Scheduling manufacturing systems with blocking: a Petri net approach

This paper introduces a Petri net-based approach for scheduling manufacturing systems with blocking. The modelling of the job routings and the resource and blocking constraints is carried out with the Petri net formalism due to their capability of representing dynamic, concurrent discrete-event dynamic systems. In addition Petri nets can detect deadlocks typically found in systems with blocking constraints. The scheduling task is performed with an algorithm that combines the classical A* search with an aggressive node-pruning strategy. Tests were conducted on a variety of manufacturing systems that included classical job shop, flexible job shop and flexible manufacturing scheduling problems. The optimisation criterion was makespan. The experiments show that the algorithm performed well in all types of problems both in terms of solution quality and computing times.     

Celeritas: a coloured Petri net approach to simulation and control of flexible manufacturing systems

In many areas of computerization today, the capabilities of hardware systems far exceed the sophistication of software systems needed for optimum control. This research is an attempt to advance software control capabilities of flexible manufacturing systems (FMSs). To this end, an FMS controller architecture, called Celeritas, has been designed and a software system conforming to this architecture has been designed and implemented. Celeritas is a generic, data-configurable FMS controller designed using the coloured Petri nets (CP-nets) modelling paradigm augmented with decision support software to provide both FMS simulation and control. Formalisms of the CP-net paradigm provide straightforward representation of both the inherent concurrency and resource conflicts present in such a complex system. Augmentations provide user-defined routines for real-time interfaces to this information which is utilized to provide resource arbitration services among jobs competing for scarce resources and overall job scheduling.     

A constructive heuristic algorithm for concurrently selecting and sequencing jobs in an FMS environment

This paper deals with the concurrent solution of the loading and scheduling problems in a flexible manufacturing system ( FMS) environment. It is assumed that the FMS environment has production planned periodically and each job in the system has a number of operations to be processed on flexible machines. A heuristic approach using a constructive scheduling method is developed to solve the FMS loading and scheduling problems concurrently. The computational results are compared to an existing procedure that considers a hierarchical approach with a similar problem environment. The comparison study shows a significant improvement over the existing hierarchical procedure. This experiment indicates that a concurrent solution approach can solve the FMS loading and scheduling problems very effectively.     

Lot streaming and scheduling multiple products in two-machine no-wait flowshops

We consider the problem of minimizing makespan in two-machine no-wait flowshops with multiple products requiring lot streaming. A “product” (or lot) consists of many identical items. Lot streaming (lot sizing) is the process of creating sublots (or transfer batches to move the completed portion of a production )sublot to downstream machines so that operations can be overlapped. The number of sublots for each product is fixed. When the flowshop produces only a single product, we obtain optimal continuous-sized sublots. It is shown that these sublot sizes are also optimal for the problem of simultaneous lot streaming and scheduling of multiple products. The optimal scheduling of products can be accomplished by application of the algorithm due to Gilmore and Gomory [1]. Then, we devise an efficient heuristic for the problem of simultaneous lot streaming (finding optimal integer-sized sublots) and scheduling of multiple products. Computational results indicate that this heuristic can consistently deliver close-to-optimal solutions for the problem. A comparison of this heuristic is also made with a heuristic that first divides items belonging to each product into nearly equal-sized sublots and then constructs a schedule for such sublots. Finally, we extend our solution procedures to a traditional and more general lot streaming model, where the number of sublots for each product is a decision variable.     

Two FMS scheduling methods based on Petri nets: A global and a local approach

We are interested in the Flexible Manufacturing System (FMS) scheduling problem. Different methods have been explored to solve this problem and to master its combinatorial complexity, which is NP-hard in the general case. In this paper we will give two different scheduling methods based on Petri nets. The first one tends to solve the general scheduling problem (acyclic schedule) using the Constraint Programming method to avoid exhaustive search. The second method is a dedicated cyclic scheduling method. The aim is not to compare the methods' performances (computation time, results' quality) because they do not solve exactly the same problem, but to compare their application domains in terms of parts number.     

Petri net based scheduling

Timed Petri nets can be used to model and analyse scheduling problems. To support the modelling of scheduling problems, we provide a method to map tasks, resources and constraints onto a timed Petri net. By mapping scheduling problems onto Petri nets, we are able to use standard Petri net theory. In this paper we will show that we can use Petri net based tools and techniques to find conflicting and redundant precedences, upper- and lower-bounds for the makespan, etc. This is illustrated by a Petri net based analysis of the notorious 10×10 problem due to Fisher & Thompson (1963)     

分布式FMS智能调度和控制系统的研究与开发

介绍了分布式ＦＭＳ智能调度和控制系统的研究与开发情况：提出了一种新的适合于分布式系统建模的网络计时Ｐｅｔｒｉ网ＮＴＰＮ；将ＮＴＰＮ模型与专家系统技术相结合，为系统控制器开发了基于工程的专家系统ＥＢＥＳ；利用面向对象的技术开发了仿真的对象类库，并实现了从仿真到控制的软件重用。     

