Petri nets and genetic algorithms for complex manufacturing systems scheduling

In this paper we propose the GAPN (genetic algorithms and Petri nets) approach, which combines the modelling power of Petri nets with the optimisation capability of genetic algorithms (GAs) for manufacturing systems scheduling. This approach uses both Petri nets to formulate the scheduling problem and GAs for scheduling. Its primary advantage is its ability to model a wide variety of manufacturing systems with no modifications either in the net structure or in the chromosomal representation. In this paper we tested the performance on both classical scheduling problems and on a real life setting of a manufacturer of car seat covers. In particular, such a manufacturing system involves features such as complex project-like routings, assembly operations, and workstations with unrelated parallel machines. The implementation of the algorithm at the company is also discussed. Experiments show the validity of the proposed approach.     

Heuristic methods for the single machine scheduling problem with different ready times and a common due date

The single machine scheduling problem with a common due date and non-identical ready times for the jobs is examined in this work. Performance is measured by the minimization of the weighted sum of earliness and tardiness penalties of the jobs. Since this problem is NP-hard, the application of constructive heuristics that exploit specific characteristics of the problem to improve their performance is investigated. The proposed approaches are examined through a computational comparative study on a set of 280 benchmark test problems with up to 1000 jobs.     

Computational method for optimal machine scheduling problem with maintenance and production

This paper considers an optimal scheduling problem of maintenance and production for a machine. Firstly, the problem is formulated as a stochastic switched impulsive optimal control problem. However, there exists the stochastic disturbance in this model. Thus, it is difficult to solve the problem by conventional optimisation techniques. To overcome this difficulty, the stochastic switched impulsive optimal control problem is transformed into a deterministic switched impulsive optimal control problem with continuous state inequality constraints. Then, by combining a time-scaling transformation, a second-order smoothing technique and a penalty function method, an improved Newton algorithm is developed for solving this problem. Convergence results indicate that the algorithm is globally convergent with quadratic rate. Finally, two numerical examples are provided to illustrate the effectiveness of the developed algorithm.     

A robust scheduling for the multi-mode project scheduling problem with a given deadline under uncertainty of activity duration

The problem of this paper deals with the multi-mode project scheduling problem under uncertainty of activity duration where only the renewable resources are taken into account and a given deadline has to be met at the cost of recruiting additional resources. A heuristic algorithm is employed to solve this problem, and to maintain the robustness of the baseline schedule, the concept of critical chain project management (CCPM) is applied in which a new definition to resource buffer is considered. A simulation methodology is used to determine the size and location of resource buffers in the schedules in which three different buffer sizes and three different uncertainty levels are considered. Results and analysis of the simulation outcomes illustrate that resource buffers are useful and should be simulated by the CCPM schedules, as they help to decrease the total duration of the project during implementation and meet the deadline of the project with more assurance.     

Application of genetic algorithms with dominant genes in a distributed scheduling problem in flexible manufacturing systems

Multi-factory production networks have increased in recent years. With the factories located in different geographic areas, companies can benefit from various advantages, such as closeness to their customers, and can respond faster to market changes. Products (jobs) in the network can usually be produced in more than one factory. However, each factory has its operations efficiency, capacity, and utilization level. Allocation of jobs inappropriately in a factory will produce high cost, long lead time, overloading or idling resources, etc. This makes distributed scheduling more complicated than classical production scheduling problems because it has to determine how to allocate the jobs into suitable factories, and simultaneously determine the production scheduling in each factory as well. The problem is even more complicated when alternative production routing is allowed in the factories. This paper proposed a genetic algorithm with dominant genes to deal with distributed scheduling problems, especially in a flexible manufacturing system (FMS) environment. The idea of dominant genes is to identify and record the critical genes in the chromosome and to enhance the performance of genetic search. To testify and benchmark the optimization reliability, the proposed algorithm has been compared with other approaches on several distributed scheduling problems. These comparisons demonstrate the importance of distributed scheduling and indicate the optimization reliability of the proposed algorithm.     

