Scheduling identical jobs on uniform parallel machines

We address the problem of scheduling n identical jobs on m uniform parallel machines to optimize scheduling criteria that are nondecreasing in the job completion times. It is well known that this can be formulated as a linear assignment problem, and subsequently solved in O ( n ³) time. We give a more concise formulation for minsum criteria, and show that general minmax criteria can be minimized in O ( n ²) time. We present faster algorithms, requiring only O ( n + m log m ) time for minimizing makespan and total completion time, O ( n log n ) time for minimizing total weighted completion time, maximum lateness, total tardiness and the weighted number of tardy jobs, and O ( n log² n ) time for maximum weighted tardiness. In the case of release dates, we propose an O ( n log n ) algorithm for minimizing makespan, and an O ( mn ^2m+1) time dynamic programming algorithm for minimizing total completion time.     

Scheduling spatially distributed jobs with degradation: Application to pothole repair

This paper considers scheduling spatially distributed jobs with degradation. A mixed integer programming (MIP) model is developed for the linear degradation case in which no new jobs arrive. Properties of the model are analyzed, following which three heuristics are developed, enhanced greedy, chronological decomposition and simulated annealing. Numerical tests are conducted to: (i) establish limits of the exact MIP solution, (ii) identify the best heuristic based on an analysis of performance on small problem instances for which exact solutions are known, (iii) solve large problem instances and obtain lower bounds to establish solution quality, and (iv) study the effect of three key model parameters. Findings from our computational experiments indicate that: (i) exact solutions are limited to instances with less than 14 jobs; (ii) the enhanced greedy heuristic followed by the application of the simulated annealing heuristic yields high quality solutions for large problem instances in reasonable computation time; and (iii) the factors “degradation rate” and “work hours” have a significant effect on the objective function. To demonstrate applicability of the model, a case study is presented based on a pothole repair scenario from Buffalo, New York, USA. Findings from the case study indicate that scheduling spatially dispersed jobs with degradation such as potholes requires: (i) careful consideration of the number of servers assigned, degradation rate and depot location; (ii) appropriate modeling of continuously arriving jobs; and (iii) appropriate incorporation of equity consideration.     

码头间集装箱拖箱业务调度系统研究

分析同一港口集装箱码头间拖箱业务产生原因的基础上,根据上海港（案例港）的实地调研数据,采用Dijkstra算法和模糊综合评判法,建立码头间集装箱拖箱业务调度模型及调度系统。用C＋＋11语言,编写了适用于港口的数字模拟平台,通过仿真,验证了设计的新调度模型比传统人工方式更有效率,为港口运营提供了切实可行的系统支持。     

Minimizing maximum lateness on one machine: computational experience and some applications

We consider the problem of scheduling jobs on a single machine subject to given release dates and precedence constraints, in order to minimize maximum lateness. The algorithms of B aker and S u (Naval Res. Logist. Quart. 21 (1974) 171–176) and of M c M ahon and F lorian (Operations Res. 23 (1975) 475–482) for the problem without precedence constraints are extended to the general case. An extensive computational comparison establishes the superiority of the latter algorithm. We describe applications to the theory of job-shop scheduling and to a practical scheduling situation.     

Evaluation of scheduling techniques for solving flowshop problems with no intermediate storage

The flowshop scheduling problem with no intermediate storage (NIS problem) was studied in this research. This problem, a modification of the classical flowshop scheduling problem, arises when a set of jobs, once started, must be processed with no wait between consecutive machines. By eliminating the need for intermediate storage, reduction of capital investment in work-in-process inventory can be achieved. This approach can be practically applied to a steel mill, in which the metal should be continuously processed in order to maintain high temperature, as well as many other similar processes.To provide insight into selecting an appropriate scheduling technique for solving the NIS problem, six methods were compared in terms of the quality and efficiency of the scheduling solutions they produced. The quality of solution was measured by makespan and the efficiency of solution was measured by the computational time requirements. The six methods examined in this study included: the Gupta algorithm, the Szwarc algorithm, an integer linear programming method, the Campbell et al. algorithm, the Dannenbring rapid access with extensive search algorithm, and a mixed integer linear programming procedure.The problem factors considered in this study were number of jobs, number of machines, and range of processing times. Relatively small-sized problems were tested with up to ten jobs, five machines, and 1–100 processing time units. Six solution techniques were selected and compared, with respect to makespan and computational time requirements, for multiple combinations of the three problem variables.The resulting test data were investigated using graphical procedures and formal statistical analyses. Initially, plots of mean values were used to graphically compare the six solution methods for the two performance criteria. Next, a multivariate analysis of variance study was conducted to investigate the quality and efficiency of the algorithms with respect to the problem factors. Then, a multiple comparison procedure was employed to analyze treatment mean differences among the six solution techniques. Results from the statistical analyses are summarized in this article.It was concluded that the two mathematical programming methods, the integer linear programming procedure and the mixed integer linear programming methods, produced the best performance in terms of makespan. These two methods, however, used a far greater amount of computational time than the other four solution techniques. Producing moderately good results as far as quality of performance, the Gupta and the Szwarc algorithms were comparable with the Campbell et al. and the Dannenbring algorithms in terms of computational efficiency. By comparison, the Campbell et al. and the Dannenbring algorithms produced the poorest performance with respect to the quality of solutions.Certain limitations were imposed for this study. The problem size considered was relatively small and the sample size was also limited to ten problems per cell. In addition, a uniform distribution function was used for generating processing times within certain ranges. These limitations were necessary in order to allow the various scheduling problems to be solved within a reasonable amount of computer time.Finally, some suggestions were provided for future research in the NIS problem area. The integer linear programming method was recommended as a standard of evaluation, owing to its best overall performance. A possible area for future research would involve the improvement of the Gupta and the Szwarc algorithms through the use of backtracking procedures within the branch-and-bound technique, so that they might be competitive with the mathematical programming methods with respect to quality of performance. Other distribution functions could be investigated in terms of the influence of the distribution of processing times on the performance measures.     

