Re-entrant Flow Shop Research Articles

Heuristics for an <i>m</i>-Machine Re-Entrant Permutation Flowshop with the Objective of Total Tardiness

We focus on an m-machine re-entrant flowshop scheduling problem with the objective of minimizing total tardiness. In the re-entrant flowshop considered here, routes of all jobs are identical as in ordinary flowshops, but the jobs must be processed multiple times on the machines. We present heuristic algorithms, which are modified from well-known existing algorithms for the general m-machine flowshop problem or newly developed in this paper. For evaluation of the performance of the algorithms, computational experiments are performed on randomly generated test problems and results are reported.

An assignment-sequencing methodology for scheduling assembly and test operations with multi-pass requirements

This article presents a three-phase methodology for scheduling assembly and test operations for semiconductor devices. The facility in which these operations are performed is a re-entrant flow shop consisting of several dozen to several hundred machines and up to a 1000 specialized tools. The semiconductor devices are contained in lots, and each lot follows a specific route through the facility, perhaps returning to the same machine multiple times. Each step in the route is referred to as a “pass.” In the first phase of the methodology an extended assignment model is solved to simultaneously assign tooling and lots to the machines. Four prioritized objectives are considered: minimize the weighted sum of key device shortages, maximize the weighted sum of lots processed, minimize the number of machines used, and minimize the makespan. In the second phase, lots are optimally sequenced on their assigned machines using the same prioritized objectives. Due to the precedent relations induced by the pass requirements, some lots may have to be delayed or removed from the assignment model solution to ensure that no machine runs beyond the planning horizon. In the third phase, machines are reset to allow additional lots to be processed when tooling is available. The methodology was tested using data provided by the Assembly and Test facility of a leading manufacturer. The results indicate that high-quality solutions can be obtained within 1 hour when compared with those obtained with a greedy randomized adaptive search procedure. Cost reductions were observed across all objectives and averaged 62% in the aggregate.

A memetic algorithm for the re-entrant permutation flowshop scheduling problem to minimize the makespan

A common assumption in the classical permutation flowshop scheduling model is that each job is processed on each machine at most once. However, this assumption does not hold for a re-entrant flowshop in which a job may be operated by one or more machines many times. Given that the re-entrant permutation flowshop scheduling problem to minimize the makespan is very complex, we adopt the CPLEX solver and develop a memetic algorithm (MA) to tackle the problem. We conduct computational experiments to test the effectiveness of the proposed algorithm and compare it with two existing heuristics. The results show that CPLEX can solve mid-size problem instances in a reasonable computing time, and the proposed MA is effective in treating the problem and outperforms the two existing heuristics.

Minimizing total tardiness in a two-machine re-entrant flowshop with sequence-dependent setup times

We consider a two-machine re-entrant flowshop scheduling problem in which all jobs must be processed twice on each machine and there are sequence-dependent setup times on the second machine. For the problem with the objective of minimizing total tardiness, we develop dominance properties and a lower bound by extending those for a two-machine re-entrant flowshop problem (without sequence-dependent setup times) as well as heuristic algorithms, and present a branch and bound algorithm in which these dominance properties, lower bound, and heuristics are used. For evaluation of the performance of the branch and bound algorithm and heuristics, computational experiments are performed on randomly generated instances, and results are reported.

Reentrant two-stage multiprocessor flow shop scheduling with due windows

Reentrant flow shop scheduling allows a job to revisit a particular machine several times. The topic has received considerable interest in recent years; with related studies demonstrating that particle swarm algorithm (PSO) is an effective and efficient means of solving scheduling problems. By selecting a wafer testing process with the due window problem as a case study, this study develops a farness particle swarm optimization algorithm (FPSO) to solve reentrant two-stage multiprocessor flow shop scheduling problems in order to minimize earliness and tardiness. Computational results indicate that either small- or large-scale problems are involved in which FPSO outperforms PSO and ant colony optimization with respect to effectiveness and robustness. Importantly, this study demonstrates that FPSO can solve such a complex scheduling problem efficiently.

