A constructive algorithm and a simulated annealing approach for solving flowshop problems with missing operations

In many practical cases of flowshop environments and especially in flowline manufacturing cells, some or all jobs may not require processing on all machines. Hence, this paper focuses on the flowshop scheduling problem with missing operations. A modification of the constructive NPS-set heuristic is proposed, which generates non-permutation schedules effectively. Furthermore, a two-phase simulated annealing (SA) method is presented that specifically considers missing operations in its procedure. The modified NPS-set heuristic and the two-phase SA are tested and statistically evaluated by an extensive computational study for total flow time criteria. The results show that the modified NPS-set heuristic as well as the specific consideration of missing operations can enhance the algorithms’ performance significantly.     

Scheduling with multi-attribute set-up times on unrelated parallel machines

This paper studies a problem in the knitting process of the textile industry. In such a production system, each job has a number of attributes and each attribute has one or more levels. Because there is at least one different attribute level between two adjacent jobs, it is necessary to make a set-up adjustment whenever there is a switch to a different job. The problem can be formulated as a scheduling problem with multi-attribute set-up times on unrelated parallel machines. The objective of the problem is to assign jobs to different machines to minimise the makespan. A constructive heuristic is developed to obtain a qualified solution. To improve the solution further, a meta-heuristic that uses a genetic algorithm with a new crossover operator and three local searches are proposed. The computational experiments show that the proposed constructive heuristic outperforms two existed heuristics and the current scheduling method used by the case textile plant.     

Effective dynamic dispatching rule and constructive heuristic for solving single-machine scheduling problems with a common due window

This study addresses the single-machine scheduling problem with a common due window (CDW) that has a constant size and position. The objective is to minimise the total weighted earliness–tardiness penalties for jobs completed out of the CDW. To determine a schedule as close to optimum as possible, this study develops a dynamic dispatching rule and an effective constructive heuristic. The better performance of the proposed heuristic is demonstrated by comparing the results of it with those of a state-of-the-art greedy heuristic on a well-known benchmark problem set. In addition, we incorporate the constructive heuristic into a best-so-far meta-heuristic to examine the benefit of the proposed heuristic. The results show that the best known solutions in 144 out of the 250 benchmark instances are improved.     

A new heuristic for the flowshop scheduling problem to minimize makespan and maximum tardiness

This paper presents a new heuristic for solving the flowshop scheduling problem that aims to minimize makespan and maximize tardiness. The algorithm is able to take into account the aforementioned performance measures, finding a set of non-dominated solutions representing the Pareto front. This method is based on the integration of two different techniques: a multi-criteria decision-making method and a constructive heuristic procedure developed for makespan minimization in flowshop scheduling problems. In particular, the technique for order preference by similarity of ideal solution (TOPSIS) algorithm is integrated with the Nawaz–Enscore–Ham (NEH) heuristic to generate a set of potential scheduling solutions. To assess the proposed heuristic's performance, comparison with the best performing multi-objective genetic local search (MOGLS) algorithm proposed in literature is carried out. The test is executed on a large number of random problems characterized by different numbers of machines and jobs. The results show that the new heuristic frequently exceeds the MOGLS results in terms of both non-dominated solutions, set quality and computational time. In particular, the improvement becomes more and more significant as the number of jobs in the problem increases.     

High-performing heuristics to minimize flowtime in no-idle permutation flowshop

In this article, the issue of production scheduling in a no-idle flowshop environment is addressed. An extensive literature review has shown that there are no heuristics specifically proposed for this problem, especially when it comes to constructive heuristic methods. In this context, this article proposes a highly efficient simple constructive heuristic to minimize the total flowtime criterion. The proposed heuristic was embedded in the high performance iterated greedy algorithm. Computational results and statistical analysis show that the proposed heuristic overperformed the main constructive methods found up to now. In addition, it is observed that the integration of the proposed heuristic with the iterated greedy algorithm provides the most efficient metaheuristic for the problem.     

