Job shop scheduling—A case study

A missile range is essentially a large-scale job-shop, involving prodigious amounts of test equipment and formidable problems of coordination. Because of its characteristics, a missile range can be considered a one-machine, N-job situation. For this problem the major scheduling methods were examined and tested, but all were discarded as unfeasible except one which used a Monte Carlo scheduling procedure adjoined with statistical stopping rules. An algorithm based on these ideas was constructed, and it has proven to be flexible and workable, providing predictably near optimum schedules for the missile range within a probabilistic and statistical framework. Even though there is not total implementation yet, considerable benefits to the missile range have already been experienced. For example, in order to automate the scheduling process, it was necessary to codify the goals of the range, something that had never been formalized before. This involved an unprecedented scrutiny and precision of definition of these goals, and from this study a reasonable numerical optimization criterion was constructed. Also, in order to use any automated scheduling algorithm, data files had to be stored on tape for ready access, which in turn has improved other operations on the missile range that were dependent on these data. Furthermore, the scheduling algorithm is providing conflict-free schedules in a few minutes of computer time.     

一种求解双目标flow shop排序问题的进化算法

提出一种求解双目标flow shop排序的递进多目标进化算法.算法采用改进的精英复制策略,在实现精英保留的前提下降低了计算复杂性;通过递进进化模式增加群体多样性,改善了算法收敛性;通过群体进化过程中对非劣解集进行竞争型可变邻域启发式搜索,增强了算法局部搜索性能.采用新算法和参照算法NSGA-II对31个标准双目标flow shop算例进行优化.研究结果表明,新算法在所有算例的求解中均获得了优于NSGA-II的非劣解集,验证了算法的有效性.     

基于改进蚂蚁算法的拉动式供应链动态调度分析

分析了拉动式供应链调度动态性的产生根源,指出由于存在供应链协作成员之间复杂的协作与竞争关系,导致了供应链动态调度的特殊性;分析了供应链动态调度过程中的两个主要瓶颈.为了合理解决瓶颈问题,在优化供应链动态调度过程中引入蚁群觅食的寻优机理,并对其进行特定的算法设计及改进,提出供应链动态调度的蚂蚁寻优算法.仿真结果验证了算法可行有效.     

等待时间受限的置换流水车间调度启发式算法

针对等待时间受限的置换流水车间调度问题,分析了其可行解与流水车间调度最优解的关系,给出了计算最大完工时间的有向图,证明了等待时间受限的置换流水车间调度问题的可逆性,并以此为基础提出了一种启发式算法.算法首先根据等待时间受限约束与无等待(no-wait)约束的相似特征,生成初始工件序列集;然后利用问题可逆性给出了复杂度为O(n2m)的插入优化机制,进一步优化初始解.数据实验的结果验证了启发式算法的可行性和有效性.     

Master Scheduling in Assemble-To-Order Environments: A Capacitated Multiobjective Lot-Sizing Model

Basic characteristics of an assemble-to-order environment make effective master scheduling extremely difficult. Limited resource capacities and dynamic customer end-item demand contribute to the complexity of the master production scheduling problem. To gain flexibility and responsiveness within this system, the master production schedule (MPS) focuses at the component level. This research proposes a master scheduling technique for manufactured components which combines a multiobjective capacitated multi-item/multi-stage lot-sizing model with an interactive multiple objective optimization solution procedure. To evaluate the model's performance as a realistic and practical master scheduling tool, this study focuses on the National Cash Register (NCR) electronics manufacturing facility in Columbia, South Carolina.     

Games and Mechanism Design in Machine Scheduling—An Introduction

We survey different models, techniques, and some recent results to tackle machine scheduling problems within a distributed setting. In traditional optimization, a central authority is asked to solve a (computationally hard) optimization problem. In contrast, in distributed settings there are several agents, possibly equipped with private information that is not publicly known, and these agents must interact to derive a solution to the problem. Usually the agents have their individual preferences, which induces them to behave strategically to manipulate the resulting solution. Nevertheless, one is often interested in the global performance of such systems. The analysis of such distributed settings requires techniques from classical optimization, game theory, and economic theory. The paper therefore briefly introduces the most important of the underlying concepts and gives a selection of typical research questions and recent results, focusing on applications to machine scheduling problems. This includes the study of the so‐called price of anarchy for settings where the agents do not possess private information, as well as the design and analysis of (truthful) mechanisms in settings where the agents do possess private information.     

多功能机床环境下的Job Shop问题研究

本文引入工序机的概念描述加工系统的资源,建立了面向多功能加工机床的Job Shop作业计划模型,用遗传算法对所建的模型进行优化。在遗传算法优化搜索的基础上,利用工件、工序机和实际机床之间的动态调度使作业计划更趋合理。最后给出数值试验结果。     

A decision support methodology for strategic planning in maritime transportation

This paper presents a decision support methodology for strategic planning in tramp and industrial shipping. The proposed methodology combines simulation and optimization, where a Monte Carlo simulation framework is built around an optimization-based decision support system for short-term routing and scheduling. The simulation proceeds by considering a series of short-term routing and scheduling problems using a rolling horizon principle where information is revealed as time goes by. The approach is flexible in the sense that it can easily be configured to provide decision support for a wide range of strategic planning problems, such as fleet size and mix problems, analysis of long-term contracts and contract terms. The methodology is tested on a real case for a major Norwegian shipping company. The methodology provided valuable decision support on important strategic planning problems for the shipping company.     