Efficient methods to schedule reentrant flowshop system

In order to apply a continuous improvement of their production systems, all managers are always trying to improve their production systems by optimizing their scheduling method. This involves the search for efficient methods for obtaining the best results according to the costs and the delay criteria for example. This paper aims to solve a specific hybrid reentrant flow shop scheduling problem. This one contains some stages with some identical parallel machines. The orders sequenced are splited in batches. Each batch is processed one or more time on the system. For the resolution, various methods have been developed. An exact method which lists all the solutions and selects the best one and approximated methods such as the genetic algorithm GA, the genetic algorithm under fuzzy controller FLCGA, the particle swarm optimization PSO and the particle swarm optimization under fuzzy controller FLCPSO. The results discussed in the paper are very interesting.

Hybrid Genetic Algorithms for Solving Reentrant Flow-Shop Scheduling with Time Windows

The semiconductor industry has grown rapidly, and subsequently production planning problems have raised many important research issues. The reentrant flow-shop (RFS) scheduling problem with time windows constraint for harddisk devices (HDD) manufacturing is one such problem of the expanded semiconductor industry. The RFS scheduling problem with the objective of minimizing the makespan of jobs is considered. Meeting this objective is directly related to maximizing the system throughput which is the most important of HDD industry requirements. Moreover, most manufacturing systems have to handle the quality of semiconductor material. The time windows constraint in the manufacturing system must then be considered. In this paper, we propose a hybrid genetic algorithm (HGA) for improving chromosomes/offspring by checking and repairing time window constraint and improving offspring by left-shift routines as a local search algorithm to solve effectively the RFS scheduling problem with time windows constraint. Numerical experiments on several problems show that the proposed HGA approach has higher search capability to improve quality of solutions.

Clustered Absolute Bottleneck Adjacent Matching Heuristic for Re-Entrant Flow Shop

The problem illustrated in this paper resembles a four machine permutation re-entrant flow shop with the process routing of M1,M2,M3,M4,M3,M4 where M1 and M4 have high tendency of being the dominant machines. Due to the re-entrant and permutation nature of the process routing, the actual bottlenecks were identified as M1 and combinations of M4+M3+M4. A constructive bottleneck-based heuristic known as C-ABAM was developed to minimise the makespan of the four machine permutation re-entrant flow shop using bottleneck analysis. The results showed that C-ABAM produces better result than the original ABAM heuristic introduced by Bareduan and Hasan in 2009. It was shown that at any P1 dominance level value, the C-ABAM heuristic was capable to produce near optimal results for the 6 jobs problem sizes studied. The C-ABAM heuristic was also capable to generate results which are very compatible to the NEH. To some extent, within 6 jobs problems simulation conducted during the study, the C-ABAM shows marginally better makespan performance compared to the NEH at strong dominance level.

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 | Cmax 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.

An enhanced model for SDBR in a random reentrant flow shop environment

This study proposed an enhanced simplified drum-buffer-rope (SDBR) model to be applied in a reentrant flow shop (RFS) in which job processing times are generated from a discrete uniform distribution and machine breakdowns are subject to an exponential distribution. In this enhanced SDBR model, the due-date assignment method, order release rule and dispatching rule were improved. The due dates and release dates of orders were determined by considering the total planned load of the capacity-constrained resource (CCR) in a random RFS. The deviation rate of buffer status is used as a dispatching rule to eliminate the influence of machine breakdowns. Simulations based on a real case company are used to evaluate the effective of the proposed model. The experimental results showed that our approach yields better performance than the other methods in terms of six due-date-related indexes when the product mix is with a large proportion of multi-reentrant orders and when the utilisation of CCR increases from 60 to 90%.

Multi-level genetic algorithm for the resource-constrained re-entrant scheduling problem in the flow shop

The re-entrant flow shop scheduling problem (RFSP) is regarded as a NP-hard problem and attracted the attention of both researchers and industry. Current approach attempts to minimize the makespan of RFSP without considering the interdependency between the resource constraints and the re-entrant probability. This paper proposed Multi-level genetic algorithm (GA) by including the co-related re-entrant possibility and production mode in multi-level chromosome encoding. Repair operator is incorporated in the Multi-level genetic algorithm so as to revise the infeasible solution by resolving the resource conflict. With the objective of minimizing the makespan, Multi-level genetic algorithm (GA) is proposed and ANOVA is used to fine tune the parameter setting of GA. The experiment shows that the proposed approach is more effective to find the near-optimal schedule than the simulated annealing algorithm for both small-size problem and large-size problem.

