This is a study of a single-machine scheduling problem with the objective of minimizing the sum of a function of earliness and tardiness called the earliness and tardiness (ET) problem. I will show that if priority weights of jobs are proportional to their processing times, and if earliness and tardiness cost functions are linear, the problem will be equivalent to the total weighted tardiness problem. This proves that the et problem is np -hard. In addition, I present a heuristic algorithm with worst case bound for the et problem based on the equivalence relation between the two. When earliness and tardiness cost functions are quadratic, I consider the problem for a common due date for all jobs and for different job due dates. In general, the et problem with quadratic earliness and tardiness cost functions and all job weights equal to one is np -hard. I show that in many cases, when weights of jobs are proportional to their processing times, the problem can be solved efficiently. In the published results on the et problem with quadratic earliness and tardiness cost functions other researchers have assumed a zero starting time for the schedule. I discuss the advantages of a nonzero starting time for the schedule.     

A FRAMEWORK FOR MACHINE SCHEDULING PROBLEMS WITH CONTROLLABLE PROCESSING TIMES

This is a study of single and parallel machine scheduling problems with controllable processing time for each job. The processing time for job j depends on the position of the job in the schedule and is a function of the number of resource units allocated to its processing. Processing time functions and processing cost functions are allowed to be nonlinear. The scheduling problems considered here have important applications in industry and include many of the existing scheduling models as special cases. For the single machine problem, the objective is minimization of total compression costs plus a scheduling measure. The scheduling measures include makespan, total flow time, total differences in completion times, total differences in waiting times, and total earliness and tardiness with a common due date for all jobs. Except when the total earliness and tardiness measure is involved, each case the problem is solved efficiently. Under an assumption typically satisfied in just-in-time systems, the problem with total earliness and tardiness measure is also solved efficiently. Finally, for a large class of processing time functions; parallel machine problems with total flow time and total earliness and tardiness measures are solved efficiently. In each case we reduce the problem to a transportation problem.     

Optimal Policy for a Stochastic Scheduling Problem with Applications to Surgical Scheduling

We consider the stochastic, single‐machine earliness/tardiness problem (SET), with the sequence of processing of the jobs and their due‐dates as decisions and the objective of minimizing the sum of the expected earliness and tardiness costs over all the jobs. In a recent paper, Baker ( 2014 ) shows the optimality of the Shortest‐Variance‐First (SVF) rule under the following two assumptions: (a) The processing duration of each job follows a normal distribution. (b) The earliness and tardiness cost parameters are the same for all the jobs. In this study, we consider problem SET under assumption (b). We generalize Baker's result by establishing the optimality of the SVF rule for more general distributions of the processing durations and a more general objective function. Specifically, we show that the SVF rule is optimal under the assumption of dilation ordering of the processing durations. Since convex ordering implies dilation ordering (under finite means), the SVF sequence is also optimal under convex ordering of the processing durations. We also study the effect of variability of the processing durations of the jobs on the optimal cost. An application of problem SET in surgical scheduling is discussed.     

COMMON DUE-WINDOW SCHEDULING

In this paper, we solve common due-window scheduling problems within the just-in-time window concept, i.e., scheduling problems including both earliness and tardiness penalties. We assume that jobs share the same due window and incur no penalty as long as they are completed within the due window. We further assume that the earliness and tardiness penalty factors are constant and that the size of the window is a given parameter. For cases where the location of the due window is a decision variable, we provide a polynomial algorithm with complexity O(n * log (n)) to solve the problem. For cases where the location of the due window is a given parameter, we use dynamic programming with pseudopolynomial complexity to solve the problem.     

A bicriteria approach to scheduling a single machine with job rejection and positional penalties

Single machine scheduling problems have been extensively studied in the literature under the assumption that all jobs have to be processed. However, in many practical cases, one may wish to reject the processing of some jobs in the shop, which results in a rejection cost. A solution for a scheduling problem with rejection is given by partitioning the jobs into a set of accepted and a set of rejected jobs, and by scheduling the set of accepted jobs among the machines. The quality of a solution is measured by two criteria: a scheduling criterion, F1, which is dependent on the completion times of the accepted jobs, and the total rejection cost, F2. Problems of scheduling with rejection have been previously studied, but usually within a narrow framework—focusing on one scheduling criterion at a time. This paper provides a robust unified bicriteria analysis of a large set of single machine problems sharing a common property, namely, all problems can be represented by or reduced to a scheduling problem with a scheduling criterion which includes positional penalties. Among these problems are the minimization of the makespan, the sum of completion times, the sum and variation of completion times, and the total earliness plus tardiness costs where the due dates are assignable. Four different problem variations for dealing with the two criteria are studied. The variation of minimizing F1+F2 is shown to be solvable in polynomial time, while all other three variations are shown to be $\mathcal{NP}$ -hard. For those hard problems we provide a pseudo polynomial time algorithm. An FPTAS for obtaining an approximate efficient schedule is provided as well. In addition, we present some interesting special cases which are solvable in polynomial time.     

