Fast local neighborhood search algorithm for the no-wait flow shop scheduling with total flow time minimization

A fast local neighbourhood search (FLNS) algorithm is proposed in this paper to minimise the total flow time in the no-wait flow shop scheduling problem, which is known to be NP-hard for more than two machines. In this work, an unscheduled job sequence is constructed firstly according to the total processing time and standard deviation of jobs on the machines. This job sequence is undergone an initial optimisation using basic neighbourhood search algorithm. Then, an innovative local neighbourhood search scheme is designed to search for the partial neighbourhood in each iterative processing and calculate the neighbourhood solution with an objective increment method. This not only improves the solution quality significantly, but also speeds up the convergence of the solution of the algorithm. Moreover, a probabilistic acceptance criterion is adopted to help our method escape from the local optima. Based on Taillard’s benchmarks, the experimental results show that the proposed FLNS algorithm is superior to major existing algorithms (IHA, IBH_LS, GA-VNS and DHS) in terms of both quality and robustness, and can provide best upper bounds. The in-depth statistical analysis demonstrates that the promising performance of our proposed algorithm is also statistically significant.     

An efficient iterated local search algorithm for the total tardiness blocking flow shop problem

This paper deals with the blocking flow shop problem and proposes an Iterated Local Search (ILS) procedure combined with a variable neighbourhood search (VNS) for the total tardiness minimisation. The proposed ILS makes use of a NEH-based procedure to generate the initial solution, and uses a local search to intensify the exploration that combines the insertion and swap neighbourhood and uses a perturbation mechanism consisting of three neighbourhood operators to diversify the search. The computational evaluation has shown the effectiveness of combining the insertion and swap neighbourhood during the search despite the insertion neighbourhood being more effective than the swap neighbourhood for this problem. Finally, the computation of this algorithm when evaluated against two other algorithms from the literature shows good performance.     

Open shop scheduling problem to minimize total weighted completion time

A given number of jobs in an open shop scheduling environment must each be processed for given amounts of time on each of a given set of machines in an arbitrary sequence. This study aims to achieve a schedule that minimizes total weighted completion time. Owing to the strong NP-hardness of the problem, the weighted shortest processing time block (WSPTB) heuristic is presented to obtain approximate solutions for large-scale problems. Performance analysis proves the asymptotic optimality of the WSPTB heuristic in the sense of probability limits. The largest weight block rule is provided to seek optimal schedules in polynomial time for a special case. A hybrid discrete differential evolution algorithm is designed to obtain high-quality solutions for moderate-scale problems. Simulation experiments demonstrate the effectiveness of the proposed algorithms.     

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.     

Scheduling a permutation flow shop with family setups to minimise total tardiness

This paper presents several procedures for scheduling a permutation flow shop with family setups when the objective is to minimise total tardiness. These procedures are tested on several problem sets with varying numbers of families, jobs, and machines, three setup time distributions, and various levels of due date tightness and variability. The results show that variable greedy algorithms are effective when solving small problems, but a neighbourhood search procedure that includes searches with a neighbourhood defined by the sequence of batches of jobs belonging to the same setup family is more effective when solving large problems. Results are also presented, showing that significant reductions in total tardiness can be obtained if the time required to perform the family setups is reduced.     

Sequence-dependent setup time flexible job shop scheduling problem to minimise total tardiness

This paper studies the problem of scheduling flexible job shops with setup times where the setups are sequence-dependent. The objective is to find the schedule with minimum total tardiness. First, the paper develops a mathematical model in the form of mixed integer linear programming and compares it with the available model in the literature. The proposed model outperforms the available model in terms of both size complexity and computational complexity. Then, an effective metaheuristic algorithm based on iterated local search is proposed and compared with a tabu search and variable neighbourhood search algorithms proposed previously for the same problem. A complete experiment is conducted to evaluate the algorithms for performance. All the results show the superiority of the proposed algorithm against the available ones.     

An effective discrete harmony search algorithm for flexible job shop scheduling problem with fuzzy processing time

This study addresses flexible job shop scheduling problem (FJSP) with fuzzy processing time. The fuzzy or uncertainty of processing time is one of seven characteristics in remanufacturing. A discrete harmony search (DHS) algorithm is proposed for FJSP with fuzzy processing time. The objective is to minimise maximum fuzzy completion time. A simple and effective heuristic rule is proposed to initialise harmony population. Extensive computational experiments are carried out using five benchmark cases with eight instances from remanufacturing. The proposed heuristic rule is evaluated using five benchmark cases. The proposed DHS algorithm is compared to six metaheuristics. The results and comparisons show the effectiveness and efficiency of DHS for solving FJSP with fuzzy processing time.     

