Scheduling parallel batch processing machines with arbitrary job sizes and incompatible job families

Motivated by a bottleneck operation in an MLCC (multi-layer ceramic capacitor) production line, we study the scheduling problem of parallel batch processing machines in which a number of jobs can be processed simultaneously in a machine as a batch. Volumes of the jobs are different from each other and each job belongs to the family in which all jobs have the same processing time. In this situation, we analyse three kinds of problems whose performance measures are makespan, total completion time, and total weighted completion time, respectively. Since these problems are known to be NP-hard, we propose a number of heuristics and design genetic algorithms for the problems. Through some computational experiments, we evaluate the performances of the heuristic algorithms proposed, including the genetic algorithms for each of three problems.     

Linguistic-based meta-heuristic optimization model for flexible job shop scheduling

In this paper, a linguistic based meta-heuristic modelling and solution approach for solving the Flexible Job Shop Scheduling Problem (FJSSP) is presented. FJSSP is an extension of the classical job-shop scheduling problem. The present problem definition is to assign each operation to a machine out of a set of capable machines ( the routing problem ) and to order the operations on the machines ( the sequencing problem ), such that a predefined performance measure is optimized. The scope of the problem is widened by taking into account the alternative process plans for each part ( process plan selection problem ) in the present study. Moreover, instead of using operations to represent product processing requirements and machine processing capabilities, machine independent capability units, which are known as Resource Elements (RE), are used. Representation of unique and shared capability boundaries of machine tools and part processing requirements is possible via RE. Using REs in scheduling can also reduce the problem size. The FJSSP is presented as a grammar and the productions in the grammar are defined as controls. Using these controls and the Giffler and Thompson (1960) priority rule-based heuristic, a simulated annealing algorithm is developed to solve FJSSP. This novel approach simplifies the modelling process of the FJSSP and enables usage of existing job shop scheduling algorithms for its solution. The results obtained from the computational study have shown that the proposed algorithm can solve this complex problem effectively within reasonable time. The results have also given some insights on the effect of the selection of dispatching rules and the flexibility level on the job shop performance. It is observed that the effect of dispatching rule selection on the job shop performance diminishes by increasing the job shop flexibility.     

Scheduling algorithms to minimise the total family flow time for job shops with job families

This paper considers the job scheduling problem in which jobs are grouped into job families, but they are processed individually. The decision variable is the sequence of the jobs assigned to each machine. This type of job shop scheduling can be found in various production systems, especially in remanufacturing systems with disassembly, reprocessing and reassembly shops. In other words, the reprocessing shop can be regarded as the job shop with job families since it performs the operations required to bring parts or sub-assemblies disassembled back to like-new condition before reassembling them. To minimise the deviations of the job completion times within each job family, we consider the objective of minimising the total family flow time. Here, the family flow time implies the maximum among the completion times of the jobs within a job family. To describe the problem clearly, a mixed integer programming model is suggested and then, due to the complexity of the problem, two types of heuristics are suggested. They are: (a) priority rule based heuristics; and (b) meta-heuristics. Computational experiments were performed on a number of test instances and the results show that some priority rule based heuristics are better than the existing ones. Also, the meta-heuristics improve the priority rule based heuristics significantly.     

Unrelated parallel machine scheduling with job splitting

Scheduling jobs on unrelated parallel machines is an activity that is very much a part of industrial scheduling. We report a methodology for minimizing the total weighted tardiness of all jobs intended to be processed on unrelated parallel machines in the presence of dynamic job releases and dynamic machine availability. More importantly, the mixed (binary) integer linear programming model formulated for the problem incorporates a couple of “hard” operational constraints to ensure that just-in-time manufacturing practices are followed by controlling the work-in-process and/or finished goods inventories generated by split jobs mandated by a tight due date, a high priority, and/or a high workload. Four different methods based on simple and composite dispatching rules are used to identify an initial solution, which is then used by the tabu-search-based heuristic solution algorithm to ultimately find the best solution. Incorporating the various tabu search features led to the development of six different heuristics that were tested on eight small problem instances to compare the quality of their solutions to the optimal solutions. The results show that the proposed heuristics are capable of obtaining solutions of good quality in a remarkably short computation time with the best performer among them recording a percentage deviation of only 1.18%. A factorial experiment based on a split-plot design is performed to test the performance of the heuristics on problem structures, ranging from nine jobs and three machines to 60 jobs and 15 machines. The results show that the newly developed composite dispatching heuristic, referred to as the modified apparent tardiness cost, is capable of obtaining initial solutions that significantly accelerate the tabu-search-based heuristics to attain the best solution. The use of a long-term memory function is proven to be advantageous in solving all problem structures. In addition, the variable tabu list size is preferred for solving the small problem structure, while the fixed tabu list size is preferred as the problem size grows from small to medium and then large.     