生产企业合同交货期确定及合同排序

讨论了企业订货合同管理中面临的决策问题以及解决途径。应用机器工件调度理论求解包括提前和延期惩罚的合同排序问题，给出了启发式排序规则和求解搜索策略。采用了3种启发式方法：1）接排序规则排序；2）对初始排序施加成对交换技术改善；3）射束搜索技术。实验结果表明，第3种求解质量具有明显优势，能得到令人满意的结果。     

基于动态约束的炼钢连铸重调度算法设计

针对炼钢连铸过程中出现的新炉次插入的重调度问题,考虑实际生产中的工艺约束,以最小化开工时间差异度、加工机器差异度的加权和为目标函数建立动态调度模型,采用回溯算法与启发式规则结合的算法。用Matlab7.8.0软件对选取的算例进行仿真,结果表明,此算法能保证重调度结果的实时性和有效性。     

An experimental comparison of human schedulers and heuristic algorithms for the traveling salesman problem

Vehicle routing and scheduling for laundry, courier, mail, and other service operations is a significant service industry problem. Several computer-based heuristic algorithms have been developed to assist schedulers in developing efficient delivery (and pick up) vehicle routes. This paper reports the results of an experiment that compared the performance of inexperienced human schedulers and seven heuristic vehicle routing algorithms. A large set of traveling salesman test problems ranging in size from 10 to 80 customers was used in the experiment. The results of the experiment suggest that inexperienced, untrained human schedulers can consistently find traveling salesman solutions as good as or better than all but one of the seven heuristic algorithms tested (including the widely used ClarkeWright distance saved heuristic and the recently published largest-angle insertion heuristic). The human schedulers found traveling salesman routes as good as the best heuristic tested (Lin 's 3-optimal) in 29 percent of the test problems. On average, the human schedulers' solution distances were only 2.8 percent above the 3-optimal heuristic solution distances.     

A note on workload-dependent due date assignment rules

For many production systems, delivery performance relative to promised job due dates is a critical evaluation criterion. Delivery performance is affected by the way in which work is dispatched on the shop floor, and also by the way the job due dates are assigned to begin with. This pape shows how information regarding congestion levels on the shop floor can be used to assign due dates to arriving jobs in such a way that the mean tardiness of jobs is decreased without increasing the average length of the promised delivery lead times.Baker and Bertrand suggested a modification of the Total Work (TWK) rule for assigning job due dates which adjusts the job flow allowance according to the level of congestion in the shop. Their method gives longer flow allowances to jobs which arrive when the system is congested. Although their modified TWK rule results in lower mean tardiness in many settings, it also generally results in a higher proportion of jobs tardy.This paper presents an alternative modification of the TWK rule which, in most cases, provides mean tardiness as low as or lower than Baker and Bertrand's rule and also results in a lower proportion of jobs tardy. The alternative rule suggested here still results in higher proportion of tardy jobs than the non-workload adjusted rule in most settings, but suggestions are made for how this problem might be addressed.     

