A tabu search algorithm for simultaneous machine/AGV scheduling problem

Machines and automated guided vehicles (AGVs) scheduling problems are two essential issues that need to be addressed for the efficiency of the overall production system. The purpose of this paper is to study the simultaneous scheduling problem of machines and AGVs in a flexible manufacturing system (FMS) since the global optimum cannot be reached by considering each of them individually. In this paper, a mixed integer linear programming (MILP) model is developed with the objective of makespan minimisation. The MILP model consists of the following two constraint sets: machines and AGVs scheduling sub-problems. As both sub-problems are known to be NP-hard, a heuristic algorithm based on tabu search (TS) is proposed to get optimal or near to optimal solution for large-size problems within reasonable computation time. The proposed algorithm includes a novel two-dimensional solution representation and the generation of two neighbour solutions, which are alternately and iteratively applied to improve solutions. Moreover, an improved lower bound calculation method is introduced for the large-size problems. Computational results show the superior performance of the TS algorithm for the simultaneous scheduling problem.     

Study on constraint scheduling algorithm for job shop problems with multiple constraint machines

This paper focuses on a job-shop scheduling problem with multiple constraint machines (JSPMC). A constraint scheduling method for the JSPMC is proposed. It divides the machines in the shop into constraint and non-constraint machines based on a new identification method, and formulates a reduced problem only for constraint machines while replacing the operations of non-constraint machines with time lags. The constraint machines are scheduled explicitly by solving the reduced problem with an efficient heuristic, while the non-constraint machines are scheduled by the earliest operation due date (EODD) dispatching rule. Extensive computational results indicate that the proposed constraint scheduling algorithm can obtain a better trade-off between solution quality and computation time compared with various versions of the shifting bottleneck (SB) methods for the JSPMC.     

Parallel machine scheduling with step-deteriorating jobs and setup times by a hybrid discrete cuckoo search algorithm

This article considers the parallel machine scheduling problem with step-deteriorating jobs and sequence-dependent setup times. The objective is to minimize the total tardiness by determining the allocation and sequence of jobs on identical parallel machines. In this problem, the processing time of each job is a step function dependent upon its starting time. An individual extended time is penalized when the starting time of a job is later than a specific deterioration date. The possibility of deterioration of a job makes the parallel machine scheduling problem more challenging than ordinary ones. A mixed integer programming model for the optimal solution is derived. Due to its NP-hard nature, a hybrid discrete cuckoo search algorithm is proposed to solve this problem. In order to generate a good initial swarm, a modified Biskup–Hermann–Gupta (BHG) heuristic called MBHG is incorporated into the population initialization. Several discrete operators are proposed in the random walk of Lévy flights and the crossover search. Moreover, a local search procedure based on variable neighbourhood descent is integrated into the algorithm as a hybrid strategy in order to improve the quality of elite solutions. Computational experiments are executed on two sets of randomly generated test instances. The results show that the proposed hybrid algorithm can yield better solutions in comparison with the commercial solver CPLEX^® with a one hour time limit, the discrete cuckoo search algorithm and the existing variable neighbourhood search algorithm.     

基于直线往复单智能RGV系统单工序调度研究

针对直线布局轨道式智能加工系统单自动引导车(rail guide vehicle, RGV)单工序作业调度进行研究。考虑到智能RGV与数控机床(CNC machine tools)的特点,建立了给定时间内RGV与CNC机床配合物料加工下料用时之和最小化为目标的非线性整数规划模型。当加工物料数目比较多时,求解该问题非常耗时。根据RGV与CNC机床加工物料调度特征,提出计算机模拟仿真算法对问题进行求解。利用3组系统参数对模型及算法的有效性和实用性进行了检验分析,最后给出了最优调度计划的实际运行结果及结论。     

Iterated beam search for the combined car sequencing and level scheduling problem

The level scheduling problem is concerned with the final stage of a multi-stage just-in-time production system so that different models of a product are evenly distributed in a discrete production sequence, thereby making the problem practically an unconstrained optimisation problem. The car sequencing problem, on the other hand, is a constraint satisfaction problem based on a number of options constricting the final assembly schedule. The combined car sequencing and level scheduling problem aims to find the optimal production schedule that evenly distributes different models over the planning horizon and satisfies all option constraints. This paper proposes a parametric iterated beam search algorithm for the combined problem that can be used either as a heuristic or as an exact optimisation method. The paper includes a computational study based on a 54-instance test bed that proves the effectiveness of the proposed algorithm.     

