Re-entrant Flow Shop Research Articles

Makespan minimization in reentrant flow shop problem with identical jobs

Makespan minimization in reentrant flow shop problem with identical jobs

Robust scheduling in a two-machine re-entrant flow shop to minimise the value-at-risk of the makespan: branch-and-bound and heuristic algorithms based on Markovian activity networks and phase-type distributions

Robust scheduling in a two-machine re-entrant flow shop to minimise the value-at-risk of the makespan: branch-and-bound and heuristic algorithms based on Markovian activity networks and phase-type distributions

Sequence- and Time-Dependent Maintenance Scheduling in Twice Re-Entrant Flow Shops

Sequence- and Time-Dependent Maintenance Scheduling in Twice Re-Entrant Flow Shops

Scheduling with lot streaming in a two-machine re-entrant flow shop

Lot streaming is splitting a job-lot of identical items into several sublots (portions of a lot) that can be moved to the next machines upon completion so that operations on successive machines can be overlapped; hence, the overall performance of a multi-stage manufacturing environment can be improved. In this study, we consider a scheduling problem with lot streaming in a two-machine re-entrant flow shop in which each job-lot is processed first on Machine 1, then goes to Machine 2 for its second operation before it returns to the primary machine (either Machine 1 or Machine 2) for the third operation. For the two cases of the primary machine, both single-job and multi-job cases are studied independently. Optimal and near-optimal solution procedures are developed. Our objective is to minimize the makespan, which is the maximum completion time of the sublots and job lots in the single-job and multi-job cases, respectively. We prove that the single-job problem is optimally solved in polynomial-time regardless of whether the third operation is performed on Machine 1 or Machine 2. The multi-job problem is also optimally solvable in polynomial time when the third operation is performed on Machine 2. However, we prove that the multi-job problem is NP-hard when the third operation is performed on Machine 1. A global lower bound on the makespan and a simple heuristic algorithm are developed. Our computational experiment results reveal that our proposed heuristic algorithm provides optimal or near-optimal solutions in a very short time.

Reentrant flow shop with identical jobs and makespan criterion

The article focuses on the problem of a reentrant flow shop with identical jobs and makespan minimisation objective. After presenting an optimal integer programming formulation for the problem, we consider the case of unit processing times. We correct two results published a few decades ago regarding two greedy heuristic algorithms. In some cases, these algorithms lead to an optimal solution, but they are generally not optimal. We point out the advantages of each of the two heuristic algorithms and, by machine learning analysis, discuss features that differentiate between them.

Learning per-machine linear dispatching rule for heterogeneous multi-machines control

ABSTRACT This paper proposes a per-machine linear dispatching rule learning approach to improve the scheduling of re-entrant flow shop such as semiconductor fab. Finding an optimal schedule of a complex manufacturing system is intractable; hence, a dispatching rule as a heuristic approach is widely used in actual practice. Also, to develop a good dispatching rule, an automated methodology for developing heuristics, also known as a hyper-heuristic, has been studied extensively. However, most of the literature has focused on finding a single-sophisticated dispatching rule, in which every machine uses the same rule. Such an approach often shows suboptimal performance when the optimal dispatching rule is different on each machine. To solve this problem, we introduce a simple and effective per-machine dispatching rule learning approach, in which each machine has one linear dispatching rule that is optimised by the Gradient-based Evolutionary Strategy (GES). This method is sample-efficient and can be applied to non-differentiable objective functions such as average Cycle Time. The proposed approach was mainly compared to two popular methods based on Genetic Programming (GP) and the Genetic Algorithm (GA) on a four-station and eight-machine re-entrant flow shop. Numerical results show that the proposed approach outperforms widely used methods.