A Contribution to the Reentrant Flow-Shop Scheduling Problem

This paper considers a flow-shop scheduling problem which is characterized by reentrants and aims on the minimization of makespan. Reentrants are events of a repeated processing of a specific job on a machine, which can occur due to, e.g., quality reasons. In the following, we focus on missing operations which did not receive adequate attention in the literature so far. After describing different types of reentrants, a specific level formulation is given in order to cope with processing times equal to zero in an appropriate way. Finally, we perform first computational tests with different problem sizes and compare our results with an already existing formulation with respect to solution quality and computation times. Our main results are as follows: (i) it turns out that our formulation is well suitable when zero processing times occur, as we derive better objective values for makespan; (ii) however, longer computation times have to be accepted compared to traditional formulations; (iii) the computation times are mainly influenced by the total number of jobs.

Study on Re-entrant Flow-shop Scheduling Problem (Optimization by Mixed Integer Programming)

A sophisticated formulation for re-entrant flow-shop scheduling problem is discussed in order to plan an optimum production schedule by mathematical programming. In the formulation, repeated operations by the same production resource are taken into account in the cyclic manufacturing process for mono-product. The general constraints of the problem are represented in linear equations composed by decision variables including both absolute starting times and relative starting times of the operations. The absolute starting times provide the sequence of the processing order in the manufacturing activity, while the relative starting times assure the appropriate handling in cyclic operation for each production resource. Since the complexity of the constraints affects the optimization, redundant decision variables have to be eliminated from the constraints. In this paper, we derive a new formulation in which the absolute starting times variables are represented implicitly by the relative starting time variables. The new formulation guides stepwise optimization approach, that is, the total number of cyclic terms is minimized before the search for the shortest complete time of the product, or the flow time. The result of the pre-optimization contributes enlargement of the problem size in optimization. The number of the total processes of the products is evaluated to verify the feasibility of the formulation and the optimization procedures by computational examinations.

Hybrid Multi-Objective Methods to Solve Reentrant Shops

This article examines the multi-objective scheduling of a reentrant hybrid flow shop. This type of shop is composed of several stages made of several identical parallel machines. When a task has to be processed on a stage, it is assigned to the machine with the smallest workload. This problem shows a reentrant structure: each task must be processed several times at each stage. In this paper, this problem is solved by minimizing two objectives: the makespan (maximum completion time of the jobs) and the total tardiness of the tasks. A new method is improved with different local searches: Adjacent and Non Adjacent Pairwise Interchange, Extract and Backward-Shifted Reinsertion, and Extract and Forward-Shifted Reinsertion. Every local search is tuned with statistical method (design of experiment) and the best one is worked out. This method is compared with the best one in several instances. The results involve three different measures.

A Genetic-based Algorithm to Find Better Estimation of Non-Dominated Solutions for a Bi-objective Re-entrant Flowshop Scheduling Problem with Outsourcing

Abstract In this paper, we present a mathematical model for a flowshop scheduling problem with two machines in which each job visits both machines twice. Due to the strict due dates, tardiness is not allowable so the scheduler needs to choose the jobs for being processed in-house and therefore outsources the remaining jobs. This decision shall be made regarding two objective functions: minimization of total completion time for in-house jobs and minimization of outsourcing cost. Since the problem is NP-hard, we propose a genetic-based algorithm to find non-dominated solutions for large-sized problems. By defining efficient dominance properties rather than Pareto and a secondary criterion for making diversification in the population different from crowding distance, we focus our search on middle part of Pareto-front as we believe that the solutions located in this part are more interesting for the decision maker. We compare the quality of solutions found by our proposed algorithm with the simplest variant of NSGA-II. Although proposed algorithm is able to find limited number of non-dominated solutions, the quality of the solutions are improved significantly.