A multi-objective vehicle routing and scheduling problem with uncertainty in customers’ request and priority

In this paper, a multi-objective vehicle routing and scheduling problem with uncertainty in priority and request of customers is presented. In the proposed model, a set of dynamic requests is received over time, and the planner does not have any information regarding their location and size until they arrive. Moreover, the routing model aims to satisfy different customers according to their specific time windows which were predefined by an expert as (being very important, important, casual or unimportant). This paper uses the proposed model as a multi-objective problem where the total required number of vehicles, the total distance travelled and the waiting time imposed on vehicles are minimized, and the total customers’ satisfaction for service is maximized. An efficient framework for solving this model is designed and its performance is evaluated in different steps for various test problems generalized from Solomon’s VRPTW benchmark problems. The various heuristics and improvement concepts incorporate local exploitation in the evolutionary search, and the concept of Pareto optimality for the multi-objective optimization is used in the proposed procedure. The computational experiments on data sets illustrate the efficiency and effectiveness of the proposed approach.     

Comparative evaluation of genetic algorithms for job-shop scheduling

Many optimization problems from the industrial engineering world, in particular the manufacturing systems, are very complex in nature and quite hard to solve by conventional optimization techniques. There has been increasing interest in imitating living beings to solve such kinds of hard optimization problems. Simulating the natural evolutionary process of human beings results in stochastic optimization tech niques called evolutionary algorithms, which can often outperform conventional optimization methods when applied to difficult real-world problems. There are currently three main avenues of this research: genetic algorithms (GAs), evolutionary programming (EP) and evolution strategies (ESs). Among them, genetic algorithms are perhaps the most widely known types of evolutionary algorithms today. During the past years, several GAs for the job-shop scheduling problems have been proposed, each with different chromosome representation. In this paper, the different GAs are collected from the literature and an attempt has been made to evaluate them. The benchmark problems available in open literature are used for evaluation and the performance measure considered is makespan. The algorithms are coded in C+ +.     

A Stochastic Goal Program for Employee Scheduling*

Deterministic goal programs for employee scheduling decisions attempt to minimize expected operating costs by assigning the ideal number of employees to each feasible schedule. For each period in the planning horizon, managers must first determine the amount of labor that should be scheduled for duty. These requirements are often established with marginal analysis techniques, which use estimates for incremental labor costs and shortage expenses. Typically, each period in the planning horizon is evaluated as an independent epoch. An implicit assumption is that individual employees can be assigned to schedules with as little as a single period of work. If this assumption violates local work rules, the labor requirements parameters for the deterministic goal program may be suboptimal. As we show in this research, this well-known limitation can lead to costly staffing and scheduling errors. We propose an employee scheduling model that overcomes this limitation by integrating the labor requirements and scheduling decisions. Instead of a single, externally determined staffing goal for each period, the model uses a probability distribution for the quantity of labor required. The model is free to choose an appropriate staffing level for each period, eliminating the need for a separate goal-setting procedure. In most cases this results in better, less costly decisions. In addition, the proposed model easily accommodates both linear and nonlinear under- and overstaffing penalties. We use simple examples to demonstrate many of these advantages and to illustrate the key techniques necessary to implement our model. We also assess its performance in a study of more than 1,700 simulated stochastic employee scheduling problems.     

Heuristic Estimation of the Efficient Frontier for a Bi-Criteria Scheduling Problem

We examine a single-machine scheduling problem where the objective is to minimize the mean and the variance of the job completion times simultaneously. We seek to identify the efficient frontier which is obtained by parametrically solving a weighted combination of the two criteria. The identification of the true efficient frontier for this problem is notoriously difficult. To estimate the frontier, we propose a heuristic procedure which is quite general and can be applied to other bi-criteria problems as well. It involves repeated applications of a relatively new technique called beam search in an adaptive manner. To evaluate the proposed procedure, we introduce two measures of performance and conduct a computational study. The results of the study indicate that the procedure is highly effective.     

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.     

基于银行授信额度的Max-NPV项目调度问题研究

本文对基于银行授信额度的Max-NPV项目调度问题进行研究.首先界定研究的假设条件并对文中所用到的符号进行定义;随后采用基于事件的研究方法构建了问题的整数规划优化模型;鉴于问题的NP-hard属性,设计了双层模拟退火搜索循环嵌套的启发式求解算法;最后对一个算例进行了求解分析,并讨论了银行授信额度及客户支付比例对项目收益的影响.结果表明:随着银行授信额度的提高,承包商安排项目进度自由度的增加使得其净现值得到改善,在支付比例较低的条件下项目完成时间也随之提前;当客户支付比例提高时,项目净现值单调上升,而项目完成时间呈先提前后延迟的变化趋势.     

