A heuristic method for two-stage hybrid flow shop with dedicated machines

This paper considers a two-stage hybrid flow shop scheduling problem with dedicated machines, in which the first stage contains a single common critical machine, and the second stage contains several dedicated machines. Each job must be first processed on the critical machine in stage one and depending on the job type, the job will be further processed on the dedicated machine of its type in stage two. The objective is to minimize the makespan. To solve the problem, a heuristic method based on branch and bound (B&B) algorithm is proposed. Several lower bounds are derived and four constructive heuristics are used to obtain initial upper bounds. Then, three dominance properties are employed to enhance the performance of the proposed heuristic method. Extensive computational experiments on two different problem categories each with various problem configurations are conducted. The results show that the proposed heuristic method can produce very close-to-optimal schedules for problems up to 100 jobs and five dedicated machines within 60 s. The comparisons with solutions of two other meta-heuristic methods also prove the better performance of the proposed heuristic method.     

An effective neighborhood search algorithm for scheduling a flow shop of batch processing machines

This paper considers scheduling problem of flow shop with many batch processing machines and objective of maximum lateness. An effective neighborhood search algorithm (NSA) is proposed for the problem, in which a job permutation and a batch permutation are used to indicate the solution of two sub-problems, respectively. Each job permutation consists of several family-permutations for the representation of jobs from the same family. Two swaps are applied to two permutations to produce new solutions. NSA is applied to a number of instances and compared with some methods, and computational results validate the good performance of NSA.     

A two-stage hybrid flow shop with dedicated machines at the first stage

This paper considers the problem of minimizing the makespan in a two-stage hybrid flow shop with dedicated machines at stage 1. There exist multiple machines at stage 1 and one machine at stage 2. Each job must be processed on a specified machine at stage 1 depending on job type, and then the job is processed on the single machine at stage 2.     

An ACO-based intercell scheduling approach for job shop cells with multiple single processing machines and one batch processing machine

Intercell transfers are inevitable for the manufacturing of complicated products, which disrupts the philosophy of cellular manufacturing and leads new challenges to the field of production scheduling. The issue of intercell scheduling is analyzed in the context of a cellular manufacturing system consisting of multiple single-processing machines and one batch-processing machine, which is derived from the actual manufacturing of complicated assemblies in the equipment manufacturing industry. Since the two types of machines are different from, even contrary to, each other in some constraint conditions, a combinational ant colony optimization (CACO) approach is developed in this paper, which designs two structures for the single-processing machines and the batch-processing machine, respectively. By updating pheromone trails integratedly and scheduling the single-processing operations and the batch-processing operations simultaneously, cooperative optimization for the two types of machines is achieved in the CACO. Minimizing the maximum completion time is taken as the scheduling objectives. Computational results show that the CACO has significant advantages comparing with other approaches and the CPLEX, and is especially suitable for the large dimension problems.     

A hybrid genetic heuristic for scheduling parallel batch processing machines with arbitrary job sizes

This paper investigates the scheduling problem of parallel identical batch processing machines in which each machine can process a group of jobs simultaneously as a batch. Each job is characterized by its size and processing time. The processing time of a batch is given by the longest processing time among all jobs in the batch. Based on developing heuristic approaches, we proposed a hybrid genetic heuristic (HGH) to minimize makespan objective. To verify the performance of our algorithm, comparisons are made through using a simulated annealing (SA) approach addressed in the literature as a comparator algorithm. Computational experiments reveal that affording the knowledge of problem through using heuristic procedures, gives HGH the ability of finding optimal or near optimal solutions in a reasonable time.     

Minimizing total completion time in two-stage hybrid flow shop with dedicated machines

We consider the problem of minimizing total completion time in a two-stage hybrid flow shop scheduling problem with dedicated machines at stage 2. There exist 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.     

A meta-heuristic approach to solve a JIT scheduling problem in hybrid flow shop

In this paper we address a hybrid flow shop scheduling problem considering the minimization of the sum of the total earliness and tardiness penalties. This problem is proven to be NP-hard, and consequently the development of heuristic and meta-heuristic approaches to solve it is well justified. So, we propose an ant colony optimization method to deal with this problem. Our proposed method has several features, including some heuristics that specifically take into account both earliness and tardiness penalties to compute the heuristic information values. The performance of our algorithm is tested by numerical experiments on a large number of randomly generated problems. A comparison with solutions performance obtained by some constructive heuristics is presented. The results show that the proposed approach performs well for this problem.     