Integrating analytical hierarchy process to genetic algorithm for re-entrant flow shop scheduling problem

This research considers a hybrid flow shop scheduling problem with dynamic re-entrant characteristics substantiated by the complexity of the problem in a repairing company. Multiple types of jobs are involved in the problem with individual buffer times that are strongly related to the previous processing job. These jobs need to go through tandem workstations, while some jobs may re-enter the processing line more than once. In order to reduce complexity, jobs are considered as basic units for scheduling. A novel combination of the analytical hierarchy process (AHP) and genetic algorithm (GA) is proposed to deal with the dynamic re-entrant scheduling problem which takes many criteria into consideration. GA is applied to obtain near-optimal schedules, while AHP works with a twofold effect. One is to fulfil the multiple criteria, while the other is adopted in the selection process of GA to fasten GA's convergence speed. The proposed model and solution algorithm are applied to solve the problem in a repairing company under a set of actual constraints. Comprehensive studies are conducted with real-life data. The results are consistent with the company operational scenario and are better than those of the manual schedules.

113 半導体製造におけるスケジューリングの最適化および実規模モデルへの適用(OS1-3 スケジューリングII)

Semiconductor manufacturing process flow is consisted of hundreds of process steps using hundreds of machines repeatedly, which is called a re-entrant flow shop, and it is very difficult to optimize the production schedule. Furthermore, in recent years, it has been becoming more difficult to use machines effectively because the product-mix becomes much more complex and the production lot size becomes much smaller. Therefore, it is indispensable to integrate a variety of scheduling methods into a solution to achieve the high production efficiency. In our previous researches we applied the well-known cooperative scheduling method, Lagrangian Decomposition and Coordination method, into an abstracted model based on the actual production line. Then we have verified the proposed method can create schedule effectively. In this paper we show the effectiveness for also larger models and make clear the issue in applying it into the actual scale model.

Using simplified drum-buffer-rope for re-entrant flow shop scheduling in a random environment

The traditional simplified drum buffer rope (SDBR) does not consider the application of re-entrant flow shop (RFS) in a random environment which might involve variable processing times and machine breakdowns. This paper proposed a weighted layer production buffer and weighted production buffer to monitor the status of the buffer deviation when applying SDBR in a RFS with non-deterministic parameters. The buffer status deviation used the overall urgency and actual urgency to estimate the influence of overall accumulated machine downtime and the influence of actual machine downtime of capacity-constrained-resource (CCR) at different layers. A dispatching rule, called SDBR_DReentry, was applied to decide the priority of all work orders by the buffer status deviation of each CCR machine with the consideration of the re-entry feature. A simulated RFS was designed and four different methods (including ours) were applied in order to demonstrate the effectiveness of our approach. The experimental results show that when compared to six performance indexes related to the due date, our approach has better performance than the other three methods when the product mix with a large proportion of multi-reentrant orders and when the CCR utilization increases from 60 to 90%. Key words: Drum-buffer-rope, simplified drum-buffer-rope, re-entrant flow shop, scheduling, random environments.

Minimizing total completion time for re-entrant flow shop scheduling problems

In this paper, we study re-entrant flow shop scheduling problems with the objective of minimizing total completion time. In a re-entrant scheduling problem, jobs may visit some machines more than once for processing. The problem is NP-hard even for machine number m = 2 . A heuristic algorithm is presented to solve the problem, in which an effective k -insertion technique is introduced as the improvement strategy in iterations. Computational experiments and analyses are performed to give guidelines of choosing parameters in the algorithm. We also provide a lower bound for the total completion time of the optimal solution when there are only two machines. Objective function values of the heuristic solutions are compared with the lower bounds to evaluate the efficiency of the algorithm. For randomly generated instances, the results show that the given heuristic algorithm generates solutions with total completion times within 1.2 times of the lower bounds in most of the cases.

Bi-objective scheduling for reentrant hybrid flow shop using Pareto genetic algorithm

This paper deals with a scheduling problem for reentrant hybrid flowshop with serial stages where each stage consists of identical parallel machines. In a reentrant flowshop, a job may revisit any stage several times. Local-search based Pareto genetic algorithms with Minkowski distance-based crossover operator is proposed to approximate the Pareto optimal solutions for the minimization of makespan and total tardiness in a reentrant hybrid flowshop. The Pareto genetic algorithms are compared with existing multi-objective genetic algorithm, NSGA-II in terms of the convergence to optimal solution, the diversity of solution and the dominance of solution. Experimental results show that the proposed crossover operator and local search are effective and the proposed algorithm outperforms NSGA-II by statistical analysis.