解决并行多机提前/拖后调度问题的混合遗传算法方法

研究了带有公共交货期的并行多机提前/拖后调度问题.提出了一种混合遗传算法 方法,以便于确定公共交货期和每台机器上加工的任务代号及其加工顺序,即找到一个最优 公共交货期和最优调度,使加工完所有任务后交货期安排的成本、提前交货成本和拖后交货 成本的总和最小.数值计算结果表明了该混合遗传算法优于启发式算法,并能适用于较大规 模并行多机提前/拖后调度问题.算法计算量小,鲁棒性强.     

Genetic algorithms for the optimal common due date assignment and the optimal scheduling policy in parallel machine earliness/tardiness scheduling problems

Earliness/tardiness scheduling problems with undetermined common due date which have wide application background in textile industry, mechanical industry, electronic industry and so on, are very important in the research fields such as industry engineering and CIMS. In this paper, a kind of genetic algorithm based on sectional code for minimizing the total cost of assignment of due date, earliness and tardiness in this kind of scheduling problem is proposed to determine the optimal common due date and the optimal scheduling policy for determining the job number and their processing order on each machine. Also, simulated annealing mechanism and the iterative heuristic fine-tuning operator are introduced into the genetic algorithm so as to construct three kinds of hybrid genetic algorithms with good performance. Numerical computational results focusing on the identical parallel machine scheduling problem and the general parallel machine scheduling problem shows that these algorithms outperform heuristic procedures, and fit for larger scale parallel machine earliness/tardiness scheduling problem. Moreover, with practical application data from one of the largest cotton colored weaving enterprises in China, numerical computational results show that these genetic algorithms are effective and robust, and that especially the performance of the hybrid genetic algorithm based on simulated annealing and the iterative heuristic fine-tuning operator is the best among them.     

提前/延期惩罚最小化互替机床调度算法

对经提前/延期（E/T）惩罚最小为目标的互替机床调度问题进行了分析，对互替机床E/T调度问题进行了描述，提出了解决调度问题的具体策略，在此基础上，建立了基于启发式的互替机床E/T调度算法，最后通过仿真实验验证了本算法的有效性和实用性。     

Parallel machine selection and job scheduling to minimize machine cost and job tardiness

This paper discusses the problem of simultaneously selecting and scheduling parallel machines to minimize the sum of machine holding cost and job tardiness cost. A combinatorial optimization model is developed for this purpose. Solving the developed model is NP-hard. A heuristic algorithm is developed to locate the optimal or near optimal solutions based on a Tabu search mechanism specially designed to control the search process in the solution neighborhood for jobs scheduled on specific machines. Numerical examples show that the solutions of the model lead to compromises between the system cost related to machine selection and the operational cost related to job tardiness penalties. The examples also show that the developed algorithm is effective and computationally efficient.     

Parallel machine earliness and tardiness scheduling with proportional weights

In this paper we study the problem of scheduling n jobs with a common due date and proportional early and tardy penalties on m identical parallel machines. We show that the problem is NP-hard and propose a dynamic programming algorithm to solve it. We also propose two heuristics to tackle the problem and analyze their worst-case error bounds.Scope and purposeScheduling problems to minimize the total weighted earliness and tardiness (WET) arise in Just-in-time manufacturing systems, where one of the objectives is to complete each job as close to its due date as possible. The earliness and tardiness weights of a job in WET tend to increase with the value of the job. Because processing time is often a good surrogate for the value of a job, it is reasonable to consider weights that are proportional to job processing times. In this paper we study the parallel identical machine WET problem with proportional weights. We propose both exact and approximation algorithms to tackle the problem.     

Scheduling job classes on uniform machines

We study a scheduling problem with job classes on parallel uniform machines. All the jobs of a given class share a common due-date. General, non-decreasing and class-dependent earliness and tardiness cost functions are assumed. Two objectives are considered: (i) minmax, where the scheduler is required to minimize the maximum earliness/tardiness cost among all the jobs and (ii) minmax-minsum, where the scheduler minimizes the sum of the maximum earliness/tardiness cost in all job classes. The problem is easily shown to be NP-hard, and we focus here on the introduction of simple heuristics. We introduce LPT (Largest Processing Time first)-based heuristics for the allocation of jobs to machines within each class, followed by a solution of an appropriate non-linear program, which produces for this job allocation an optimal schedule of the classes. We also propose a lower bound, based on balancing the load on the machines. Our numerical tests indicate that the heuristics result in very small optimality gaps.     