Scheduling two-stage hybrid flow shop with availability constraints

Most of the literature on scheduling assumes that machines are always available. However, in real life industry, machines may be subject to some unavailability periods due to maintenance activities such as breakdowns (stochastic case) and preventive maintenance (deterministic case). In this paper we investigate the two-stage hybrid flow shop scheduling problem with only one machine on the first stage and m machines on the second stage to minimize the makespan. We consider that each machine is subject to at most one unavailability period. The start time and the end time of each period are known in advance (deterministic case) and only the non-resumable case is studied. First we discuss the complexity of the problem. Afterwards, we give the Branch and Bound model for this problem. Last, we calculate the worst-case performances of three heuristics: LIST algorithm, LPT algorithm and H-heuristic.     

A simulated annealing algorithm approach to hybrid flow shop scheduling with sequence-dependent setup times

One of the scheduling problems with various applications in industries is hybrid flow shop. In hybrid flow shop, a series of n jobs are processed at a series of g workshops with several parallel machines in each workshop. To simplify the model construction in most research on hybrid flow shop scheduling problems, the setup times of operations have been ignored, combined with their corresponding processing times, or considered non sequence-dependent. However, in most real industries such as chemical, textile, metallurgical, printed circuit board, and automobile manufacturing, hybrid flow shop problems have sequence-dependent setup times (SDST). In this research, the problem of SDST hybrid flow shop scheduling with parallel identical machines to minimize the makespan is studied. A novel simulated annealing (NSA) algorithm is developed to produce a reasonable manufacturing schedule within an acceptable computational time. In this study, the proposed NSA uses a well combination of two moving operators for generating new solutions. The obtained results are compared with those computed by Random Key Genetic Algorithm (RKGA) and Immune Algorithm (IA) which are proposed previously. The results show that NSA outperforms both RKGA and IA.     

A hybrid approach to large-scale job shop scheduling

A decomposition based hybrid optimization algorithm is presented for large-scale job shop scheduling problems in which the total weighted tardiness must be minimized. In each iteration, a new subproblem is first defined by a simulated annealing approach and then solved using a genetic algorithm. We construct a fuzzy inference system to calculate the jobs’ bottleneck characteristic values which depict the characteristic information in different optimization stages. This information is then utilized to guide the process of subproblem-solving in an immune mechanism in order to promote the optimization efficiency. Numerical computational results show that the proposed algorithm is effective for solving large-scale scheduling problems.     

An improved ant colony algorithm for dynamic hybrid flow shop scheduling with uncertain processing time

In this article the scheduling problem of dynamic hybrid flow shop with uncertain processing time is investigated and an ant colony algorithm based rescheduling approach is proposed. In order to reduce the rescheduling frequency the concept of due date deviation is introduced, according to which a rolling horizon driven strategy is specially designed. Considering the importance of computational efficiency in the dynamic environment, the traditional ant colony optimization is improved. On the one hand, a strategy of available routes compression to restrict ants’ movement is proposed so that the ants’ searching cycle for new solutions could be shorten. On the other hand, illuminating function in state transfer possibility is improved to facilitate the exploration of low pheromone trail. Performance of rolling horizon procedure and rescheduling algorithm are evaluated respectively through simulations, the results show the best parameters of rolling horizon procedure and demonstrate the feasibility and efficiency of rescheduling algorithm. An example from the practical production is addressed to verify the effectiveness of the proposed approach.     

Improved bounds for hybrid flow shop scheduling with multiprocessor tasks

In this paper, we investigate the problem of minimizing makespan in a multistage hybrid flow-shop scheduling with multiprocessor tasks. To generate high-quality approximate solutions to this challenging NP-hard problem, we propose a discrepancy search heuristic that is based on the new concept of adjacent discrepancies. Moreover, we describe a new lower bound based on the concept of dual feasible functions. The proposed lower and upper bounds are assessed through computational experiments conducted on 300 benchmark instances with up to 100 jobs and 8 stages. For these instances, we provide evidence that the proposed bounds consistently outperform the best existing ones. In particular, the proposed heuristic successfully improved the best known solution of 75 benchmark instances.     