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.     

A comparison of metaheuristic procedures to schedule jobs in a permutation flow shop to minimise total earliness and tardiness

This paper considers the problem of scheduling jobs in a permutation flow shop with the objective of minimising total earliness and tardiness. A genetic algorithm is proposed for the problem. This procedure and five other procedures were tested on problem sets that varied in terms of number of jobs, machines and the tightness and range of due dates. It was found that the genetic algorithm procedure was consistently effective in generating good solutions relative to the other procedures.     

Incorporating preventive maintenance into the m-machine no-wait flow-shop scheduling problem with total flow-time minimization: a computational study

In this article, the impact of preventive maintenance policies on the constructive heuristics performance for the no-wait flow-shop problem with total flow-time minimization is evaluated. The main constructive heuristics for the m-machine no-wait flow-shop scheduling problem with total flow-time minimization are compared through computational experiments with a set of 5760 problems. The results show that the adopted parameters significantly affect the performance of the constructive heuristics; also, the computational effort required to solve the problems increases owing to the complexity of the function-objective calculation. Heuristics proposed by Laha and Sapkal (LSH) and Framinan, Nagano and Moccellin (FNMH) provide the best solutions for both evaluated policies.     

Re-entrant flow shop scheduling problem with time windows using hybrid genetic algorithm based on auto-tuning strategy

The re-entrant flow shop scheduling problem considering time windows constraint is one of the most important problems in hard-disc drive (HDD) manufacturing systems. In order to maximise the system throughput, the problem of minimising the makespan with zero loss is considered. In this paper, evolutionary techniques are proposed to solve the complex re-entrant scheduling problem with time windows constraint in manufacturing HDD devices with lot size. This problem can be formulated as a deterministic Fm?|?fmls, rcrc, temp?|?C_max problem. A hybrid genetic algorithm was used for constructing chromosomes by checking and repairing time window constraints, and improving chromosomes by a left-shift heuristic as a local search algorithm. An adaptive hybrid genetic algorithm was eventually developed to solve this problem by using fuzzy logic control in order to enhance the search ability of the genetic algorithm. Finally, numerical experiments were carried out to demonstrate the efficiency of the developed approaches.     

A lever concept integrated with simple rules for flow shop scheduling

The development of more efficient and better performing priority dispatching rules (PDRs) for production scheduling is relevant to modern flow shop scheduling practice because they are simple, easy to apply and have low computational complexity, especially for large-scale problems. While the current research trend in scheduling is towards finding superior solutions through meta-heuristics, they are computationally expensive and many meta-heuristics also use PDRs to generate starting points. In this paper, we analyse the properties of flow shop scheduling problems to minimise maximum completion time, and generate a new dominance rule that is complementary to Szwarc’s rule. These dominance rules indicate that a weighting factor should be included in sequencing to account for the possibility that a single job’s processing time can generate idle time repeatedly within a flow line. Two new PDRs with a leveraged weighting factor are proposed to minimise makespan and average completion time. Computational results on Taillard’s benchmark problems and on historical operating room data show that the proposed PDRs perform much better than established PDRs without an increase in computational complexity.     

A multi-objective scatter search for a bi-criteria no-wait flow shop scheduling problem

The flow shop problem as a typical manufacturing challenge has gained wide attention in academic fields. This article considers a bi-criteria no-wait flow shop scheduling problem (FSSP) in which weighted mean completion time and weighted mean tardiness are to be minimized simultaneously. Since a FSSP has been proved to be NP-hard in a strong sense, a new multi-objective scatter search (MOSS) is designed for finding the locally Pareto-optimal frontier of the problem. To prove the efficiency of the proposed algorithm, various test problems are solved and the reliability of the proposed algorithm, based on some comparison metrics, is compared with a distinguished multi-objective genetic algorithm (GA), i.e. SPEA-II. The computational results show that the proposed MOSS performs better than the above GA, especially for the large-sized problems.     

Scheduling on a two-machine permutation flow shop under time-of-use electricity tariffs

We consider a two-machine permutation flow shop scheduling problem to minimise the total electricity cost of processing jobs under time-of-use electricity tariffs. We formulate the problem as a mixed integer linear programming, then we design two heuristic algorithms based on Johnson’s rule and dynamic programming method, respectively. In particular, we show how to find an optimal schedule using dynamic programming when the processing sequence is fixed. In addition, we propose an iterated local search algorithm to solve the problem with problem-tailored procedures and move operators, and test the computational performance of these methods on randomly generated instances.     

