Two-stage hybrid batching flowshop scheduling with blocking and machine availability constraints using genetic algorithm

This research investigates a two-stage hybrid flowshop scheduling problem in a metal-working company. The first stage consists of multiple parallel machines and the second stage has only one machine. Four characteristics of the company have substantiated the complexity of the problem. First, all machines in stage one are able to process multiple jobs simultaneously but the jobs must be sequentially set up one after another. Second, the setup time of each job is separated from its processing time and depends upon its preceding job. Third, a blocking environment exists between two stages with no intermediate buffer storage. Finally, machines are not continuously available due to the preventive maintenance and machine breakdown. Two types of machine unavailability, namely, deterministic case and stochastic case, are identified in this problem. The former occurs on stage-two machine with the start time and the end time known in advance. The latter occurs on one of the parallel machine in stage one and a real-time rescheduling will be triggered. Minimizing the makespan is considered as the objective to develop the optimal scheduling algorithm. A genetic algorithm is used to obtain a near-optimal solution. The computational results with actual data are favorable and superior over the results from existing manual schedules.     

A two-machine flowshop scheduling problem with a separated maintenance constraint

This paper considers a two-machine flowshop scheduling problem with a separated maintenance constraint. This means that the machine may not always be available during the scheduling period. It needs a constant time to maintain the machine after completing a fixed number of jobs at most. The objective is to find the optimal job combinations and the optimal job schedule such that the makespan is minimized. The proposed problem has some practical applications, for example, in electroplating process, the electrolytic cell needs to be cleaned and made up a deficiency of medicine. In this paper, we propose a heuristic algorithm to solve this problem. Some polynomially solvable cases and computational experiments are also provided.     

An improved NEH-based heuristic for the permutation flowshop problem

NEH is an effective heuristic for solving the permutation flowshop problem with the objective of makespan. It includes two phases: generate an initial sequence and then construct a solution. The initial sequence is studied and a strategy is proposed to solve job insertion ties which may arise in the construct process. The initial sequence which is generated by combining the average processing time of jobs and their standard deviations shows better performance. The proposed strategy is based on the idea of balancing the utilization among all machines. Experiments show that using this strategy can improve the performance of NEH significantly. Based on the above ideas, a heuristic NEH-D (NEH based on Deviation) is proposed, whose time complexity is O(mn²), the same as that of NEH. Computational results on benchmarks show that the NEH-D is significantly better than the original NEH.     

A Constructive Genetic Algorithm for permutation flowshop scheduling

The general flowshop scheduling problem is a production problem where a set of n jobs have to be processed with identical flow pattern on m machines. In permutation flowshops the sequence of jobs is the same on all machines. A significant research effort has been devoted for sequencing jobs in a flowshop minimizing the makespan. This paper describes the application of a Constructive Genetic Algorithm (CGA) to makespan minimization on flowshop scheduling. The CGA was proposed recently as an alternative to traditional GA approaches, particularly, for evaluating schemata directly. The population initially formed only by schemata, evolves controlled by recombination to a population of well-adapted structures (schemata instantiation). The CGA implemented is based on the NEH classic heuristic and a local search heuristic used to define the fitness functions. The parameters of the CGA are calibrated using a Design of Experiments (DOE) approach. The computational results are compared against some other successful algorithms from the literature on Taillard’s well-known standard benchmark. The computational experience shows that this innovative CGA approach provides competitive results for flowshop scheduling problems.     