Ant colony optimisation algorithms for two-stage permutation flow shop with batch processing machines and nonidentical job sizes

This paper focuses on minimising the maximum completion time for the two-stage permutation flow shop scheduling problem with batch processing machines and nonidentical job sizes by considering blocking, arbitrary release times, and fixed setup and cleaning times. Two hybrid ant colony optimisation algorithms, one based on job sequencing (JHACO) and the other based on batch sequencing (BHACO), are proposed to solve this problem. First, max-min pheromone restriction rules and a local optimisation rule are embedded into JHACO and BHACO, respectively, to avoid trapping in local optima. Then, an effective lower bound is estimated to evaluate the performances of the different algorithms. Finally, the Taguchi method is adopted to investigate and optimise the parameters for JHACO and BHACO. The performances of the proposed algorithms are compared with that of CPLEX on small-scale instances and those of a hybrid genetic algorithm (HGA) and a hybrid discrete differential evolution (HDDE) algorithm on full-scale instances. The computational results demonstrate that BHACO outperforms JHACO, HDDE and HGA in terms of solution quality. Besides, JHACO strikes a balance between solution quality and run time.     

Iterated greedy algorithms to minimize the total family flow time for job-shop scheduling with job families and sequence-dependent set-ups

This study addresses a variant of job-shop scheduling in which jobs are grouped into job families, but they are processed individually. The problem can be found in various industrial systems, especially in reprocessing shops of remanufacturing systems. If the reprocessing shop is a job-shop type and has the component-matching requirements, it can be regarded as a job shop with job families since the components of a product constitute a job family. In particular, sequence-dependent set-ups in which set-up time depends on the job just completed and the next job to be processed are also considered. The objective is to minimize the total family flow time, i.e. the maximum among the completion times of the jobs within a job family. A mixed-integer programming model is developed and two iterated greedy algorithms with different local search methods are proposed. Computational experiments were conducted on modified benchmark instances and the results are reported.     

Strength and adaptability of problem-space based neighborhoods for resource-constrained scheduling

In this paper, Resource Constrained Scheduling (RCS) consists of scheduling activities on scarce resources, each activity may require more than one resource at a time, and each resource is available in the same quantity throughout the planning period. This paper described a methodology for RCS that can be easily adapted to consider different regular measures of performance. The solution approach is local search using a recent development published in the literature; namely, problem-space based neighborhoods. Computational results are encouraging when searching these spaces using simple local search techniques. Further improvements are explored through the use of a genetic algorithm. In both cases, close-to-optimal solutions are found for standard problems from the literature. The adaptability of the methodology is demonstrated using makespan and mean tardiness as performance measures.     

A duplication heuristic for static scheduling of tasks on distributed memory multiprocessors

Abstract

A task duplication heuristic, DSH, was proposed in [11]. The underlying concept of the task duplication heuristic is duplicating some tasks on processors such that the earliest start time of tasks on processors can be reduced, that is, tasks on processors can be executed sooner. This leads to a better scheduling length. In this paper, we propose a more general task duplication heuristic, bottom‐up top‐down duplication heuristic (BTDH), for static scheduling of directed‐acyclic graphs (DAGs) on distributed memory multiprocessors. The key difference between BTDH and DSH is the method used for duplicating tasks. BTDH allows tasks to be duplicated on processors even though the duplication of tasks will temporarily increase the earliest start time of some tasks. DSH only allows those duplications which will reduce the earliest start time of tasks. Simulation results show that, for coarse‐grain DAGs, the scheduling length of BTDH is almost the same as the scheduling length of DSH. However, for medium‐grain and fine‐grain DAGs, BTDH produces better scheduling length than DSH.     