A scatter search approach to sequence-dependent setup times job shop scheduling

Scheduling jobs on multiple machines is a difficult problem when real-world constraints such as the sequence setup time, setup times for jobs and multiple criteria are used for solution goodness. It is usually sufficient to obtain a near-optimal solution quickly when an optimal solution would require days or weeks of computation. Common scheduling heuristics such as Shortest Processing Time can be used to obtain a feasible schedule quickly, but are not designed for multiple simultaneous objectives. We use a new meta-heuristic known as a scatter search (SS) to solve these types of job shop scheduling problems. The results are compared with solutions obtained by common heuristics, a tabu search, simulated annealing, and a genetic algorithm. We show that by combining the mechanism of diversification and intensification, SS produces excellent results in a very reasonable computation time. The study presents an efficient alternative for companies with a complicated scheduling and production situation.     

Makespan minimisation for a parallel machine scheduling problem with preemption and job incompatibility

In this paper, an extension of the graph colouring problem is introduced to model a parallel machine scheduling problem with job incompatibility. To get closer to real-world applications, where the number of machines is limited and jobs have different processing times, each vertex of the graph requires multiple colours and the number of vertices with the same colour is bounded. In addition, several objectives related to scheduling are considered: makespan, number of pre-emptions and summation over the jobs’ throughput times. Different solution methods are proposed, namely, two greedy heuristics, two tabu search methods and an adaptive memory algorithm. The latter uses multiple recombination operators, each one being designed for optimising a subset of objectives. The most appropriate operator is selected dynamically at each iteration, depending on its past performance. Experiments show that the proposed algorithm is effective and robust, while providing high-quality solutions on benchmark instances for the graph multi-colouring problem, a simplification of the considered problem.     

Flexible job shop with continuous material flow

A new scheduling problem, the continuous flow flexible job shop (CF-FJS) is proposed. The formulation combines the well-known flexible job shop (FJS) problem and a dedicated continuous material flow model (MFM). In the MFM, operations are represented by material flow functions derived by integration of arbitrarily defined speed patterns. Two main concepts of the MFM formalism, i.e. variable speed of processing and continuous material flow, lead to position-dependent processing times and overlapping in operations which extend standard FJS formulation. Properties of the CF-FJS are investigated. A tabu search sched uling algorithm utilising these properties is proposed. Effective neighbourhood functions are defined based on elimination approaches. Two auxiliary procedures: search intensification level switching and fast feasibility detection are added to improve algorithm efficiency. The algorithm is verified using dedicated benchmark instances which comprise non-trivial representations of the CF-FJS specific features, i.e. machine efficiency patterns and minimum inter-operation buffers. The research is motivated by task scheduling in a fastener factory, but the presented results can be useful in many domains, such as production of granular goods, steel details, glass and fluids. The solution can be used in real-world applications. The published results can be helpful in testing new CF-FJS scheduling algorithms.     

Heuristics for the two-machine flowshop scheduling problem to minimise makespan with bounded processing times

The two-machine flowshop scheduling problem of minimising makespan is addressed where jobs have random processing times that are bounded within certain intervals. The probability distributions of job processing times within intervals are not known. The only known information about job processing times is the lower and upper bounds. The decision concerning the solution to the problem, i.e. finding a sequence, has to be made based on these bounds. Different heuristics using the bounds are proposed, and the proposed heuristics are compared based on randomly generated data. Computational analysis has shown that three of the proposed heuristics perform well with an overall average error of less than one percent. Moreover, for symmetric distributions, it is also shown that one of the heuristics, which applies Johnson's algorithm to the average of the lower and upper bounds, performs best with an overall average percentage error of 0.71. The obtained results are also shown to be consistent with recent results reported in the literature.     