Multi-objective distributed reentrant permutation flow shop scheduling with sequence-dependent setup time

The distributed reentrant permutation flow shop (DRPFS) is a combination of the reentrant flow shop problem and distributed scheduling. The DRPFS is a NP-hard problem that consists of two subproblems: (1) assigning a set of jobs to a set of available factories and (2) determining the operation sequence of jobs in each factory. This paper is the first study to consider the inclusion of sequence-dependent setup time in the DRPFS. The industrial applications of flow shop indicate that the machine setup time to process a job may depend on the previously processed jobs. Particularly, in DRPFS, the effect of sequence-dependent setup time is intensified due to its reentrant characteristic. An improved version of the multi-objective adaptive large neighborhood search (MOALNS) is proposed as a solution method for the sequence-dependent DRPFS with the aim to minimize the makespan, production cost, and tardiness. The proposed algorithm enhances the standard MOALNS by embedding an improved solution acceptance and non-dominated set updating criteria to assist the algorithm in finding the near-optimal Pareto front of the factory allocation and scheduling problems. To address the multiple objectives and the issue of non-uniform setup time, a new set of destroy and repair heuristics are developed. Further, the numerical experiments demonstrate the efficiency of IMOALNS in finding high-quality solutions in a relatively short time.

A modified column generation algorithm for scheduling problem of reentrant hybrid flow shops with queue constraints

This paper investigates a two-stage reentrant hybrid flow shops scheduling problem. In this problem, each product is processed layer by layer with different processing time. To be more practical, the queue time between the parallel machines and the batch processing machine is restricted. The objective is to minimise the total completion time. A column generation algorithm is proposed to solve the scheduling problem by decomposing this problem into main problem and workpiece level sub-problem. In the proposed method, dynamic programming with multiple decision-making is designed to solve each sub-problem and the adaptive accelerating strategy is provided creatively to effectively improve the convergence of the algorithm. In the branch-and-bound method to generate feasible solution, the innovative method of neighbourhood mutation is employed. Computational experiments demonstrate that the proposed method for the two-stage hybrid flow shops problem is quite stable and effective compared with other conventional formulation.

A decentralized coordination algorithm for multi-objective linear programming with block angular structure

ABSTRACT This article considers linear multi-objective programming problems with block angular structure, which are analogous to multi-disciplinary optimization environments where disciplines must collaborate to achieve a common overall goal. In this decentralized environment, a mechanism to guide locally optimized decision makers’ solutions to a Pareto-optimal solution without sharing the entire local information is developed. The mechanism is based on an augmented Lagrangian approach to generate a solution and is separated into two phases: phase I determines an ideal point for each of the single objectives and phase II searches for a compromise solution starting from a single ideal point. Theoretical results show that the algorithm converges and the solution generated is Pareto optimal. The algorithm’s effectiveness is demonstrated via an illustrative example and a real-world bi-objective re-entrant flow-shop production planning problem. The real-world experimental results showed that the decentralized method had an average 50% better performance compared to other centralized methods.

Considering stockers in reentrant hybrid flow shop scheduling with limited buffer capacity

Diversification of products has increased the involvement of reentrant manufacturing processes, in which a job returns multiple times to a machine at the preceding workflow stage to continue the manufacturing process. Reentrant flow shop manufacturing can substantially improve manufacturing efficiency when scheduled properly. In practice, advanced manufacturing companies (e.g., semiconductor foundries) have introduced automated material handling system (AMHS), including stockers that serve as centralized inventory buffer space for temporarily storing the inventories owing to limited buffer capacity of each machine. However, no previous studies on reentrant flow shop scheduling have considered the impact of limited buffer capacity or stockers on scheduling efficiency. Consequently, this study investigated the application of stockers in solving the reentrant hybrid flow shop scheduling problem with limited buffer capacity. With the objective of optimizing the makespan and mean flowtime of a schedule, this problem is NP-hard because it generalizes the flow shop problem. Therefore, this study developed a hybrid harmony search and genetic algorithm (HHSGA) for the problem, in which limited buffer capacity and stockers cause solution decoding to be non-trivial. Experimental comparison on scheduling problems with different numbers of jobs showed that the HHSGA performed better than conventional algorithms. Moreover, among three manufacturing conditions (i.e., with buffers and stockers, with buffers only, and with stockers only), the results indicated that the condition using inventory buffers and stockers was more beneficial.