A tardiness-augmented approximation scheme for rejection-allowed multiprocessor rescheduling

In the multiprocessor scheduling problem to minimize the total job completion time, an optimal schedule can be obtained by the shortest processing time rule and the completion time of each job in the schedule can be used as a guarantee for scheduling revenue. However, in practice, some jobs will not arrive at the beginning of the schedule but are delayed and their delayed arrival times are given to the decision-maker for possible rescheduling. The decision-maker can choose to reject some jobs in order to minimize the total operational cost that includes three cost components: the total rejection cost of the rejected jobs, the total completion time of the accepted jobs, and the penalty on the maximum tardiness for the accepted jobs, for which their completion times in the planned schedule are their virtual due dates. This novel rescheduling problem generalizes several classic NP-hard scheduling problems. We first design a pseudo-polynomial time dynamic programming exact algorithm and then, when the tardiness can be unbounded, we develop it into a fully polynomial time approximation scheme. The dynamic programming exact algorithm has a space complexity too high for truthful implementation; we propose an alternative to integrate the enumeration and the dynamic programming recurrences, followed by a depth-first-search walk in the reschedule space. We implemented the alternative exact algorithm in C and conducted numerical experiments to demonstrate its promising performance.

     

A note on pre-emptive scheduling with earliness and tardiness costs

The option of pre-emption seems to have escaped the attention of existing literature on scheduling problems with earliness and tardiness costs. This note presents an attempt to accommodate pre-emption in such settings. The focus is on models with a common due date for all jobs under different cost structures ( job dependent versus job independent), and different objectives ( minsum and minmax). It appears that only one of these cases is not polynomially solvable: the case of minsum objective and job-dependent ( linear) cost. An exact dynamic programming algorithm is introduced for this problem, as well as an efficient heuristic, which is shown to perform extremely well in our numerical tests.     

Single-machine batch delivery scheduling with an assignable common due window

This paper addresses a batch delivery single-machine scheduling problem in which jobs have an assignable common due window. Each job will incur an early (tardy) penalty if it is early (tardy) with respect to the common due window under a given schedule. There is no capacity limit on each delivery batch, and the cost per batch delivery is fixed and independent of the number of jobs in the batch. The objective is to find the optimal size and location of the window, the optimal dispatch date for each job, as well as an optimal job sequence to minimize a cost function based on earliness, tardiness, holding time, window location, window size, and batch delivery. We show that the problem can be optimally solved in O(n⁸)$O(n^8)$ time by a dynamic programming algorithm under a reasonable assumption on the relationships among the cost parameters. A computational experiment is also conducted to evaluate the performance of the proposed algorithm. We also show that some special cases of the problem can be optimally solved by lower order algorithms.     

A NOTE ON “COMMON DUE WINDOW SCHEDULING”

Kramer and Lee recently addressed a common due window scheduling problem with earliness and tardiness penalties, where earliness and tardiness penalty factors are constant and the common window size is given. They showed that the problem is polynomial when the location of the due window is a decision variable. For the case where the location of the due window is given, the problem is also polynomial when the latest due date is greater than or equal to the makespan, and they proposed a pseudopolynomial dynamic programming algorithm to find an optimal schedule when the latest due date is less than the makespan. In this note we address the problem for the case where the location of the due window is given. Specifically, we show that the problem is polynomial if the window location is unrestricted, and present a more efficient dynamic program algorithm to optimally solve the problem if the window location is restricted. The concepts of unrestricted and restricted window locations are defined in this note.     

A two-agent single machine scheduling problem with due-window assignment and a common flow-allowance

We study a single-machine scheduling model combining two competing agents and due-date assignment. The basic setting involves two agents who need to process their own sets of jobs, and compete on the use of a common processor. Our goal is to find the joint schedule that minimizes the value of the objective function of one agent, subject to an upper bound on the value of the objective function of the second agent. The scheduling measure considered in this paper is minimum total (earliness, tardiness and due-date) cost, based on common flow allowance, i.e., due-dates are defined as linear functions of the job processing times. We introduce a simple polynomial time solution for this problem (linear in the number of jobs), as well as to its extension to a multi-agent setting. We further extend the model to that of a due-window assignment based on common flow allowance.