Bi-criteria SDST hybrid flow shop scheduling with learning effect of setup times: water flow-like algorithm approach

In studies on automatic scheduling problems, processing times do not differ according to repetition of job or process sequences so it may also be necessary to consider processing times independent from setup times. While considering setup times, the human factor has an important effect on setup, so by the processing of similar tasks frequently worker skills improve and they are able to perform setup at a greater pace. This fact is known as the ‘learning effect’ in the literature. This paper deals with sequence-dependent setup times (SDSTs) hybrid flow shop scheduling with learning effect of setup times for minimising weighted sum of makespan and total tardiness. A mathematical programming model that incorporates these aspects of the problem is developed which belongs to the NP-hard class. Thus, because of the intensive computation, we propose a novel meta-heuristic approach called water flow-like algorithm (WFA) which has the feature of multiple and dynamic numbers of solution agents. Various parameters of the problem and the WFA are reviewed by means of Taguchi experimental design. For the evaluation of the proposed WFA, problem data was generated to compare it against a random key genetic algorithm (RKGA). The results demonstrate the high performance of the WFA with respect to the RKGA.     

Scheduling job shop problems with sequence-dependent setup times

In this work we consider job shop problems where the setup times are sequence dependent under minimisation of the maximum completion time or makespan. We present a genetic algorithm to solve the problem. The genetic algorithm is hybridised with a diversification mechanism, namely the restart phase, and a simple form of local search to enrich the algorithm. Various operators and parameters of the genetic algorithm are reviewed to calibrate the algorithm by means of the Taguchi method. For the evaluation of the proposed hybrid algorithm, it is compared against existing algorithms through a benchmark. All the results demonstrate that our hybrid genetic algorithm is very effective for the problem.     

A novel hybrid meta-heuristic algorithm for a no-wait flexible flow shop scheduling problem with sequence dependent setup times

In this paper, we contemplate the problem of scheduling a set of n jobs in a no-wait flexible flow shop manufacturing system with sequence dependent setup times to minimising the maximum completion time. With respect to NP-hardness of the considered problem, there seems to be no avoiding application of metaheuristic approaches to achieve near-optimal solutions for this problem. For this reason, three novel metaheuristic algorithms, namely population based simulated annealing (PBSA), adapted imperialist competitive algorithm (AICA) and hybridisation of adapted imperialist competitive algorithm and population based simulated annealing (AICA?+?PBSA), are developed to solve the addressed problem. Because of the sensitivity of our proposed algorithm to parameter's values, we employed the Taguchi method as an optimisation technique to extensively tune different parameters of our algorithm to enhance solutions accuracy. These proposed algorithms were coded and tested on randomly generated instances, then to validate the effectiveness of them computational results are examined in terms of relative percentage deviation. Moreover, some sensitive analyses are carried out for appraising the behaviour of algorithms versus different conditions. The computational evaluations manifestly support the high performance of our proposed novel hybrid algorithm against other algorithms which were applied in literature for related production scheduling problems.     

Heuristics for permutation flow shop scheduling with batch setup times

In this paper we consider permutation flow shop scheduling problems with batch setup times. Each job has to be processed on each machine once and the technological routes are identical for all jobs. The set of jobs is divided into groups. There are given processing timest _ij of jobi on machinej and setup timess _rj on machinej when a job of ther-th group is processed after a job of another group. It is assumed that the same job order has to be chosen on each machine. We consider both the problems of minimizing the makespan and of minimizing the sum of completion times, where batch or item availability of the jobs is assumed. For these problems we give various constructive and iterative algorithms. The constructive algorithms are based on insertion techniques combined with beam search. We introduce suitable neighbourhood structures for such problems with batch setup times and describe iterative algorithms that are based on local search and reinsertion techniques. The developed algorithms have been tested on a large collection of problems with up to 80 jobs.Supported by Deutsche Forschungsgemeinschaft (Project ScheMA) and by the International Association for the Promotion of Cooperation with Scientists from the Independent States of the Former Soviet Union (Project INTAS-93-257)     

A hybrid water flow algorithm for multi-objective flexible flow shop scheduling problems