Hybrid sliding level Taguchi-based particle swarm optimization for flowshop scheduling problems

A hybrid sliding level Taguchi-based particle swarm optimization (HSLTPSO) algorithm is proposed for solving multi-objective flowshop scheduling problems (FSPs). The proposed HSLTPSO integrates particle swarm optimization, sliding level Taguchi-based crossover, and elitist preservation strategy. The novel contribution of the proposed HSLTPSO is the use of a PSO to explore the optimal feasible region in macro-space, the use of a systematic reasoning mechanism of the sliding level Taguchi-based crossover to exploit the better solution in micro-space, and the use of the elitist preservation strategy to retain the best particles of multi-objective population for next iteration. The sliding level Taguchi-based crossover is embedded in the PSO to find the best solutions and consequently enhance the PSO. Using the systematic reasoning way of the Taguchi-based crossover with considering the influence of tuning factors α, β and γ is presented in this study to solve the conflicting problem of non-feasible solutions and to find the better particles. As a result, it exhibits a significant improvement in Pareto best solutions of the FSP. By combining the advantages of exploration and exploitation, from the computational experiments of the six test problems, the HSLTPSO provides better results compared to the existing methods reported in the literature when solving multi-objective FSPs. Therefore, the HSLTPSO is an effective approach in solving multi-objective FSPs.     

Stochastic proportionate flowshop scheduling with setups

This paper addresses the problem of scheduling n jobs on a proportionate two-machine flowshop where the machines are subject to random breakdowns and setup times are considered separate from processing times. The considered performance measure is makespan. Sequences that minimize makespan with probability 1 are obtained when the first or the second machine is subject to random breakdowns without making any assumptions about downtime distributions or counting processes. It is assumed that the processing and setup times on one machine dominate the corresponding times on the other machine. In the case that processing and setup times on the first and second machines are proportionate, it is shown that the longest processing time (LPT) rule gives an optimal solution when only the first machine is subject to breakdowns, while the shortest processing time (SPT) rule yields an optimal solution when only the second machine suffers breakdowns.     

Computational complexity and solution algorithms for flowshop scheduling problems with the learning effect

In this paper, we analyze the two-machine flowshop problem with the makespan minimization and the learning effect, which computational complexity was not determined yet. First, we show that an optimal solution of this problem does not have to be the ‘permutation’ schedule if the learning effect is taken into consideration. Furthermore, it is proved that the permutation and non-permutation versions of this problem are NP-hard even if the learning effect, in a form of a step learning curve, characterizes only one machine. However, if both machines have learning ability and the learning curves are stepwise then the permutation version of this problem is strongly NP-hard. Furthermore, we prove the makespan minimization problem in m-machine permutation proportional flowshop environment remains polynomially solvable with identical job processing times on each machine even if they are described by arbitrary functions (learning curves) dependent on a job position in a sequence. Finally, approximation algorithms for the general problem are proposed and analyzed.     

A two-machine flowshop makespan scheduling problem with deteriorating jobs

In traditional scheduling problems, the job processing times are assumed to be known and fixed from the first job to be processed to the last job to be completed. However, in many realistic situations, a job will consume more time than it would have consumed if it had begun earlier. This phenomenon is known as deteriorating jobs. In the science literature, the deteriorating job scheduling problems are relatively unexplored in the flowshop settings. In this paper, we study a two-machine flowshop makespan scheduling problem in which job processing times vary as time passes, i.e. they are assumed as increasing functions of their starting times. First, an exact algorithm is established to solve most of the problems of up to 32 jobs in a reasonable amount of time. Then, three heuristic algorithms are provided to derive the near-optimal solutions. A simulation study is conducted to evaluate the performances of the proposed algorithms. In addition, the impact of the deterioration rate is also investigated.     

Heuristics for a two-stage assembly flowshop with bicriteria of maximum lateness and makespan

We consider a two-stage assembly flowshop scheduling problem with the objective of minimizing a weighted sum of makespan and maximum lateness. The problem is known to be NP-hard, and therefore, we propose heuristics to solve the problem. The proposed heuristics are Tabu search (Tabu), particle swarm optimization (PSO), and self-adaptive differential evolution (SDE). An extensive computational experiment is conducted to compare performances of the proposed heuristics. The computational experiment reveals that both PSO and SDE are much superior to Tabu. Moreover, it is statistically shown that PSO performs better than SDE. The computation times of both PSO and SDE are close to each other and they are less than 40 and 45 s, respectively, for the largest size problem considered.     