公共交货期窗口下提前/拖期问题的多机调度算法

提出了求公共交货期窗口下提前／拖期都有惩罚的单机零件排序问题最优解的新算法,建立了相应多机零件排序问题的数学模型。在证明关于单机问题最优排序和最优公共交货期性质的若干定理的基础上,给出了求解多机问题的一个启发式算法。数值例子表明,该算法有较为理想的优化效果和工程实用价值。     

Lagrangian bounds for just-in-time job-shop scheduling

We study the job-shop scheduling problem with earliness and tardiness penalties. We describe two Lagrangian relaxations of the problem. The first one is based on the relaxation of precedence constraints while the second one is based on the relaxation of machine constraints. We introduce dedicated algorithms to solve the corresponding dual problems. The second one is solved by a simple dynamic programming algorithm while the first one requires the resolution of an NP-hard problem by branch and bound. In both cases, the relaxations allow us to derive lower bounds as well as heuristic solutions. We finally introduce a simple local search algorithm to improve the best solution found. Computational results are reported.     

Minimizing total earliness and tardiness through unrelated parallel machine scheduling using distributed release time control

Using unrelated parallel machine scheduling to minimize the total earliness and tardiness of jobs with distinct due dates is a nondeterministic polynomial-hard problem. Delayed customer orders may result in penalties and reduce customer satisfaction. On the other hand, early completion creates inventory storage costs, which increase the total cost. Although parallel machines can increase productivity, machine assignments also increase the complexity of production. Therefore, the challenge in parallel machine scheduling is to dynamically adjust the machine assignment to complete the job within the shortest possible time. In this paper, we address an unrelated parallel machine scheduling problem for jobs with distinct due dates and dedicated machines. The objective is to dynamically allocate jobs to unrelated parallel machines in order to minimize the total earliness and tardiness time. We formulate the problem as a mixed integer linear programming (MILP) model and develop a modified genetic algorithm (GA) with a distributed release time control (GARTC) mechanism to obtain the near-optimal solution. A preliminary computational study indicates that the developed GARTC not only provides good quality solutions within a reasonable amount of time, but also outperforms the MILP model, a classic GA and heuristic approaches described in the literature.     

Minmax scheduling problems with a common due-window

This paper focuses on a minmax due-window assignment problem. The goal is to schedule the jobs and the due-window such that the highest cost among all jobs is minimized. The objective function contains four cost components: for earliness, tardiness, due-window starting time and due-window size. We present a polynomial time solution for the case of a single machine and for a two-machine flow-shop. The cases of parallel identical machines and uniform machines are NP-hard, and simple heuristics and lower bounds are introduced and tested numerically.     

解并行多机提前/拖后调度问题的并行遗传算法

为有效地解决带有公共交货期的非等同并行多机提前/拖后调度问题,设计了一种分段扩展排列编码的混合遗传算法,使遗传编码能同时反映调度方案和公共交货期,并对其初始种群产生、交叉和变异方法也进行了研究。同时为了更好地适应调度实时性和解大规模此类问题的需要,基于遗传算法自然并行性特点的基础上,实现了主从式控制网络模式下并行混合遗传算法。计算结果表明,此算法是有效的,优于启发式算法和遗传算法,有着较高的并行性,并能适用于大规模非等同并行多机提前/拖后调度问题。     

解不同交货期并行机调度问题的并行遗传算法

为有效地解决不同交货期窗口下的非等同并行多机提前/拖后调度问题,设计了一种分段编码的混合遗传算法。此编码方式能反映工件的分配序列,并利用调度优先级规则和最好适应值规则相结合的启发式算法对其顺序进行了调整,加快了收敛速度。同时为了更好地适应调度实时性和解大规模此类问题的需要,基于遗传算法自然并行性特点的基础上,实现了主从式控制网络模式下并行混合遗传算法。计算结果表明,此算法是有效的,优于遗传算法,有着较高的并行性,并能适用于大规模不同交货期窗口下非等同并行多机提前/拖后调度问题。     

A genetic algorithm for minimizing the makespan in the case of scheduling identical parallel machines

Identical parallel machine scheduling problem for minimizing the makespan is a very important production scheduling problem, but there have been many difficulties in the course of solving large scale identical parallel machine scheduling problem with too many jobs and machines. Genetic algorithms have shown great advantages in solving the combinatorial optimization problem in view of its characteristic that has high efficiency and that is fit for practical application. In this article, a kind of genetic algorithm based on machine code for minimizing the makespan in identical machine scheduling problem is presented. Several different scale numerical examples demonstrate the genetic algorithm proposed is efficient and fit for larger scale identical parallel machine scheduling problem for minimizing the makespan, the quality of its solution has advantage over heuristic procedure and simulated annealing method.     

A Neural Network Model For The Common Due Date Job Scheduling On Unrelated Parallel Machines

This paper presents an approach for scheduling under a common due date on parallel unrelated machine problems based on artificial neural network. The objective is to allocate and sequence the jobs on the machines so that the total cost is minimized. The total cost is the sum of the total earliness and the total tardiness cost. The multilayer Perceptron (MLP) neural network is a suitable model in our study due to the fact that the problem is NP-hard. In our study, neural network has been proven to be effective and robust in generating near optimal solutions to the problem.     

