Simulation optimization with GA and OCBA for semiconductor back-end assembly scheduling

This paper investigates the multistage hybrid flow shop (HFS) scheduling problems using the new bat algorithm. A HFS is the generalisation of flowshop with multiple machines. HFS is one of the important scheduling problems that represent many industries like iron and steel, chemical, textile and ceramic industries. The HFS scheduling problems have been proved to be NP-hard. A recently developed bat meta-heuristic algorithm is proposed to solve the HFS problems. The proposed algorithm is validated with a well-chosen set of benchmark problems in the literature. Computational results indicate that the proposed bat algorithm is more efficient than the genetic algorithm and particle swarm optimisation.

Much of the research on operations scheduling problems has either ignored setup times or assumed that setup times on each machine are independent of the job sequence. Furthermore, most scheduling problems which have been discussed in the literature are under the assumption that machines are continuously available. Nevertheless, in most real life industries, a machine can be unavailable for many reasons, such as unanticipated breakdowns, i.e., stochastic unavailability, or due to a scheduled preventive maintenance where the periods of unavailability are known in advance, i.e., deterministic unavailability. This paper deals with the hybrid flow shop scheduling problems in which there are sequence-dependent setup times, commonly known as the SDST, and machines which suffer stochastic breakdown to optimize objectives based on expected makespan. This type of production system is found in industries such as chemical, textile, metallurgical, printed circuit board, and automobile manufacture. With the increase in manufacturing complexity, conventional scheduling techniques for generating a reasonable manufacturing schedule have become ineffective. The genetic algorithm can be used to tackle complex problems and produce a reasonable manufacturing schedule within an acceptable time. This paper describes how we can incorporate simulation into genetic algorithm approach to the scheduling of a SDST hybrid flow shop with machines that suffer stochastic breakdown. An overview of the hybrid flow shops and scheduling under stochastic unavailability of machines are presented. Subsequently, the details of incorporated simulation into genetic algorithm approach are described and implemented. Consequently, the results obtained are analyzed with Taguchi experimental design.

With the rapid development of computer technology and related softwares for mathematical models, mathematical modelling of scheduling problems is receiving growing attention from researchers. In this work, the hybrid flow shop scheduling problem with unrelated parallel machines (HFSP-UPM) with the objective aimed to minimise the makespan is studied. According to the characteristics of the HFSP-UPM, eight mixed integer linear programming (MILP) models are formulated in order to obtain optimal solutions based on different modelling ideas. Then, these models are extended to solve HFSP-UPM with sequence-dependent setup times (HFSP-UPM-SDST), no-wait HFSP-UPM (HFSP-UPM-NW) and HFSP-UPM with blocking (HFSP-UPM-B). All the proposed models and the existing model are detailedly compared and evaluated under three aspects namely modelling process, size complexity and computational complexity. Numerical experiments show that MILP models dependent on diverse modelling ideas perform very differently. The model developed based on stage precedence is the best one and should be given preference in future applications. In addition, the proposed models of HFSP-UPM-NW and HFSP-UPM-B improve several best known solutions for the test instances in the existing literature.

Improved cuckoo search algorithm for hybrid flow shop scheduling problems to minimize makespan

Much of the research on operations scheduling problems has either ignored setup times or assumed that setup times on each machine are independent of the job sequence. Furthermore, most scheduling problems that have been discussed in the literature are under the assumption that machines are continuously available. Nevertheless, in most real-life industries a machine can be unavailable for many reasons, such as unanticipated breakdowns (stochastic unavailability), or due to scheduled preventive maintenance where the periods of unavailability are known in advance (deterministic unavailability). This paper deals with hybrid flow shop scheduling problems in which there are sequence-dependent setup times (SDSTs), and machines suffer stochastic breakdowns, to optimise objectives based on the expected makespan. With the increase in manufacturing complexity, conventional scheduling techniques for generating a reasonable manufacturing schedule have become ineffective. An immune algorithm (IA) can be used to tackle complex problems and produce a reasonable manufacturing schedule within an acceptable time. In this research, a computational method based on a clonal selection principle and an affinity maturation mechanism of the immune response is used. This paper describes how we can incorporate simulation into an immune algorithm for the scheduling of a SDST hybrid flow shop with machines that suffer stochastic breakdowns. The results obtained are analysed using a Taguchi experimental design.