Adaptive production scheduling of virtual production systems using object-oriented Petri nets with changeable structure

Virtual Production Systems (VPSs) are logically constructed by organizing production resources belonging to one or more physical manufacturing systems. VPSs can enhance the agility of manufacturing systems. However, an effective scheduling approach is required to cope with disturbance and changes to these systems. An adaptive production scheduling method is proposed. Object-oriented Petri nets with changeable structure (OPNs-CS) formulate the scheduling problem of VPSs. To resolve resource constraints in a VPS, the OPNs-CS is modified by introducing limited token available time and by revising the enabling and firing rules. The artificial intelligent heuristic search (A*) algorithm is modified and applied to generate the optimal or near optimal schedule. When a VPS encounters any disturbance, an estimate of the effects of the disturbance can be estimated by simulation on the OPNs-CS model. If the scheduling target (completion time) is not affected, rescheduling is not required. Whenever there is a change to the VPS, the TOPNs-CS model is updated to refresh VPS schedule. A case study is presented to demonstrate the procedures for applying the proposed scheduling approach. The given case study shows that the proposed approach is capable of scheduling a VPS dynamically in response to disturbances and changes are involved.     

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.     

A coloured Petri net-based hybrid heuristic search approach to simultaneous scheduling of machines and automated guided vehicles

To achieve a significant improvement in the overall performance of a flexible manufacturing system, the scheduling process must consider the interdependencies that exist between the machining and transport systems. However, most works have addressed the scheduling problem as two independent decision making problems, assuming sufficient capacity in the transport system. In this paper, we study the simultaneous scheduling (SS) problem of machines and automated guided vehicles using a timed coloured Petri net (TCPN) approach under two performance objectives; makespan and exit time of the last job. The modelling approach allows the evaluation of all the feasible vehicle assignments as opposed to the traditional dispatching rules and demonstrates the benefits of vehicle-controlled assignments over machine-controlled for certain production scenarios. In contrast with the hierarchical decomposition technique of existing approaches, TCPN is capable of describing the dynamics and evaluating the performance of the SS problem in a single model. Based on TCPN modelling, SS is performed using a hybrid heuristic search algorithm to find optimal or near-optimal schedules by searching through the reachability graph of the TCPN with heuristic functions. Large-sized instances are solved in relatively short computation times, which were a priori unsolvable with conventional search algorithms. The algorithm’s performance is evaluated on a benchmark of 82 test problems. Experimental results indicate that the proposed algorithm performs better than the conventional ones and compares favourably with other approaches.     

The G-group heuristic to solve the multi-product,sequencing, lot sizing and scheduling problem in flow shops

This paper presents a new heuristic to solve the problem of making sequencing, lot sizing and scheduling decisions for a number of products manufactured in a flow shop environment, so as to minimize the sum of setup and inventory holding costs while a given demand is fulfilled without backlogging. The proposed solution method first determines sequencing decisions then lot sizing and scheduling decisions are simultaneously determined. This heuristic, called the G-group method, divides the set of products into G groups and requires that products belonging to the same group have the same cycle time. Also, the cycle time of each group is restricted to be an integer multiple of a basic period. For each basic period of the global cycle, the products to be produced during this period and the production sequence to be used are chosen. Then, a non-linear program is solved to determine lot sizes and to construct a feasible production schedule. To evaluate its performance, the G-group method was compared to four other methods. Numerical results show that the proposed heuristic outperforms all these methods.     

含不一致任务重量的同型熔炼炉批调度优化

为求解含不一致任务重量的同型熔炼炉批调度问题,建立了最小化最大任务完工时间优化模型,设计了一种混合粒子群算法（HPSO）。算法使用随机生成的任务序列作为粒子,采用批首次匹配（BFF）规则对任务序列分批,最长加工时间（LPT）规则将批分配到批处理机,并提出了一种最小完工时间差（MCD）规则对LPT调度结果进行优化;为避免早熟,算法引入交叉和变异操作搜索最优解。通过仿真实验与SA、GA算法对比,实验结果表明算法具有良好的性能。     

Hybrid branch and bound algorithms for the two-stage assembly scheduling problem with separated setup times

This article proposes hybrid branch and bound algorithms to minimise the makespan for the two-stage assembly scheduling problem with separated setup times. In the studied problem, there are multiple machines at the first stage, each of which produces a component of a job. When all components are available, a single assembly machine at the second stage completes the job. Existing algorithms are based on the state space search and hence suffer from the state space explosion problem. In order to reduce the search space, lower and upper bounds for a partial schedule are proposed. Also, a heuristic function and a dominance rule are developed to guide the search process. Moreover, accelerated factors are introduced to increase the speed of the search. Experimental results indicate that our algorithms outperform an existing method, and can find the optimal or near-optimal schedules in a short time for all tested problems with up to ten thousand jobs and nine first-stage machines.     