Integrated process planning and scheduling for large-scale flexible job shops using metaheuristics

In this paper, we discuss an integrated process planning and scheduling problem in large-scale flexible job shops (FJSs). We assume that products can be manufactured in different ways, i.e. using different bills of materials (BOM) and routes for the same product. The total weighted tardiness is the performance measure of interest. A Mixed Integer Programming formulation is provided for the researched problem. Because of the NP-hardness of the investigated problem, an iterative scheme is designed that is based on variable neighbourhood search (VNS) on the process planning level. Appropriate neighbourhood structures for VNS are proposed. Because the evaluation of each move within VNS requires the solution of a large-scale FJS scheduling problem instance, efficient heuristics based on local search from previous research are considered on the scheduling level. Extensive computational experiments based on new randomly generated problem instances are conducted. In addition, a parallel version of the VNS is investigated within the computational experiments. The proposed iterative scheme is benchmarked against a genetic algorithm (GA) from the literature that simultaneously considers process planning and scheduling for the special case where a single BOM is available for each product. It turns out that the new iterative scheme outperforms the GA and a memetic algorithm based on the GA. It is able to solve even large-size problem instances in reasonable amount of time.     

Scheduling job shop associated with multiple routings with genetic and ant colony heuristics

The general job shop problem is one of the well known machine scheduling problems, in which the operation sequence of jobs are fixed that correspond to their optimal process plans and/or resource availability. Scheduling and sequencing problems, in general, are very difficult to solve to optimality and are well known as combinatorial optimisation problems. The existence of multiple job routings makes such problems more cumbersome and complicated. This paper addresses a job shop scheduling problem associated with multiple job routings, which belongs to the class of NP hard problems. To solve such NP-hard problems, metaheuristics have emerged as a promising alternative to the traditional mathematical approaches. Two metaheuristic approaches, a genetic algorithm and an ant colony algorithm are proposed for the optimal allocation of operations to the machines for minimum makespan time criterion. ILOG Solver, a scheduler package, is used to evaluate the performance of the proposed algorithms. The comparison reveals that both the algorithms are capable of providing solutions better than the solution obtained with ILOG Solver.     

Heuristic algorithms for scheduling heat-treatment furnaces of steel casting industries

This paper addresses a research problem of scheduling parallel, non-identical batch processors in the presence of dynamic job arrivals, incompatible job-families and non-identical job sizes. We were led to this problem through a real-world application involving the scheduling of heat-treatment operations of steel casting. The scheduling of furnaces for heat-treatment of castings is of considerable interest as a large proportion of the total production time is the processing times of these operations. In view of the computational intractability of this type of problem, a few heuristic algorithms have been designed for maximizing the utilization of heat-treatment furnaces of steel casting manufacturing. Extensive computational experiments were carried out to compare the performance of the heuristics with the estimated optimal value (using the Weibull technique) and for relative effectiveness among the heuristics. Further, the computational experiments show that the heuristic algorithms proposed in this paper are capable of obtaining near (statistically estimated) optimal utilization of heat-treatment furnaces and are also capable of solving any large size real-life problems with a relatively low computational effort.     

Bi-objective partial flexible job shop scheduling problem: NSGA-II,NRGA, MOGA and PAES approaches

This paper deals with a problem of partial flexible job shop with the objective of minimising makespan and minimising total operation costs. This problem is a kind of flexible job shop problem that is known to be NP-hard. Hence four multi-objective, Pareto-based, meta-heuristic optimisation methods, namely non-dominated sorting genetic algorithm (NSGA-II), non-dominated ranked genetic algorithm (NRGA), multi-objective genetic algorithm (MOGA) and Pareto archive evolutionary strategy (PAES) are proposed to solve the problem with the aim of finding approximations of optimal Pareto front. A new solution representation is introduced with the aim of solving the addressed problem. For the purpose of performance evaluation of our proposed algorithms, we generate some instances and use some benchmarks which have been applied in the literature. Also a comprehensive computational and statistical analysis is conducted in order to analyse the performance of the applied algorithms in five metrics including non-dominated solution, diversification, mean ideal distance, quality metric and data envelopment analysis are presented. Data envelopment analysis is a well-known method for efficiently evaluating the effectiveness of multi-criteria decision making. In this study we proposed this method of assessment of the non-dominated solutions. The results indicate that in general NRGA and PAES have had a better performance in comparison with the other two algorithms.     

Cyclic scheduling heuristics for a re-entrant job shop manufacturing environment

Two efficient cyclic scheduling heuristics for re-entrant job shop environments were developed. Each heuristic generated an efficient and feasible cyclic production schedule for a job shop in which a single product was produced repetitively on a set of machines was to determine an efficient and feasible cyclic schedule which simultaneously minimized flow time and cycle time. The first heuristic considered a repetitive production re-entrant job shop with a predetermined sequence of operations on a single product with known processing times, set-up and material handling times. The second heuristic was a specialization of the first heuristic where the set-up for an operation could commence even while the preceding operation was in progress. These heuristics have been extensively tested and computational results are provided. Also, extensive analysis of worst-case and trade-offs between cycle time and flow time are provided. The results indicate that the proposed heuristics are robust and yield efficient and superior cyclic schedules with modest computational effort.     