This research addresses scheduling problem of n jobs on a Hybrid Flow Shop (HFS) with unrelated parallel machines in each stage. A monolithic mixed integer linear programming (MILP) model is presented to minimize the maximum completion time (makespan). As the research problem is shown to be strongly NP-hard, a Lagrangian relaxation (LR) algorithm is developed to handle the HFS scheduling problem. We design two approaches, simplification of subproblems and dominance rules, to solve the subproblems which are generated in each iteration. For evaluation purposes, numerical experiments with small and large size problems are randomly generated with up to 50 jobs and four stages. The experimental results show that the Lagrangian relaxation approaches outperform the MILP model with respect to CPU time. Furthermore, from the results, it can be conclude that the simplification of subproblems shows slightly better solutions in comparison with dominance rules to solve the subproblems.

This paper is survey of hybrid flow shop scheduling problems. An HFS scheduling problem is a classical flow-shop in which parallel machines are available to perform the same operation. Most real world scheduling problems are NP-hard in nature. The hybrid flow shop scheduling problems have received considerable research attention. The several optimization and heuristic solution procedures are available to solve a variety of hybrid flow shop scheduling problems. It discusses and reviews sustainability of several variants of the hybrid flow shop scheduling problem for economical analysis, each in turn considering different assumptions, constraints and objective functions. Sustainability is the long-term maintenance of responsibility, which analysis the economics and encompasses the concept of stewardship. The Hybrid flow shop problem has sustained for several decades with multi – objective constraints. The paper shows some fruitful directions for future research and opportunities in the area of hybrid flow shop.

Distributed scheduling is seldom investigated in hybrid flow shops. In this study, distributed two-stage hybrid flow shop scheduling problem (DTHFSP) with sequence-dependent setup times is considered. A collaborative variable neighborhood search (CVNS) is proposed to simultaneously minimize total tardiness and makespan. DTHFSP is simplified by incorporating factory assignment into machine assignment of a prefixed stage, and its solution is newly represented with a machine assignment string and a scheduling string. CVNS consists of two cooperated variable neighborhood search (VNS) algorithms, and neighborhood structures and global search have collaborated in each VNS. Eight neighborhood structures and two global search operators are defined to produce new solutions. The current solution is periodically replaced with a member of the archive farthest from it. Experiments are conducted , and the computational results validate that CVNS has good advantages over the considered DTHFSP.

This paper investigates a multi-stage hybrid flow shop scheduling problem in a real-world printed circuit board (PCB) assembly shop. Some distinct characteristics such as calendar constraints, sequence-dependent setup times, unrelated parallel machines and stage skipping are taken into account. Besides, lot-sizing is introduced to split an order of PCBs into a number of smaller sub-lots to improve the utilization of the assembly lines. This article develops an effective hierarchical approach to reduce the complexity of such a complicated PCB scheduling problem by decomposing it into two highly coupled sub-problems of job sequencing and batch scheduling with lot-sizing. A two-stage ant colony algorithm with lot-sizing is proposed to evolve best results for makespan criterion. Extensive computational experiments have been conducted to compare the performance with two other algorithms. The results demonstrate that the proposed two-stage ant colony algorithm with lot-sizing is competitive in terms of computational result, computational time and stability.

The hybrid flow shop scheduling problem (HFSP), as a realistic extension of the classical flow shop scheduling problem, widely exists in real-world industrial production systems. In practice, the fact that machines are unrelated is important and cannot be neglected. This study focuses on the HFSP with unrelated parallel machines (HFSP-UPM) to minimize the makespan. To address this problem, a hybrid representation that combines single-sequence coding and full-sequence coding is developed to search for solution space that is not covered by common encoding methods. An initialization block integrating random heuristic strategies is proposed for improving the quality of the initial sparrow swarm. To improve the diversity of a sparrow swarm further, a perturbation block embedded with a set of historical best positions and an enhancement strategy are developed. A critical set based local search block is designed for high-intensity local exploitation of promising regions when necessary. Several benchmark cases from the literature as well as some randomly generated instances characterized by the distribution of real data from factory studies are employed to participate in the test. The test results reveal the effectiveness of the proposed perturbation block and local search block. Compared to state-of-the-art metaheuristic algorithms, the enhanced sparrow search algorithm (ESSA) demonstrates higher convergence accuracy when handling instances. The value of the gap between a solution found by the ESSA and a feasible solution found by the mixed-integer programming (MIP) model can reach 0.6%.