Minimizing makespan on parallel machines with release time and machine eligibility restrictions

Scheduling in the presence of machine eligibility restrictions when not all machines can process all the jobs is a practical problem into which there has been little research. Pinedo demonstrated that the least flexible job (LFJ) rule was optimal for minimizing makespan in a parallel machine environment (with equal processing times) when there are machine eligibility restrictions, the machine eligibility sets are nested, and no release time constraint exists. The results presented in this paper demonstrate that for the more realistic case when the machine eligibility sets are not nested (with unequal processing times known when a job is released), the longest processing time (LPT) rule performs better than the LFJ rule in the presence or absence of release time stipulations. The experimental results show that the order (job selection first or machine selection first) does not matter, which is consistent with Pinedo’s observation. The new heuristics that are evaluated in this paper provide important results for the parallel machine scheduling problem and their applications in the semiconductor industry, which motivated this research.     

Dynamic co-ordinated scheduling in the supply chain under a process modernisation

A new dynamic model for co-ordinated scheduling of interlinked processes in a supply chain under a process modernisation is presented. Such a problem is vital in many of the supply chain management domains. This problem is represented as a special case of the scheduling problem with dynamically distributed jobs. The peculiarity of the proposed approach is the dynamic interpretation of scheduling based on a natural dynamic decomposition of the problem and its solution with the help of a modified form of continuous maximum principle blended with combinatorial optimisation. The special properties of the developed model allow using methods of discrete optimisation for the schedule calculation. Optimality and sufficiency conditions as well as structural properties of the model are investigated. Advantages and limitations of the proposed approach are discussed. With the developed approach, an explicit inclusion of a process modernisation in the SC co-ordinated decisions for a wide ranges of possible applications as well as a dynamic model and a tractable algorithm for optimal discrete time scheduling on the basis of continuous maximum principle have been obtained.     

Parallel machine scheduling problem with ready times,due times and sequence-dependent setup times using meta-heuristic algorithms

This article considers a parallel machine scheduling problem with ready times, due times and sequence-dependent setup times. The objective of this problem is to determine the allocation policy of jobs and the scheduling policy of machines to minimize the weighted sum of setup times, delay times and tardy times. A mathematical model for optimal solution is derived. An in-depth analysis of the model shows that it is very complicated and difficult to obtain optimal solutions as the problem size becomes large. Therefore, two meta-heuristics, genetic algorithm (GA) and a new population-based evolutionary meta-heuristic called self-evolution algorithm (SEA), are proposed. The performances of the meta-heuristic algorithms are evaluated through comparison with optimal solutions using several randomly generated examples.     

A branch and bound algorithm for optimal cyclic scheduling in a robotic cell with processing time windows

A branch and bound algorithm is described for optimal cyclic scheduling in a robotic cell with processing time windows. The objective is to minimise the cycle time by determining the exact processing time on each machine which is limited within a time window. The problem is formulated as a set of prohibited intervals of the cycle time, which is usually applied in the robotic cyclic scheduling problem with fixed processing times. Since both bounds of these prohibited intervals are linear expressions of the processing times, we divide these prohibited intervals into a series of the subsets and transform the problem into enumerating the non-prohibited intervals of cycle time in each subset. This enumeration procedure is completed by an efficient branch and bound algorithm, which could find an optimal solution by enumerating partial non-prohibited intervals. Computational results on the benchmark instances and randomly generated test instances indicate that the algorithm is effective.     