A new heuristic for integrated process planning and scheduling in reconfigurable manufacturing systems

Integrated process planning and scheduling (IPPS) is a manufacturing strategy that considers process planning and scheduling as an integrated function rather than two separated functions performed sequentially. In this paper, we propose a new heuristic to IPPS problem for reconfigurable manufacturing systems (RMS). An RMS consists mainly of reconfigurable machine tools (RMTs), each with multiple configurations, and can perform different operations with different capacities. The proposed heuristic takes into account the multi-configuration nature of machines to integrate both process planning and scheduling. To illustrate the applicability and the efficiency of the proposed heuristic, a numerical example is presented where the heuristic is compared to a classical sequential process planning and scheduling strategy using a discrete-event simulation framework. The results show an advantage of the proposed heuristic over the sequential process planning and scheduling strategy.     

A genetic algorithm for solving the economic lot scheduling problem in flow shops

In this study, we propose a hybrid genetic algorithm (HGA) to solve the economic lot scheduling problem in flow shops. The proposed HGA utilizes a so-called Proc PLM heuristic that tests feasibility for the candidate solutions obtained in the evolutionary process of genetic algorithm. When a candidate solution is infeasible, we propose to use a binary search heuristic to ‘fix’ the candidate solution so as to obtain a feasible solution with the minimal objective value. To evaluate the performance of the proposed HGA, we randomly generate a total of 2100 instances from seven levels of utilization rate ranged from 0.45 to 0.80. We solve each of those 2100 instances by the proposed HGA and the other solution approaches in the literature. Our experiments show that the proposed HGA outperforms traditional methods for solving the economic lot scheduling problem in flow shops.     

Flexible job shop scheduling with lot streaming and sublot size optimisation

Models and optimisation approaches are developed for a flexible job shop scheduling problem with lot streaming and lot sizing of the variable sublots. A two-stage optimisation procedure is proposed. First, the makespan value is minimised with the smallest sublots defined for the problem instance. This makes it possible to shorten the makespan significantly, because each sublot is transferred separately to the next operation of a job. In the second stage, the sizes of the sublots are maximised without increasing the obtained makespan value. In this way, the quantity of sublots and transport activities is limited together with the related manufacturing cost. Two objectives are defined for the second stage. The first one is the maximisation of the sum of the sublot sizes of all operations, the second one is the maximisation of the number of the operations which do not need to be split at all. Mixed-integer linear programming, constraint programming and graph-based models are implemented for the problem. Two optimisation approaches are developed and compared in computational experiments for each stage and objective, one approach is based on a third-party solver, and the second one on an independent own implementation, namely a tabu search and a greedy constructive heuristic.     

Hybrid genetic algorithm for the economic lot-scheduling problem

The economic lot-scheduling problem (ELSP) is an important production scheduling problem that has been intensively studied over 40 years. Numerous heuristic algorithms have been developed since the problem is NP-hard. Dobson's heuristic has been regarded as the best in its performance. The present paper provides a hybrid genetic algorithm based on the time-varying lot sizes approach in the ELSP literature. Numerical experiments show that the hybrid genetic algorithm outperforms Dobson's heuristic.     

蚁群系统结合指派规则求解HFS调度问题

以NP-难的最小化时间表长为目标的混合流水车间调度问题为研究对象。把工件在第1阶段开始加工的排序问题转化为旅行商问题,采用蚁群系统求得初始排序;在第1阶段后各阶段采用工件先到先服务规则选择工件、最先空闲机器优先规则选择机器以构建初始工件的机器指派与排序;充分利用已知的机器布局和工件加工时间特点,确定工件加工瓶颈阶段,并以此为基础对工件的机器指派与排序进行改进。用Carlier和Neron设计的Benchmark算例仿真后与著名的NEH算法比较,表明这种算法是有效的。     

Closed loop control-based real-time dispatching heuristic on parallel batch machines with incompatible job families and dynamic arrivals

In this paper, a real-time closed loop control dispatching heuristic (RCLC) algorithm is proposed to address the scheduling problem of parallel batch machines with incompatible job families, limited waiting time constraints, re-entrant flow and dynamic arrivals in the diffusion and oxidation areas of a semiconductor wafer fabrication system (SWFS), which is known to be strongly NP-hard. The basis of this algorithm is the information of lots in the buffer when the parallel batch machines are idle and available. In RCLC, if the number of any family lots is less than the maximum batch size, the dispatching heuristic can be seen as a pull–pull–push–push (P⁴) strategy; otherwise, a genetic algorithm (GA). A look-itself strategy, P⁴ strategy and GA can build a closed loop control system. The experiments are implemented on the Petri nets-based real-time scheduling simulation platform of SWFS, and demonstrate the effectiveness of our proposed method.