Scheduling in flowshops to minimize total tardiness of jobs

The problem of scheduling in static flowshops is considered with the objective of minimizing mean or total tardiness of jobs. A heuristic algorithm based on the simulated annealing (SA) technique is developed. The salient features of the proposed SA algorithm are the development of two new perturbation schemes for use in the proposed SA algorithm and a new improvement scheme to improve the quality of the solutions. The proposed algorithm is evaluated by using the benchmark problems available in the literature. The performance of the proposed SA algorithm is found to be very good, and the proposed heuristic performs better than the existing heuristics.     

Scheduling a flow-line manufacturing cell: a tabu search approach

The performance of two heuristic procedures for the scheduling of a flow-line manufacturing cell was compared. We propose a procedure based on a combinatorial search technique known as tabu search. The new procedure is compared with a heuristic based on simulated annealing which was proposed in earlier research. The scheduling problem addressed here differs from the traditional flow-shop scheduling problem in the sense that we are interested in sequencing part families (i.e. groups of jobs which share a similar setup) as well as individual jobs within each family. The results reveal that the tabu search heuristic outperforms the simulated annealing heuristic by generating 'better solutions' in less computation time.     

A computational study of heuristics for two-stage flexible flowshops

We consider the scheduling of two-stage flexible flowshops. This manufacturing environment involves two machine centres representing two consecutive stages of production. Each machine centre is composed of multiple parallel machines. Each job has to be processed serially through the two machine centres. In each machine centre, a job may be processed on any of the machines. There are n independent jobs to be scheduled without preemption. The jobs can wait in between the two machine centres and the intermediate storage is unlimited. Our objective will be to minimize the maximum completion time of the jobs. We formulate the problem as a mixed integer program. Given this problem class is NP-hard in the strong sense, we present three lower bounds to estimate the optimal solution. We then propose a sequence-first, allocate-second heuristic approach for its solution. We heuristically decompose the problem by first creating a priority list to order the jobs and then assign the jobs to the available machines in each machine centre based on this order. We describe seven rules for the sequencing phase. The assignment phase consists of a heuristic which attempts to minimize each partial schedule length while looking ahead at the future assignment of the currently unscheduled jobs. The computational performance of the heuristic approach was evaluated by comparing the value of each heuristic variant to the best among the three lower bounds. Its effectiveness was tested on scenarios pertinent to flexible flowshop environments, such as cellular manufacturing, by conducting a computational study of over 3400 problems. Our computational results indicate that the most effective approach used Johnson's rule to provide the priority list for job assignment. This provided integrality gaps which on the average were less than 0·73%.     

Effective hybrid genetic algorithm for minimizing makespan on a single-batch-processing machine with non-identical job sizes

The paper addresses minimizing makespan by a genetic algorithm (GA) for scheduling jobs with non-identical sizes on a single-batch-processing machine. A batch-processing machine can process up to B jobs simultaneously. The processing time of a batch is equal to the longest processing time among all jobs in the batch. Two different GAs are proposed based on different encoding schemes. The first is a sequence-based GA (SGA) that generates random sequences of jobs using GA operators and applies the batch first fit heuristic to group the jobs. The second is a batch-based hybrid GA (BHGA) that generates random batches of jobs using GA operators and ensures feasibility by using knowledge of the problem based on a heuristic procedure. A greedy local search heuristic based on the problem characteristics is hybridized with a BHGA that has the ability of steering efficiently the search toward the optimal or near-optimal schedules. The performance of proposed GAs is compared with a simulated annealing (SA) approach proposed by Melouk et al. (Melouk, S., Damodaran, P. and Chang, P.Y., Minimizing makespan for single machine batch processing with non-identical job sizes using simulated annealing. Int. J. Prod. Econ., 2004, 87, 141–147) and also against a modified lower bound proposed for the problem. Computational results show that BHGA performs considerably well compared with the modified lower bound and significantly outperforms the SGA and SA in terms of both quality of solutions and required runtimes.     