Simultaneous scheduling of production and maintenance tasks in the job shop

This paper deals with the job shop problem of simultaneous scheduling of production operations and preventive maintenance tasks. To solve this problem, we develop an elitist multi-objective genetic algorithm that provides a set of Pareto optimal solutions minimising the makespan and the total maintenance cost. A deep study was made to choose the best encoding, operators, and the different probabilities. Some lower bounds of the adopted criteria are developed. The computational experiments carried out on a set of published instances validate the efficiency 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.     

A hybrid algorithm for total tardiness minimisation in flexible job shop: genetic algorithm with parallel VNS execution

This paper addresses the flexible-job-shop scheduling problem (FJSP) with the objective of minimising total tardiness. FJSP is the generalisation of the classical job-shop scheduling problem. The difference is that in the FJSP problem, the operations associated with a job can be processed on any set of alternative machines. We developed a new algorithm by hybridising genetic algorithm and variable neighbourhood search (VNS). The genetic algorithm uses advanced crossover and mutation operators to adapt the chromosome structure and the characteristics of the problem. Parallel-executed VNS algorithm is used in the elitist selection phase of the GA. Local search in VNS uses assignment of operations to alternative machines and changing of the order of the selected operation on the assigned machine to increase the result quality while maintaining feasibility. The purpose of parallelisation in the VNS algorithm is to minimise execution time. The performance of the proposed method is validated by numerical experiments on several representative problems and compared with adapted constructive heuristic algorithms’ (earliest due date, critical ratio and slack time per remaining operation) results.     

A genetic search algorithm to optimize job sequencing under a technological constraint in a rolling-mill facility

This article presents some results from the application of a genetic search algorithm to solve a job scheduling problem where setup costs depend on the order of the jobs. An empirical study shows that, for small problems, the solutions given by the genetic algorithm are as good as those obtained with a mixed-integer linear program. For larger problems that are computationally infeasible, we benchmark the genetic solutions against traditional scheduling heuristics. We also study different population management strategies that can improve the performance of the algorithm. Finally, future research avenues are discussed.     

Minimizing total tardiness on a batch processing machine with incompatible job families

Motivated by an application in semiconductor manufacturing, we study the problem of minimizing total tardiness on a batch processing machine with incompatibl8e job families, where all jobs of the same family have identical processing times and jobs of different families cannot be processed together. We present a dynamic programming algorithm which has polynomial time complexity when the number of job families and the batch machine capacity are fixed. We also examine various heuristic solution procedures which can provide near optimal solutions in a reasonable amount of computation time.     

Dynamic job shop scheduling using variable neighbourhood search

In this paper a scheduling method based on variable neighbourhood search (VNS) is introduced to address a dynamic job shop scheduling problem that considers random job arrivals and machine breakdowns. To deal with the dynamic nature of the problem, an event-driven policy is selected. To enhance the efficiency and effectiveness of the scheduling method, an artificial neural network with a back propagation error learning algorithm is used to update parameters of the VNS at any rescheduling point according to the problem condition. The proposed method is compared with some common dispatching rules that have been widely used in the literature for the dynamic job shop scheduling problem. Results illustrate the high efficiency and effectiveness of the proposed method in a variety of shop floor conditions.     

An efficient hybrid evolutionary heuristic using genetic algorithm and simulated annealing algorithm to solve machine loading problem in FMS

In this paper, a machine loading problem in a flexible manufacturing system (FMS) is discussed, with bi-criterion objectives of minimising system imbalance and maximising system throughput in the occurrence of technological constraints such as available machining time and tool slots. A mathematical model is used to select machines, assign operations and the required tools in order to minimise the system's imbalance while maximising the throughput. An efficient evolutionary algorithm by hybridising the genetic algorithm (GA) and simulated annealing (SA) algorithm called GASA is proposed in this paper. The performance of the GASA is tested by using 10 sample dataset and the results are compared with the heuristics reported in the literature. The influence of genetic operators on the evolutionary search in GASA is studied and reported. Two machine selection heuristics are proposed and their influence on the quality of the solution is also studied. Extensive computational experiments have been carried out to evaluate the performance of the proposed evolutionary heuristics and the results are presented in tables and figures. The results clearly support the better performance of GASA over the algorithms reported in the literature.