An effective formulation for optimal scheduling of multistage multi-product batch plant based on due dates

A mathematical formulation for optimal scheduling of multistage multi-product batch plant with parallel units is presented. The allocations of tasks, units and stages are described by a set of binary variables. The sequence-dependent setup times of orders and the ready times of units are considered. Based on the due dates and the processing times of orders, the predefined processing sequence of orders is achieved. The continuous time representation mode is also used in the proposed model. The computations on several classic scheduling examples and comparisons with other existing models in the literatures demonstrate the proposed scheduling model can obtain the optimal solutions in a shorter time and has much fewer binary variables.     

Some recent results in the analysis of greedy algorithms for assignment problems

We survey some recent developments in the analysis of greedy algorithms for assignment and transportation problems. We focus on the linear programming model for matroids and linear assignment problems with Monge property, on general linear programs, probabilistic analysis for linear assignment and makespan minimization, and on-line algorithms for linear and non-linear assignment problems.This is an expanded version of a survey lecture presented at the DGOR/NSOR Symposium, Amsterdam, 1993     

Comparisons of bi-objective genetic algorithms for hybrid flowshop scheduling with sequence-dependent setup times

This paper addresses the scheduling problems in a hybrid flowshop with two objectives of minimising the makespan and total tardiness. Since this problem is NP-hard, evolutionary algorithms based on the genetic algorithm (GA) namely; BOGAW, BOGAC, BOGAT, and BOGAS are proposed for searching the Pareto-optimal frontier. In these algorithms, we propose to generate a section of solutions for the next generation using a neighbourhood search structure on the best individual in each generation. The selection procedure selects the best chromosome based on an evaluation mechanism used in the algorithm (i.e., weighted sum, crowding distance, TOPSIS and single-objective). The aim of this paper is to clarify that the cited characteristic is efficient and it enhances the efficiency of algorithms. Therefore, we perform a comparison between the proposed algorithms to find the best alternative. Data envelopment analysis is used to evaluate the performance of approximation methods. The obtained result from the comparison shows that, BOGAC is the more efficient. To continue, since the efficiency of our idea is not clear, we compare our efficient algorithm with other efficient algorithms in the literature (namely PGA-ALS and MOGLS). The final persuasive results support the idea that BOGAC in comparison with PGA-ALS and MOGLS is more effective and efficient.     

Solution algorithms for the number of tardy jobs minimisation scheduling with a time-dependent learning effect

This paper deals with a single-machine scheduling problem with a time-dependent learning effect. The goal is to determine the job sequence that minimise the number of tardy jobs. Two dominance properties, two heuristic algorithms and a lower bound to speed up the search process of the branch-and-bound algorithm are proposed. Computational experiments show that the branch-and-bound algorithm can solve instances up to 18 jobs in a reasonable amount of time, and the proposed heuristic algorithm MFLA performs effectively and efficiently     

Optimal scheduling of logistical support for an emergency roadway repair work schedule

The completion of every disaster rescue task performed by repair work teams relies on the in-time supply of materials to the rescue workers. Up to now, logistical support planning for emergency repair work in Taiwan has been done manually, which is neither effective nor efficient. To remedy the problem, this study presents a logistical support scheduling model for the given emergency repair work schedule. The objective is to minimize the short-term operating cost subject to time constraints and other related operating constraints. This model is formulated as an integer multiple-commodity network flow problem which is characterized as NP-hard. A heuristic algorithm, based on the problem decomposition and variable fixing techniques, is also proposed to efficiently solve this problem. Computational tests are performed using data from Taiwan's 1999 Chi-Chi earthquake. The results show that the model and the solution algorithm would be useful for the logistical support scheduling.     

A new multi-objective optimization model for preventive maintenance and replacement scheduling of multi-component systems

In this article, a new multi-objective optimization model is developed to determine the optimal preventive maintenance and replacement schedules in a repairable and maintainable multi-component system. In this model, the planning horizon is divided into discrete and equally-sized periods in which three possible actions must be planned for each component, namely maintenance, replacement, or do nothing. The objective is to determine a plan of actions for each component in the system while minimizing the total cost and maximizing overall system reliability simultaneously over the planning horizon. Because of the complexity, combinatorial and highly nonlinear structure of the mathematical model, two metaheuristic solution methods, generational genetic algorithm, and a simulated annealing are applied to tackle the problem. The Pareto optimal solutions that provide good tradeoffs between the total cost and the overall reliability of the system can be obtained by the solution approach. Such a modeling approach should be useful for maintenance planners and engineers tasked with the problem of developing recommended maintenance plans for complex systems of components.     