In this article, the multi-objective flexible flow shop scheduling problem with limited intermediate buffers is addressed. The objectives considered in this problem consist of minimizing the completion time of jobs and minimizing the total tardiness time of jobs. A hybrid water flow algorithm for solving this problem is proposed. Landscape analysis is performed to determine the weights of objective functions, which guide the exploration of feasible regions and movement towards the optimal Pareto solution set. Local and global neighbourhood structures are integrated in the erosion process of the algorithm, while evaporation and precipitation processes are included to enhance the solution exploitation capability of the algorithm in unexplored neighbouring regions. An improvement process is used to reinforce the final Pareto solution set obtained. The performance of the proposed algorithm is tested with benchmark and randomly generated instances. The computational results and comparisons demonstrate the effectiveness and efficiency of the proposed algorithm.     

Genetic algorithm for job-shop scheduling with machine unavailability and breakdowns

The job-shop scheduling problem (JSSP) is considered to be one of the most complex combinatorial optimisation problems. In our previous attempt, we hybridised a Genetic Algorithm (GA) with a local search technique to solve JSSPs. In this research, we propose an improved local search technique, Shifted Gap-Reduction (SGR), which improves the performance of GAs when solving relatively difficult test problems. We also modify the new algorithm for JSSPs with machine unavailability and breakdowns. We consider two scenarios of machine unavailability. First, where the unavailability information is available in advance (predictive) and, secondly, where the information is known after a real breakdown (reactive). We show that the revised schedule is mostly able to recover if the interruptions occur during the early stages of the schedules.     

A hybrid artificial bee colony algorithm for a flexible job shop scheduling problem with overlapping in operations

Overlapping in operations is an effective technology for productivity improvement in modern manufacturing systems. Thus far, however, there are still rare works on flexible job shop scheduling problems (FJSPs) concerning this strategy. In this paper, we present a hybrid artificial bee colony (hyABC) algorithm to minimise the total flowtime for a FJSP with overlapping in operations. In the proposed hyABC, a dynamic scheme is introduced to fine-tune the search scope adaptively. In view of poor exploitation ability of artificial bee colony algorithm, a modified migrating birds optimisation algorithm (MMBO) is developed and integrated into the search process for better balancing global exploration and local exploitation. In MMBO, a forward share strategy with one-job based crossover is designed to make good use of valuable information from behind solutions. Besides, an improved downward share scheme is adopted to increase diversification of the population, and thus alleviate the premature convergence. Extensive experiments based on benchmark instances with different scales are carried out and comparisons with other recent algorithms identify the effectiveness of the proposed hyABC.     

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.     

Two-stage flow shop scheduling with dedicated machines

This study is concerned with the manufacturing model that has a common machine at stage one and two parallel dedicated machines at stage two. All jobs need to be processed on the stage-one common machine. After the stage-one processing, the jobs of type 1 (type 2) will route to the first (second) dedicated machine at stage two. We first elaborate several published works on makespan minimisation which are not known to other streams of recent works. While the minimisation of maximum lateness is strongly NP-hard, we develop a linear-time algorithm to solve the case where two sequences of the two job types are given a priori.     

Hierarchical production control for a flow shop with dynamic setup changes and random machine breakdowns

In this paper, we study a manufacturing system consisting of two machines separated by two intermediate buffers, and capable of producing two different products. Each product requires a constant processing time on each of the machines. Each machine requires a constant non-negligible setup change time from one product to the other. The demand rate for each product is considered to be piecewise constant. Each machine undergoes failure and repair. The time-to-failure and time-to-repair are exponentially distributed random variables. The setup change and processing operations are resumable. We model our system as a continuous time, continuous flow process. An optimal control problem is formulated for the system to minimize the total expected discounted cost over an infinite horizon. To determine the optimal control policy structure, a discrete version of the problem is solved numerically using a dynamic programming formulation with a piecewise linear penalty function. A real-time control algorithm is then developed with the objective of maintaining low work-in-process inventory and keeping the production close to the demand. The algorithm uses a hierarchical control structure to generate the loading times for each product on each machine in real time and to respond to random disruptions in the system. The system is simulated using this algorithm to study its performance. The performance of the algorithm is also compared to alternative policies.     