Reentrant hybrid flow shop scheduling problem with non-anticipatory sequence-dependent setup time

This paper studies a hybrid flow shop scheduling problem originated from a steam turbine rotor production. Reentrance and non-anticipatory sequence-dependent setup time are considered. The objectives are to minimise makespan and total tardiness. A mixed integer linear programming model is formulated. A bi-objective simulated annealing algorithm is developed to solve problems with real size. A modified version of the Nawaz-Enscore-Ham algorithm is applied to find a good initial solution and a Pareto search mechanism is introduced to find the Pareto set. The proposed bi-objective simulated annealing algorithm is compared with a single-objective algorithm. Experimental results demonstrate the superiority of the bi-objective algorithm. Sensitivity analysis provides valuable managerial insights for real production.

Reentrant Flow Shop Scheduling considering Multiresource Qualification Matching

With the development of technology and industry, new research issues keep emerging in the field of shop scheduling. Most of the existing research assumes that one job visits each machine only once or ignores the multiple resources in production activities, especially the operators with skill qualifications. In this paper, we consider a reentrant flow shop scheduling problem with multiresource considering qualification matching. The objective of the problem is to minimize the total number of tardy jobs. A mixed integer programming (MIP) model is formulated. Two heuristics, namely, the hill climbing algorithm and the adapted genetic algorithm (GA), are then developed to efficiently solve the problem. Numerical experiments on 30 randomly generated instances are conducted to evaluate the performance of proposed MIP formulation and heuristics.

A performance analysis of dispatch rules for semiconductor assembly & test operations

The purpose of this paper is to statistically compare six dispatch rules for semiconductor assembly & test operations with respect to two hierarchical objectives: minimise the weighted sum of key device (chip) shortages and maximise the weighted throughput of lots processed. Three factors affecting system performances are studied: the different rules, whether the machines are set up at time zero, and whether the maximum number of changeovers is restricted over the planning horizon. System performance is determined with both a discrete event AutoSched AP simulation model and a greedy randomised adaptive search procedure (GRASP) for 30 real and randomly generated data sets. A full factorial design with common random numbers was conducted to concurrently investigate the interaction among the three factors. The statistical analysis showed that the two rules designed to process as many hot lots (i.e., key device lots) as possible performed the best in minimising the weighted shortage. We also found that initial setups and limiting the number of setups over a 2- to 3-day planning horizon can significantly weaken the rules’ performance but in some cases the interaction of these factors mitigated their negative impacts. Due to the general nature of the models, the results should be applicable to most reentrant flow shops. The GRASP is now being used by the sponsoring company and the most promising dispatch rules are being studied in an experimental environment.

On the Use of Genetic Algorithm for Solving Re-entrant Flowshop Scheduling with Sum-of-processing-times-based Learning Effect to Minimize Total Tardiness

Most research studies on scheduling problems assume that a job visits certain machines only one time. However, this assumption is invalid in some real-life situations. For example, a job may be pro...

Online Scheduling of 2-Re-entrant Flexible Manufacturing Systems

Online scheduling of operations is essential to optimize productivity of flexible manufacturing systems (FMSs) where manufacturing requests arrive on the fly. An FMS processes products according to a particular flow through processing stations. This work focusses on online scheduling of re-entrant FMSs with flows using processing stations where products pass twice and with limited buffering between processing stations. This kind of FMS is modelled as a re-entrant flow shop with due dates and sequence-dependent set-up times. Such flow shops can benefit from minimization of the time penalties incurred from set-up times. On top of an existing greedy scheduling heuristic we apply a meta-heuristic that simultaneously explores several alternatives considering trade-offs between the used metrics by the scheduling heuristic. We identify invariants to efficiently remove many infeasible scheduling options so that the running time of online implementations is improved. The resulting algorithm is much faster than the state of the art and produces schedules with on average 4.6% shorter makespan.