A hybrid scheduling approach for a two-stage flexible flow shop with batch processing machines

In this paper, we discuss a flexible flow shop scheduling problem with batch processing machines at each stage and with jobs that have unequal ready times. Scheduling problems of this type can be found in semiconductor wafer fabrication facilities (wafer fabs). We are interested in minimizing the total weighted tardiness of the jobs. We present a mixed integer programming formulation. The batch scheduling problem is NP-hard. Therefore, an iterative stage-based decomposition approach is proposed that is hybridized with neighborhood search techniques. The decomposition scheme provides internal due dates and ready times for the jobs on the first and second stage, respectively. Each of the resulting parallel machine batch scheduling problems is solved by variable neighborhood search in each iteration. Based on the schedules of the subproblems, the internal due dates and ready times are updated. We present the results of designed computational experiments that also consider the number of machines assigned to each stage as a design factor. It turns out that the proposed hybrid approach outperforms an iterative decomposition scheme where a fairly simple heuristic based on time window decomposition and the apparent tardiness cost dispatching rule is used to solve the subproblems. Recommendations for the design of the two stages with respect to the number of parallel machines on each stage are given.     

Local and global dominance conditions for the weighted earliness scheduling problem with no idle time

In this paper, we present dominance conditions for the single machine weighted earliness scheduling problem with no idle time. We also propose an algorithm that can be used to improve upper bounds for the weighted earliness criterion and lower bounds for an earliness/tardiness problem. The computational tests show that the algorithm is superior to an initial heuristic schedule and an existing adjacency condition.     

A genetic algorithm with sub-indexed partitioning genes and its application to production scheduling of parallel machines

Production scheduling seeks optimal combination of short manufacturing time, stable inventory, balanced human and machine utilization rate, and short average customer waiting time. Since the problem in general has been proven as NP-hard, we focus on suboptimal scheduling solutions for parallel flow shop machines where jobs are queued in a bottleneck stage. A Genetic Algorithm with Sub-indexed Partitioning genes (GASP) is proposed to allow more flexible job assignments to machines. Our fitness function considers tardiness, earliness, and utilization rate related variable costs to reflect real requirements. A premature convergence bounce is added to traditional genetic algorithms to increase permutation diversity. Finally, a production scheduling system for an electronic plant based on GASP is implemented and illustrated through real production data. The proposed GASP has demonstrated the following advantages: (1) the solutions from GASP are better and with smaller deviations than those from heuristic rules and genetic algorithms with identical partitioning genes; (2) the added premature convergence bounce helps obtain better solutions with smaller deviations; and (3) the consideration of variable costs in the fitness function helps achieve better performance indicators.     

Local and global dominance conditions for the weighted earliness scheduling problem with no idle time

In this paper, we present dominance conditions for the single machine weighted earliness scheduling problem with no idle time. We also propose an algorithm that can be used to improve upper bounds for the weighted earliness criterion and lower bounds for an earliness/tardiness problem. The computational tests show that the algorithm is superior to an initial heuristic schedule and an existing adjacency condition.     

A branch-and-bound algorithm to minimize total weighted completion time on identical parallel machines with job release dates

In this paper, we consider an identical parallel machine scheduling problem with release dates. The objective is to minimize the total weighted completion time. This problem is known to be strongly NP-hard. We propose some dominance properties and two lower bounds. We also present an efficient heuristic. A branch-and-bound algorithm, in which the heuristic, the lower bounds and the dominance properties are incorporated, is proposed and tested on a large set of randomly generated instances.     

Single machine scheduling with controllable processing times to minimize total tardiness and earliness

In most deterministic scheduling problems job processing times are considered as invariable and known in advance. Single machine scheduling problem with controllable processing times with no inserted idle time is presented in this study. Job processing times are controllable to some extent that they can be reduced or increased, up to a certain limit, at a cost proportional to the reduction or increase. In this study, our objective is determining a set of compression/expansion of processing times in addition to a sequence of jobs simultaneously, so that total tardiness and earliness are minimized. A mathematical model is proposed firstly and afterward a net benefit compression–net benefit expansion (NBC–NBE) heuristic is presented so as to acquire a set of amounts of compression and expansion of jobs processing times in a given sequence. Three heuristic techniques in small problems and in medium-to-large instances two meta-heuristic approaches, as effective local search methods, as well as these heuristics are employed to solve test examples. The single machine total tardiness problem (SMTTP) is already NP-hard, so the considered problem is NP-hard obviously. The computational experiments demonstrate that our proposed heuristic is efficient approach for such just-in-time (JIT) problem, especially equipped with competent heuristics.