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.     

Multi-product continuous plant scheduling: combination of decomposition,genetic algorithm,and constructive heuristic

We propose a polylithic method for medium-term scheduling of a large-scale industrial plant operating in a continuous mode. The method combines a decomposition approach, a genetic algorithm (GA) and a constructive MILP-based heuristic. In the decomposition, decisions are made at two levels, using the rolling horizon approach. At the upper level, a reduced set of products and the time period is chosen to be considered in the lower level. At the lower level, a short-term scheduling MILP-model with event-based representation is used. A heuristic solution to the lower level problem is found using a constructive Moving Window heuristic guided by a genetic algorithm. The GA is applied for finding efficient utilisation of critical units in the lower level problem. For solving the one unit scheduling problem, a parallel dynamic programming algorithm is proposed. Implementation of the dynamic programming algorithm for a graphics processing unit (GPU) is incorporated in the GA for improving its performance. The experimental study of the proposed method on a real case of a large-scale plant shows a significant improvement of the solution quality and the solving time comparing to the pure decomposition algorithm proposed in the earlier study, and confirmed suitability of the proposed approach for the real-life production scheduling. In particular, the reduction of the number of changeovers and their duration in the obtained solution as well as the CPU time of solving the problem was about 60% using the new approach.     

A heuristic for scheduling in flowshop and flowline-based manufacturing cell with multi-criteria

The problem of scheduling in flowshop and flowline-based manufacturing cell is considered with the bicriteria of minimizing makespan and total flowtime of jobs, The formulation of the scheduling problems for both the flowshop and the flowline-based manufacturing cell is first discussed. We then present the development of the proposed heuristic for flowshop scheduling. A heuristic preference relation is developed as the basis for the heuristic so that only the potential job interchanges are checked for possible improvement with respect to bicriteria, The proposed heuristic algorithm as well as the existing heuristic are evaluated in a large number of randomly generated large-sized flowshop problems. We also investigate the effectiveness of these heuristics with respect to the objective of minimizing total machine idletime. We then modify the proposed heuristic for scheduling in a cell, and evaluate its performance.     

Approximation algorithms for common due date assignment and job scheduling on parallel machines

We consider the problem of assigning a common due date to a set of jobs and scheduling the jobs on a set of parallel machines so that the weighted sum of the due date, total earliness, and total tardiness is minimized. A heuristic is developed to solve this problem, and an absolute performance ratio is provided for this heuristic. Another heuristic with a better worst-case performance bound is presented for the case with a zero earliness penalty. A fully polynomial approximation scheme is also developed.     

Bottleneck-based heuristics to minimize tardy jobs in a flexible flow line with unrelated parallel machines

This paper develops new bottleneck-based heuristics with machine selection rules to solve the flexible flow line problem with unrelated parallel machines in each stage and a bottleneck stage in the flow line. The objective is to minimize the number of tardy jobs in the problem. The heuristics consist of three steps: (1) identifying the bottleneck stage; (2) scheduling jobs at the bottleneck stage and the upstream stages ahead of the bottleneck stage; (3) using dispatching rules to schedule jobs at the downstream stages behind the bottleneck stage. A new approach is developed to find the arrival times of the jobs at the bottleneck stage, and two decision rules are developed to schedule the jobs on the bottleneck stage. This new approach neatly overcomes the difficulty of determining feasible arrival times of jobs at the bottleneck stage. In order to evaluate the performance of the proposed heuristics, six well-known dispatching rules are examined for comparison purposes. Six factors are used to design 729 production scenarios, and ten test problems are generated for each scenario. Computational results show that the proposed heuristics significantly outperform all the well-known dispatching rules. An analysis of the experimental factors is also performed and several interesting insights into the heuristics are discovered.     