A two-stage three-machine assembly scheduling problem with deterioration effect

The two-stage assembly scheduling problem has received growing attention in the research community. Furthermore, in many two-stage assembly scheduling problems, the job processing times are commonly assumed as a constant over time. However, it is at odds with real production situations some times. In fact, the dynamic nature of processing time may occur when machines lose their performance during their execution times. In this case, the job that is processed later consumes more time than another one processed earlier. In view of these observations, we address the two-stage assembly linear deterioration scheduling problem in which there are two machines at the first stage and an assembly machine at the second stage. The objective is to complete all jobs as soon as possible (or to minimise the makespan, implies that the system can yield a better and efficient task planning to limited resources). Given the fact that this problem is NP-hard, we then derive some dominance relations and a lower bound used in the branch-and-bound method for finding the optimal solution. We also propose three metaheuristics, including dynamic differential evolution (DDE), simulated annealing (SA) algorithm, and cloud theory-based simulated annealing (CSA) algorithm for find near-optimal solutions. The performances of the proposed algorithms are reported as well.     

基于资源限制的多目标网络计划优化模型

目前网络计划优化研究要么没有考虑资源限定的柔性,要么只是集中于单纯的工期优化或资源优化等单目标优化。本文针对传统网络计划建模资源限制缺少柔性、优化目标单一等问题进行了深入的研究。在柔性资源的限制下,为使得工程网络计划达到总体最优,考虑工程项目的工期、成本、项目净现值、资源的均衡等多个目标,建立其网络计划优化模型,并采用粒子群算法予以求解。根据拓扑排序算法生成满足时序约束的活动序列并计算活动的时间参数。对于产生资源冲突的活动,依照执行优先权解决冲突资源的执行顺序,更新时间参数。采用随机权重的方法,让粒子群算法种群的多个个体进行随机转化,从而保持解的多样性。采用国际上通用的Patterson问题库中benchmark算例对本文提出的方法进行验证。结果表明,与初始方案相比,优化后的方案分别在工期上缩减了20%,成本上缩减了11.17%,净现值增加了11.82%,资源均衡度减少了18.29%。由此可见,提出的基于粒子群算法的优化模型对资源限制下的网络计划中的工期、成本、净现值、资源均衡度等多个目标均实现了不同程度的优化。     

Flow shop scheduling in serial multi-product processes with transfer and set-up times

Short-term production scheduling is a widely seen problem in multi-product batch operations. In this paper, an effective heuristic algorithm for scheduling a set of different tasks to be processed on serial processors is presented that provides an approach towards minimizing the entire makespan and improving productivity. Flow shops with an interstage storage policy, non-zero transfer times, and non-zero setup times are considered. The performance of the proposed algorithm was evaluated through numerous simulated problems. Statistical analysis of the output data indicates that in the situation containing up to seven tasks, the algorithm provides optimal or near optimal solutions and needs very short computation time. For a larger number of tasks, it gives up to 20% better solutions than a well-known existing algorithm.     

A Three Phased Approach To Final Exam Scheduling

A multi-phase examination scheduling process applicable to large university settings in general and SUNY at Buffalo (SUNYAB) in particular is proposed. Each scheduling phase is considered an integral part of the overall scheduling process and solved independently. Phase one of scheduling process is wth the assignment of examinations to exam blocks (each containing one or more exams). The objective of this phase is to minimize the number of students taking more than one exam in the same exam block. The problem is solved using a variation of the quadratic assignment problem. Phase two of the scheduling process uses the results from phase one as input. The exam blocks are assigned to exam days in such a way that some measure of students' comfort is maintained. Phase two of the scheduling process is formulated as a set covering problem with an extra constraint. Phase three of the scheduling process which is involved wt h the assignment of exam blocks to exam periods in each day and optimal ordering of exam days is solved heuristically using a traveling salesman problem as part of solution procedure. The performance of the algorithms devised for the multi-phase scheduling process are tested both in terms of quality of the solutions obtained and the computer time to generate these solutions.     

A generic resource distribution and test scheduling scheme for embedded core-based SoCs

We present a novel test scheduling algorithm for embedded core-based system-on-chips based on a graph-theoretic formulation. Given a system integrated with a set of cores and a set of test resources, we select a test for each core from a set of alternative test sets, and schedule it in a way to evenly balance the resource usage and to ultimately reduce the test application time. Improvements to the basic algorithm are sought by grouping the cores and assigning higher priorities to those with smaller number of alternate test sets. The algorithm is also extended for solving the general test scheduling problem where multiple test sets are selected for each core from a set of alternatives to facilitate the testing for various fault models. A simulation study is performed to quantify the performance of the proposed scheduling approach.     