A novel discrete artificial bee colony algorithm for the hybrid flowshop scheduling problem with makespan minimisation

This paper proposes a new improvement of the NEH heuristic named I-NEH to solve a hybrid flow shop scheduling problem with assembly operations and unrelated parallel machines. The objective was to either minimise total tardiness or makespan. The novelty of I-NEH was to integrate two features into the original NEH heuristic, by applying four rules to break a tie in the machine selection process, and applying either total tardiness or makespan, to break a tie in a job insertion process. There were three main steps for I-NEH. The first step was to schedule jobs by a dispatching rule. The second step was to apply the job insertion and the machine selection processes iteratively. The last step was to apply the forward heuristic in order to reduce the earliness and flow time, whereas the total tardiness obtained from the first two steps must be maintained. Exhaustive experiments were conducted to evaluate the efficiency of I-NEH through the average relative percentage deviation index (ARPD). For the case studies, the results showed that I-NEH outperformed the dispatching rules that have been proven previously to obtain good solutions, with ARPD values of 34.46% for total tardiness and 17.43% for makespan. In addition, the proposed I-NEH heuristic reduced the maximum tardiness with the ARPD value of 19.84% when the objective was to minimise total tardiness, and the computational time of I-NEH was within a reasonable range.

With the rapid development of make-to-order pattern including E-commerce and takeout and catering service in restaurants, the study of integrated scheduling and distribution receives more and more attentions. Based on a practical order picking and distribution system, a three-stage hybrid flow shop scheduling problem with distribution is studied. Each order is processed on the hybrid flow shop which consists of identical parallel machines with sequence-dependent setup times at stage 1, identical parallel machines at stage 2 and dedicated machines at stage 3, followed by a multi-trip traveling salesman problem with capacitated vehicles for customers of different destination areas. A mixed-integer linear programming model is formulated to minimize the maximum delivery completion time. A variable neighborhood search (VNS)-based method, a four-layered constructive heuristic method (denoted by $$CH_{VNS}$$) and a hybrid heuristic method (denoted by $$CONS_{VNS}$$) which combines the VNS method and the $$CH_{VNS}$$ method are developed to solve the problems with practical size. Computational experiments show the effectiveness and efficiency of the proposed methods.

In this research, a bi-criteria group scheduling problem is investigated in a hybrid flow shop (HFS) environment, wherein the parallel machines are unrelated. The objective of the problem is to minimize a linear combination of the total weighted completion time being mindful of the producer and the total weighted tardiness being mindful of the customers. The underlying assumption is that the jobs are released into the system in dynamic times. The machine ready times are considered to be dynamic as well. Sequence-dependent setup times are required for changing the process between groups of jobs. The runtimes of jobs are assumed to be decreasing as the workers learn how to process similar jobs. A mixed-integer linear programing model is developed for the problem. However, since the problem is non-deterministic polynomial-time hard (NP-hard), it may not be solved to optimality within a reasonable time. This research comprehensively addresses the question of what type of meta-heuristic algorithm is more appropriate for solving these problems. In particular, local search algorithms are compared to the population-based algorithms with respect to the permutation or non-permutation properties of the optimal solution. Three algorithms based on tabu search as well as three algorithms based on simulated annealing are developed to represent the local search algorithms. Two other algorithms are developed based on genetic algorithm (GA) to exemplify the population-based algorithms. The results of a comprehensive experimental design reveal that GA-based algorithms have greater potential for identifying better quality solutions in HFS scheduling problems compared to the local search algorithms.

In this paper, a hybrid flow shop scheduling problem with a new approach considering time lags and sequence-dependent setup time in realistic situations is presented. Since few works have been implemented in this field, the necessity of finding better solutions is a motivation to extend heuristic or meta-heuristic algorithms. This type of production system is found in industries such as food processing, chemical, textile, metallurgical, printed circuit board, and automobile manufacturing. A mixed integer linear programming (MILP) model is proposed to minimize the makespan. Since this problem is known as NP-Hard class, a meta-heuristic algorithm, named Genetic Algorithm (GA), and three heuristic algorithms (Johnson, SPTCH and Palmer) are proposed. Numerical experiments of different sizes are implemented to evaluate the performance of presented mathematical programming model and the designed GA in compare to heuristic algorithms and a benchmark algorithm. Computational results indicate that the designed GA can produce near optimal solutions in a short computational time for different size problems.