A heuristic procedure for loading problems in flexible manufacturing systems

The loading problem in a flexible manufacturing system (FMS) is viewed as selecting a subset of jobs from a job pool and allocating the jobs among machines. In this paper a heuristic solution to the loading problem has been suggested by developing the concept of essentiality ratio for the objective of minimizing the system unbalance and thereby maximizing the throughput. The proposed heuristic is tested on ten problems and the results show that the algorithm developed is very reliable and efficient.     

Hybrid flowshop scheduling with family setup time and inconsistent family formation

This research considers a hybrid flowshop scheduling problem where jobs are organised in families according to their machine settings and tools. The family setup time arises when a machine shifts from processing one job family to another. The problem is compounded by the challenges that the formation of job families is different in different stages and only a limited number of jobs can be processed within one setup. This type of problem is common in the production process of standard metal components. This paper aims to propose two approaches to solve this problem. One is a metaheuristic in the form of a genetic algorithm and the other is a heuristic. The proposed approaches are compared and contrasted against the two relevant metaheuristic and heuristic adapted from solving a generalised sequence-dependent setup flowshop problem. Comparative results indicate that the proposed genetic algorithm has better performance on minimising makespan and the heuristic is more effective on reducing family setup time.     

An improved branch and bound procedure for scheduling a flow line manufacturing cell

This paper presents a new branch and bound procedure for scheduling a flow-line manufacturing cell. This procedure and an existing procedure are tested on several problem sets with varying numbers of families, jobs and machines, and varying setup time distributions. The results show that the new procedure solves small problems dramatically faster than the existing procedure. Three heuristic procedures, based on the new branch and bound procedure, are developed. These heuristic procedures as well as a tabu search procedure are tested on problem sets with larger problem sizes. The results show that one of the new procedures generates solutions with improved makespans compared to the tabu search procedure.     

Solution algorithms for single-machine group scheduling with ready times and deteriorating jobs

This article considers the single-machine group scheduling problem with deterioration effect and ready times. The objective of this problem is to determine the sequence of groups and the sequence of jobs to minimize the makespan. To solve the problem, an algorithm based on enumeration, an heuristic algorithm and a branch-and-bound algorithm are developed and exhaustively tested. The computational results show that the performance of the heuristic algorithm is fairly accurate in obtaining near-optimal solutions and the branch-and-bound algorithm is very effective in obtaining optimal solutions.     

A review and evaluation on constructive heuristics to optimise product mix based on the Theory of Constraints

In this paper, we address the problem of defining the product mix in order to maximise a system's throughput. This problem is well known for being NP-Complete and therefore, most contributions to the topic focus on developing heuristics that are able to obtain good solutions for the problem in a short CPU time. In particular, constructive heuristics are available for the problem such as that by Fredendall and Lea, and by Aryanezhad and Komijan. We propose a new constructive heuristic based on the Theory of Constraints and the Knapsack Problem. The computational results indicate that the proposed heuristic yields better results than the existing heuristic.     

A mathematical model and heuristic procedure to schedule printed circuit packs on sequencers

This paper considers the NP-hard problem of scheduling printed circuit packs (PCPs) on sequencers to minimize the total number of changeovers of input tapes required to produce PCPs. A mathematical model for this problem is given. However, when the size of the problem increases, the model will not be computationally feasible. An effective and fast heuristic to solve this problem is presented. The heuristic has shown its effectiveness over two previous heuristics found in the literature. It has been tested on a problem with 45 PCPs, two sequencers, each with seven dispensing heads, and a total of 20 input tape types. Comparison results showed that the heuristic reduced the total number of changeovers by 34% and 23% over previous heuristics. In addition, the proposed heuristic provided balanced workload across available sequencers. To investigate the efficiency of our heuristic further, we tested it against data sets from the literature. The proposed heuristic performs reasonably well compared with the reported results. In printed circuit packs' environment, set-up reduction is a main concern. Set-up is composed of the time required to changeover input tapes on sequencers when switching from PCP type to another. The proposed heuristic is more effective in reducing the number of changeovers of input tapes than heuristics found in the literature. The same heuristic can be used to schedule jobs on CNC machines so that total amount of tool switching is minimized.