A job shop distributed scheduling based on Lagrangian relaxation to minimise total completion time

This paper considers a distributed job shop scheduling problem where autonomous sub-production systems share common machines with each other. Each sub-production system is responsible for the scheduling of a set of jobs to minimise the total completion time on shared machines. A sub-production system has ultimate responsibility on maintaining private information such as objective function, processing time and routings on shared machines. Also sub-production systems must cooperate each other in order to achieve a global goal while sharing minimum of private information. In this research, we propose a distributed cooperation method in which sub-production systems and shared machines interact with one another to find a compromised solution between a locally optimised solution and a system-wide solution. We tested the proposed method for small, medium and large size of job shop scheduling problems and compared to a global optimal solutions. The proposed method shows promising results in terms of solution qualities and computational times.     

A note on minimising total absolute deviation of job completion times on a two-machine no-wait proportionate flowshop

A popular measure used in service systems is that of total absolute deviation of job completion times (TADC). It is relevant to settings where the objective is to balance the level of service provided to different customers. During the last decade, TADC has been studied in various machine settings, and under various assumptions on the job processing times. In this note, we study TADC on a two-machine no-wait proportionate flow shop, i.e. a flow shop with machine-independent processing times, and with no buffer between the machines. A very surprising and unique result is introduced: a simple index policy (the well-known largest processing time (LPT) first sequence) is shown to be optimal for instances of no more than seven jobs. This property does not hold for larger instances. We show that for instances of eight and nine jobs, there are exactly two schedules which are candidates for optimality. For the 10-job instance, the number of candidates increases. This uncommon behaviour of the optimal solution and, consequently, the complexity of the problem studied here, remain open questions, and are challenging topics for future research.     

A new complexity proof for the two-stage hybrid flow shop scheduling problem with dedicated machines

This paper considers a two-stage hybrid flow shop scheduling problem with dedicated machines at stage 2. The objective is to minimise the makespan. There is one machine at stage 1 and two machines at stage 2. Each job must be processed on the single machine at stage 1 and, depending upon the job type, the job is processed on either of the two machines at stage 2. We first introduce this special type of the two-stage hybrid flow shop scheduling problem and present some preliminary results. We then present a counter example to the known complexity proof of Riane et al. [Riane, F., Artiba, A. and Elmaghraby, S.E., 2002. Sequencing a hybrid two-stage flowshop with dedicated machines. International Journal of Production Research, 40, 4353–4380.] Finally, we re-establish the complexity of the problem.     

Minimizing makespan in a two-stage flow shop with parallel batch-processing machines and re-entrant jobs

Against a background of heat-treatment operations in mould manufacturing, a two-stage flow-shop scheduling problem is described for minimizing makespan with parallel batch-processing machines and re-entrant jobs. The weights and release dates of jobs are non-identical, but job processing times are equal. A mixed-integer linear programming model is developed and tested with small-scale scenarios. Given that the problem is NP hard, three heuristic construction methods with polynomial complexity are proposed. The worst case of the new constructive heuristic is analysed in detail. A method for computing lower bounds is proposed to test heuristic performance. Heuristic efficiency is tested with sets of scenarios. Compared with the two improved heuristics, the performance of the new constructive heuristic is superior.     

Iterative algorithms for batching and scheduling to minimise the total job tardiness in two-stage hybrid flow shops

This study considers the batching and scheduling problem in two-stage hybrid flow shops in which each job with a distinct due-date is processed through two serial production stages, each of which has identical machines in parallel. Under the fundamental trade-off that large batch sizes with less frequent changeovers may reduce setup costs and hence increase machine utilisation, while small batch sizes may reduce job flow times and hence improve scheduling performance, the problem is to determine the number of batches, the batch compositions, the allocation of batches to the parallel machines at each stage, and the sequence of the batches allocated to each machine for the objective of minimising the total job tardiness. A mixed integer programming model is developed for the reduced problem in which the number of batches is given, and then, three iterative algorithms are proposed in which batching and scheduling are done repeatedly until a good solution is obtained. To show the performance of the algorithms, computational experiments were done on a number of test instances, and the results are reported. In particular, we show that the number of batches decreases as the ratio of the batch setup time to the job processing time increases.