Multi-objective process planning and scheduling using controlled elitist non-dominated sorting genetic algorithm

The integration of process planning and scheduling is considered as a critical component in manufacturing systems. In this paper, a multi-objective approach is used to solve the planning and scheduling problem. Three different objectives considered in this work are minimisation of makespan, machining cost and idle time of machines. To solve this integration problem, we propose an improved controlled elitist non-dominated sorting genetic algorithm (NSGA) to take into account the computational intractability of the problem. An illustrative example and five test cases have been taken to demonstrate the capability of the proposed model. The results confirm that the proposed multi-objective optimisation model gives optimal and robust solutions. A comparative study between proposed algorithm, controlled elitist NSGA and NSGA-II show that proposed algorithm significantly reduces scheduling objectives like makespan, cost and idle time, and is computationally more efficient.     

随机型双边装配线平衡问题的一种启发式算法

为有效求解随机型双边装配线第Ⅰ类平衡问题(STALBP 1),在分析双边装配线平衡特点的基础上,考虑各任务操作时间的随机性,提出了一种启发式算法。在该启发式算法中,假定各任务的操作时间服从正态分布,运用具有操作方位约束的任务优先分配等规则来进行任务的选择和分配,通过改变预设超限概率,在不同生产节拍下,分别得到不同的平衡方案。实例验证了算法的有效性。     

An improved multi-objective evolutionary algorithm based on decomposition for energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time

With the increasing attention on environment issues, green scheduling in manufacturing industry has been a hot research topic. As a typical scheduling problem, permutation flow shop scheduling has gained deep research, but the practical case that considers both setup and transportation times still has rare research. This paper addresses the energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time to minimise both makespan as economic objective and energy consumption as green objective. The mathematical model of the problem is formulated. To solve such a bi-objective problem effectively, an improved multi-objective evolutionary algorithm based on decomposition is proposed. With decomposition strategy, the problem is decomposed into several sub-problems. In each generation, a dynamic strategy is designed to mate the solutions corresponding to the sub-problems. After analysing the properties of the problem, two heuristics to generate new solutions with smaller total setup times are proposed for designing local intensification to improve exploitation ability. Computational tests are carried out by using the instances both from a real-world manufacturing enterprise and generated randomly with larger sizes. The comparisons show that dynamic mating strategy and local intensification are effective in improving performances and the proposed algorithm is more effective than the existing algorithms.     

Parallel machine scheduling with limited controllable machine availability

Most machine scheduling models assume that either the machines are available all the time, or the time of their unavailability is fixed as a constraint. In this paper, we study the problem that neither the unavailability length nor the start time of machine unavailability is fixed. Instead, they would be determined in order to minimise the total cost involved with the completion time and the unavailable time. This model could represent a more realistic and complex situation, in which jobs and machines’ availability operations should be optimised simultaneously. After the model is formulated, some properties of the problem are presented. Then a branch and bound algorithm based on column generation approach is proposed to solve the problem. The computation results show that, within a reasonable computation time, the proposed algorithm can solve medium sized problems optimally.     

A note on resource allocation scheduling with group technology and learning effects on a single machine

In this article, single-machine group scheduling with learning effects and convex resource allocation is studied. The goal is to find the optimal job schedule, the optimal group schedule, and resource allocations of jobs and groups. For the problem of minimizing the makespan subject to limited resource availability, it is proved that the problem can be solved in polynomial time under the condition that the setup times of groups are independent. For the general setup times of groups, a heuristic algorithm and a branch-and-bound algorithm are proposed, respectively. Computational experiments show that the performance of the heuristic algorithm is fairly accurate in obtaining near-optimal solutions.     

有模具约束的并行机批量流调度问题研究

大多数调度问题均假设产品以单个或整批的方式进行生产,而实际生产过程中,会把产品分批后再进行生产。但当考虑模具约束时,对如何解决产品分批以及制定合理调度方案的问题,本文以最小化最大完工时间为优化目标,建立了考虑模具约束的并行机批量流调度模型,并提出了一种基于遗传算法和差分算法结合的混合差分遗传算法（DEGA）,实现分批与调度两个问题并行优化。最后通过对算例测试,DEGA算法得到更优的解,证明了该算法的优越性和稳定性。结合实际案例,验证了模型和算法的可行性。