Job shop scheduling with modified due dates

This paper introduces a new dispatching rule to job shop scheduling, extending earlier results to a multi-machine environment. This new rule, which uses modified due dates is compared to other popular dispatching methods over a range of due date tightnesses at two utilization levels. The results for mean tardiness indicate that the modified operation due date (MOD) rule compares very favorably with other prominent dispatching methods.The modified due date is a job's original due date or its early finish time, whichever is larger. For an individual operation, it is the operation's original due date or the operation's early finish time, whichever is larger. A comparison of the job-based version with the operation-based version indicated that the operation-based version tended to be more effective at meeting due dates.The main performance measure was mean job tardiness, although the proportion of tardy jobs was also reported, and the two measures together imply the conditional mean tardiness. The MOD rule was compared to several well-known tardiness-oriented priority rules, such as minimum slack-per-operation (S/OPN), smallest critical ratio (SCR), and COVERT. The MOD rule tended to achieve lower levels of mean tardiness than the other rules, except under conditions where due dates were quite loose. In this situation, very little tardiness occurs for any of the rules. The MOD rule appeared to be more robust than the other rules to changes in the tightness of due dates, and similar results occurred at both high and low utilizations.     

货物配装问题两种算法的比较研究

货物配装问题是NP-难问题，对这类问题如何求解，学术界提出了多种算法，这些算法可归结为2大类：精确算法和启发式算法。通过对这2类算法中最具代表性的几种算法的分析、比较和总结，指出了各种算法的优缺点、适用范围和场合、存在的问题以及改进的方案，为货物配装问题求解过程中算法的选择提供了依据和参考.     

卷烟厂制丝车间自动排产问题研究

以卷烟厂为研究背景,对制丝车间生产特点和排产需求进行分析,提出了基于规则的启发式算法,以解决卷烟厂制丝车间排产问题。以生产均衡为目标,构建以工段为整体的倒序排产的制丝车间排产算法,并将该算法应用于某卷烟厂。经实际数据验证,该算法可很好地满足制丝排产的需求。     

配送计划的优化编制方法

讨论了在时间、距离和载重量等多种约束条件下，编制配送计划的优化方法。先给出配送问题的数学模型，并设计了一个带时间和距离约束条件的启发式算法来求解该模型，求得问题的近似解；然后再采用分枝定界法得到配送问题的最优解：最后，考查近似解与最优解在总的运行距离的相对误差，以此检验这个近似解的有效性。     

Use of the net present value criterion in a random job shop where early shipments are forbidden

Both practitioners and researchers in the field of Operations Management have suggested that shop scheduling should be an integral component in both the strategic and tactical plans for an organization's assets. This paper examines the use of an accepted measure of return on assets, net present value (NPV), in a simulated shop scheduling environment where early shipment of jobs before their due dates is forbidden. In addition, early shipment of raw materials to the shop is also forbidden. This shop environment is consistent with the prevalent practice in industry of accepting orders only on a just-in-time basis to reduce purchased parts inventories. The NPV measure provides a means of balancing a variety of performance criteria that have been treated as separate objectives previously, including work-in-process inventory, finished goods inventory, mean flow time and mean tardiness, while also providing a means of measuring monetarily the value of various shop scheduling approaches.The NPV performance of priority scheduling rules and order release policies is measured in this research through the simulation of a random job shop under a variety of environmental conditions. It is found in a comparison of priority rules that use time-based information with those that use job value information that the Critical Ratio rule provides higher average performance than the three other rules used in the study. However, in some situations that are consistent with JIT practice, value-based priority rules also perform well. The use of a mechanism for delaying the release of jobs to each work center in the shop provided higher average NPV when shop utilization was set at a low level of 80%, while immediate release of work upon its arrival to the shop provided superior performance at a higher shop utilization level of 94%. While JIT materials delivery and costing yields higher NPV, it did not alter the relative ranking of priority rule/release policy combinations. In addition, it was found that environmental factors, including average job length, average number of tasks per job and level of tardiness penalty, resulted in greater variations in NPV performance than the institution of a JIT raw materials delivery policy.     

A heuristic rule for routing customers to parallel servers

A practically important problem is the assignment of stochastically arriving service requests to one of several parallel service groups so as to minimize the long-run average sojourn time per service request. An exact solution of this multi-dimensional optimization problem is computationally infeasible. A simple heuristic solution method yielding a good suboptimal rule will be given for the case of server groups with different and generally distributed service times. This solution method is based on a decomposition approach and first principles from Markov decision theory. The main idea of the heuristic method is to apply one step of policy improvement to the best Bernoulli-splitting rule.     

Scientific planning of urban cordon sanitaire for desired queuing time

The outbreak of the COVID-19 pandemic disrupted ofur normal life. Many cities enforced a cordon sanitaire as a countermeasure to protect densely inhabited areas. Travelers can only cross the cordon after being checked. To minimize the waiting time in the queue, this paper proposes a method to determine the scientific planning of urban cordon sanitaire for desired queuing time, which is a significant problem that has not been explored. A novel two-stage optimization model is proposed where the first stage is the transportation system equilibrium problem to predict traffic inflow, and the second stage is the queuing network design problem to determine the allocation of test stations. This method aims to minimize the total health infrastructure investment for the desired maximum queuing time. Note that queuing theory is used to represent the queuing phenomenon at each urban entrance. A heuristic algorithm is designed to solve the proposed model where the Method of Successive Averages (MSA) is adopted for the first stage, and the Genetic Algorithm (GA) with elite strategy is adopted for the second stage. An experimental study with sensitivity analysis is conducted to demonstrate the effectiveness of the proposed methods. The results show that the methods can find a good heuristic optimal solution. This research is helpful for policymakers to determine the optimal investment and planning of cordon sanitaire for disease prevention and control, as well as other criminal activities such as drunk driving, terrorists, and smuggling.     