A mathematical formulation and anarchic society optimisation algorithms for integrated scheduling of processing and transportation operations in a flow-shop environment

This paper addresses a permutation flow-shop scheduling problem where there are a finite number of transporters to carry jobs from each machine to its subsequent machine. The problem is first formulated as a mixed-integer linear programme, and then two anarchic society optimisation (ASO) algorithms are developed to solve large-sized instances of the problem. The numerical experience shows that the ASO algorithms are considerably effective and efficient. Finally, a sensitivity analysis is carried out to study the performance of the manufacturing system versus the transportation times and the number of transporters.     

Asymptotic optimality of shortest processing time-based algorithms for flow shop and open shop problems with nonlinear objective functions

This article investigates the criterion of minimizing total k-power completion time (TKCT) in flow shop and open shop scheduling. For these NP-hard problems, the asymptotic optimality of the shortest processing time-based algorithms is proven for a sufficiently large problem scale. To numerically evaluate the convergence of the algorithms, new lower bounds with performance guarantees are presented for the flow shop TKCT problem. Computational results demonstrate the performance of the proposed algorithms and the effectiveness of the nonlinear objective. In addition, theoretical results on the single-machine TKCT problem are obtained for mathematical deduction.     

The extended resource task network: a framework for the combined scheduling of batch processes and CHP plants

The issue of energy has emerged as one of the greatest challenges facing mankind. In an industrial perspective, the development of site utility systems (generally combined heat and power (CHP) systems) for the generation and management of utilities provides a great potential source for energy savings. However, in most industrial sites, a master–slave relationship usually governs this kind of system and limits the potential operating capacity of CHP. To improve the decision-making process, Agha et al. (2010. Integrated production and utility system approach for optimising industrial unit operation. Energy, 35, 611–627) have proposed an integrated approach that carries out simultaneous and consistent scheduling of batch production plants and site utility systems. The modelling of the problem relies on a mixed integer linear programming (MILP) formulation. Nevertheless, although it is a powerful mathematical tool, it still remains difficult to use for non-expert engineers. In this framework, a graphical formalism based on existing representations (STN, RTN) has been developed: the extended resource task network (ERTN). Combined with an efficient and generic MILP formulation, it permits various kinds of industrial problems, including production and consumption of utility flows to be modelled homogenously. This paper focuses on the semantic elements of the ERTN formalism and illustrates their use through representative examples.     

Using genetic algorithms (GA) and a coloured timed Petri net (CTPN) for modelling the optimization-based schedule generator of a generic production scheduling system

The semiconductor manufacturing industry is one of the most complicated manufacturing systems in the world. Considering its complex problem nature, such as the unrelated parallel machine environment, dynamic job arrival, non-pre-emption, inseparable sequence-dependent set-up time, multiple-resource requirements, general precedence constraint, and job recirculation, this study proposed the optimization-based schedule generator (OptSG) for solving the generalized scheduling problems arising from the semiconductor manufacturing environment. The separation of the problem structure and problem configuration in OptSG contributes to the structural independence, making OptSG robust and convenient in analysis and problem-solving in real settings with changing properties. Meanwhile, an MILP model was proposed as a benchmark to estimate the validity of OptSG. Inseparable sequence-dependent set-up time and multiple-resource requirements that have not been addressed simultaneously in the literature were considered in this model. By using different evaluation criteria, including makespan, total completion time and maximum tardiness, experiments were conducted to compare the solutions of the MILP model, OptSG and dispatching rule-based heuristics (DRBH). The results validated the solution quality of OptSG.