An improved approximation algorithm for the two-machine open shop scheduling problem with family setup times

We consider the problem of scheduling families of jobs in a two-machine open shop so as to minimize the makespan. The jobs of each family can be partitioned into batches and a family setup time on each machine is required before the first job is processed, and when a machine switches from processing a job of some family to a job of another family. For this NP-hard problem the literature contains (5/4)-approximation algorithms that cannot be improved on using the class of group technology algorithms in which each family is kept as a single batch. We demonstrate that there is no advantage in splitting a family more than once. We present an algorithm that splits one family at most once on a machine and delivers a worst-case performance ratio of 6/5.     

A hybrid differential evolution algorithm for a two-stage flow shop on batch processing machines with arbitrary release times and blocking

Batch processing machines (BPMs) have important applications in a variety of industrial systems. This paper considers the problem of scheduling two BPMs in a flow shop with arbitrary release times and blocking such that the makespan is minimised. The problem is formulated as a mixed integer programming model. Subsequently, a hybrid discrete differential evolution (HDDE) algorithm is proposed. In the algorithm, individuals in the population are first represented as discrete job sequences, and mutation and crossover operators are applied based on the representation. Second, after using the first-fit rule to form batches, a novel least idle/blocking time heuristic is developed to schedule the batches in the flow shop. Furthermore, an effective local search technique is embedded in the algorithm to enhance the exploitation ability. The performance of the proposed algorithm is evaluated by comparing its results to a commercial solver (CPLEX), a genetic algorithm and a simulated annealing algorithm. Computational experiments demonstrate the superiority of the HDDE algorithm in terms of solution quality, robustness and run time.     

Robust scheduling of a two-stage hybrid flow shop with uncertain interval processing times

This paper studies the makespan minimisation scheduling problem in a two-stage hybrid flow shop. The first stage has one machine and the second stage has m identical parallel machines. Neither the processing time nor probability distribution of the processing time of each job is uncertain. We propose a robust (min–max regret) scheduling model. To solve the robust scheduling problem, which is NP-hard, we first derive some properties of the worst-case scenario for a given schedule. We then propose both exact and heuristic algorithms to solve this problem. In addition, computational experiments are conducted to evaluate the performance of the proposed algorithms.     

Scheduling a dynamic flexible flow line with sequence-dependent setup times: a simulation analysis

This paper presents a simulation-based experimental study of scheduling rules for scheduling a dynamic flexible flow line problem considering sequence-dependent setup times. A discrete-event simulation model is presented as well as eight adapted heuristic algorithms, including seven dispatching rules and one constructive heuristic, from the literature. In addition, six new proposed heuristics are implemented in the simulation model. Simulation experiments are conducted under various conditions such as setup time ratio and shop utilisation percentage. One of the proposed rules performs better for the mean flow time measure and another one performs better for the mean tardiness measure. Finally, multiple linear regression based meta-models are developed for the best performing scheduling rules.     

A hybrid artificial bee colony algorithm for flexible job shop scheduling with worker flexibility

The traditional flexible job shop scheduling problem (FJSP) considers machine flexibility but not worker flexibility. Given the influence and potential of human factors in improving production efficiency and decreasing the cost in practical production systems, we propose a mathematical model of an extended FJSP with worker flexibility (FJSPW). A hybrid artificial bee colony algorithm (HABCA) is presented to solve the proposed FJSPW. For the HABCA, effective encoding, decoding, crossover and mutation operators are designed, and a new effective local search method is developed to improve the speed and exploitation ability of the algorithm. The Taguchi method of Design of Experiments is used to obtain the best combination of key parameters of the HABCA. Extensive computational experiments carried out to compare the HABCA with some well-performing algorithms from the literature confirm that the proposed HABCA is more effective than these algorithms, especially on large-scale FJSPW instances.     