基于扫描算法的启发式构造方法比较

针对车辆路径问题,基于扫描算法第一阶段的解,应用启发式算法中的最近插入算法、凸包算法和最远插入算法求解第二阶段。通过仿真实验,从总里程和算法运行时间两个方面对各算法性能给出评价。结果显示,在应用扫描算法进行聚类后,求解路径排程阶段,凸包算法虽然用时多于其它两种算法,但在里程上有明显优势,最远插入算法与最近插入算法在运行时间上没有显著差别,但在总里程上,前者较好。     

A new three-dimensional manufacturing service composition method under various structures using improved Flower Pollination Algorithm

With the growing complexity of customer requirements and the increasing scale of manufacturing services, how to select and combine the single services to meet the complex demand of the customer has become a growing concern. This paper presents a new manufacturing service composition method to solve the multi-objective optimization problem based on quality of service (QoS). The proposed model not only presents different methods for calculating the transportation time and transportation cost under various structures but also solves the three-dimensional composition optimization problem, including service aggregation, service selection, and service scheduling simultaneously. Further, an improved Flower Pollination Algorithm (IFPA) is proposed to solve the three-dimensional composition optimization problem using a matrix-based representation scheme. The mutation operator and crossover operator of the Differential Evolution (DE) algorithm are also used to extend the basic Flower Pollination Algorithm (FPA) to improve its performance. Compared to Genetic Algorithm, DE, and basic FPA, the experimental results confirm that the proposed method demonstrates superior performance than other meta heuristic algorithms and can obtain better manufacturing service composition solutions.     

一种解决配送规划问题的改进节约算法

车辆优化调度问题（VSP）是物流配送中广泛存在的一类问题，VSP问题属于NP一困难问题。在描述了简单VSP模型的基础上，对启发式算法中的C-W节约算法进行改进，将AK算法的思想运用其中，使计算结果的优化程度明显提高。     

Scheduling of re-entrant flow shops

We propose and develop a scheduling system for a very special type of flow shop. This flow shop processes a variety of jobs that are identical from a processing point of view. All jobs have the same routing over the facilities of the shop and require the same amount of processing time at each facility. Individual jobs, though, may differ since they may have different tasks performed upon them at a particular facility. Examples of such shops are flexible machining systems and integrated circuit fabrication processes. In a flexible machining system, all jobs may have the same routing over the facilities, but the actual tasks performed may differ; for instance, a drilling operation may vary in the placement or size of the holes. Similarly, for integrated circuit manufacturing, although all jobs may follow the same routing, the jobs will be differentiated at the photolithographic operations. The photolitho-graphic process establishes patterns upon the silicon wafers where the patterns differ according to the mask that is used.The flow shop that we consider has another important feature, namely the job routing is such that a job may return one or more times to any facility. We say that when a job returns to a facility it reenters the flow at that facility, and consequently we call the shop a re-entrant flow shop. In integrated circuit manufacturing, a particular integrated circuit will return several times to the photolithographic process in order to place several layers of patterns on the wafer. Similarly, in a flexible machining system, a job may have to return to a particular station several times for additional metal-cutting operations.These re-entrant flow shops are usually operated and scheduled as general job shops, ignoring the inherent structure of the shop flow. Viewing such shops as job shops means using myopic scheduling rules to sequence jobs at each facility and usually requires large queues of work-in-process inventory in order to maintain high facility utilization, but at the expense of long throughput times.In this paper we develop a cyclic scheduling method that takes advantage of the flow character of the process. The cycle period is the inverse of the desired production rate (jobs per day). The cyclic schedule is predicated upon the requirement that during each cycle the shop should perform all of the tasks required to complete a job, although possibly on different jobs. In other words, during a cycle period we require each facility to do each task assigned to it exactly once. With this requirement, a cyclic schedule is just the sequencing and timing on each facility of all of the tasks that that facility must perform during each cycle period. This cyclic schedule is to be repeated by each facility each cycle period. The determination of the best cyclic schedule is a very difficult combinatorial optimization problem that we cannot solve optimally for actual operations. Rather, we present a computerized heuristic procedure that seems very effective at producing good schedules. We have found that the throughput time of these schedules is much less than that achievable with myopic sequencing rules as used in a job shop. We are attempting to implement the scheduling system at an integrated circuit fabrication facility.