Minimising total tardiness in the m-machine flowshop problem: A review and evaluation of heuristics and metaheuristics

In this work, a review and comprehensive evaluation of heuristics and metaheuristics for the m-machine flowshop scheduling problem with the objective of minimising total tardiness is presented. Published reviews about this objective usually deal with a single machine or parallel machines and no recent methods are compared. Moreover, the existing reviews do not use the same benchmark of instances and the results are difficult to reproduce and generalise. We have implemented a total of 40 different heuristics and metaheuristics and we have analysed their performance under the same benchmark of instances in order to make a global and fair comparison. In this comparison, we study from the classical priority rules to the most recent tabu search, simulated annealing and genetic algorithms. In the evaluations we use the experimental design approach and careful statistical analyses to validate the effectiveness of the different methods tested. The results allow us to clearly identify the state-of-the-art methods.     

Resource-constrained flowshop scheduling with separate resource recycling operations

This paper considers the relocation problem arising from public re-development projects cast as a two-machine flowshop scheduling problem. In such a project, some buildings need to be torn down and re-constructed. The two processes of tearing down and re-constructing each building are often viewed as a single operation. However, under certain circumstances, the re-construction process, i.e., the resource recycling process, can be viewed as a separate operation. In this paper we regard these two processes as separate on the assumption that they are handled by different working crews. We formulate the problem as a resource-constrained two-machine flowshop scheduling problem with the objective of finding a feasible re-development sequence that minimizes the makespan. We provide problem formulations, discuss the complexity results, and present polynomial algorithms for various special cases of the problem.     

An improved particle swarm optimization algorithm for flowshop scheduling problem

The flowshop scheduling problem has been widely studied and many techniques have been applied to it, but few algorithms based on particle swarm optimization (PSO) have been proposed to solve it. In this paper, an improved PSO algorithm (IPSO) based on the “alldifferent” constraint is proposed to solve the flow shop scheduling problem with the objective of minimizing makespan. It combines the particle swarm optimization algorithm with genetic operators together effectively. When a particle is going to stagnate, the mutation operator is used to search its neighborhood. The proposed algorithm is tested on different scale benchmarks and compared with the recently proposed efficient algorithms. The results show that the proposed IPSO algorithm is more effective and better than the other compared algorithms. It can be used to solve large scale flow shop scheduling problem effectively.     

An ant colony optimization approach to a permutational flowshop scheduling problem with outsourcing allowed

This paper deals with the scheduling problem of minimizing the makespan in a permutational flowshop environment with the possibility of outsourcing certain jobs. It addresses this problem by means of the development of an ant colony optimization-based algorithm. This new algorithm, here named as flowshop ant colony optimization is composed of two combined ACO heuristics. The results show that this new approach can be used to solve the problem efficiently and in a short computational time.     

Heuristics for minimizing regular performance measures in unrelated parallel machine scheduling problems

This research compares the performance of various heuristics and one metaheuristic for unrelated parallel machine scheduling problems. The objective functions to be minimized are makespan, total weighted completion time, and total weighted tardiness. We use the least significant difference (LSD) test to identify robust heuristics that perform significantly better than others for a variety of parallel machine environments with these three performance measures. Computational results show that the proposed metaheuristic outperforms other existing heuristics for each of the three objectives when run with a parameter setting appropriate for the objective.     

New simple constructive heuristic algorithms for minimizing total flow-time in the permutation flowshop scheduling problem

This paper develops a set of new simple constructive heuristic algorithms to minimize total flow-time for an $n$-jobs×$m$-machines permutation flowshop scheduling problem. We first propose a new iterative algorithm based on the best existing simple heuristic algorithm, and then integrate new indicator variables for weighting jobs into this algorithm. We also propose new decision criteria to select the best partial sequence in each iteration of our algorithm. A comprehensive numerical experiment reveals that our modifications and extensions improve the effectiveness of the best existing simple heuristic without affecting its computational efficiency.     