An improved multi-objective evolutionary algorithm based on decomposition for energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time

With the increasing attention on environment issues, green scheduling in manufacturing industry has been a hot research topic. As a typical scheduling problem, permutation flow shop scheduling has gained deep research, but the practical case that considers both setup and transportation times still has rare research. This paper addresses the energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time to minimise both makespan as economic objective and energy consumption as green objective. The mathematical model of the problem is formulated. To solve such a bi-objective problem effectively, an improved multi-objective evolutionary algorithm based on decomposition is proposed. With decomposition strategy, the problem is decomposed into several sub-problems. In each generation, a dynamic strategy is designed to mate the solutions corresponding to the sub-problems. After analysing the properties of the problem, two heuristics to generate new solutions with smaller total setup times are proposed for designing local intensification to improve exploitation ability. Computational tests are carried out by using the instances both from a real-world manufacturing enterprise and generated randomly with larger sizes. The comparisons show that dynamic mating strategy and local intensification are effective in improving performances and the proposed algorithm is more effective than the existing algorithms.     

A hybrid electromagnetism-like algorithm for two-stage assembly flow shop scheduling problem

This paper presents a study on the two-stage assembly flow shop scheduling problem for minimising the weighed sum of maximum makespan, earliness and lateness. There are m machines at the first stage, each of which produces a component of a job. A single machine at the second stage assembles the m components together to complete the job. A novel model for solving the scheduling problem is built to optimise the maximum makespan, earliness and lateness simultaneously. Two optimal operation sequences of jobs are determined and verified. As the problem is known to be NP-hard, a hybrid variable neighbourhood search – electromagnetism-like mechanism (VNS-EM) algorithm is proposed for its handling. To search beyond local optima for a global one, VNS algorithm is embedded in each iteration of EM, whereby the fine neighbourhood search of optimum individuals can be realised and the solution is thus optimised. Simulation results show that the proposed hybrid VNS-EM algorithm outperforms the EM and VNS algorithms in both average value and standard deviation.     

An estimation of distribution algorithm for hybrid flow shop scheduling under stochastic processing times

The estimation of distribution algorithm (EDA) has recently emerged as a promising alternative to traditional evolutionary algorithms for solving combinatorial optimisation problems. This paper presents a novel two-phase simulation-based EDA (TPSB-EDA) for minimising the makespan of a hybrid flow shop under stochastic processing times. To address the stochastic scheduling problem efficiently, the proposed TPSB-EDA incorporates a two-phase simulation model to estimate the performance of candidate solutions. In this model, an optimal back propagation network is firstly applied to identify a set of roughly good solutions, and then the selected solutions are further evaluated by a discrete-event simulation algorithm. Moreover, an annealing selection mechanism (ASM) is adopted to preserve the population diversity of EDA. Different from the selection operators of common EDAs, the ASM uses Boltzmann probability in the annealing algorithm to select part of population to establish the probabilistic model. Computation results indicate that the TPSB-EDA provides good solutions in the aspects of solution quality and computational efficiency.     

A hybrid nested partitions algorithm for scheduling flexible resource in flow shop problem

Production scheduling with flexible resources is critical and challenging in many modern manufacturing firms. This paper applies the nested partitions (NP) framework to solve the flexible resource flow shop scheduling (FRFS) problem using an efficient hybrid NP algorithm. By considering the domain knowledge, the ordinal optimisation principle and the NEH heuristics are integrated into the partitioning scheme to search the feasible region. An efficient resource-allocation procedure is built into the sampling scheme for the FRFS problem. A large number of benchmark examples with flexible resources are tested. The test results show that the hybrid NP algorithm is more efficient than either generic NP or heuristics alone. The algorithm developed in this study is capable of selecting the most promising region for a manufacturing system with a high degree of accuracy. The algorithm is efficient and scalable for large-scale problems.     

A heuristic model for dynamic flexible job shop scheduling problem considering variable processing times

In real scheduling problems, unexpected changes may occur frequently such as changes in task features. These changes cause deviation from primary scheduling. In this article, a heuristic model, inspired from Artificial Bee Colony algorithm, is proposed for a dynamic flexible job-shop scheduling (DFJSP) problem. This problem consists of n jobs that should be processed by m machines and the processing time of jobs deviates from estimated times. The objective is near-optimal scheduling after any change in tasks in order to minimise the maximal completion time (Makespan). In the proposed model, first, scheduling is done according to the estimated processing times and then re-scheduling is performed after determining the exact ones considering machine set-up. In order to evaluate the performance of the proposed model, some numerical experiments are designed in small, medium and large sizes in different levels of changes in processing times and statistical results illustrate the efficiency of the proposed algorithm.