MODELING, OPTIMISATION AND ANALYSIS OF RE-ENTRANT FLOWSHOP JOB SCHEDULING WITH FUZZY PROCESSING TIMES

This paper presents a makespan minimization of -jobs -machines re-entrant flow shop scheduling problem (RFSP) under fuzzy uncertainties using Genetic Algorithm. The RFSP objective is formulated as a mathematical programme constrained by number of jobs and resources availability with traditional scheduling policies of First Come First Serve (FCFS) and the First Buffer First Serve (FBFS). Jobs processing times were specified by fuzzy numbers and modelled using triangular membership function representations. The modified centroid defuzzification technique was used at different alpha-cuts to obtain fuzzy processing times (FPT) of jobs to explore the importance of uncertainty. The traditional GA schemes and operators were used together with roulette wheel algorithm without elitism in the selection process based on job fuzzy completion times. A test problem of five jobs with specified Job Processing and Transit Times between service centres, Job Start Times and Job Due times was posed. Results obtained using the deterministic and fuzzy processing times were compared for the two different scheduling policies, FCFS and FBFS. The deterministic optimal makespan for FBFS schedule was 61.2% in excess of the FCFS policy schedule.  The results also show that schedules with fuzzy uncertainty processing times provides shorter makespans than those for deterministic processing times and those under FCFS performing better than those under FBFS policy for early jobs while on the long run the FBFS policy performs better. The results underscore the need to take account of comprehensive fuzzy uncertainties in job processing times as a trade-off between time and costs influenced by production makespan. http://dx.doi.org/10.4314/njt.v36i3.21

Re-Entrant Flowshop Scheduling With Learning Considerations to Minimize The Makespan

In the more recent days, topics of scheduling re-entrant flowshop settings and scheduling models with learning consideration have received growing attention separately in research areas. However, scheduling with both the learning and re-entrant concept is relatively unexplored. Motivated by this limitation, this paper considers re-entrant permutation flowshop scheduling of jobs associated with a sum-of-processing-times-based learning function to minimize the makespan. Because the same problem without learning or re-entrant has been proved NP-hard, we thus propose four heuristics and a simulated annealing (SA) to search for approximate solutions. In the first stage, Johnson’s rule (JH) combined with four local search methods, which are namely the NEH method, pairwise interchange (PI), backward-shifted re-insertion (BACK), and forward-shifted re-insertion (FOR), is tackled in this problem. They are referred to the four heuristics as JH + NEH, JH + PI, JH + BACK, and JH + FOR, respectively. In the second stage, a simulated annealing algorithm seeded with four good different initials obtained from the first stage is provided for finding a good quality of solutions. Finally, the experimental results are tested to assess the performances of all the proposed algorithms as job size changes or machine number or learning effect or the number of re-entrant time.

Heuristic algorithms for two-machine re-entrant flowshop scheduling problem with jobs of two classes

Heuristic algorithms for two-machine re-entrant flowshop scheduling problem with jobs of two classes

Two machines flow shop with reentrance and exact time lag

This paper considers a reentrant flow shop with two machines and exact time lag L , in which each task may be processed in this order M 1 , M 2 , M 1 and there is an identical time lag between the completion time of the first operation and the start time of the second operation on the first machine. The objective is to minimize the total completion time. We prove the NP-hardness of a special case and we give some special subproblems that can be solved in polynomial time.

Solving Re-entrant No-wait Flowshop Scheduling Problem

In this study, we consider the production environment of no-wait reentrant flow shop with the objective of minimizing makespan of the jobs. In a reentrant flow shop, at least one job should visit at least one of the machines more than once. In a no-wait flowshop scheduling problem, when the process of a specific job begins on the first machine, it should constantly be processed without waiting in the line of any machine until its processing is completed on the last one. Integration of the properties of both of these environments, which is applied in many industries such as robotic industries, is not investigated separately. First, we develop a mathematical model for the problem and then we present three methods to solve it. Therefore, we construct simulated annealing (SA), genetic algorithm (GA) and a bottleneck based heuristic (BB) algorithms that solve the problem. Finally, the efficiency of the proposed methods is numerically analyzed.