Bi-criteria minimization for the permutation flowshop scheduling problem with machine-based learning effects

In traditional scheduling problems, the processing time for the given job is assumed to be a constant regardless of whether the job is scheduled earlier or later. However, the phenomenon named “learning effect” has extensively been studied recently, in which job processing times decline as workers gain more experience. This paper discusses a bi-criteria scheduling problem in an m-machine permutation flowshop environment with varied learning effects on different machines. The objective of this paper is to minimize the weighted sum of the total completion time and the makespan. A dominance criterion and a lower bound are proposed to accelerate the branch-and-bound algorithm for deriving the optimal solution. In addition, the near-optimal solutions are derived by adapting two well-known heuristic algorithms. The computational experiments reveal that the proposed branch-and-bound algorithm can effectively deal with problems with up to 16 jobs, and the proposed heuristic algorithms can yield accurate near-optimal solutions.     

A three-phase algorithm for flowshop scheduling with blocking to minimize makespan

This paper proposes a three-phase algorithm (TPA) for the flowshop scheduling problem with blocking (BFSP) to minimize makespan. In the first phase, the blocking nature of BFSP is exploited to develop a priority rule that creates a sequence of jobs. Using this as the initial sequence and a variant of the NEH-insert procedure, the second phase generates an approximate solution to the problem. Then, utilizing a modified simulated annealing algorithm incorporated with a local search procedure, the schedule generated in the second phase is improved in the third phase. A pruning procedure that helps evaluate most solutions without calculating their complete makespan values is introduced in the local search to further reduce the computational time needed to solve the problem. Results of the computational experiments with Taillard's benchmark problem instances show that the proposed TPA algorithm is relatively more effective and efficient in minimizing makespan for the BFSP than the state-of-the-art procedures. Utilizing these results, 53 out of 60 new tighter upper bounds have been found for large-sized Taillard's benchmark problem instances.     

Modeling realistic hybrid flexible flowshop scheduling problems

This paper aims to contribute to the recent research efforts to bridge the gap between the theory and the practice of scheduling by modelizing a realistic manufacturing environment and analyzing the effect of the inclusion of several characteristics in the problem formulation. There are several constraints and characteristics that affect the scheduling operations at companies. While these constraints are many times tackled in the literature, they are seldom considered together inside the same problem formulation. We propose a formulation along with a mixed integer modelization and some heuristics for the problem of scheduling n jobs on m stages where at each stage we have a known number of unrelated machines. The jobs might skip stages and, therefore, we have what we call a hybrid flexible flowshop problem. We also consider per machine sequence-dependent setup times which can be anticipatory and non-anticipatory along with machine lags, release dates for machines, machine eligibility and precedence relationships among jobs. Manufacturing environments like this appear in sectors like food processing, ceramic tile manufacturing and several others. The optimization criterion considered is the minimization of the makespan. The MIP model and the heuristics proposed are tested against a comprehensive benchmark and the results evaluated by advanced statistical tools that make use of decision trees and experimental designs. The results allow us to identify the constraints that increase the difficulty.     

A tabu search algorithm with a new neighborhood structure for the job shop scheduling problem

Tabu search (TS) algorithms are among the most effective approaches for solving the job shop scheduling problem (JSP) which is one of the most difficult NP-complete problems. However, neighborhood structures and move evaluation strategies play the central role in the effectiveness and efficiency of the tabu search for the JSP. In this paper, a new enhanced neighborhood structure is proposed and applied to solving the job shop scheduling problem by TS approach. Using this new neighborhood structure combined with the appropriate move evaluation strategy and parameters, we tested the TS approach on a set of standard benchmark instances and found a large number of better upper bounds among the unsolved instances. The computational results show that for the rectangular problem our approach dominates all others in terms of both solution quality and performance.