A hybrid harmony search algorithm for the flexible job shop scheduling problem

In this paper, a novel hybrid harmony search (HHS) algorithm based on the integrated approach, is proposed for solving the flexible job shop scheduling problem (FJSP) with the criterion to minimize makespan. First of all, to make the harmony search (HS) algorithm adaptive to the FJSP, the converting techniques are developed to convert the continuous harmony vector to a kind of discrete two-vector code for the FJSP. Secondly, the harmony vector is mapped into a feasible active schedule through effectively decoding the transformed two-vector code, which could largely reduce the search space. Thirdly, a resultful initialization scheme combining heuristic and random strategies is introduced to make the initial harmony memory (HM) occur with certain quality and diversity. Furthermore, a local search procedure is embedded in the HS algorithm to enhance the local exploitation ability, whereas HS is employed to perform exploration by evolving harmony vectors in the HM. To speed up the local search process, the improved neighborhood structure based on common critical operations is presented in detail. Empirical results on various benchmark instances validate the effectiveness and efficiency of our proposed algorithm. Our work also indicates that a well designed HS-based method is a competitive alternative for addressing the FJSP.     

Two-stage hybrid flowshop scheduling with simultaneous processing machines

Simultaneous processing machines, common in processing industries such as steel and food production, can process several jobs simultaneously in the first-in, first-out manner. However, they are often highly energy-consuming. In this paper, we study a new two-stage hybrid flowshop scheduling problem, with simultaneous processing machines at the first stage and a single no-idle machine with predetermined job sequence at the second stage. A mixed integer programming model is proposed with the objective of minimizing the total processing time to reduce energy consumption and improve production efficiency. We give a sufficient and necessary condition to construct feasible sequencing solutions and present an effective approach to calculate the time variables for a feasible sequencing solution. Based on these results, we design a list scheduling heuristic algorithm and its improvement. Both heuristics can find an optimal solution under certain conditions with complexity O(nlogn), where n is the number of jobs. Our experiments verify the efficiency of these heuristics compared with classical heuristics in the literature and investigate the impacts of problem size and processing times.     

Two-stage hybrid flow shop scheduling with dynamic job arrivals

Motivated by applications in semiconductor manufacturing industry, we consider a two-stage hybrid flow shop where a discrete machine is followed by a batching machine. In this paper, we analyze the computational complexity of a class of two-machine problems with dynamic job arrivals. For the problems belonging to P we present polynomial algorithms. For the NP-complete problems we propose the heuristics, and then establish the upper bounds on the worst case performance ratios of the heuristics. In addition, we give the improved heuristics that can achieve better performances.     

A hybrid quantum-inspired genetic algorithm for multiobjective flow shop scheduling.

This paper proposes a hybrid quantum-inspired genetic algorithm (HQGA) for the multiobjective flow shop scheduling problem (FSSP), which is a typical NP-hard combinatorial optimization problem with strong engineering backgrounds. On the one hand, a quantum-inspired GA (QGA) based on Q-bit representation is applied for exploration in the discrete 0-1 hyperspace by using the updating operator of quantum gate and genetic operators of Q-bit. Moreover, random-key representation is used to convert the Q-bit representation to job permutation for evaluating the objective values of the schedule solution. On the other hand, permutation-based GA (PGA) is applied for both performing exploration in permutation-based scheduling space and stressing exploitation for good schedule solutions. To evaluate solutions in multiobjective sense, a randomly weighted linear-sum function is used in QGA, and a nondominated sorting technique including classification of Pareto fronts and fitness assignment is applied in PGA with regard to both proximity and diversity of solutions. To maintain the diversity of the population, two trimming techniques for population are proposed. The proposed HQGA is tested based on some multiobjective FSSPs. Simulation results and comparisons based on several performance metrics demonstrate the effectiveness of the proposed HQGA.