New Methods for Resolving Conflicting Requests with Examples from Medical Residency Scheduling

In scheduling medical residents, the objective is often to maximize resident satisfaction across the space of feasible schedules, relative to the many hard constraints that ensure appropriate patient coverage, adequate training opportunities, etc. A common metric of resident satisfaction is the number of time‐off requests that are granted. Simply maximizing this total, however, may lead to undesirable schedules since some requests have higher priority than others. For example, it might be better to grant one resident's request for a family member's wedding in place of two residents’ requests to attend a rugby game. Another approach is to assign a weight to each request and maximize the total weight of granted requests, but determining weights that accurately represent residents’ and schedulers’ preferences can be quite challenging. Instead, we propose to identify the exhaustive collection of maximally feasible and minimally infeasible sets of requests which can then be used by schedulers to select their preferred solution. Specifically, we have developed two algorithms, which we call Sequential Request Selection Via Cuts (Sequential RSVC) and Simultaneous Request Selection Via Cuts (Simultaneous RSVC), to identify these sets by solving two sequences of optimization problems. We present these algorithms along with computational results based on a real‐world problem of scheduling residents at the University of Michigan C.S. Mott Pediatric Emergency Department. Although we focus our exposition on the problem of resident scheduling, our approach is applicable to a broad class of problems with soft constraints.     

一种差异工件单机批调度问题的蚁群优化算法

由于在利用蚁群算法构建差异工件(即工件有尺寸差异)单机批调度问题的解时,批的加工时间是不确定的.从而不能类似于经典调度问题的蚁群算法把批加工时间的倒数作为蚁群算法中的启发式信息,引入批的利用率和批的负载均衡率作为蚁群算法中的启发式信息,提出了JACO(ant colony optimization based a job sequence)和BACO(ant colony optimization based a batch sequence)两种蚁群优化算法.在算法JACO中,解的编码为工件序列,它对应着用BF(best fit)分批规则生成的调度方案,信息素代表工件间的排列顺序;在算法BACO中,解的编码为批序列,信息素代表工件间的批相关性,由此信息素通过中间信息素量来构造相应的解,并引入特定的局部优化策略,提高了算法的搜索效率.实验表明,与以往文献中的SA(simula-ted annealing)、GA(genetic algorithm)算法以及FFLPT(first-fit longest processing time)、BFLPT (best-fit longest processing time)启发式规则相比,算法JACO和BACO明显优于它们,且BACO算法比JACO算法效果更好.     

Just-in-time scheduling with controllable processing times on parallel machines

We study scheduling problems with controllable processing times on parallel machines. Our objectives are to maximize the weighted number of jobs that are completed exactly at their due date and to minimize the total resource allocation cost. We consider four different models for treating the two criteria. We prove that three of these problems are NP\mathcal{NP} -hard even on a single machine, but somewhat surprisingly, the problem of maximizing an integrated objective function can be solved in polynomial time even for the general case of a fixed number of unrelated parallel machines. For the three NP\mathcal{NP} -hard versions of the problem, with a fixed number of machines and a discrete resource type, we provide a pseudo-polynomial time optimization algorithm, which is converted to a fully polynomial time approximation scheme.     

An Evaluation of Tour Scheduling Heuristics with Differences in Employee Productivity and Cost

This study focuses on the manpower tour scheduling problem using data from a lockbox system of a commercial bank. The lockbox system uses employees who differ in productivity, hourly cost, number of available working hours per week, and days-off constraints. These specific problem characteristics require a more general problem formulation and solution procedure for the manpower tour scheduling problem than addressed in previous research. Four heuristic methods for solving the problem (three developed here and a simple round-up procedure) are tested on a set of forty problems. The results of this study show the effort to develop sophisticated heuristic methods for this class of problems is well justified.     

An exchange heuristic for resource constrained scheduling with consideration given to opportunities for parallel processing

This paper describes a heuristic which produces efficient makespans for resource-constrained scheduling problems with parallel processing capabilities. This heuristic was initially developed for the scheduling of army battalion training exercises. The original heuristic has also been successfully applied to solve problems in project scheduling with limited resources, generalized job shop scheduling, and resource-constrained scheduling. The exchange heuristic requires an initial feasible solution upon which it improves the makespan by efficiently and systematically shuffling activities while maintaining feasibility. The method has recently been modified twice, termed the intelligent version and naive version, respectively, such that its ability to reduce the initial makespan is enhanced. In this study     

Real-time part dispatching within manufacturing cells using fuzzy logic

A new fuzzy logic dispatching method is presented ff which o ers an improvement over certain existing common dispatching rules with respect to the performance measures, number of late parts, maximum part lateness, average producff tion times and machine bu er levels. The fuzzy logic dispatcher incorporates a wider range of scheduling issues than those considered by most dispatching rules, considers certain control ff issues that e ect scheduling, contains mechanisms for optimization and also allows for the addition of more control or scheduling rules.